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공학박사학위논문

전륜 가속도 센서 기반 승차감 향상을

위한 능동 현가 시스템 예측 제어

Wheelbase Preview Active Suspension Control to

Improve Vehicle Ride Comfort based on Front-Wheel

Acceleration Sensing

2018년 8월

서울대학교 대학원

기계항공공학부

권 백 순

i

Abstract

Wheelbase Preview Active Suspension

Control to Improve Vehicle Ride

Comfort based on Front-Wheel Acceleration Sensing

Baek-soon Kwon

School of Mechanical and Aerospace Engineering

The Graduate School

Seoul National University

Active and semi-active suspension systems for passenger vehicles have been

a very active area of research for several decades owing to their potential to

improve the ride comfort and handling performance. It is well known that active

suspensions provide better performance and more functions compared to semi-

active suspensions. The main functions of active suspensions are vehicle height

adjustment, ride quality improvement, and attitude control. Some active

suspensions have been implemented and commercialized on high performance

and luxury vehicle these days. For example, Hydractive suspension by Citroen,

active body control (ABC) system by Mercedes-Benz, and anti-roll control

(ARS) system by BMW have been developed. Active suspensions have even

greater potential if preview information of the oncoming road height profile is

available. There are various ongoing projects which are trying to achieve better

driving performance using road preview information. Mercedes-Benz

introduced the world’s first actively preview controlled suspension system by

detecting road surface undulations in advance. BMW is trying to develop video

image processing system for suspension control. Volkswagen has undertaken

researches to prepare and operate suspension parts by road sensing with radar/

ii

laser sensors. Honda holds a patent for adaptive active suspension and aware

vehicle network system.

From a careful review of considerable amount of literature, active suspension

and preview control technology has the potential to promote both safety and

convenience of passengers. However, the current state-of-the-art in preview

active suspension technology has two main challenges. First, the developed

suspension control approaches require information on signals which may be

difficult to access such as suspension stroke speed or tire deflection. Second, it

requires precise, expensive sensors to detect road information such as a laser

scanner. While the cost of these sensors is going down, integrating these sensors

include special considerations and represent yet another barrier to adoption.

Therefore, this dissertation focused on developing a partial preview control

algorithm for low-bandwidth active suspension systems. In order to cope with

the unknown road disturbance, a novel vertical vehicle model has been adopted.

The state variables for suspension control were estimated using easily

accessible measurements. The vertical acceleration information of front wheels

is used to obtain preview control inputs for rear suspension actuators. From the

present driving mode by a mode selector, the control objective is determined to

be height control, attitude control, or ride comfort control.

In the remainder of this thesis, we will provide an overview of the overall

architecture of the proposed active suspension control algorithm. The

performance of the proposed algorithm has been verified via computer

simulations and vehicle tests. The results show the enhanced vehicle driving

performance by the proposed suspension control and state estimation algorithm.

Keywords: Active suspension control, Reduced vertical full-car model, Kalman

filter, Linear quadratic regulator, Optimal linear preview control, Model

predictive control, Electro-mechanical suspension

Student Number: 2013-23053

iii

List of Figures

Figure 2.1. Schematic diagram of the electro-mechanical suspension control

algorithm for a vehicle. The proposed control algorithm consists of mode

selector, upper-level and lower-level controllers, and suspension state

observer. .......................................................................................... 14

Figure 3.1. Quarter-car model of a high-bandwidth active suspension. ........ 16

Figure 3.2. Quarter-car model of a medium-bandwidth active suspension. ... 16

Figure 3.3. Quarter-car model of a low-bandwidth active suspension .......... 16

Figure 3.4. The 7-DOF vertical full-car model ........................................... 22

Figure 3.5. The height profile of the road for model validation ................... 26

Figure 3.6. Comparison of vehicle body motion of actual and simulated

vehicle ............................................................................................. 27

Figure 3.7. Comparison of suspension deflection of actual and simulated

vehicle ............................................................................................. 28

Figure 4.1. Block diagram of suspension state observer.............................. 30

Figure 4.2. Two sensor configurations for measurement............................. 32

Figure 4.3. The relation between the suspension velocity and the damping

force used in simulation given in Carsim® ......................................... 40

Figure 4.4. Comparisons of actual and estimated states by disturbance-

coupled observer and the proposed observer for single bump road test . 42

Figure 4.5. Comparisons of actual and estimated suspension velocities by

disturbance-coupled observer and the proposed observer for single bump

road test. .......................................................................................... 43

Figure 4.6. Semi-active suspension system of front side and mounted sensors

for the field test ................................................................................ 45

Figure 4.7. The damping force versus suspension velocity curves of the semi-

active damper prototype .................................................................... 45

Figure 4.8. Comparisons of reference data and estimated states for single

iv

bump road case................................................................................. 48

Figure 4.9. Comparisons of reference data and estimated suspension velocities

for single bump road case.................................................................. 49

Figure 4.10. Comparisons of reference data and estimated states for off-road

case ................................................................................................. 50

Figure 4.11. Comparisons of reference data and estimated suspension

velocities for off-road case ................................................................ 51

Figure 4.12. Comparisons of measured and estimated acceleration of rear

wheels for off-road case .................................................................... 52

Figure 5.1. Bode plots from symmetric road elevation input to delayed front

left wheel acceleration and that of rear left wheel acceleration in full-car

model .............................................................................................. 60

Figure 5.2. Delayed front left wheel acceleration and that of rear left wheel

acceleration generated by sinusoidal road disturbance simulation ......... 62

Figure 5.3. Wheelbase preview disturbance information. ............................ 64

Figure 5.4. Schematic of MPC concept ..................................................... 66

Figure 5.5. Frequency response of the passive vehicle at 10 kph ................. 71

Figure 5.6. Frequency response of the heave acceleration of the controlled

vehicle at 10 kph .............................................................................. 72

Figure 5.4. Frequency response of the pitch acceleration of the controlled

vehicle at 10 kph .............................................................................. 73

Figure 6.1. A quarter-car model with electro-mechanical actuator. .............. 76

Figure 6.2. Belt-driven ball screw actuator model ...................................... 77

Figure 6.3. Circuit diagram of the motor ................................................... 79

Figure 6.4. A vertical full-car model with EMS.......................................... 80

Figure 6.5. Accumulator spring stiffness to incorporate the actuator stroke

limit................................................................................................. 82

Figure 6.6. Mode and desired height level decision algorithm..................... 88

Figure 7.1. Comparison of ride comfort improvement simulation................ 97

Figure 7.2. Comparison of ride comfort improvement simulation...............101

Figure 7.3. Comparison of ride comfort improvement simulation for

v

unconstrained EMS system ..............................................................106

Figure 7.4. Comparison of ride comfort improvement simulation for

constrained EMS system .................................................................. 110

Figure 7.5. Simulation scenario for evaluation of the proposed EMS control

algorithm ........................................................................................ 111

Figure 7.6. Simulation scenario for evaluation of the proposed EMS control

algorithm ........................................................................................ 113

Figure 7.7. Heave acceleration of the vehicle body ................................... 114

Figure 7.8. Pitch angel of the vehicle ....................................................... 114

Figure 7.9. Roll angel of the vehicle ........................................................ 114

Figure 7.10. FL suspension displacement ................................................. 116

Figure 7.11. RR suspension displacement................................................. 116

Figure 7.12. FL actuator stroke ................................................................ 117

Figure 7.13. RR actuator stroke ............................................................... 117

Figure 7.14. Estimated FL suspension speed at double lane change ............ 117

vi

Contents

Chapter 1 Introduction ........................................................1

1.1. Background and Motivation ..................................................... 1

1.2. Previous Researches.................................................................. 4

1.3. Thesis Objectives .................................................................... 10

1.4. Thesis Outline ......................................................................... 11

Chapter 2 Description of an Electro-mechanical Suspension

(EMS) system ............................................ 12

Chapter 3 An Active Suspension System Model ................. 15

3.1. Model Reduction of a Quarter-car Suspension System .......... 17

3.1.1. Conventional quarter-car model ............................................... 17

3.1.2. Model reduction...................................................................... 19

3.2. A Reduced Vertical Full-car Model......................................... 21

3.2.1. Model reduction of 7-DOF full-car model................................. 21

3.2.2. Model validation ..................................................................... 26

Chapter 4 Suspension State Estimation .............................. 29

4.1. Design of a Suspension State Estimator ................................. 30

4.1.1. Sensor configurations .............................................................. 31

4.1.2. Estimation of rear wheel acceleration ....................................... 33

4.1.3. Suspension state estimator ....................................................... 35

4.1.4. Algorithm to estimate sensor bias............................................. 37

4.2. Performance Evaluation of Estimator ..................................... 39

4.2.1. Simulation results ................................................................... 39

4.2.2. Vehicle test results .................................................................. 44

Chapter 5 Design of Active Suspension Control Algorithm. 53

vii

5.1. Linear Quadratic Optimal Control .......................................... 54

5.2. Wheelbase Preview Control .................................................... 57

5.2.1. Wheelbase preview information ............................................... 57

5.2.2. Optimal preview control .......................................................... 63

5.2.3. Model predictive control ......................................................... 65

5.3. Frequency Response Analysis of Controlled Vehicle ............. 70

Chapter 6 An Electro-mechanical Active Suspension

System....................................................... 75

6.1. EMS system modeling ............................................................ 77

6.1.1. Electro-mechanical actuator modeling ...................................... 77

6.1.2. Reduced vertical full-car model with EMS................................ 80

6.2. EMS System Control Algorithm ............................................. 87

6.2.1. Driving mode decision ............................................................ 87

6.2.2. Desired suspension state decision............................................. 93

6.2.3. Desired motor voltage decision ................................................ 94

Chapter 7 Performance Evaluation .................................... 96

7.1. Ride Comfort Control Performance ........................................ 97

7.1.1. Carsim® simulation results ...................................................... 99

7.1.2. EMS system simulation results ...............................................102

7.2. Mode Control Performance....................................................111

Chapter 8 Conclusions and Future works ......................... 118

Bibliography .................................................................. 120

Abstract in Korean.......................................................... 128

1

Chapter 1 Introduction

1.1. Background and Motivation

An automotive suspension system is one of the major components in a

vehicle. In general, a vehicle has one suspension for each wheel; hence a vehicle

has four wheels, it also has four suspensions. Within the available suspension

travel, aims of a vehicular suspension are: (a) to isolate the vehicle body from

external disturbances coming from irregular road surfaces and internal

disturbances created by cornering, acceleration, or deceleration, in order to

have ride comfort; (b) to carry the weight of the vehicle body; (c) to

accommodate variations in load, due to changes in the number of passengers

and luggage, or from internal disturbances; and (d) to keep a firm contact

between the road and the tires, for good handling performance thus improving

drive safety. One can say that the suspension system plays major role in safety

and ride comfort of a vehicle [Williams'94, Appleyard'95, Cao'08]. Thereby,

research and development of vehicular suspensions have been being concerned,

in order to meet ever-strengthening user requirements on ride quality and drive

safety [Xue'11].

It is well known that conventional passive suspensions represent a trade-off

between conflicting performance metrics such as the ride comfort and the road

holding. Since the late 1960s, vehicle suspension systems have been widely

investigated and studied because of their potential to improve the ride quality

2

[Els'07, Huang'06, Yoshimura'01]. An ideal vehicle suspension system should

be able to reduce the acceleration and the displacement of the vehicle body to

achieve ride comfort. Meanwhile an acceptable level of suspension deflection

and tire deflection should also be maintained as handling measures.

Active suspension systems for passenger vehicles have been a very active

area of research for several decades owing to their potential to improve the ride

comfort and handling performance. This is because active systems offer

additional functionalities and therefore enlarge the full driving dynamics

potential of a vehicle by employing different types of actuator such as

magnetorheological actuators and hydraulic actuators. Although an active

system shows an outstanding performance, it consumes heavy amount of power

compared to a semi-active or a passive system.

Performance improvements and power consumption is a tradeoff in active

system [Singal'13]. Since active control requires extra energy compared to

passive and semi-active system, it has not been widely considered in the real

world. This challenge must be faced and solved due to the fact that the active

system is indispensable in the future to maximize ride quality and handling

performance [Yoshihiro'96].

Recently, Daimler AG introduced the world’s first actively controlled

hydraulic suspension system called active body control, which has been

successfully implemented in several Mercedes–Benz models [Rajala'11].

Another example is the system by BMW, which has developed an anti-roll

control hydraulic actuator in the center of the rear anti-roll bar [Strassberger'04].

3

Active suspensions have even greater potential if preview information of the

oncoming road height profile is available. There are various ongoing projects

trying to achieve better driving performance using road preview information.

Mercedes-Benz introduced the world’s first actively preview controlled

suspension system by detecting road surface undulations in advance. BMW is

trying to develop video image processing system for suspension control.

Volkswagen has undertaken researches to prepare and operate suspension parts

by road sensing with radar/ laser sensors. Honda holds a patent for adaptive

active suspension and aware vehicle network system.

From a careful review of considerable amount of literature, preview active

suspension control technology has the potential to promote passenger’s safety

and convenience simultaneously. However, the current state-of-the-art in

preview active suspension control technology has main challenge on obtaining

road preview information. It requires precise, expensive sensors to detect road

information such as a laser scanner. While the cost of these sensors is going

down, integrating them into series production vehicles will increase the price

and represent yet another barrier to market.

Therefore, this dissertation focused on developing a partial preview control

algorithm using road information with less detail. Still this would include

acceleration information of front wheels which was used to obtain preview

control inputs for rear suspension actuators.

4

1.2. Previous Researches

The main objective of active suspension systems is to reduce motions of the

sprung mass. Use of optimal control theory for designing active vehicle

suspension systems have been proposed by many researchers. Davis and

Thompson obtained optimal control by measurement of axle acceleration and

of axle to body displacement, and the incorporation of a term corresponding to

the integral of the axle to body displacement has achieved zero steady state

response to both static body forces and ramp road inputs [Davis'88]. Krtolica et

al. developed a complete analytical solution for a two-dimensional half-car

model in which the unsprung masses have not been included [Krtolica'90].

Shirahatt et al. obtained the optimal suspension parameters of a passive

suspension and active suspension for a passenger car which satisfies the

performance as per ISO 2631 standards by genetic algorithm [Shirahatt'08].

To understand the performance improvement more realistically, the existing

actuator limitation should be incorporated when designing the controller. For

active suspension systems, the bump stoppers mechanically constrain the

suspension deflections; thus constraining the actuator displacements at the

same time. Also the controller design should consider rate of the actuator

displacement, too. The linear quadratic regulator (LQR) controller design is

suitable at minimizing a linear cost function without explicitly incorporating

hard constraints. Köse et al. proposed state and output feedback scheduled

controllers with sufficient conditions to satisfy a parameter-dependent

performance measure, without violating the saturation bounds [KöSe'03]. Sun

5

et al. proposed a saturated adaptive robust control strategy to handle the

saturation constraints by anti-windup compensation approach [Sun'13].

It is shown that using a force control loop to compensate the hydraulic

dynamics can destabilize the system [Alleyne'98]. This full nonlinear control

problem of active suspensions has been investigated using several approaches

including optimal control. Moreover, several assumptions of linearity in the

parameters are needed, which actual systems may not satisfy. The use of fuzzy

logic systems has accelerated in recent years in many areas, including feedback

control. Cal and Konik proposed a fuzzy logic approach for the active control

of a hydro-pneumatic actuator [Cal'96]. Particularly important in fuzzy logic

control are the universal function approximation capabilities of the systems

[Kosko'92, Kosko'94]. Given these recent results, some rigorous design

techniques for fuzzy logic feedback control based on adaptive control

approaches have now been given [Wang'92, Wang'94]. Fuzzy logic systems

offer significant advantages over adaptive control, including no requirement for

linearity in the parameters assumptions and no need to compute a regression

matrix for each specific system. Fuzzy logic control schemes have been used to

control suspension systems. For example, Salem and Aly designed a quarter-

car system on the basis of the concept of a four-wheel independent suspension

system. They proposed a fuzzy control for active suspension system to improve

the ride comfort [Salem'09].

In active suspension systems, inevitable uncertainties often emerge. Roughly

speaking, the uncertainties can be classified into two categories: parametric

uncertainties and general uncertainties. Gaspar et al. have used a robust

6

controller for a full vehicle linear active suspension system using the mixed

parameter synthesis [Gaspar'03]. Chamseddine et al. developed a method for

the purpose of sensor fault diagnosis and accommodation [Chamseddine'06]. A

sliding mode technique is designed for a linear full vehicle active suspension

system. Yagiz et al. designed a sliding mode controller for a non-linear seven

degrees of freedom vehicle model [Yagiz'00]. Yagiz and Yuksek designed an

SMC for a linear model [Yagiz'01]. In these two studies, the robustness of the

controller has been shown by varying the vehicle parameters such as the vehicle

mass and the damper ratios.

Due to inherent strong nonlinearities in the damper and spring components,

inevitably the nonlinear effect must be taken into account in designing the

controller for practical active suspension systems. Suspension control design

mainly focuses on the following three motions of the vehicle: vertical

movement at center of gravity, pitching movement and rolling movement. An

intelligent controller can be used to design a control system for a full vehicle

nonlinear active suspension system such as neural controller. Neural networks

are capable of handling complex and nonlinear problems, process information

rapidly and can reduce the engineering effort required in controller model

development. These methods provide an extensive freedom for control

engineers to deal with practical problems of vagueness, uncertainty, or

imprecision. These intelligent methods are good candidates for alleviating the

problems associated with active suspension control systems [Rumelhart'86,

Narendra'90].

Active suspensions have even greater potential if preview information of the

7

oncoming road height profile is available. An optimal control for previewing

active suspension systems can be derived using the Hamilton function [Hac'92,

Balzer'81]. This is the common optimal preview control (OPC) approach in the

current literature and results in a LQR as a state feedback and a preview

feedforward term calculated from the oncoming road height profile

[Thompson'98, Louam'92, Youn'00, Kang'09, Martinus'96, Huisman'93a,

Huisman'93b, Marzbanrad'04, Senthil'96].

Furthermore, model predictive control (MPC) is a promising design scheme,

since information about the future is available and actuator constraints can be

explicitly incorporated [Mehra'97, Cho'99, Cho'05, Göhrle'12, Göhrle'13,

Göhrle'14, Göhrle'15].

Most of these researches above assume that all state variables are available.

However, implementation of these suspension control laws requires

information on states which may be difficult to access. Indeed, one of issues in

active / semi-active suspension control is to estimate states of the suspensions

from easily accessible and inexpensive measurements such as accelerations or

angular velocities for on-board suspension control applications. This requires

observer that can produce estimates of the states such as suspension deflection

and velocity using reduced number of sensors. The implementation of the

observer with low cost sensors is one of the main challenges to car

manufacturers that aim at equipping mass-produced cars with controlled

suspension systems.

Observers to estimate suspension states have been developed in many

researches. J.K. Hedrick et al. proposed disturbance-decoupled observers for

8

semi-active and fully active suspension systems [Hedrick'94]. R. Rajamani and

J.K. Hedrick proposed an adaptive observer for a class of nonlinear suspension

systems [Rajamani'93]. In deterministic case, K. Yi provided a bilinear observer

for semi-active suspension systems whose estimation error is independent of

the unknown disturbance [Yi'95]. The disturbance-decoupled observer for

semi-active suspension was developed in stochastic case by K. Yi and B.S.

Song [Yi'99]. N. Pletschen and K. J. Diepold proposed a nonlinear state

estimation approach which combines Kalman filter theory and Takagi-Sugeno

modelling and applied to a hybrid vehicle suspension [Pletschen'17]. In these

works, the observers were provided for estimation of quarter car model states

only.

However, relatively little work has been done about observers with full-car

model. L. Dugard et al. proposed a H∞ observer with 7-DOF full-car model

[Dugard'12]. In their work, the observer was designed by minimizing the

unknown disturbance effect on the estimated state variables. However, effects

of measurements noise were not considered in the design process. H. Ren et al.

proposed a suspension state observer based on unscented Kalman filter to

improve the robustness against parameters variation of the semi-active

suspension control strategy and to be adaptive to different types of unknown

road disturbances [Ren'16]. In their work, the road disturbance is considered as

system process noise, however, the sensitivity to unknown disturbance is not

discussed analytically.

From a careful review of considerable amount of literature, preview active

suspension control technology has the potential to promote both safety and

9

convenience simultaneously. However, the current state-of-the-art in preview

active suspension control technology has main challenge on obtaining road

preview information. It requires detailed road information that currently can be

obtained by only expensive sensors such as a laser scanner or a precision level

of road information from stereo vision sensors. While the cost of these sensors

is going down, integrating them into cars will increase the price and represent

yet another barrier to adoption. Moreover, a drawback of “look-ahead” sensor

is that they are vulnerable to water, snow, or other soft obstacles on the road.

For example, they recognize a heap of leaves as a serious obstacle, while a

pothole filled with water, will not detected at all.

Therefore, this dissertation would focus on developing a partial preview rear

suspension control algorithm without information. The measured vertical

acceleration information of front wheels is used to obtain preview control

inputs for rear suspension actuators. This wheelbase preview is relatively

reliable and economical compared with look-ahead sensor. A novel 3-DOF full-

car model is adopted to design a road disturbance-decoupled suspension state

observer. The vertical acceleration measurements of the front wheels and

estimated vertical acceleration of the rear wheels are regarded as system inputs

in the time process model. Two sensor configurations are considered to make

measurement information which is easily accessible and convenient to use for

active / semi-active suspensions.

10

1.3. Thesis Objectives

This dissertation focused on developing a partial preview control algorithm

with limited road preview information to improve the driving performance.

From a considerable amount of literature, preview active suspension control

technology has the potential to promote both ride comfort and safety of

passengers. However, the current state-of-the-art in preview active suspension

control technology has main challenge on obtaining road preview information

and state estimation.

Mainly three research issues are considered: how to cope with the unknown

road disturbance, how to estimate the suspension state variable, and how to

control the vehicle. In the remainder of this thesis, we will provide an overview

of the overall architecture of the proposed preview active suspension control

algorithm and the experimental results which shown the effectiveness of the

proposed state estimation algorithm. The effectiveness of the proposed preview

active suspension control algorithm has been evaluated via computer

simulations. The results show the improved ride comfort and handling

performance on scenarios such as bump, double lane change, J-turn, squat and

dive.

11

1.4. Thesis Outline

This dissertation is structured in the following manner. An overall

architecture of the proposed active suspension control algorithm is described in

Chapter 2. In Chapter 3, a conventional active suspension model is introduced

and model reduction is conducted. In Chapter 4, a suspension state estimator is

introduced and shows the experiment results for the evaluation of the estimation

performance. In Chapter 5, the concept of preview information for rear

suspension from front suspension is introduced. Then an algorithm for

wheelbase preview active suspension control is designed based on OPC and

MPC approaches. In Chapter 6, an electro-mechanical suspension (EMS)

system and control algorithm are introduced. The proposed modeling and

control methods in previous chapters are applied. Chapter 7 shows the

simulation results for the evaluation of the performance of the proposed EMS

control algorithm. Then the conclusion which describes the summary and

contribution of the proposed active suspension control algorithm and future

works is presented in Chapter 8.

12

Chapter 2 Description of an Electro-

mechanical Suspension (EMS) system

All active suspensions implemented in automobiles today are based on

hydraulic or pneumatic operation. Although hydraulic systems have already

proved their potential in commercial systems, there are three main

disadvantages: inefficiency due to the continuously pressurized system, a

relatively high system time constant and environmental pollution issues

because of hose leaks and ruptures. An electro-mechanical suspension system

can resolve the disadvantages of hydraulic systems since continuous power is

not needed, control is easy and no fluids are present. In this research, a control

algorithm for an electro-mechanical suspension system is proposed to improve

the driving performance of a vehicle.

From a considerable amount of literature, preview active suspension control

technology has the potential to promote not only safety of passengers but also

convenience. However, the current state-of-the-art in preview active suspension

control technology has main challenge on obtaining road preview information

and state estimation. It requires precise, expensive sensors to detect road

information such as a laser scanner or a stereo camera. While the cost of these

sensors is going down, integrating them into cars will increase the price and

represent yet another barrier to adoption. Moreover, a drawback of “look-ahead”

13

sensor is that they are vulnerable, potentially confused by water, snow, or other

soft obstacles.

Therefore, in this research, we focus on developing a partial preview control

algorithm without road information. As aforementioned, mainly three research

issues are considered: how to cope with the unknown road disturbance, how to

estimate the suspension state variable, and how to control the vehicle. The

system architecture of the algorithm is outlined in Figure 2.1. The proposed

control algorithm consists of mode selector, upper-level and lower-level

controllers, and suspension state observer. The mode selector determines a

present driving mode and desired height level of the vehicle. The upper-level

controller determines the desired suspension state considering the actuator

stroke limit. The electro-mechanical actuator is driven by a motor which is

controlled by a motor voltage controller, so the lower level controller calculates

the voltage at each actuator motor using estimated state by the observer and the

calculated desired state. A novel 3-DOF full-car model is adopted to design a

road disturbance-decoupled suspension state observer and lower level

controller. To improve the ride comfort performance, the vertical acceleration

information of front wheels is used to obtain preview control inputs for rear

suspension actuators.

In the remainder of this thesis, we will provide an overview of the overall

architecture of the proposed EMS control algorithm and the experimental and

simulation results which shown the effectiveness of the proposed algorithm.

14

Mode

Selector Lower

Level

Controller

Actuator

Vehicle

Sensor

State

Observer

EMS Control Algorithm

Upper

Level

Controller

Figure 2.1. Schematic diagram of the electro-mechanical suspension control

algorithm for a vehicle. The proposed control algorithm consists of mode

selector, upper-level and lower-level controllers, and suspension state observer.

15

Chapter 3 An Active Suspension System

Model

An active suspension is one including an actuator that can supply active force,

which is regulated by a control algorithm using data from sensors attached to

the vehicle. An active suspension is composed of an actuator and a mechanical

spring, or an actuator, a mechanical spring and a damper. It belongs to the high-

bandwidth active suspension controlling both the sprung mass and the unsprung

mass if the active actuator works mechanically in parallel with the spring. It is

the low-bandwidth active suspension controlling the sprung mass if the active

actuator works mechanically in series with the spring and the damper. In general,

the frequency of the unsprung mass lies in the range of 10 ~ 15 Hz, and the

frequency of the sprung mass lies in the range of 1 ~ 2 Hz. Due to supplying

active force control, active suspensions provide the possibility to fully

accomplish the aims of automotive suspensions. Three typical quarter-car

models of active suspensions according to the actuator bandwidth are illustrated

in Figure 3.1 ~ 3.3 [Xue'11]. The main objective of suspension systems is to

reduce motions of the sprung mass against to the uneven road surface. An

appropriate control input is calculated through modeling process.

16

ms

mu

Figure 3.1. Quarter-car model of a high-bandwidth active suspension.

ms

mu

Figure 3.2. Quarter-car model of a medium-bandwidth active suspension.

ms

mu

Figure 3.3. Quarter-car model of a low-bandwidth active suspension.

17

3.1. Model Reduction of a Quarter-car Suspension

System

In this section, a conventional quarter-car model is formulated for active

suspension control. Then, model reduction is conducted to cope with the

unknown road disturbance and state estimation.

3.1.1. Conventional quarter-car model

In many previous literature, the common approach is to use quarter-car

[Canale'06], half-car [Marzbanrad'04], or full-car models [Unger'11] with

sprung mass and unsprung mass. This approach can regulate motions of both

vehicle body and wheel because both dynamics are incorporated in model

representation. For example, equations of quarter-car model of a medium-

bandwidth active suspension shown in Figure 3.2 is given as follows:

s s s u s u a

u u s u s u t u r a

m z k z z c z z f

m z k z z c z z k z z f

(3.1)

where the subscript s, u, t, and r denote vehicle body, wheel, tire, and road,

respectively. m denotes the mass, k denotes the spring stiffness, c denotes the

damping coefficient, z denotes the vertical displacement which respect to the

static equilibrium position, and fa denotes the control force from actuator. The

state-space formulation from (3.1) is obtained as follows:

wx = Ax+ Bu + B w (3.2)

where the state vector consists of the vehicle body displacement from the wheel,

the wheel displacement from the road, absolute velocity of the body, and

18

absolute velocity of the wheel. The controlled input of the system is force from

actuator, and absolute velocity of the road surface is disturbance to the system

as follows:

T

s u u r s u

a

r

x z z z z z z

u f

w z

The system matrix, input matrix, and disturbance input matrix is given as

follows:

0 0 1 1 0

00 0 0 1 0

110 , ,

0

1 0

w

s s s s

t

uu u u u

k c cA B B

m m m m

kk c c

mm m m m

This conventional state-space representation for quarter-car model has two

limitations from a practical point of view. First, some state variables such as

suspension deflection, absolute velocity of the body and wheel are difficult to

access directly [Davis'88]. Second, the disturbance input, absolute velocity of

the road surface, is unknown or hard to know. It requires precise, expensive

sensors to detect road information such as a laser scanner or a stereo camera.

Moreover, a drawback of such sensor is that they are vulnerable, potentially

confused by water, snow, or other soft obstacles [Arunachalam'03]. In these

reasons, the conventional model is not suitable for controller implementation

of active suspension system.

19

3.1.2. Model reduction

A model reduction is conducted to overcome the limitation of conventional

quarter car model. The model reduction is proposed from the fact that the

electro-mechanical actuator considered in this research has a much lower

operating frequency (~ 5 Hz) than eigenfrequency of the wheel (10 ~ 15 Hz).

Using the conventional model, a suspension controller calculates high-

frequency control signals to influence wheel dynamics, which cannot be

realized by the actuator [Göhrle'14]. Hence, only the vehicle body dynamics is

considered and wheel dynamics is ignored. This approach has been hardly

proceeded in the literature [Krtolica'90, Göhrle'15]. In their works, however,

the unknown road disturbance still remains. A novel state-space representation

for reduced quarter-car model which is free from unknown disturbance is

proposed in this research.

From (3.1), using only the vehicle body dynamics equation, the state-space

representation for reduced quarter-car model is obtained as follows:

,reduced r reduced r w r reducedx = A x + B u + B w (3.3)

where the state vector consists of vehicle body displacement and its velocity

from the wheel. The controlled input of the system is force from actuator, and

the vertical wheel acceleration is disturbance to the system as follows:

T

reduced s u s u

a

reduced u

x z z z z

u f

w z

The system matrix, input matrix, and disturbance input matrix is given as

20

follows:

,

0 1 00

, ,11

r r w r

s s s

A B Bk c

m m m

When compared with the conventional model, the reduced one has half-size

system matrix because of ignoring wheel dynamics. Therefore, the wheel

deflection, absolute velocity of the body, and absolute velocity of the wheel are

no states of the reduced model and hence do not have to be observed for

controller implementation. Moreover, it is noted the disturbance input can be

measured easily by accelerometers on the wheel. From the measured

disturbance, it is possible to design a suspension state observer which is

independent from unknown road disturbance. Using the reduced model without

modeled wheel dynamics, the controller calculates control signals in a feasible

frequency range.

21

3.2. A Reduced Vertical Full-car Model

3.2.1. Model reduction of 7-DOF full-car model

The classical linearized 7-DOF full-car model considered heave, pitch, and

roll motions of the sprung mass and vertical motions of the four unsprung

masses [Esmailzadeh'97, ElBeheiry'96]. In Figure 3.4, a typical 7-DOF vertical

full-car model is shown. The variables of the model and nominal parameter

values of typical sedan given in Carsim® are given in Table 3.1. The equations

of body motion of the full-car model are given as follows:

1 1 1 2 2 2 3 3 3 4 4 4

1 1 1 2 2 2 3 3 3 4 4 4

1 2 3 4

1 1 1 2 2 2 3 3 3 4 4 4

1 1 1

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

s s s u s u s u s u

s u s u s u s u

xx s u f s u f s u r s u r

s u

m z k z z k z z k z z k z z

c z z c z z c z z c z z

f f f f

I k z z t k z z t k z z t k z z t

c z z

2 2 2 3 3 3 4 4 4

, , 1 2 3 4

1 1 1 2 2 2 3 3 3 4 4 4

1 1 1 2 2 2 3 3 3 4

( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( )

f s u f s u r s u r

roll f roll r f f r r

yy s u f s u f s u r s u r

s u f s u f s u r

t c z z t c z z t c z z t

K K t f t f t f t f

I k z z l k z z l k z z l k z z l

c z z l c z z l c z z l c

4 4

1 2 3 4

( )

( ) ( )

s u r

f r

z z l

l f f l f f

(3.4)

The dynamic equations of bounce motion of wheels are given as follows:

1 1 1 1 1 1 1 1 1 1

2 2 2 2 2 2 2 2 2 2

3 3 3 3 3 3 3 3 3 3

4 4 4 4 4 4 4 4 4 4

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

u u s u s u t u r

u u s u s u t u r

u u s u s u t u r

u u s u s u t u r

m z k z z c z z k z z f

m z k z z c z z k z z f

m z k z z c z z k z z f

m z k z z c z z k z z f

(3.5)

22

X

Y

Z

zu1

zs1

zu2zu3

k1,c1

k2,c2

k3,c3

k4,c4

zs2

zs3

zs4

2tf

2tr

lf

lr

zs

zu4

ms,Ixx,Iyy

zr1

zr3

zr2

zr4

f1

f3

f2

f4

Figure 3.4. The 7-DOF vertical full-car model.

Table 3.1. The variables and nominal parameters of full-car model used in

simulation study.

Parameter/

variable Description Value

ms Sprung mass 1653 kg

mu Unsprung mass 45 kg

Ixx, Iyy Roll and pitch moment of inertia 614, 2765 kg∙m2

k1,2 Front suspension stiffness 25222 N/m

k3,4 Rear suspension stiffness 29220 N/m

k t Tire stiffness 230000 N/m

Kroll,f ,r Roll stiffness of front and rear axle 22000 N∙m/rad

c1,2 Front damping ratio 4721 N∙s/m

c3,4 Rear damping ratio 3979 N∙s/m

tf ,tr Distance from C.G. to front/rear left tire 0.8, 0.8 m

lf Distance from C.G. to front axle 1.402 m

lr Distance from C.G. to rear axle 1.646 m

L The wheel base 3.048 m

zs Vertical displacement of C.G. of sprung mass

zsi Vertical displacement of i-th point of sprung mass i=1…4

zui Vertical displacement of unsprung masses i=1…4

zri Vertical displacement of road under every wheel i=1…4

θ Sprung mass pitch angle

ϕ Sprung mass roll angle

fi Controlled force from i-th actuator i=1…4

23

The linearized kinematic equations involved with vertical displacement at

each corner of sprung mass and vertical displacement/attitude of C.G of the

sprung mass are given as follows:

1

2

3

4

s s f f

s s f f

s s r r

s s r r

z z l t

z z l t

z z l t

z z l t

(3.6)

In the proposed reduced full-car model, vertical motions of the four unsprung

masses are not considered as mentioned in chapter 3.1.2, but their vertical

accelerations are regarded as disturbance input to the system. From (3.4) and

(3.6), the state-space representation for reduced full-car model is obtained as

follows:

wx Ax Bu B w (3.7)

where the state vector consists of suspension displacement and its velocity at

each corner, and vertical, roll, and pitch velocity of the body. The controlle d

input vector of the system consists of force from each actuator, and the vertical

acceleration at each wheel is disturbance to the system as follows:

1 1 1 1 2 2 2 2

3 3 3 3 4 4 4 4

1 2 3 4

1 2 3 4

s u s u s u s u

T

s u s u s u s u

T

T

u u u u

z z z z z z z z

z z z z z z z z z

f f f f

z z z z

x

u

w

(3.8)

The system matrix, input matrix, and disturbance input matrix is given as

follows:

24

0 0 0 0

1 0 0 0

0 0 0 0

0 1 0 0

0 0 0 0

, , 0 0 1 0

0 0 0 0

0 0 0 1

0 0 0 0

0 0 0 0

0 0 0 0

1 1

2 2

3 3

4 4

5 5

w6 6

7 7

8 8

9 9

10 10

11 11

A B

A B

A B

A B

A B

A B BA B

A B

A B

A B

A B

A B

where

2 2 2 2 2 2

1 1 2 21 1 1 2 2 2

3 3 4 43 3 3 4 4 4

0 1 0 0 0 0 0 0 0 0 0

0 0 0

0 0 0 1 0 0

f f f f f f

s yy s xx yy s yy s xx yy

f r f r f r f r f r f r

s yy s xx yy s yy s xx yy

l t l l t lk c k ca k c c a k c c

m I m I I m I m I I

l l t t l l l l t t l lk c k cb k c c b k c c

m I m I I m I m I I

1

2

3

A

A

A

2 2 2 2 2 2

1 1 2 21 1 1 2 2 2

3 3 4 43 3 3 4 4 4

0 0 0 0 0

0 0 0

0 0 0 0 0 1 0 0 0 0 0

f f f f f f

s yy s xx yy s yy s xx yy

f r f r f r f r f r f r

s yy s xx yy s yy s xx yy

l t l l t lk c k ca k c c a k c c

m I m I I m I m I I

l l t t l l l l t t l lk c k cb k c c b k c c

m I m I I m I m I I

4

5

6

A

A

A

1 1 2 21 1 1 2 2 2

2 2 2 2 2 2

3 3 4 43 3 3 4 4 4 0 0 0

0 0 0 0 0 0 0 1 0 0 0

f r f r f r f r f r f r

s yy s xx yy s yy s xx yy

r r r r r r

s yy s xx yy s yy s xx yy

l l t t l l l l t t l lk c k cc k c c c k c c

m I m I I m I m I I

k cl t l k l c t ld k c c d k c c

m I m I I m I m I I

7A

25

1 1 2 21 1 1 2 2 2

2 2 2 2 2 2

3 3 4 43 3 3 4 4 4

1 1 2 2

0 0 0

f r f r f r f r f r f r

s yy s xx yy s yy s xx yy

r r r r r r

s yy s xx yy s yy s xx yy

s s s s

l l t t l l l l t t l lk c k cc k c c c k c c

m I m I I m I m I I

k cl t l k l c t ld k c c d k c c

m I m I I m I m I I

k c k c

m m m m

8

9

A

A 3 3 4 4

1 2 3 4

1 1 2 2 3 3 4 4

0 0 0

0 0 0

0 0 0

s s s s

f f r r

f xx f xx f xx f xx

f f f f r r r r

yy yy yy yy yy yy yy yy

k c k c

m m m m

t c t c t c t ca a b b

t I t I t I t I

l k l c l k l c l k l c l k l c

I I I I I I I I

10

11

A

A

, ,, ,

1 3 1 32 2 2 2

f roll f f roll froll r roll rr rf r f r

xx f xx r xx f xx r

t K t KK Kt ta k t b k t c k t d k t

I t I t I t I t

2 2 2 2

2 2 2 2

0 0 0 0

1 1 1 1

1 1 1 1

1

f f f f f r f r f r f r

s xx yy s xx yy s xx yy s xx yy

f f f f f r f r f r f r

s xx yy s xx yy s xx yy s xx yy

f r f

s xx

t l t l t t l l t t l l

m I I m I I m I I m I I

t l t l t t l l t t l l

m I I m I I m I I m I I

t t l l

m I

1 3 5 7

2

4

6

B B B B

B

B

B2 2 2 2

2 2 2 2

1 1 1

1 1 1 1

1 1 1 1

r f r f r r r r r

yy s xx yy s xx yy s xx yy

f r f r f r f r r r r r

s xx yy s xx yy s xx yy s xx yy

s s s s

f f r r

xx xx xx xx

t t l l t l t l

I m I I m I I m I I

t t l l t t l l t l t l

m I I m I I m I I m I I

m m m m

t t t t

I I I I

8

9

10

B

B

B

f f r r

yy yy yy yy

l l l l

I I I I

11B

26

3.2.2. Model validation

The derived vehicle model (3.7) is validated via simulation with vehicle

software Carsim® and MATLAB/Simulink. Therefore, it is driven with the test

vehicle in Carsim® with actuator force equal to zero over a road, where the

height profile was pre-defined. The measured vertical wheel acceleration from

the test vehicle was input to the proposed model simultaneously. Hence,

simulated heave, roll, and pitch motion and suspension state are compared to

the values measured in the vehicle.

An irregular and asymmetric road height profile used in model validation is

shown in Figure 3.5. The speed of test vehicle was 20 kph. Figure 3.6 and 3.7

show that the vehicle body motion and suspension deflection calculated from

the proposed vertical full-car model. It is shown that the results from the model

correspond well with the actual values. A small error is occurred mainly from

nonlinear damping characteristics of the test vehicle which is not considered in

the linear model. However, the error is tolerable for suspension control in the

interesting frequency range up to about 5 Hz.

Figure 3.5. The height profile of the road for model validation.

27

Figure 3.6. Comparison of vehicle body motion of actual and simulated

vehicle. (a) vertical displacement, (b) roll angle, and (c) pitch angle

28

Figure 3.7. Comparison of suspension deflection of actual and simulated

vehicle. (a) FL, (b) FR, (c) RL, and (d) RR suspension

29

Chapter 4 Suspension State Estimation

In recent decades, many suspension control approaches to improve ride

quality and handling performance were developed assuming that all states are

available. Implementation of these suspension control laws requires

information on states which may be difficult to access. Indeed, one of issues in

active / semi-active suspension control is to estimate states of the suspensions

from easily accessible and inexpensive measurements such as accelerations or

angular velocities for on-board suspension control applications. This requires

observer that can produce estimates of the states such as suspension deflection

and velocity using reduced number of sensors. The implementation of the

observer with low cost is one of the main challenges to car manufacturers aim

at equipping mass-produced cars with controlled suspension systems.

In this chapter, a road disturbance-decoupled suspension state observer is

designed based on the reduced full-car model. Two sensor configurations are

considered to make measurement information which is easily accessible and

convenient to use for active / semi-active suspensions. The estimation

performance of the proposed observer has been examined via simulation study

and field tests.

30

4.1. Design of a Suspension State Estimator

The overall structure of suspension state observer with reduced full-car model

is shown in Figure 4.1. The proposed system involves three elements:

measurement of body and front wheel motion, estimation of rear wheel

acceleration, and suspension state observer. The functions and relationship

between the three elements can be summarized as follows.

The suspension states (x) and acceleration of wheels (�̈�𝒖) are influenced by

the vertical road displacement input (𝒛𝒓). The body motion is measured by

accelerometers or gyroscopes which is represented by y in Figure 4.1. The

acceleration of front wheels is measured by accelerometers which is

represented by �̈�𝒖,𝒇∗ in Figure 4.1. These measurements are utilized in

suspension state observer and rear wheel acceleration estimator. Two sensor

configurations are introduced in subsection 4.1.1.

Vehicle

Reduced full car model

Body and front wheel motion sensors

Measurement update

Rear wheel acceleration estimator

Suspension state observer

Figure 4.1. Block diagram of suspension state observer.

31

The acceleration of rear wheels should be estimated because no

accelerometer is mounted at rear wheels in this research. The estimated

acceleration of rear wheels (�̂̈�𝒖,𝒓) is utilized in suspension state observer. This

estimator can be replaced by additional accelerometers, but using the least

sensors is one of goal in this work. The estimation algorithm and its analysis

are described in subsection 4.1.2.

The suspension state observer utilizes measured acceleration of front wheels

and estimated acceleration of rear wheels in time process model. The measured

body motion is utilized in measurement update to estimate the suspension state.

The priori state estimate and posteriori estimate are represented by �̂�− and �̂�+,

respectively in Figure 4.1. The Kalman filter to minimize the estimation error

covariance is designed in subsection 4.1.3.

4.1.1. Sensor configurations

As shown in Figure 4.2, two sensor configurations which are inexpensive to

be mounted are introduced in this section. Two accelerometers at front wheels

are used for the road disturbance input measurements in all sensor

configurations. The road disturbance input measurements are given in (4.1).

* * *

1 2 3 4

1 1 2 2 3 3 4 4

ˆ ˆ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

T

u u u u

T

u u u u

t z t z t z t z t t t

z t t z t t z t t z t t

w w ξ (4.1)

where ξi, i=1…4, are assumed to be zero mean stationary white noise processes.

32

X

Y

Z3 point body acceleration

Front wheel acceleration

X

Y

Z

Front wheel acceleration

Z-axis acceleration

X, Y-axis Angular velocities

(a) sensor configuration 1 (b) sensor configuration 2

Figure 4.2. Two sensor configurations for measurement.

From the sensor configuration 1, the body motion is measured from three

accelerometers mounted at three corners of the sprung mass. The measurement

equation is given in (4.2).

1 2 3( ) [ ( ) ( ) ( )] ( )

( ) ( ) ( )

( ) ( ) ( )

T

s s s

T TT T T T T T

t z t z t z t t

t t t

t t t

1 1

2 4 6 2 4 6 1

1 1 1

y v

A A A x B B B u v

H x J u v

(4.2)

From the sensor configuration 2, the body motion is measured from two gyros

and one accelerometers mounted at center of gravity point of the sprung mass.

The measurement equation is given in equation (4.3).

2 9 2 2

( ) [ ( ) ( ) ( )] ( )

( ) ( ) ( )0

( ) ( ) ( )

T

s

TT T T

t z t t t t

t t tI

t t t

2 2

9

9 10 11 2

2 2 2

y v

Ax B B B u v

H x J u v

(4.3)

where the measurement noise vectors v1 and v2 are assumed to be zero mean

stationary white noise processes.

33

4.1.2. Estimation of rear wheel acceleration

In the reduced full-car model as written in (3.7), each acceleration of wheels

is applied to the system as disturbance input and should be obtained. The exact

way to obtain the disturbance information is the acceleration measurement by

accelerometers mounted at each wheels. To reduce the number of sensors, only

two accelerometers at front wheels are used for the road disturbance input

measurements. Then the acceleration of the rear wheels should be estimated

and two estimation methods are proposed in this research.

The first method for estimation of acceleration of rear wheels is time delaying

of measured acceleration of front wheels. This time delay concept was proposed

in many previous work [Marzbanrad'04, Marzbanrad'02]. In these work, the

road disturbance input to front wheels is delayed equally to rear wheels. This

can be reasonable when the vehicle speed is constant. On the additional

assumption that the tire grip on the road is keeping with no tire deflection, the

acceleration of front wheels would be delayed to rear wheels as follows:

3 4 1 2ˆ ˆ( ) ( ) ( ) ( )

T T

u u u delay u delayz t z t z t t z t t (4.4)

where �̂̈�𝒖𝟑(𝒕) and �̂̈�𝒖𝟒(𝒕) are estimated rear left and right wheel acceleration,

respectively. tdelay is the delayed time which is represented with the longitudinal

velocity vx and the wheel base L as written in (4.5).

delay

x

Lt

v (4.5)

The time delaying method for estimation of acceleration of rear wheels is

based on the assumption of constant speed. When the vehicle speed is low, the

delayed time step is strongly influenced by the slight change of the speed. In

34

this case, the time delay method is not suitable and another method is proposed

to reduce the estimation error.

The second method for estimation of acceleration of rear wheels is using

estimated suspension velocity and body motion. For example, the rear left

suspension velocity which is the 6-th state variable in the reduced full-car

model as defined in (3.8) can be represented as (4.6) from the time derivative

of equation (3.6).

6 3 3

3

s u

s r r u

x z z

z l t z

(4.6)

From time derivative of equation (4.6), the acceleration of rear left wheel is

represented as follows:

3 6u s r r

dz z l t x

dt (4.7)

The estimated acceleration of rear left wheel can be written with the estimated

state variables as follows:

3 6

ˆ ˆˆ ˆ ˆu s r r

dz z l t x

dt (4.8)

In the same way, the estimated acceleration of rear right wheel can be

obtained as follows:

4 8

ˆ ˆˆ ˆ ˆu s r r

dz z l t x

dt (4.9)

If the present vehicle speed is higher than threshold value, the rear wheel

acceleration is estimated with the first method. Otherwise, the second method

is used in the rear wheel acceleration estimator.

35

4.1.3. Suspension state estimator

Considering the computing period of ECU, the discrete-time Kalman filter is

designed to minimize the estimation error covariance matrix. The continuous

system represented in (3.7) is transformed into a discrete-time system of which

the time step is T as follows:

k k-1 k-1 w k-1x Fx Gu G w (4.10)

where

1

1

T

T

T

e T

e T

e T

A

A

A

w w w

F I A

G F I A B B

G F I A B B

In this process, the real road disturbance input vector wk is substituted by the

measured and estimated wheel acceleration vector w* in (4.1). The

measurement noise vector ξk-1 is regarded as the process noise vector and then

the time process equation is represented as follows:

* k k-1 k-1 w k-1 k-1

x Fx Gu G w ξ (4.11)

The measurement equation (4.2), and (4.3) are also transformed into

discretized equations.

i i i i ,k k k ,ky H x J u v (4.12)

where the subscript i means the i-th sensor configuration hereinafter. The noise

processes ξk and vi,k are white, zero-mean, uncorrelated, and have known

covariance matrices Q and Ri, respectively:

36

, , ,

,

~ 0, ,

~ 0, ,

T

k j

T

i i i i i k j

T

i

E

E

E

k k j

k k j

k j

ξ Q ξ ξ Q

v R v v R

ξ v 0

After a posteriori estimated states �̂�𝟎+ and a posteriori error covariance

matrix 𝐏𝟎+ are initialized, the following equations are computed for each time

step [Simon'06]. A priori error covariance matrix 𝐏𝐤− is updated as follows:

T - +

k k-1P FP F Q (4.13)

The optimal Kalman gain is obtained by (4.14).

1T T

i i i i

- -

k k kK P H H P H R (4.14)

A time update, a posteriori estimation, and a posteriori error covariance

matrix are obtained by (4.15).

*

,

ˆ ˆ

ˆ ˆ ˆi i i

i

- +

k k-1 k-1 w k-1

k k k k k k

+ -

k k k

x Fx Gu G w

x x K y H x J u

P I K H P

(4.15)

The optimal Kalman gain is computed each step and the real-time matrix

inversions are conducted. This is a drawback of Kalman filter when the system

matrix size is large such as the full-car model. The steady-state Kalman filter is

not optimal, however, this can save a lot of computational effort and the

estimation performance is nearly indistinguishable from that of the optimal

Kalman filter. One way to determine the steady-state Kalman gain is finding

the steady-state value of the estimation error covariance matrix as written in

(4.16) which called a discrete algebraic Riccati equation (DARE).

37

1

T T T T

i i i i i

P FP F FP H H P H R H P F Q (4.16)

Once 𝐏∞ is obtained, the steady-state Kalman gain 𝐊∞ is obtained by

substitution of 𝐏∞ for 𝐏𝐤− in (4.14) as follows:

1T T

i i i i

K P H H P H R (4.17)

4.1.4. Algorithm to estimate sensor bias

In our work, because the sensor measurement is used for system disturbance

input, the sensor bias generates drift of the estimated states. To deal with the

unknown but constant sensor bias, a recursive algorithm to estimate the sensor

bias is considered. In B. Friedland’s work, the optimum estimate of the state

and constant bias for linear system is proposed [Friedland'69]. The main results

can be summed up as follows.

The dynamic equations and observation equation are written as (4.18).

1

1

k k k k k k

k k

k k k k k k

x A x B b

b b

y H x C b

(4.18)

where xk is the original process state, bk is the bias vector, ξk is process noise

vector, and ηk is observation noise vector. The ξk and ηk are white, zero-mean,

and uncorrelated.

The optimum estimate of the state can be expressed as

ˆˆ ( )k k x kx x V k b (4.19)

Where �̃�𝒌 is the bias-free estimate, computed as if no bias were present, �̂�𝒌

is the optimum estimate of the bias, and 𝑽𝒙(𝒌) is a matrix which can be

38

interpreted as the ratio of the covariance of �̃�𝒌 and �̂�𝒌. The bias-free state and

the bias estimation equations are written as follows:

1 1 1 1

1 1 1 1 1 1

( )

ˆ ˆ ˆ ˆˆ( ) ( )

k k k x k k k k

k k b k k k k k k k k

x A x K k y H A x

b b K k y H A x B b C b

(4.20)

where �̃�𝒌(𝒌) is the bias-free gain and 𝑲𝒃(𝒌) is the bias gain.

The results presented in his work are based on expressing the solution of the

estimation error variance equation of the problem with bias present in terms of

the solution of the variance equation for bias-free estimation and other matrices

which depend only on the bias-free computations. By this technique the

estimation of the bias is essentially decoupled from the computation of the bias-

free estimate of the state.

39

4.2. Performance Evaluation of Estimator

To evaluate the estimation performance of proposed observer, a simulation

study has been conducted by using the vehicle software Carsim® and

MATLAB/Simulink. Then the observer and semi-active damper prototype have

been implemented on a test vehicle.

4.2.1. Simulation results

Passing a single bump without actuator control scenario has been simulated

to evaluate the performance of the observer. The single bump road height

profile described by equation (4.21) is applied to the right wheels only so that

the roll and pitch motions are generated simultaneously.

2

1 cos ( 10) 10, 10( )

0

r b

r b

h X for X Lz X L

otherwise

(4.21)

where zr is road elevation, X is longitudinal displacement, hr is a half of the

bump height, and Lb is the bump width. In this study, hr =0.05 m and Lb=3.6 m

were used. The simulated vehicle speed was 20 kph. The nominal parameters

of simulated vehicle given in Carsim® are shown in Table 3.1 which is used to

design the observer. The nonlinear relation between the suspension velocity and

the damping force used in simulation study is shown in Figure 4.3.

40

Figure 4.3. The relation between the suspension velocity and the damping

force used in simulation given in Carsim® .

The proposed observer described in section 4.1 was designed to completely

decouple the unknown road disturbance. In other works, the road disturbance

was not completely removed and was considered as unknown input

[Pletschen'16, Dugard'12, Ren'16]. A disturbance-coupled observer with full-

car model has been designed to compare the estimation performance as written

as follows:

ˆ ˆ ˆ

o o o o o

o o o o

o o o o o o o o o

x A x B w

y H x v

x A x B w K y H x

(4.22)

where the state xc and disturbance input wc are defined as follows:

1~4 1~4 1~4

1 2 3 4

T

u s u u r

T

r r r r

z z z z z z

z z z z

o

o

x

w

The states are composed with bounce, roll, pitch velocities of the body, each

41

unsprung mass velocity, each suspension deflection, each tire deflection. The

unknown disturbance input is the derivative of road elevation, which is

considered as system process noise when the Kalman gain Ko is computed.

In Figure 4.4 and 4.5, comparison of some estimated states by the proposed

disturbance-decoupled observer (DDO) and disturbance-coupled observer

(DCO) and actual states (heaving acceleration, heaving, rolling, pitching

velocities, and suspension velocities) for the single bump simulation are shown.

The legend “actual” indicates that the signals have been obtained by Carsim®

outputs, and the legends “estimated, DDO” and “estimated, DCO” indicate that

the signals have been computed by the proposed disturbance-decoupled

observer and disturbance-coupled observer, respectively. The titles FL, FR, RL,

and RR represent the front left, front right, rear left, and rear right suspensions,

respectively. Both observers are designed with the sensor configuration 1. The

RMS noise value of accelerometer used in simulations are 0.049 m/s2. It is

illustrated that the estimation performance of the proposed DDO is much better

than that of the DCO because the proposed observer completely removes the

effect of unknown road disturbance on the estimation error. It is shown that the

estimated states by the proposed DDO are quite close to the actual states. In

Figure 4.5, it is also shown that the front suspension velocity is estimated more

accurately than rear suspension velocity by DDO. This estimation error is

mainly caused by the assumption that the road disturbance input is equally

delayed from front to rear wheels.

42

Figure 4.4. Comparisons of actual and estimated states by disturbance-

coupled observer and the proposed observer for single bump road test. (a)

heaving acceleration, (b) heaving, (c) rolling, and (d) pitching velocities.

43

Figure 4.5. Comparisons of actual and estimated suspension velocities by

disturbance-coupled observer and the proposed observer for single bump road

test. (a) FL, (b) FR, (c) RL, and (d) RR suspension.

44

4.2.2. Vehicle test results

In Figure 4.6, prototype of semi-active suspension system and sensors

mounted on front side of the test car are shown. Four semi-active damper

prototypes have been installed at each corner of the test car. The semi-active

damping force curves used in field test are shown in Figure 4.7. The damping

rate of each damper was controlled by unknown control strategy in real time

during the experiment. The proposed observer in this work would be used for

semi-active suspension control strategy, but the experiment has been conducted

to evaluate the estimation performance only. Therefore, the control logic was

assumed to be unknown. The measurement from accelerometers at three

corners of the sprung mass was used for state estimation and the measurement

from linear variable differential transformer (LVDT) was used for getting

reference data only. Using the LVDT data for state estimation is not suitable for

mass-produced cars because the deflection sensor is expensive and has a short

life-time. One accelerometer and two gyros have been mounted on the center

of gravity point of the sprung mass for measurement of heaving acceleration,

pitching and rolling velocity, respectively. These three body-mounted sensors

were used for getting reference data or state estimation.

Two test cases, single bump and low speed off-road, have been used to

evaluate the performance of the observer. In single bump case, the vehicle speed

was about 30 kph and the acceleration of rear wheels was estimated from time

delaying of measured acceleration of front wheels. In off-road case, the vehicle

speed was less than 5 kph and the acceleration of rear wheels was estimated by

using estimated suspension velocity and body motion.

45

Sprung mass

LVDT

Accelerometer

Semi-active damper prototype

Spring

Accelerometer

Figure 4.6. Semi-active suspension system of front side and mounted sensors

for the field test.

Figure 4.7. The damping force versus suspension velocity curves of the semi-

active damper prototype.

46

In Figure 4.8 ~ 4.11, comparisons of some estimated and measured states for

the single bump case and the off-road case are shown. The “reference” indicates

that the signals have been obtained by additional sensors, and the legends

“estimated1” and “estimated2” indicate that the signals have been computed by

the observers using the sensor measurements with the sensor configuration 1

and 2, respectively. In Figure 4.8 and 4.10, the reference data of heaving

velocity was obtained by numerical integration of measured acceleration from

body-mounted sensor. In Figure 4.9 and 4.11, the reference data of suspension

velocity was obtained by numerical differentiation of measured suspension

deflection from LVDT. In both test cases, it is illustrated that the estimated

states are quite close to the actual states for all sensor configurations and

therefore the estimation results can be used for semi-active suspension control

strategy in real-time. The root-mean-square errors of estimated states by

observers with the sensor configuration 1 and 2 are compared in Table 4.1. The

estimation performance of heaving, rolling, and pitching motion by observer

with sensor configuration 2 is better than that of observer with sensor

configuration 1 because the body motion measurement is used for state

estimation directly. The vertical acceleration measurement from accelerometers

at three corners of the sprung mass is distorted as rolling or pitching motion is

generated, while the measurement from accelerometer and gyros mounted on

the center of gravity point of the sprung mass is not influenced. The suspension

velocity is the most important state because many semi-active control strategies

are based on this signal. In general, the estimation performance of front

suspension velocity is better than that of rear suspension velocity because the

47

front wheel acceleration is measured directly whereas the rear wheel

acceleration is estimated to reduce the number of sensors. The suspension

velocity estimation performance of observer with the sensor configuration 1 is

similar to that of observer with the sensor configuration 2, relatively.

Table 4.1. The experimental estimation results

Estimated state

RMSEa

Single bump case Off-road case

S.C.b 1 S.C. 2 S.C. 1 S.C. 2

Heaving acceleration (m/s2) 0.297 0.053 0.309 0.013

Heaving velocity (m/s) 0.030 0.002 0.012 0.001

Rolling velocity (deg/s) 1.026 0.393 1.107 0.488

Pitching velocity (deg/s) 1.589 0.697 0.577 0.296

Suspension velocity, FL (mm/s) 42.2 28.5 37.7 28.4

Suspension velocity, FR (mm/s) 42.1 49.1 35.5 25.6

Suspension velocity, RL (mm/s) 58.8 61.6 39.0 41.3

Suspension velocity, RR (mm/s) 48.6 52.8 30.1 37.1

a Root-mean-square error

b Sensor configuration

48

Figure 4.8. Comparisons of reference data and estimated states for single

bump road case. (a) heaving acceleration (b) heaving velocity, (c) rolling

velocity, and (d) pitching velocity.

49

Figure 4.9. Comparisons of reference data and estimated suspension velocities

for single bump road case. (a) FL, (b) FR, (c) RL, and (d) RR suspension.

50

Figure 4.10. Comparisons of reference data and estimated states for off-road

case. (a) heaving acceleration (b) heaving velocity, (c) rolling velocity, and

(d) pitching velocity.

51

Figure 4.11. Comparisons of reference data and estimated suspension

velocities for off-road case. (a) FL, (b) FR, (c) RL, and (d) RR.

52

In Figure 4.12, the estimated acceleration of rear wheels by the two methods

discussed in subsection 4.1.2 for the off-road case is shown. The legends

“delayed” and “estimated” indicate that the signals have been computed by the

time delaying method and by the proposed method using estimated suspension

velocity and body motion, respectively. The reference data has been acquired

from additional accelerometers mounted on rear wheels. Because the vehicle

speed is low and not constant, the phase and magnitude of front wheel

acceleration is not equally delayed to rear wheel. In this case, the proposed

estimation algorithm has improved the estimation performance of the rear

wheel acceleration and suspension states.

Figure 4.12. Comparisons of measured and estimated acceleration of rear

wheels for off-road case. (a) RL, (b) RR

53

Chapter 5 Design of Active Suspension

Control Algorithm

From a careful review of considerable amount of literature, preview active

suspension systems have even greater potential than feedback systems.

However, the current state-of-the-art in preview active suspension control

technology has main challenge on obtaining road preview information. It

requires precise, expensive sensors to detect road information such as a laser

scanner or a stereo camera. Moreover, a drawback of “look-ahead” sensor is

that they are vulnerable, potentially confused by water, snow, or other soft

obstacles.

In this Chapter, active suspension control algorithm based on the reduced

vertical full-car model is introduced. The main control objective of low-

bandwidth active suspension control is ride comfort improvement such as

isolation of the vehicle body from external disturbances coming from irregular

road surfaces and internal disturbances created by cornering, acceleration, or

deceleration. A feedback control approach for ride comfort is considered, then

a partial preview control without road information is developed. The wheel base

preview is relatively reliable and economical when compared with look-ahead

sensor. The vertical acceleration information of front wheels was used to obtain

preview control inputs for rear suspension actuators.

54

5.1. Linear Quadratic Optimal Control

A time invariant linear system can always be stabilized by a linear feedback

if it is controllable or stabilizable. A linear quadratic (LQ) optimal control for

the reduced quarter-car model is introduced before it is extended to the reduced

vertical full-car model.

The reduced quarter-car suspension system in (3.3) is controllable. It can be

easily proved from that the controllability matrix written as (5.1) has full rank.

.

2

10

1

s

cont r r r

s s

mR B A B

c

m m

(5.1)

Therefore, the system can be stabilized by LQ optimal control. To find an

input that suffices both the requirement of fast control and does not require

infinite control power, an optimization problem has to be solved. A very useful

criterion is the quadratic integral criterion as follows:

0

lim

f

f

t

T T

c ct

J y t Qy t u t Ru t dt

(5.2)

where yc is the interested output variable and Q and R is a diagonal non-negative

weighting matrix containing the weighting factors. For ride comfort

improvement and regulation of the suspension rattle space, the yc can be

formulated as follows:

s

c reduced

s u

zy Cx Du

z z

(5.3)

55

where C and D is written as follows:

1

,

1 0 0

s s s

k c

m m mC D

Now consider (5.3), substituting this into (5.2) results in

0

0

0

lim

lim

lim

f

f

f

f

f

f

t

T T

reduced reducedt

t T T

T T

reduced reducedT Tt

t

c cT T

reduced reducedTt

c c

J Cx Du Q Cx Du u Ru dt

C QC C QDx u x u dt

D QC D QD R

Q Nx u x u dt

N R

(5.4)

If (Ar, C) is observable, then the optimal closed loop control system written

in (5.5) is stable.

1 T T

reduced r r c c r reducedx A B R N B P x (5.5)

where P (strictly positive definite) is the solution of the Riccati equation as

follows:

1 1

1 1 0

TT T

r r c c r r c c

T T

r c r c c c c

P A B R N A B R N P

PB R B P Q N R N

(5.6)

The control law is obtained as a state feedback

c reducedu K x (5.7)

with feedback gain, 1 T T

c c c rK R N B P .

The LQ optimal control can be applied to the reduced vertical full-car model

in (3.7). In reduced full-car model, the heave, roll, and pitch motion of the body

56

and suspension motion are interested output for ride comfort as follows:

1~4 1~4( ) ( )T

s s u s uz z z z z

cy Cx Du

(5.8)

with

TT T T T T T T T T T T

TT T T

9 10 11 1 3 5 7 2 4 6 8

9 10 11

C A A A Π Π Π Π Π Π Π Π

D B B B 0 0

where iΠ denotes a 𝟏 × 𝟏𝟏 matrix with a unity located in the i-th columns

and with remaining elements equal to zero. The output can be incorporated into

the quadratic integral criterion as follows:

0

0

lim

lim

f

f

f

f

t

T T

t

t

T T

t

J t t t t dt

dt

c c

c c

T

c c

y Qy u Ru

Q Nx u x u

N R

(5.9)

From a similar process, the feedback control law for the reduced full-car

suspension system is obtained as follows:

cu K x (5.10)

The feedback gain can be given as follows:

1 T T

c

c c

K R N B P (5.11)

Where P is the solution of the Riccati equation as follows:

1 1

1 1

TT T

T T

c c c c

c c c c c

P A BR N A BR N P

PBR B P Q N R N 0 (5.12)

57

5.2. Wheelbase Preview Control

In order to develop a preview control algorithm without road information,

the road disturbance delay between the front and the rear wheels is considered.

The wheelbase preview control algorithm using delayed disturbance has been

introduced before [Moran'93, Marzbanrad'02, Marzbanrad'03]. However, in

their work, the algorithm still has limitations from a practical point of view such

as assumption that suspension state and road disturbance is available. In our

work, the vertical acceleration information of front wheels can be used to obtain

preview control inputs for rear suspension actuators because it is the

disturbance input of the proposed reduced full-car model.

5.2.1. Wheelbase preview information

In (4.4), the vertical acceleration of front wheels is delayed equally to rear

wheels with assumptions that the vehicle speed is constant and the tire grip on

the road is keeping with no tire deflection. Considering the tire dynamics in

(3.5), an analysis of the time delay method is conducted on frequency domain.

Taking Laplace transforms for (3.4) and (3.5) without control input, the

following equation (5.13) and (5.14) can be obtained.

58

2

1 1 1 2 2 2 3 3 3

4 4 4 1 1 1 2 2 2

3 3 3 4 4 4

2

1 1 1 2 2 2 3 3 3

4 4

( ) ( ) ( ) ( ) ( ) ( ) ( )

( s ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( s ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

( )

s s s s s

s u u

u u

xx f s f s r s

m s Z s c s k Z s c s k Z s c s k Z s

c k Z s c s k Z s c s k Z s

c s k Z s c k Z s

I s s c s k t Z s c s k t Z s c s k t Z s

c s k

4 1 1 1 2 2 2

3 3 3 4 4 4

2

1 1 1 2 2 2 3 3 3

4 4 4 1 1 1 2 2 2

3 3

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( )

r s f u f u

r u r u

yy f s f s r s

r s f u f u

r u

t Z s c s k t Z s c s k t Z s

c s k t Z s c s k t Z s

I s s c s k l Z s c s k l Z s c s k l Z s

c s k l Z s c s k l Z s c s k l Z s

c s k l Z

3 4 4 4( ) ( ) ( )r us c s k l Z s

(5.13)

2

1 1 1 1 1 1 1 1

2

2 2 2 2 2 2 2 2

2

3 3 3 3 3 3 3 3

2

4 4 4 4 4 4 4 4

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

u t u s t r

u t u s t r

u t u s t r

u t u s t r

m s c s k k Z s c s k Z s k Z s

m s c s k k Z s c s k Z s k Z s

m s c s k k Z s c s k Z s k Z s

m s c s k k Z s c s k Z s k Z s

(5.14)

With parameter assumptions of k i = k (i=1…4), ci = c (i=1…4), tf = tr, and lf

= lr, for simplicity, Laplace transformation of bounce, roll, and pitch position

of center of sprung mass with respect to road disturbance can be expressed as

follows:

1 2 3 42

1 2 3 42

1 2 3 42

( )( ) ( ( ) ( ) ( ) ( ))

( ) B( )

( ) /( ) ( ( ) ( ) ( ) ( ))

( ) B( )

( ) /( ) ( ( ) ( ) ( ) ( ))

( ) B( )

s r r r r

s

f

r r r r

x

f

r r r r

y

C sZ s Z s Z s Z s Z s

m s A s s

C s ts Z s Z s Z s Z s

m s A s s

C s ls Z s Z s Z s Z s

m s A s s

(5.15)

where

2 2

2 2

( ) , ( ) 4( )( )

( ) , / , /

u t u t

t t x xx f y yy f

A s m s cs k k B s m s k cs k

C s ck s kk m I t m I l

59

Laplace transformation of wheel accelerations with respect to road

disturbance can be expressed as follows:

11 12 13 14 11

21 22 23 24 22

31 32 33 34 33

41 42 43 44 44

( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( )( )

ru

ru

ru

ru

G s G s G s G s Z sZ s

G s G s G s G s Z sZ s

G s G s G s G s Z sZ s

G s G s G s G s Z sZ s

(5.16)

where

11

2

11 12

13 14

23 14 24 13 34 12

( ) ( ), 1,...,4

( ) ( ), , 1,...,4

( ) ( ) ( ) ( ) , ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ), ( ) ( ) ( ) ( )

( ) ( ), ( ) ( ), ( ) ( )

ii

ij ji

t

G s G s for i

G s G s for i j

k sG s D s E s F s G s D s E s F s

A s

G s D s E s F s G s D s E s F s

G s G s G s G s G s G s

where

2 2

2 2

2

2

( ) / ( ) /( ) ( )( ) , ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) / ( )( )

( ) ( ) ( )

t t

s x

t

y

s C s k s C s kC s C sD s E s

A s m s A s B s A s m s A s B s

s C s k C sF s

A s m s A s B s

The validation of the time delayed method can be conducted by analysis of

transfer functions. For example, from equation (5.16), the Laplace

transformation of time delayed front left wheel acceleration can be expressed

as follows:

1

2

1 11 12 13 14

3

4

( )

( )( )( ) ( ) ( ) ( ) ( )

( )

( )

delay

r

t s r

u delay

r

r

Z s

Z sZ t t s e G s G s G s G s

Z s

Z s

(5.17)

On the assumption that symmetric road disturbance of left and right wheels,

the road input can be expressed as follows:

60

1 2

3 4

(s) Z ( ) Z ( )

(s) (s) (s)delay

r r r

t s

r r r

Z s s

Z Z e Z

(5.18)

In this case, the transfer function of delayed front left wheel acceleration and

that of rear left wheel acceleration can be expressed as follows:

1

11 12 13 14

1_

331 32 33 34 3

( )( )( ( ) ( ) ( ) ( ))

( )

( )

( )( ( ) ( ) ( ) ( )) ( )

( )

delay delay delay

delay delay

t s t s t su delay

r

delay

t s t su

r

Z t t se G s G s e G s e G s

Z s

G s

Z sG s G s e G s e G s G s

Z s

(5.19)

The Bode plot of transfer functions in (5.19) is shown in Figure 5.1.

Figure 5.1. Bode plots from symmetric road elevation input to delayed front

left wheel acceleration and that of rear left wheel acceleration in full-car

model.

61

It is noted that magnitude gap between delayed front wheel acceleration and

rear wheel acceleration is caused by the frequency of road disturbance, but their

phase gap is negligible. As shown in figure 5.1, the magnitude of delayed front

wheel acceleration is expected to be larger than that of actual rear wheel

acceleration under 2.5 Hz road disturbance situation. An opposite result is

expected under 9 Hz road disturbance situation. The acceleration magnitude

gap according to the road disturbance was found by simulation with Carsim®.

In Figure 5.2, delayed front wheel acceleration and rear wheel acceleration

generated by symmetric sinusoidal road disturbance input in simulation are

compared. The simulation result shows the expected acceleration magnitude

gap and little phase gap. From the analysis of the acceleration time delay from

front to rear wheels, it is reasonable that the vertical acceleration information

of front wheels can be used to preview control for rear active suspension.

62

Figure 5.2. Delayed front left wheel acceleration and that of rear left wheel

acceleration generated by sinusoidal road disturbance simulation. (a) 2 Hz and

(b) 9 Hz road disturbance input, respectively.

63

5.2.2. Optimal preview control

The optimal linear preview control problem for active suspension was

considered by Bender, Tomizuka, and Foag. Solution of the problem calls for

linear feedback of the full state vector and feedforward of another variable that

depends on the future road inputs measured directly in the preview scheme. The

main results can be summed up as follows [Hac'92].

Consider the suspension system pre-defined by (3.7) where the state vector

x(t) is fully available, x0 is deterministically given and w(t) can be measured

exactly up to tp time units ahead of time t (i.e. 𝐰(𝝉), 𝛕 ∈ [𝒕, 𝒕 + 𝒕𝒑] is known).

Consider also the quadratic integral criterion as follows:

01 12 2

1( ) ( )

2

1[ ]

2

T

T

TT T T T T

p pt

J T T

dt

x P x

x Q x 2x N u u R u 2x Q w w Q w

(5.20)

where Q1, Rp, PT, and Q2 are symmetric, time-invariant weighting matrices such

that Rp is positive definite and 1

1

T

n p p p

Q Q N R N nonnegative definite. Then

the problem of determining an input which minimize the criterion (5.20),

0 0( ) [ ( ), ( ), , ]pt f t t t t t u x w , is called the deterministic

linear optimal preview control problem. Suppose now that the problem duration,

T, approaches infinity. In this case, instead of J, consider the cost rate 𝑱′ = 𝑱 𝑻⁄ .

When T is finite, the optimal control that minimizes J also minimizes J'. Then

the optimal control uo(t) that minimize 𝑱∞′ = 𝐥𝐢𝐦

𝑻→∞𝑱 𝑻⁄ is given by

1( ) [( ) ( ) ( )]T T T

o p pt t t u R N B P x B r (5.21)

64

where P is a nonnegative definite symmetric solution of the algebraic Riccati

equation as follows:

1T T

n n p n

0 PA A P PBR B P Q (5.22)

where 1 T

n p p

A A BR N and the preview control vector r(t) is given by

120

( ) ( ) (p

ct

t t d

TA

wr e PB Q w (5.23)

where 1 T

c n p

A A BR B P is asymptotically stable if the pair (A, B) is

stabilizable and (An, T) is detectable where T

n Q T T .

The concept of wheelbase preview disturbance information is shown in

Figure 5.3. No preview information for front suspension is provided and

vertical acceleration history of front wheels is used to preview information for

rear suspension as equation (5.24).

1

2

0

0( ) , [0, ]

( )

( )

delay delay

u delay

u delay

t tz t t

z t t

w (5.24)

65

Figure 5.3. Wheelbase preview disturbance information.

Using the same quadratic integral criterion in (5.9), the wheelbase preview

control input using optimal preview control approach is obtained as follows:

1

1

( ) [( ) ( ) ( )]

( ) ( )

T T T

opc delay

T

delay

t t t

t t

c c

c c

u R N B P x B r

K x R B r (5.25)

where the wheelbase preview control vector rdelay(t) is given by

0( ) (

delayd

t

delay delayt t d

TA

wr e PB w (5.26)

where P is the solution of the Riccati equation above in (5.12), and

1 1T T

d c

c c

A A BR N BR B P (5.27)

5.2.3. Model predictive control

In LQ optimal control approach, hard constraints cannot be explicitly

incorporated and hence have to be minimized in the cost function. For active

suspension systems, the constraints on suspension rattle space in order not to

reach the bump stoppers, the mechanically limited actuator displacements and

also the constrained of the actuator force should be considered in controller

design. Since vertical acceleration history of front wheels can be used to

preview information for rear suspension, furthermore constraints on control

variables should explicitly be incorporated and the optimization has to be

carried out in real-time, model predictive control (MPC) seems to be the

appropriate controller design scheme. MPC approaches for active suspensions

with preview road information based on a quarter-car model [CHO'99], a half-

car model [Mehra'97], and full-car model [Göhrle'15] were introduced. The

66

main results can be summed up as follows.

y(k)

past future

k k+1 k+2 k+N k+P

yr(k+i)

yp(k+i)

wp(k+i)

u*(k+i)

... ...

Control horizon, N

Prediction horizon, P

Figure 5.4. Schematic of MPC concept.

Consider the discretized suspension system pre-defined in (4.10) and (5.8).

( 1) ( ) ( ) ( )

( ) ( ) ( )

k k k k

k k k

wx Fx Gu G w

y Cx Du (5.28)

At each sample time, a set of N control moves u(k), u(k+1), …, u(k+N-1) are

computed by solving the following optimization problem:

2

( ), ( 1)... ( 1)1

12

0

min [ ( ) ( )]

[ ( )]

P

i p rk k k N

i

N

i

i

Q k i k i

R k i

u u uy y

u

(5.29)

such that

EU b (5.30)

67

where yp(k+i) are the predicted values of the controlled variable at the i-th future

sample time. The inequalities in (5.30) represent constraints such a rate and/or

absolute bounds on control/output variables.

The optimization problem in (5.29) can be represented as the following

equivalent vector space quadratic programming (QP) formulation.

minT TJ Q R

uy y u u (5.31)

where

[ ( 1) ( )]

[ ( ) ( )]

[ ( ) ( 1)]

( ( 1) ( ))

( ( ) ( ))

T

T

T

k k P

k k N

k k P

Q diag Q k Q k P

R diag R k R k N

y y y

u u u

w w w

and relationship among �⃗⃗� , x(k), �⃗⃗⃗� , and �⃗⃗� is given by

( ) u wk y x u w (5.32)

where Λ, Γu, and Γw are all matrices that can be constructed from the state space

model given by (5.28). Then the equation (5.31) is represented as follows:

min ( ( ) ) ( ( ) )

( )

2 2 2

T T

u w u w

T T T T T T

u u w w

T T T T T

w u w u

J k Q k R

Q Q R Q

Q Q Q

ux u w x u w u u

x x u u w w

x w x u w u

(5.33)

In the above, we can drop the terms not containing �⃗⃗� since they have no

effect on the minimization problem. We can now write the minimizat ion

problem in the standard QP formulation as follows:

1min ( ) ( )

2

T T T T T

u u u w uJ Q R Q Q u

u u x w u (5.34)

Input constraints are immediately addressed in QP algorithms which allow

68

for bounds on the design variable, i.e. the elements of �⃗⃗� . State and output

constraints may be incorporated in the following manner. Define an output

vector of constraints as follows:

, ,( )c c u c w ck y x u w (5.35)

where �⃗⃗� 𝒄, Δc, Γu,c, and Γw,c is obtained similar to (5.32).

Consider constraints of the form,

c cL U cy (5.36)

which implies

, ,

, ,

( )u c w cc c

u c c c w c

U k

L

xu

w (5.37)

The equation (5.34) and (5.37) are the standard QP optimization problem

formulation which allows us to utilize available generic QP algorithms. In the

absence of constraints, �⃗⃗� 𝒎𝒑𝒄 is immediately found by setting 𝝏𝑱

𝝏�⃗⃗� to zero and

solving for �⃗⃗� as follows:

1( ) ( ( ) )T T

mpc u u u wQ R Q k u x w (5.38)

The control law at each time step k is obtained as follows:

1 2 3 4 0 1( ) [ , , , ] ( ) [ ]pk k u x w (5.39)

where

1

1 2 3 4

1

0 1

[ , , , ] [1,0 0]( )

[ ] [1,0 0]( )

T T

u u u

T T

p u u u w

Q R Q

Q R Q

For the wheelbase preview control, the �⃗⃗⃗� in the above is constituted with

69

the wheelbase preview disturbance given in (5.24). In this research, to solve

MPC problem in MATLAB, CVXGEN which is designed to be utilizable in

MATLAB is used as solver [Mattingley'12].

70

5.3. Frequency Response Analysis of Controlled

Vehicle

The Laplace transformation of bounce, roll, and pitch position of the passive

(uncontrolled) vehicle model with respect to road disturbance can be expressed

as (5.15). With assumptions that the vehicle goes straight with constant speed

and the tire grip on the road is keeping, the delayed out-of-phase road elevation

inputs into the vehicle front and rear wheels. On the assumption that symmetric

road disturbance of left and right wheels written in (5.18), the vehicle model is

converted from a multi-input multi-output (MIMO) system to a single-input

multi-output (SIMO) system. Then transfer functions between the road input,

Zr(s), and the body motions can be obtained.

The frequency responses of the heave and pitch acceleration of the passive

vehicle at 10 kph is illustrated in Figure 5.5. It is noted that the heave and pitch

acceleration humps are occurred alternately in the magnitude plot due to phase

difference of the delayed road elevation inputs to front and rear wheels. The

acceleration magnitude has humps when the phase difference corresponding to

the multiple of one wavelength is occurred, while the pitch acceleration

magnitude has humps when the phase difference corresponding to the multiple

of a half-wavelength is occurred. The modal peak frequencies are speed-

dependent because the delayed time is a speed function (tdelay = L/vx).

71

Figure 5.5. Frequency response of the passive vehicle at 10 kph.

With some controlled forces, the Laplace transformation of the body motions

can be expressed as (5.40). To analyze the frequency response of the controlled

vehicle, the LQ optimal feedback control and the wheelbase preview control

for ride comfort improvement based on the reduced vertical full-car model

proposed in chapter 5.1 and 5.2 have been adopted. With the same assumptions

above, the frequency responses of the heave and pitch acceleration of the

controlled vehicle at 10 kph are illustrated in Figure 5.6 and 5.7, respectively.

72

1 2 3 42

2 2

1 2 3 42

1 2 3 42

2 2

1 2 3 42

( )( ) ( ( ) ( ) ( ) ( ))

( ) B( )

( ) ( ) ( ) ( )( ) B( )

( ) /( ) ( ( ) ( ) ( ) ( ))

( ) B( )

/( ) ( ) ( ) (

( ) B( )

s r r r r

s

u t

s

f

r r r r

x

u t f

s

C sZ s Z s Z s Z s Z s

m s A s s

s m s kF s F s F s F s

m s A s s

C s ts Z s Z s Z s Z s

m s A s s

s m s k tF s F s F s F s

m s A s s

1 2 3 42

2 2

1 2 3 42

)

( ) /( ) ( ( ) ( ) ( ) ( ))

( ) B( )

/( ) ( ) ( ) ( )

( ) B( )

f

r r r r

y

u t f

s

C s ls Z s Z s Z s Z s

m s A s s

s m s k lF s F s F s F s

m s A s s

(5.40)

Figure 5.6. Frequency response of the heave acceleration of the controlled

vehicle at 10 kph.

73

Figure 5.7. Frequency response of the pitch acceleration of the controlled

vehicle at 10 kph.

The magnitudes of both heave and pitch acceleration of the feedback

controlled vehicle are reduced compared to the passive vehicle within the

frequency range of about 0.5 to 50 Hz. This means that even with control

algorithm ignoring the wheel dynamics, vehicle ride comfort can be improved.

For performance comparison, the results of full preview controlled vehicle are

also shown assuming that 1-seconds of future road information is available. It

is shown that a significant ride comfort improvement is achieved by the full

preview control algorithm. The performance of the proposed wheelbase

74

preview control is superior to that of the feedback control but inferior to the full

preview control performance as expected. It is noted that the body motion

cannot be influenced by any control algorithms around the frequency of about

12 Hz which is known as a wheel-hop frequency [Hedrick'90]. The ride comfort

can be improved significantly by the proposed control algorithm within the

frequency range of about 0.5 to 5 Hz which is appropriate to low-bandwidth

actuators.

75

Chapter 6 An Electro-mechanical Active

Suspension System

All active suspensions implemented in automobiles today are based on

hydraulic or pneumatic operation. Although hydraulic systems have already

proved their potential in commercial systems, there are three main

disadvantages: inefficiency due to the continuously pressurized system, a

relatively high system time constant and environmental pollution issues

because of hose leaks and ruptures. An electro-mechanical suspension (EMS)

system can resolve the disadvantages of hydraulic systems since continuous

power is not needed, control is easy and no fluids are present.

Over the last decade, EMS systems for automobiles has been proposed

[Suda'00, Suda'03]. The electro-mechanical actuator consists of DC motor and

the ball screw mechanism. The tunable damping force on an electromagnetic

damper allows high controllability to be achieved [Kawamoto'07]. The

performance of the EMS has been discussed on the energy consumption,

vibration isolation, and vehicle maneuverability [Kawamoto'08]. J. Seo et al.

proposed a control algorithm for the motorized active suspension damper

(MASD). In their work, the MASD system significantly improves the ride

comfort compared with conventional CDC [Seo '14]. D. Shin et al. reduces the

actuator power consumption by changing its control mode according to the

driving conditions [Shin'16].

76

In this chapter, a control algorithm for an electro-mechanical suspension

system is proposed to improve the driving performance of a vehicle. A vehicle

height adjustment is one of the main salient features of EMS systems. The EMS

system lifts the sprung mass to improve ride comfort and to protect the vehicle

bottom during off road driving and lowers the sprung mass to reduce air drag

and to enhance safety during high-speed driving. Another main function of the

EMS system is isolation of the body against to road disturbance and roll, pitch

compensation.

A quarter-car model with the EMS in this research has been illustrated in

Figure 6.1. A typical low-bandwidth active suspension has been adopted in this

research which is primarily concerned with dominant (body) modes and

associated characteristics because the electro-mechanical actuator has a low

operating frequency (~ 5 Hz).

ms

mu

mb

Figure 6.1. A quarter-car model with electro-mechanical actuator.

77

6.1. EMS system modeling

6.1.1. Electro-mechanical actuator modeling

As shown in Figure 6.1, the actuator is inserted between sprung mass and

unsprung mass. An accumulator spring parallel to the actuator is necessary to

minimize the actuator loads in steady-state. The bottom of actuator is mounted

on the unsprung mass and the top of actuator, a ball nut, is attached in series to

the main spring and damper. A free body diagram of belt-driven ball screw

mechanism is shown in Figure 6.2 and parameters of the model are given in

Table 6.1. The motor and ball screw are attached at the unprung mass. The ball

nut is driven by the motor with a belt whose gear ratio is n, so that the driven

torque at ball nut is amplified as n times as much than output torque of motor.

A stroke motion of the actuator can be described by 1) rotary to axial

transformation of the ball screw and 2) rotor dynamics of the ball nut.

Motorrotor

Ball nut

Ball screw

Fixed to Unsprung mass

Figure 6.2. Belt-driven ball screw actuator model.

78

Table 6.1. The variables and nominal parameters of rotor dynamics of actuator

and quarter car model.

Parameter/variable Description Value

ωm Angular velocity of motor

ωb Angular velocity of ball nut

�̇�𝒃 − �̇�𝒖 Actuator stroke speed

Jm Moment of inertia of motor rotor 0.00025 kg∙m2

Jb Moment of inertia of ball nut 0.0025 kg∙m2

l Lead of the ball screw 0.01 m

n Reduction gear ratio of the belt 5

Efficiency of the belt 0.95

fr Coefficient of dynamic friction

In the following modelling procedure, the following items are assumed

[Kawamoto'07].

∙ Motor rotor and ball screw mechanism are assumed to be rigid.

∙ Backlash and torsion of ball screw are not considered.

From these assumptions, equation of rotary to axial transformation of the ball

screw is written as follows:

2( )b b uz z

l

(6.1)

The equation of rotor dynamics of ball nut with reduction gear ratio of the

belt is written as follows:

b b m aJ n (6.2)

where τm is the motor output torque, and τa is output torque of the actuator.

Using the equilibrium of force, the output force in the axial direction, fa, is

written as follows:

2a af

l

(6.3)

Considering the dynamic friction of the actuator and substituting (6.1) and

(6.3) into (6.2) yields following the output force [Seo '14].

79

2

( )a m r b u rf n m z z f f xl

(6.4)

where

2 sgn( ) 0.01 /

2,

0.01 /0.01 2

b u b u

r b b ub u

z z when z z m s

m J f x z zl sin when z z m s

Figure 6.3 shows that the motor circuit is modelled as the equivalent DC

motor circuit, while Table 6.2 gives the parameters of the model. The motor is

connected to a power supply, and the voltage is controlled. The circuit equation

is obtained as (6.5). The limit for the variable voltage of power supply is ±12

V.

motor motor e

diV L R i V

dt (6.5)

where Ve is the electromotive force which is proportional to the motor speed (=

n times the angular velocity of the ball nut) as written in (6.6).

+

-

M

Figure 6.3. Circuit diagram of the motor.

Table 6.2. The variables and nominal parameters of circuit model.

Parameter/variable Description Value

i Current

V Variable voltage of power supply ±12 V

Lmotor Inductance 0.01523 H

Rmotor Resistance 0.1523 Ω

Kt Motor torque constant 0.0455 Nm/A

Ke Induced voltage constant 0.0349 V∙sec/rad

80

2( )e e m e b e b uV K K n K n z z

l

(6.6)

Assuming that the output torque of the motor is proportional to the motor

current, i, it is obtained as (6.7).

m tK i (6.7)

6.1.2. Reduced vertical full-car model with EMS

Figure 6.4 shows that to design the EMS control algorithm, the EMS system

described in the above is modelled in a vertical full-car model. Throughout the

paper, the subscript i ∈{1,2,3,4} stands for front left, front right, rear left, and

rear right corner, respectively, of the vehicle. Table 6.3 gives the supplementary

to variables and nominal parameters in Table3.1. The equations of body motion

are given in (6.8) ~ (6.10).

x

y

z

zr1

zu1

zs1

zr3

zu3

k1,c1

k2,c2 k3,c3

k4,c4

zs2 zs3

zs4

2tf

2tr

lf

lr

zs

zr2

zu2

ka

kaka

ka

zb1

zb3zb2

kt

kt

kt

kt

fa1

fa2

fa3

fa4

Mx My

Figure 6.4. A vertical full-car model with EMS.

81

Table 6.3. The supplementary variables and nominal parameters of the full-car

model used in the simulation study.

Parameter/

variable Description Value

mb Ball nut mass 1 kg

ka Spring stiffness of accumulator spring 25000 N/m

zbi Displacement of i-th corner of ball nut i=1…4

ax, ay Longitudinal and lateral acceleration of sprung mass

1 1 1 2 2 2 3 3 3 4 4 4

1 1 1 2 2 2 3 3 3 4 4 4

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

s s b s b s b s b

s b s b s b s b

m z k z z k z z k z z k z z

c z z c z z c z z c z z

(6.8)

1 1 1 2 2 2 3 3 3 4 4 4

1 1 1 2 2 2 3 3 3 4 4 4

, ,

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

xx s b f s b f s b r s b r

s b f s b f s b r s b r

roll f roll r s roll y s roll

I k z z t k z z t k z z t k z z t

c z z t c z z t c z z t c z z t

K K m h a m gh

(6.9)

1 1 1 2 2 2 3 3 3 4 4 4

1 1 1 2 2 2 3 3 3 4 4 4

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

yy s b f s b f s b r s b r

s b f s b f s b r s b r

s pitch x s pitch

I k z z l k z z l k z z l k z z l

c z z l c z z l c z z l c z z l

m h a m gh

(6.10)

The equation of ball nut motion is given as follows:

( ) ( ) ( ) , 1, 4b bi i si bi i si bi a bi ui aim z k z z c z z k z z f for i (6.11)

where fai is the output force of each actuator, which is given as follows:

2( ) sgn( ), 1, 4ai t i r bi ui r bi uif nK i m z z f z z for i

l

(6.12)

where ii is the current of each motor from the circuit equation given as follows:

2( ), 1, 4i

i motor motor i e bi ui

diV L R i K n z z for i

dt l

(6.13)

The operational range of the ball screw mechanism is about ±30 mm. Figure

6.5 shows that to incorporate this stroke limit in the model, the accumulator

spring stiffness is dramatically increased beyond the range.

82

Actuator stroke [mm]

Accumulator spring

stiffness

30 33-33 -30

ka

40·ka

Figure 6.5. Accumulator spring stiffness to incorporate the actuator stroke limit.

The state-space representation for reduced full-car model with EMS is

obtained as follows:

a a a a a wa ax A x B u B w (6.14)

where the state vector consists of displacement between body and ball nut and

its velocity, the actuator stroke and its velocity at each corner, and the motor

current at each actuator. The controlled input vector of the system consists of

motor voltage at each actuator, and the vertical acceleration at each wheel and

longitudinal, lateral acceleration of the body is disturbance to the system as

follows:

1 1 1 1 2 2 2 2 3 3 3 3

4 4 4 4 1 1 1 1 2 2 2 2

3 3 3 3 4 4 4 4 1 2 3 4

1 2 3 4

1 2 3 4

s b s b s b s b s b s b

s b s b b u b u b u b u

T

b u b u b u b u

T

T

u u u u x y

z z z z z z z z z z z z

z z z z z z z z z z z z

z z z z z z z z i i i i

V V V V

z z z z a a

a

a

a

x

u

w

(6.15)

The system matrix, input matrix, and disturbance input matrix is given as

83

follows:

, ,

a1 a1 wa1

a2 a2 wa2

a a wa

a20 a20 wa20

A B B

A B BA B B

A B B

where

, 1,3,5,7,9,11,13,15for ai iA Π i

where iΠ denotes a 𝟏 × 𝟐𝟎 matrix with a unity located in the i-th columns

and with remaining elements equal to zero.

2 2 2 2

1 1 1 1 21 1 1 2

2 2

3 32 42 2 3 3 3 4

44 4

f f f f

f

s yy b r s xx yy b r s yy

f f f r f r f r f r

f

s xx yy s yy s xx yy s yy

f r f r a

s xx yy b

l t l lk k c c ka k l e c c a k

m I m m m I I m m m I

t l l l t t l l l lk cc kc c b k l e c c b k

m I I m I m I I m I

t t l l kcc c

m I I m

a2A

1 3 1 3

2 2 2 2

1 1 2 21 1 1 2

2 2

3 32 22 2 3

20 0 0 0

2 2

T

s roll s roll tf f

r xx xx b r

f f f f

f

s yy s xx yy s yy b r

f f f r f

f

s xx yy b r s yy s

m gh m gh nKl e l e

m I I l m m

l t l lk c k ka k l e c c a k

m I m I I m I m m

t l l l t tk cc cc c b k l e

m I I m m m I m

a4A

43 3 4

44 4 1 4 1 2

1 1 2 21 1 1 2

20 0 0 0

2 2

r f r f r

xx yy s yy

T

f r f r s roll a s roll tf f

s xx yy xx b r xx b r

f r f r f r f r

r

s yy s xx yy s yy s

l l l lkc c b k

I I m I

t t l l m gh k m gh nKcc c l e l e

m I I I m m I l m m

l l t t l l l l tk c k cc k l e c c c k

m I m I I m I m

a6A

2 2

2 2 2 2

3 3 3 3 43 3 3 4

2 2

44 4 1 5

20 0 0 0

2 2

f r f r

xx yy

r r r rr

s yy b r s xx yy b r s yy

T

s roll r s roll r a tr rr r

s xx yy xx f xx f b r b r

t l lc c

I I

k k c cl t l k ld k l e c c d k

m I m m m I I m m m I

m gh t m gh t k nKc t lc c l e l e

m I I I t I t m m l m m

84

1 1 2 21 1 1 2 2 2

2 2 2 2

3 3 343 3 3 4

2 2

344 4

f r f r f r f r f r f r

r

s yy s xx yy s yy s xx yy

r r r rr

s yy s xx yy s yy b r

sr r

s xx yy b r

l l t t l l l l t t l lk c k cc k l e c c c k c c

m I m I I m I m I I

k c kl t l k ld k l e c c d k

m I m I I m I m m

c m gc t lc c

m I I m m

a8A

1 4

, ,,

1 3 1

,

3

0 0 0 02 2

2

, ,2 2 2

2

roll r s roll r ar r

xx f xx f b r

T

t

b r

f roll f s roll f roll f s rollroll r rf r f

xx f xx r xx f

roll rrr

xx r

h t m gh t kl e l e

I t I t m m

nK

l m m

t K m gh t K m ghK ta k t b k t c k t

I t I t I t

Ktd k t

I t

1 1

2 2

3 3

,

0 0 0 0 0 0 0

20 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

20 0 0 0 0 0 0

s pitch

yy

a

b r b r b r

T

t

b r

b r b r

T

a t

b r b r

b r b r

a t

b r

m ghe

I L

kk c

m m m m m m

nK

l m m

k c

m m m m

k nK

m m l m m

k c

m m m m

k nK

m m l m

a10

a12

a14

A

A

A

4 4

0

0 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

T

b r

b r b r

T

a t

b r b r

e

motor

T

motor

motor

m

k c

m m m m

k nK

m m l m m

K n

lL

R

L

a16

a17

A

A

85

0 0 0 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0

T

e motor

motor motor

T

e motor

motor motor

T

e motor

motor motor

K n R

lL L

K n R

lL L

K n R

lL L

a18

a19

a20

A

A

A

0 0 0 0 , 1,2,...,16

10 0 0

10 0 0

10 0 0

10 0 0

0 0 0 0 , 1,3,5,7,9,11,13,15,17,18,19,20

0 0 0

motor

motor

motor

motor

s pitch f s roll fr

b r yy xx

for

L

L

L

L

for

m h l m h tm

m m I I

ai

a17

a18

a19

a20

wai

a2

B i

B

B

B

B

B i

B

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

s pitch f s roll fr

b r yy xx

s pitch r s roll rr

b r yy xx

s pitch r s roll rr

b r yy xx

b

b r

b

b r

m h l m h tm

m m I I

m h l m h tm

m m I I

m h l m h tm

m m I I

m

m m

m

m m

a4

a6

a8

a10

a12

B

B

B

B

B

86

0 0 0 0 0

0 0 0 0 0

b

b r

b

b r

m

m m

m

m m

a14

a16

B

B

87

6.2. EMS System Control Algorithm

In this section, vehicle height levelling and ride comfort control algorithm of

the EMS as shown in Figure 2.1 is designed. The mode selector determines a

present driving mode and desired height level of the vehicle. The upper-level

controller determines the desired suspension state considering the actuator

stroke limit. The lower level controller calculates the target motor voltage at

each actuator using estimated state by the observer.

6.2.1. Driving mode decision

As shown in Figure 6.6, the mode selector determines a present driving mode

and desired height level of the vehicle, (𝒛𝒔 − 𝒛𝒖)𝒅, from the vehicle sensor

signals of longitudinal speed (vx), SWA, APS, BPS, and vertical acceleration of

wheels (�̈�𝒖). To reflect the driver’s intention and the road disturbance, the mode

selector classify the current situation into six modes: normal mode, attitude

control mode, bump mode, off-road mode, high-speed straightway mode, and

high-speed attitude control mode. Also, to prevent the chattering phenomenon

of the mode conversion, the driving mode in the previous step is used at the

same time. The mode decision condition and target height level are given in

Table 6.4.

88

Attitude control

mode

Bump mode

Normal mode

Mode Decision

Off-road mode

High-speed

attitude control

mode

High-speed

straightway mode

Figure 6.6. Mode and desired height level decision algorithm.

Table 6.4. Driving mode decision condition and desired height level.

mode situation Mode decision condition height level

1 Normal

vx ≤ 90 kph &

�̈�𝒖_𝑹𝑴𝑺 ≤ 2 m/s2 &

(APS & BPS & SWA)_RMS ≤ threshold_1

0 mm

2 Attitude control

vx ≤ 90 kph &

�̈�𝒖_𝑹𝑴𝑺 ≤ 2 m/s2 &

(APS | BPS | SWA)_RMS > threshold_1

0 mm

3 Bump vx ≤ 40 kph &

�̈�𝒖_𝑹𝑴𝑺 > 2 m/s2 0 mm

4 Off-road Staying at mode 3 for 2 sec + 30 mm

5 High-speed

straightway

vx > 90 kph &

(APS & BPS & SWA)_RMS ≤ threshold_2 - 30 mm

6 High-speed

attitude control

vx > 90 kph &

(APS | BPS | SWA)_RMS > threshold_2 - 30 mm

89

Each driving mode and corresponding situation is described as follows:

1) Normal mode, mode 1

The normal mode is a mild driving situation in which the driver's input is

small on a general flat road, not on a highway road. As a condition for

determining the non-high speed region and the flat road, the value of vehicle

speed is selected to be 90 kph or less, and the root mean square (RMS) value of

the vertical acceleration of the unsprung mass, �̈�𝒖, is selected to be 2 m/s2 or

less. As a condition for determining the mild driving situation, the RMS values

of APS, BPS, and SWA are less than 0.1, 0.1, and 30°, respectively. In the

normal mode, the target height level is selected as 0 mm, at which the vehicle

height is maintained by suspension spring and accumulator spring without

control to reduce the amount of control input.

2) Attitude control mode, mode 2

The attitude control mode is acceleration or cornering situation by the driver

on a general flat road, not on a highway road. The condition for determining

the non-high-speed region and the flat road is the same as in the case mode 1,

and the condition for making decision that the vehicle attitude control is

necessary due to the driver's input is that either of the RMS value of APS, BPS,

and SWA is greater than 0.1, 0.1, and 30°. In the attitude control mode, a

relatively large amount of control input is used to reduce roll and pitch angles

during cornering or acceleration. In order to secure both the negative and

positive range of the actuator, the target height level is selected as 0 mm.

3) Bump mode, mode 3

The bump mode is a situation in which the vehicle passes through the bump

90

and a large heave motion is instantaneously generated. Under the assumption

that the driver runs at low speed on the bump, the speed condition for

determining the bump road is selected as 40 kph or less. Also, the condition for

making decision that the ride control is required against the road disturbance is

that the RMS value of the �̈�𝒖 is larger than 2 m/s2. In the bump passing mode,

a relatively large amount of control input is used to reduce the vertical

acceleration of the sprung mass or reduce roll and pitch angles to improve ride

comfort. In order to secure both the negative and positive range of the actuator,

the target height level is selected as 0 mm.

4) Off-road mode, mode 4

The off-road mode is a situation in which the vehicle passes through the

rough road and a persistent irregular heave motion is generated. The perception

condition for the rough road is selected as the duration of the mode 3 is greater

than 2 seconds. The target height is selected as +30 mm to protect the vehicle

bottom.

5) High-speed straightway mode, mode 5

It is a high-speed straight-ahead driving situation in which the driver's input

is small on the highway. As a condition for determining the high speed region,

the vehicle speed is selected to be higher than 90 kph. As a condition for

determining the mild driving situation, the RMS values of APS, BPS, and SWA

are less than 0.2, 0.1, and 15°, respectively. The target height level is selected

to be -30 mm to reduce the air resistance and to improve fuel efficiency.

6) High-speed attitude control mode, mode 6

It is acceleration or cornering situation by the driver on the highway. The

91

condition for determining the high-speed region is the same as in the mode 5,

but the condition for making decision that the vehicle attitude control is

necessary due to the driver's input is that either of the RMS value of APS, BPS,

and SWA is greater than 0.2, 0.1, and 15°. The target height level is selected to

be -30 mm to reduce the air resistance and to enhance safety.

Some threshold values of the signal are used in the mode conversion

algorithm given in Table 6.4. This simple mode conversion algorithm can cause

unintentional chattering phenomenon of mode and height level near the

threshold value. Therefore, the chattering prevention algorithm considering the

driving mode in the previous step and the conservative threshold value is added

as Table 6.5. The added hysteresis of threshold value prevents the mode from

changing rapidly. Also, when the switching between the mode 2 and the mode

6 occurs, the previous target height level is maintained to ensure safety.

92

Table 6.5. Driving mode chattering prevention algorithm.

Previous

mode

Present

mode condition Mode decision height level

2 1 (APS & BPS & SWA)_RMS

≤ 0.5×threshold_1 1 0 mm

2 1 (APS & BPS & SWA)_RMS

> 0.5×threshold_1 2 0 mm

3 1 or 2 �̈�𝒖_𝑹𝑴𝑺 ≤ 0.5 m/s2 1 or 2 0 mm

3 1 or 2 �̈�𝒖_𝑹𝑴𝑺 > 0.5 m/s2 3 0 mm

4 1 or 2 �̈�𝒖_𝑹𝑴𝑺 ≤ 0.5 m/s2 1 or 2 0 mm

4 1 or 2 �̈�𝒖_𝑹𝑴𝑺 > 0.5 m/s2 4 +30 mm

4 3 - 4 +30 mm

5 1 vx ≤ 60 kph 1 0 mm

5 2 vx ≤ 60 kph 2 -30 mm

5 1 or 2 vx > 60 kph 5 -30 mm

6 1 vx ≤ 60 kph 1 0 mm

6 2 vx ≤ 60 kph 2 -30 mm

6 1 or 2 vx > 60 kph 6 -30 mm

6 5 (APS & BPS & SWA)_RMS

≤ 0.5×threshold_2 5 -30 mm

6 5 (APS & BPS & SWA)_RMS

> 0.5×threshold_2 6 -30 mm

93

6.2.2. Desired suspension state decision

The upper-level controller determines xad, the desired suspension state

variable of equation (6.15). If the target height level, h, is determined from the

mode selector, the xad is expressed as equation (6.16) except for the case of the

high-speed attitude control mode.

,2

, , , , 9,11,13,15,

Ta

ijkl h h h h h

t

k lk h k h k h k h k

nK

for i j k l respectively

adx Π (6.16)

where ijklΠ denotes a 𝟏 × 𝟏𝟔 matrix with the target height value h located

in the i,j,k ,l-th columns and with remaining elements equal to zero. hk h

denotes a steady state current to maintain the actuator stroke, h.

The xad in equation (6.16) is the steady-state variable to keep the height level

at h. In case of the high-speed attitude control mode, actuator is driven

restrictively due to the actuator stroke limit of -30 mm. In this case, an

additional target displacement within operational range, (ha)1~4, is applied to the

operable actuator for attitude control. The (ha)1~4 is obtained by multiplying

linear gains on the longitudinal and lateral accelerations of the vehicle as

follows:

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3

0& 0 : 0, , ,

0& 0 : , 0, ,

0& 0 : , , 0,

0& 0 : , , ,

y x y x

y y x x

x y x y

y x x y

y x a a a y a a x a a y a x

y x a a y a a a y a x a a x

y x a a x a a y a x a a a y

y x a a y a x a a x a a y

a a h h G a h G a h G a G a

a a h G a h h G a G a h G a

a a h G a h G a G a h h G a

a a h G a G a h G a h G a h

4 0a

(6.17)

94

where the gain values are determined as the magnitude of the longitudinal and

lateral accelerations, which generate suspension displacement by 30 mm of a

passive vehicle. Using the compensation as described in equation (6.17), the xad

in the case of the high-speed attitude control mode is expressed as (6.18).

1 8 1 2 3 4

1 2 3 4

0 0 0 0a a a a

T

h a h a h a h a

h h h h h h h h

k h h k h h k h h k h h

adx 0 (6.18)

6.2.3. Desired motor voltage decision

The LQ optimal control can be applied to the reduced vertical full-car model

with EMS system in (6.14). The heave, roll, and pitch motion of the body are

related to ride comfort control. The actuator stroke at each corner is related to

vehicle height and attitude control. The interested output of the model can be

represented in (6.19) and incorporated into the quadratic integral criterion as

follows:

1~4( )T

s b uz z z ay (6.19)

0

2 2 2 2 2

0

lim

lim ( )

f

f

f

sf

t

T T

t

t

z s i bi ui j jt

J t t t t dt

z z z V dt

a a a a a ay Q y u R u

(6.20)

where 𝝆𝒛𝒔, 𝝆𝝓, 𝝆𝜽, 𝝆𝒊, 𝝆𝒋 are weighting factors that are diagonal elements

of the Qa and Ra matrix. If the current driving mode is 1, 4 or 5, the control

objective is a smooth vehicle height adjustment, so the values of 𝝆𝒊 and 𝝆𝒋 is

tuned to be relatively large. If the current driving mode is 2 or 6, the control

95

objective is roll and pitch compensation, so the values of 𝝆𝒊 is tuned to be

relatively large. If the current driving mode is 3, the control objective is ride

comfort improvement, so the values of 𝝆𝒛𝒔 , 𝝆𝝓 , and 𝝆𝜽 are tuned to be

relatively large. Table 6.6 gives the sets of weights using in simulation study.

The solution to the optimal control problem that minimizes the cost (6.20)

using the estimated suspension state is written as follows:

1 2 3 4ˆ

TV V V V

a a a adu K x x (6.21)

At ride comfort control mode, the wheelbase preview control algorithm

proposed in section 5 is also adopted in the simulation study. The state variable

of the EMS system is estimated by proposed observer in section 4 with using

measurement of suspension deflection, motor voltage, vertical wheel

acceleration, longitudinal and lateral acceleration of the body.

Table 6.6. Weighting factors for each driving mode.

Mode

Value of weighting factors

𝝆𝒛𝒔 𝝆𝝓 𝝆𝜽 𝝆𝒊 𝝆𝒋

1, 4, 5 (height control) 0 0 0 1 1×10-1

2, 6 (attitude control) 0 0 0 1×101 1×10-2

3 (ride comfort control) 1×102 1×101 1×101 1 1×10-2

96

Chapter 7 Performance Evaluation

To evaluate the EMS system control algorithm, simulation studies have been

conducted. The computer simulation was conducted using MATLAB/Simulink

and vehicle software Carsim®. The fully nonlinear vehicle model used in

simulation consists of engine model, transmission model, steering model,

suspension model, brake model, tire model, and vehicle body model. The

samling time to calculate the overall vehicle motion was 0.001 sec, while the

control input was computed every 0.01 sec. The proposed wheelbase preview

control algorithm has been evaluated through bump test. The proposed mode

control algorithm has been evaluated through various driving situation test such

as acceleration/deceleration, double lane change, J-turn, and off-road. The

driving performance of controlled vehicle with EMS system is compared with

that of passive vehicle which has a passive suspension system, composed of the

non-controlled spring and the shock-absorbing damper.

97

7.1. Ride Comfort Control Performance

The vertical acceleration of a human is a good indication of the ride comfort.

The international standard ISO 2631-1 specifies a method of evaluation of the

ride comfort by weighting the root-mean square (r.m.s) acceleration with

human vibration sensitivity curves [ISO'97]. The human vibration sensitivity

curve is shown in Figure 7.1. As it shown, humans are most sensitive to

vibrations in frequncy range from 4 to 10 Hz.

Figure 7.1. The human sensitivity to vertical vibrations.

98

In Zuo’s work [Zuo'02], this acceleration weighting filter is approximated by

a quasi-least-fifth order continuous-time filter as (7.1).

4 3 2(5)

5 4 3 2

87.72 1138 11336 5453 5509( )

92.6854 2549.83 25969 81057 79783

s s s sW s

s s s s s

(7.1)

The magnitude frequency response of the approximated acceleration

weighting filter is also shown in Figure 7.1. The weighted r.m.s. acceleration is

expressed as (7.2).

1/2

2

,0

1 T

w rms wa a t dtT

(7.2)

where aw and T denote the weighted acceleration and the duration of the

measurement, respectively.

In Table 7.1, the following values give approximate indications of ride

comfort in public transport proposed by ISO 2631-1. Quantitative evaluation of

the ride comfort improvement according to the criteria given in Table 7.1 would

be conducted through single bump test in subsections below.

Table 7.1. Criteria for evaluation of the ride comfort in public transport.

The r.m.s value of the frequency-weighted acceleration Evaluation

Less than 0.315 m/s2 not uncomfortable

0.315 m/s2 to 0.63 m/s2 a little uncomfortable

0.5 m/s2 to 1 m/s2 fairly uncomfortable

0.8 m/s2 to 1.6 m/s2 uncomfortable

1.25 m/s2 to 2.5 m/s2 very uncomfortable

Greater than 2 m/s2 extremely uncomfortable

99

7.1.1. Carsim® simulation results

Passing a single bump at a speed of 30 kph scenario has been simulated with

vehicle software Carsim® and MATLAB/Simulink to evaluate the performance

of the ride comfort enhancement. The single bump road height profile described

by equation (4.21) was applied to the left and right wheels. The feedback

controller was designed based on the system model descried as equation (3.7)

and the optimal preview control algorithm described in subsection 5.2.2 was

adopted to ride comfort improvement.

In Figure 7.2, the simulation results of proposed ride comfort improvement

control algorithms have been compared. The figures are indicating the heave

acceleration of the body, pitch angle, front and rear actuator forces. The legends

“passive”, “feedback”, “wheelbase preview”, and “full preview” indicate the

signals obtained by the passive vehicle, by the LQ optimal feedback control in

(5.10), by the proposed wheelbase preview control (WPC) in equation (5.25),

and by the full preview control (FPC) assuming that 0.3-seconds of future road

information is available. It is shown that noticeable reduction of heave

acceleration and pitch angle is achieved by both the feedback and preview

control input, compared to the passive vehicle. Regarding ride comfort, these

simulation results are indicating a huge potential for improvement, which

would be obvious by the driver. The FPC has the best potential to promote ride

comfort by driving actuator 0.3 seconds (preview time) earlier than the

feedback and WPC algorithms. The performance of proposed WPC algorithm

without preview road information is superior to that of the feedback control. In

Figure 7.2-(c) and (d), the controlled actuator force has been shown. For

100

comparison, the damping force of the passive vehicle has been also indicated.

It is evident that both the front and rear control forces by the FPC algorithm are

driven earlier than the others due to preview road information. The front

actuator forces of feedback control and WPC algorithms are similar to each

other, but the rear actuator force of the WPC is generated by the wheelbase

preview information from front wheels. As a results, the rear actuator forces of

FPC and WPC algorithms are similar to each other.

101

Figure 7.2. Comparison of ride comfort improvement simulation. (a) heave

acceleration, (b) pitch angle, (c) front and (d) rear actuator force

While the vehicle is fully passed through the bump, the weighted r.m.s.

values of vertical acceleration of drivers, aw,rms, have been compared and given

in Table 7.2. From the simulation results above, the proposed wheelbase

preview control algorithm has shown a better potential for ride comfort

improvement than the feedback control, but not better than full preview control

algorithm.

102

Table 7.2. Evaluation of the ride comfort improvement.

aw,rms [m/s2] Evaluation

Passive 1.175 Uncomfortable

Feedback 0.4235 A little uncomfortable

Wheelbase preview 0.2974 Not uncomfortable

Full preview 0.2017 Not uncomfortable

7.1.2. EMS system simulation results

In LQ optimal control approach, hard constraints cannot be explicitly

incorporated and hence have to be minimized in the cost function. For the EMS

systems, the constraints on actuator stoke and actuator voltage can cause

performance deterioration of the LQ optimal controller. In this case, the

constraints on control variables should explicitly be incorporated and the

optimization has to be carried out in real-time, therefore the MPC is the

appropriate controller design scheme.

To evaluate the improvement of ride comfort performance of the proposed

EMS system, the same bump scenario above has been simulated with the

nonlinear vehicle model constructed in MATLAB/Simulink. For comparison, a

feedback controller and an optimal preview control with wheelbase preview

information were designed based on the system model descried as equation

(6.14) and the model predictive algorithm described in subsection 5.2.3 was

adopted to ride comfort improvement. The simulation has been carried out in

two different cases. In the first simulation case, no constraint on the actuator

stoke and the actuator voltage is assumed, so it is an ideal case. And the second

simulation case, the limit for the variable voltage of power supply is ±12 V, and

103

the ±30 mm operational range of the ball screw mechanism is assumed as

shown in Figure 6.5.

a) Unconstraint case

In Figure 7.3, the simulation results of proposed ride comfort improvement

control algorithms for the vehicle with EMS system without constraint case

have been compared. The figures are indicating the heave acceleration of the

body, pitch angle, actuator stroke and voltage, and actuator stroke speed vs axial

force. The legends “passive”, “LQR”, “OPC”, and “MPC” indicate the signals

obtained by the passive vehicle, by the LQ optimal feedback control (LQR), by

the proposed wheelbase optimal preview control (OPC), and by the proposed

wheelbase model predictive control (MPC). It is shown that noticeable

reduction of heave acceleration and pitch angle is achieved by both the

feedback and preview control input, compared to the passive vehicle. The

performance of proposed OPC and MPC algorithm without preview road

information is superior to that of the LQR. In Figure 7.3-(c) and (d), the

controlled actuator strokes have been shown. It is noted that all actuator strokes

are over the operational range of ± 30 mm. In Figure 7.3-(e) and (f), the

controlled motor voltages have been shown. It is also noted that all desired rear

motor voltages are beyond the operational range of ±12 V. In Figure 7.3-(g)

and (h), the actuator stroke speeds vs axial forces have been shown. The bold

lines in the first and third quadrant represent the boundary of the modeled

actuator power constraint. In the first and third quadrant, further region from

the origin than the boundary line cannot be reached by the performance of the

104

motor under consideration. Due to the constraints, actual performance of ride

comfort improvement is not expected as Figure 7.3-(a) and (b).

105

106

Figure 7.3. Comparison of ride comfort improvement simulation for

unconstrained EMS system. (a) heave acceleration, (b) pitch angle, (c) front,

(d) rear actuator stroke, (e) front, (f) rear actuator voltage, (g) front, and (h)

rear actuator stroke speed VS axial force.

b) Constraints on actuator stoke and voltage case

In Figure 7.4, the simulation results of proposed ride comfort improvement

control algorithms for the vehicle with EMS system with constraint case have

been compared. The figures are indicating the same properties in Figure 7.3.

The legends “passive”, “LQR”, “OPC”, and “MPC” indicate the signals

obtained by the passive vehicle, by the LQ optimal feedback control (LQR), by

the proposed wheelbase optimal preview control (OPC), and by the proposed

107

wheelbase model predictive control (MPC). In this MPC design, hard

constraints on actuator stroke (±30 mm) and voltage (±12 V) are considered.

It is shown that reduction of heave acceleration and pitch angle is achieved by

both the feedback and preview control input, compared to the passive vehicle.

However, less performance improvement of ride comfort is achieved by the

controller, compared to the unconstrained case because of less actuator power.

The performance of proposed OPC and MPC algorithm without preview road

information is still superior to that of the LQR, however the performance gap

is reduced, compared to the unconstrained case. The weighted r.m.s. values of

vertical acceleration of drivers, aw,rms, have been compared and given in Table

7.3. It is noted that both ride comfort evaluations of vehicles controlled by the

LQR and OPC approaches are same each other as fairly uncomfortable. The

proposed MPC algorithm has shown a better potential for ride comfort

improvement than LQ optimal approaches due to considering hard constraint

in the design process.

In Figure 7.4-(c) and (d), the controlled actuator strokes have been shown.

It is noted that actuator strokes of the MPC are within the operational range of

±30 mm, while those of the LQR and OPC are enlarged to the boundary of the

range. Near the operating range boundary, the actuator stoke cannot be

increased or decreased due to the dramatically increased accumulator spring

stiffness as shown in Figure 6.5. As shown in Figure 7.4-(a), the actuator stroke

limitation causes huge acceleration chattering phenomenon of the LQR and

OPC in which the hard stroke constraint cannot be explicitly incorporated. In

Figure 7.4-(e) and (f), the controlled motor voltages have been shown. It is also

108

noted that all desired rear motor voltages are within the operational range of

±12 V. The MPC algorithm finds the optimal control input in the accessible

control region, but the OPC does not. In Figure 7.4-(g) and (h), the actuator

stroke speeds vs axial forces have been shown. In the first and third quadrant,

as expected, the actuators are driven by the all control algorithms within the

actuator power boundary.

Table 7.3. Evaluation of the ride comfort improvement by the EMS system.

aw,rms [m/s2] Evaluation

Passive 1.376 Very uncomfortable

LQR 0.7941 Fairly uncomfortable

OPC 0.6391 Fairly uncomfortable

MPC 0.4868 A little uncomfortable

109

110

Figure 7.4. Comparison of ride comfort improvement simulation for

constrained EMS system. (a) heave acceleration, (b) pitch angle, (c) front, (d)

rear actuator stroke, (e) front, (f) rear actuator voltage, (g) front, and (h) rear

actuator stroke speed VS axial force.

111

7.2. Mode Control Performance

A scenario for evaluation of the proposed EMS control algorithm is shown

in Figure 7.5. In the scenario, a vehicle starting at a low speed of 30 kph passes

through a bump. After passing the bump, the vehicle accelerates to above 90

kph and performs double lane change simultaneously. After that, the vehicle

decelerates to 50 kph to perform a J-turn. At the end, the vehicle decelerates to

10 kph and passes over a rough road.

30 [kph] 90 [kph] 50 [kph]

50 [

kp

h]

Off-road

Bump Acceleration & DLC Deceleration

J-turn

Deceleration

60 [kph]30 [kph]

10

[k

ph

]

Figure 7.5. Simulation scenario for evaluation of the proposed EMS control

algorithm.

112

Figure 7.6 shows the driving mode change and target height level according

to each driving condition in the simulated situation. The results comparison of

passive vehicle and controlled vehicle are shown in Figure 7.7 ~ 7.11. The

legend “passive” and “control” means the signals obtained by passive

suspension system and EMS system, respectively. Vertical acceleration, pitch

angle, and roll angle of the body are shown in Figure 7.7 ~ 7.9. The vertical

acceleration of the body in Figure 7.7 shows that the vehicle travels through the

bump from 15 to 17 sec and travels over the off-road from 80 to 100 sec. The

pitch angle of Figure 7.8 shows that the vehicle accelerates from 20 to 39.5 sec,

decelerates from 50 to 57 sec, and decelerates from 72 to 77 sec. The roll angle

of Figure 7.9 shows that the vehicle performs double lane change from about

26 to 34 seconds, performs J-turn from 58 to 68 sec.

The driving mode begins with mode 1 and it is converted to mode 3 by

passing through the bump. It can be seen that the driving mode changes to mode

2 due to acceleration after passing the bump. Then, the mode is converted to

mode 6 when the vehicle speed exceeds 90 kph at about 38 sec, and the mode

is changed to mode 5 due to mild driving from 39.5 to 50 sec. When the vehicle

speed drops below 90 kph at about 50 sec, the mode is not directly converted

from mode 6 to mode 2 by the mode chattering prevention algorithm. After the

speed drops below 60 kph, the mode is converted mode 2 at about 55 sec. From

55 to 80 sec, the mode is changed between mode 1 and 2 due to J-turn and

deceleration. After the vehicle passes over the rough road, the driving mode is

converted to mode 3 firstly, then the mode is switched to mode 4 by staying in

mode 3 for more than 2 seconds.

113

The target height level starts at 0 mm, which corresponds to mode 1, and is

maintained until the mode is changed to mode 5 by the chattering prevention

algorithm. Although the mode is changed from mode 2 to mode 6 at about 38

sec, the target height level is lowered to -30 mm at about 39.5 sec. The lowered

target height is restored to 0 mm after changing to mode 1 at about 57 sec. This

prevents undesirable intervention of control input during the attitude control by

maintained target height from 50 to 57 sec. The target height is kept at +30 mm

from 82 sec when the mode is changed to mode 4 to protect the lower end of

the vehicle.

For the acceleration, deceleration, double lane change, and J-turn situations,

it can be seen that the pitch and roll angle of the vehicle with the controlled

EMS are reduced by about 30% compared to the passive vehicle.

Figure 7.6. Simulation scenario for evaluation of the proposed EMS control

algorithm.

114

Figure 7.7. Heave acceleration of the vehicle body.

Figure 7.8. Pitch angel of the vehicle.

Figure 7.9. Roll angel of the vehicle.

115

Figure 7.10 and 7.11 show the suspension displacement and target height

levels of the front left (FL) and rear right (RR) corners of the vehicle. It can be

seen that the controlled vehicle is lowered and raised at the high-speed driving

and passing the off-road. At the time about 37.5, 57, and 82 sec, the suspension

displacement is controlled to gradually reach the target height within three

seconds. It can be also seen that when the pitch and roll angle are generated by

acceleration or turning, the suspension displacement is less generated by the

attitude control as compared with the passive vehicle.

Figures 7.12 and 7.13 show the actuator strokes of the FL and RR corners.

Suspension displacement occurs as much as the actuator stroke in height control

on the flat road. In mode 2, the phase of the actuator stroke is opposite to that

of the suspension displacement, so that the roll and pitch angle is generated less

than the passive vehicle.

In the case of the deceleration while the height level is lowered to -30 mm

from 50 to 57 sec (mode 6), an additional target displacement is applied to the

front actuator by the upper level controller as written in the above equation

(6.17) to reduce the pitch angle. Figure 7.10 and 7.12 show that the front

actuator is operated to push the body during the simulation time of 50 to 57 sec,

so that the front suspension displacement is maintained unchanged relatively

than the passive vehicle. On the other hand, the rear actuator stroke is kept close

to limit of -30 mm, so that the shape of the rear suspension displacement is

similar to that of the passive vehicle.

Representatively, the estimated FL suspension speed used in controller at

the double lane change is detailed in Figure 7.14. The numerical differentiation

116

value of the deflection sensor signal is also illustrated. While the differentiation

value is too noisy to be used in controller because of sensor noise, the estimated

value calculated by the state observer is quite similar to the actual value and the

noise is reduced.

Figure 7.10. FL suspension displacement.

Figure 7.11. RR suspension displacement.

117

Figure 7.12. FL actuator stroke.

Figure 7.13. RR actuator stroke.

Figure 7.14. Estimated FL suspension speed at double lane change.

118

Chapter 8 Conclusions and Future works

This dissertation has proposed a feasible active suspension control

algorithm to improve the driving performance. The reduced full-car model

which is free from unknown disturbance has been proposed to design the

control algorithm and the suspension state observer. The reduced model is

appropriate for a low-bandwidth controller design to concern primarily with

dominant (body) modes and associated characteristics. To improve the ride

comfort performance, a partial preview control algorithm without road

information has proposed. The wheelbase preview is relatively reliable and

cheap when compared with look-ahead sensor. The vertical acceleration

information of front wheels was used to obtain preview control inputs for rear

suspension actuators.

Finally, the reduced model and control algorithm has been adopted to the

electro-mechanical suspension (EMS) system. The main function of the EMS

system is ride height adjustment, roll and pitch compensation, and ride comfort

improvement. The proposed EMS control algorithm consists of the mode

selector, upper-level and lower-level controllers, and the suspension state

observer. The mode selector determines a present driving mode and the desired

height level of the vehicle. The upper-level controller determines the desired

suspension state considering the actuator stroke limit. The lower level controller

calculates the voltage at each actuator motor using the estimated state by the

observer and the calculated desired state. From the present driving mode, the

119

control objective is determined to be height control, attitude control, or ride

comfort control.

The effectiveness of the proposed estimation and control algorithm has been

evaluated via vehicle tests and simulations. It has been proven that the proposed

observer could estimate the suspension state well without regard to the effect

of unknown road disturbance by the field tests. From the simulation study, it

has been shown that the driving mode and target height level are changed

adaptively according to each driving condition. It has been proven that

suspension state can be estimated with good accuracy by the proposed observer.

The vehicle height was controlled to gradually reach the target height in height

control mode. The roll and pitch angle was reduced by actuator holding control

in attitude control mode. The ride comfort enhancement performance of the

proposed wheelbase preview control algorithm was superior to that of the

feedback control. The model predictive control algorithm could consider hard

constraints on control variables in design process, as a result, the higher

performance could be achieved than LQ optimal control algorithm in the case

of the actuator limitation.

In the future intelligent transportation system environment, an active

suspension control with preview information through vehicle-to-vehicle (V2V)

or vehicle-to-infrastructure (V2I) communications is imperative to achieve

further improvement of the driving performance.

120

Bibliography

R.A. Williams, "Electronically controlled automotive suspensions", Computing &

Control Engineering Journal, 5.3, 1994, pp. 143-148.

M. Appleyard and P.E. Wellstead, "Active suspensions: some background", IEE Proc.-

Control 7heory Appl., 142.2, March 1995, pp. 123-128.

J. Cao, H. Liu, P. Li, and D. J. Brown, "State of the Art in Vehicle Active Suspension

Adaptive Control Systems Based on Intelligent Methodologies", IEEE

TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS,

VOL. 9, NO. 3, SEPTEMBER 2008, pp. 392- 405.

X.D. Xue, K. W. E. Cheng, Z. Zhang, J. K. Lin, D. H. Wang, Y. J. Bao, M. K. Wong,

and N. Cheung, "Study of art of automotive active suspensions.", Power

Electronics Systems and Applications (PESA), 2011 4th International

Conference on, 2011, IEEE, pp. 1-7.

P.S. Els, N.J. Theron, P.E. Uys, M.J. Thoresson, "The ride comfort vs. handling

compromise for off-road vehicles", Journal of Terramechanics, 44.4, 2007,

pp. 303-317.

S.J. Huang and H. Y. Chen, "Adaptive sliding controller with self-tuning fuzzy

compensation for vehicle suspension control.", Mechatronics, 16.10, 2006, pp.

607-622.

T. Yoshimura, A. Kume, M. Kurimmoto, and J. Hino, "Construction of an ac tive

suspension system of a quarter car model using the concept of sliding mode

control." Journal of Sound and Vibration , 239.2, 2001, pp. 187-199.

K. Singal and R. Rajamani, "Zero-Energy Active Suspension System for Automobiles

With Adaptive Sky-Hook Damping", Journal of Vibration and

Acoustics,135.1, 2013, 011011.

S. Yoshihiro and T. Shiiba, "A new hybrid suspension system with active control and

energy regeneration.", Vehicle System Dynamics 25.S1, 1996 pp. 641-654.

S. Rajala, "H∞ control design of an active vehicle suspension system.", Thesis,

Tampere University of Technology, Tampere, Finland, 2012.

121

M. Strassberger and J. Guldner, "BMW's dynamic drive: an active stabilizer bar

system.", IEEE control systems 24.4, 2004, pp. 28-29.

B.L.J. Gysen, J.J.H. Paulides, J. L. G. Janssen, and E. A. Lomonova, "Active

electromagnetic suspension system for improved vehicle dynamics.", IEEE

Transactions on Vehicular Technology, 59.3, 2010, pp. 1156-1163.

B.R. Davis and A.G. Thompson, "Optimal linear active suspensions with integral

constraint.", Vehicle System Dynamics, 17.6, 1988 pp. 357-366.

R. Krtolica, and D. Hrovat, "Optimal active suspension control based on a half-car

model.", Decision and Control, Proceedings of the 29th IEEE Conference on.

IEEE, 1990, pp. 2238-2243.

A. Shirahatti, P.S.S. Prasad, P. Panzade, and M.M. Kulkarni, "Optimal design of

passenger car suspension for ride and road holding.", Journal of the Brazilian

Society of Mechanical Sciences and Engineering, 30.1, 2008, pp. 66-76.

I.E. KöSe and F. Jabbari, "Scheduled controllers for linear systems with bounded

actuators.", Automatica, 39.8, 2003, pp. 1377-1387.

W. Sun, Z. Zhao, and H. Gao, "Saturated adaptive robust control for active suspension

systems", IEEE Transactions on Industrial Electronics, 60.9, 2013, pp. 3889-

3896.

A. Alleyne, R. Liu, and H. Wright, "On the limitations of force tracking control for

hydraulic active suspensions", Proceeding of the 1998 American Control

Conference, Philadelphia Penn, 1998, pp. 43-47.

B. Cal, and D. Konik, "Intelligent Vehicle Active Suspension Control using Fuzzy

Logic", IFAC Triennial World Congress, Sydney, Australia, 1996, pp. 51-56.

B. Kosko, Neural Networks and Fuzzy Systems, Prentice Hall, New Jersey, 1992

B. Kosko, "Fuzzy systems as universal approximators", IEEE Trans. Computers, 43.10,

1994 pp. 1-4.

L.X. Wang, and J.M. Mendel, "Fuzzy basis functions, universal approximation, and

orthogonal least-squares learning, " IEEE Trans. Neural Networks, 3.5, 1992,

pp. 807-814.

122

L.X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis,

Prentice-Hall, New Jersey, 1994

M.M.M. Salam and Ayman A. Aly, "Fuzzy control of a quarter-car suspension system",

International Conference in Mechanical Engineering, ICME, Tokyo, Japan,

May 27-29, 2009, pp. 258-263.

P. Gaspar, I. Szaszi, and J. Bokor, "Design of Robust controller for Active vehicle

Suspension Using the Mixed μ Synthesis", Vehicle System Dynamics, 40.4,

2003, pp. 193-228.

A. Chamseddine, H. Noura, and T. Raharijana, "Control of linear Full Vehicle Active

Suspension System Using Sliding Mode Techniques", Proceedings of the

2006 IEEE, International Conference on Control Applications, Munich,

Germany, 2006.

N. Yagiz, I. Yuksek, S. Sivrioglu, "Robust Control of Active Suspensions for a Full

Vehicle Model Using Sliding Mode Control", JSME Int. Journal. Series C:

Mechanical Systems, Machine elements and Manufacturing , 43.2, 2000, pp.

253-258.

N. Yagiz and I. Yuksek, "Sliding Mode Control of Active Suspensions for a Full

Vehicle Model", Int. Journal of Vehicle Design, 26.2-3, 2001, pp. 265-276.

D. Rumelhart, G. Hinton, and R. Willams, "Learning representations by back-

propagation error", Nature, 1986, pp. 533-536

K. Narendra, and K. Parthasarathy, "Identification and Control of Dynamical Systems

Using Neural Network", IEEE Transaction on Neural Network , 1.1, 1990, pp.

4-27.

A. Hac, "Optimal linear preview control of active vehicle suspension", Vehicle system

dynamics, 21.1, 1992, pp. 167-195.

L. A. Balzer, "Optimal control with partial preview of disturbances and rate penalties

and its application to vehicle suspension", International Journal of Control,

33.2, 1981, pp. 323-345.

123

A. G. Thompson, and C. E. Pearce, "Physically realisable feedback controls for a fully

active preview suspension applied to a half-car model", Vehicle System

Dynamics, 30.1, 1998, pp. 17-35.

N. Louam, D. Wilson, and R. Sharp, "Optimization and performance enhancement of

active suspensions for automobiles under preview of the road", Vehicle System

Dynamics, 21.2, 1992, pp. 39–63.

I. Youn, "Optimal design of discrete time preview controllers for semiactive and active

suspension systems, " KSME international journal, 14.8, 2000, pp. 807-815.

O. Kang, Y. Park, Y.-S. Park, and M. Suh, "Look-ahead preview control application to

the high-mobility tracked vehicle model with trailing arms", Journal of

mechanical science and technology, 23.4, 2009, pp. 914-917.

Martinus, Donny, Benjamin Soenarko, and Yul Y. Nazaruddin. "Optimal control design

with preview for semi-active suspension on a half-vehicle model", Decision

and Control, 1996., Proceedings of the 35th IEEE Conference on. Vol. 3. IEEE,

1996, pp. 2798-2803.

R. G. M. Huisman, F. Veldpaus, H. Voets, and J. Kok, "An optimal continuous time

control strategy for active suspensions with preview" , Vehicle System

Dynamics, 22.1, 1993, pp. 43-55.

R. Huisman, F. Veldpaus, J. Van Heck, and J. Kok, "Preview estimation and control

for (semi-) active suspensions", Vehicle System Dynamics, 22.5-6, 1993, pp.

335-346.

J. Marzbanrad, G. Ahmadi, H. Zohoor, and Y. Hojjat, "Stochastic optimal preview

control of a vehicle suspension", Journal of sound and vibration , 275.3-5,

2004, pp. 973-990.

S. Senthil, and S. Narayanan, "Optimal preview control of a two-dof vehicle model

using stochastic optimal control theory", Vehicle system dynamics, 25.6, 1996,

pp. 413-430.

R. Mehra, J. Amin, K. Hedrick, C. Osorio, and S. Gopalasamy, "Active suspension

using preview information and model predictive control", Control

124

Applications, 1997., Proceedings of the 1997 IEEE International Conference

on. IEEE, 1997, pp. 860-865.

B. K. Cho, "Active suspension controller design using MPC with preview information."

KSME International Journal, 13.2, 1999, pp. 168-174.

B.K. Cho, G. Ryu, and S. J. Song, "Control strategy of an active suspension for a half

car model with preview information", International journal of automotive

technology, 6.3, 2005, pp. 243–249.

C. Göhrle, A.Wagner, A. Schindler, and O. Sawodny, "Active suspension controller

using MPC based on a full-car model with preview information", American

Control Conference, 2012. IEEE, 2012, pp.497-502.

C. Göhrle, A. Schindler, A. Wagner, and O. Sawodny, "Model predictive control of

semi-active and active suspension systems with available road preview", in

Proc. IEEE Eur. Control Conf., 2013, pp. 1499–1504.

C. Göhrle, A. Schindler, A. Wagner, and O. Sawodny, "Design and vehicle imple -

mentation of preview active suspension controllers", IEEE Transactions on

Control Systems Technology, 22.3, 2014, pp. 1135-1142.

C. Göhrle, A. Schindler, A. Wagner, and O. Sawodny, "Road profile estimation and

preview control for low-bandwidth active suspension systems", IEEE/ASME

Transactions on Mechatronics, 20.5, 2015, pp. 2299-2310.

J. K. Hedrick, R. Rajamani, and K. Yi, "Observer Design for Electronic Suspension

Applications", Vehicle System Dynamics, 23.1, 1994, pp.413-440.

R. Rajamani, J. K. Hedrick, "Adaptive observer for active automotive suspensions."

American Control Conference, 1993. IEEE, San Francisco, USA, June, 1993,

pp.706-710.

K. Yi, "Design of disturbance decoupled bilinear observers", KSME Journal, 9.3, 1995,

pp.344-350.

K. Yi, B. S. Song, "Observer design for semi-active suspension control", Vehicle

System Dynamics, 32.2-3, 1999, pp.129-148.

125

N. Pletschen, K. J. Diepold, "Nonlinear state estimation for suspension control

applications: A Takagi-Sugeno Kalman filtering approach", Control

Engineering Practice, 61, 2017, pp.292-306.

L. Dugard, O. Sename, S. Aubouet, and B. Talon, "Full vertical car observer design

methodology for suspension control applications", Control Engineering

Practice, 20.9, 2012, pp.832-845

H. Ren, S. Chen, Y. Zhao, G. Liu, and L. Yang, "State observer-based sliding mode

control for semi-active hydro-pneumatic suspension", Vehicle System

Dynamics, 54.2, 2016, pp.168-190.

M. Canale, M. Milanese, and C. Novara, "Semi-active suspension control using ‘fast’

model-predictive techniques", IEEE Transactions on control systems

technology, 14.6, 2006, pp. 1034-1046

A. Unger, F. Schimmack, B. Lohmann, and R. Schwarz, "Application of LQ based

semi-active suspension control in a vehicle", IFAC Proceedings Volumes, 44.1,

2011, pp. 1808-1813.

K. Arunachalam, P. Mannar Jawahar, and P. Tamilporai, "Active suspension system

with preview control-A review", No. 2003-28-0037, SAE Technical Paper,

2003.

E. Esmailzadeh and F. Fahimi, "Optimal adaptive active suspensions for a full car

model", Vehicle System Dynamics, 27.2, 1997, pp. 89-107

E. M. ElBeheiry, D. C. Karnopp, M. E. ElAraby, and A. M. AbdelRaaouf, "Suboptimal

control design of active and passive suspensions based on a full car model",

Vehicle System Dynamics, 26.3, 1996, pp. 197-222.

J. Marzbanrad, G. Ahmadi, Y. Hojjat, and H. Zohoor, "Optimal active control of vehicle

suspension system including time delay and preview for rough roads", Journal

of Vibration and Control, 8.7, 2002, pp. 967-991

D. Simon, "Optimal state estimation: Kalman, H infinity, and nonlinear approaches.”

John Wiley & Sons, 2006.

A. Moran and M. Nagai, "Optimal preview control of rear suspension using nonlinear

neural networks", Vehicle System Dynamics, 22.5-6, 1993, pp. 321-334.

126

J. MATTINGLEY, and S. BOYD, "CVXGEN: a code generator for embedded convex

optimization", Optimization and Engineering , 13, 2012, pp. 1-27.

Hedrick, J. Karl, and T. Butsuen, "Invariant properties of automotive suspensions.",

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of

Automobile Engineering, 204.1, 1990, pp. 21-27.

Y. Suda, K. Suematsu, K. Nakano, and T. Shiiba, "Study on Electromagnetic

suspension for automobiles – simulation and experiments of performance."

Proc. of AVEC’00, International Symposium on Advanced Vehicle Control,

Michigan, USA, September, 2000, pp.699-704.

Y. Suda, T. Shiiba, K. Hio, Y. Kawamoto, T. Kondo, and H. Yamagata, "Study on

electromagnetic damper for automobiles with nonlinear damping force

characteristics (road test and theoretical analysis)", Proceeding of the 18th

IAVSD Symposium, Vehicle System Dynamics Suppl., 41, 2004, pp. 637–646.

Y. Kawamoto, Y. Suda, H. Inoue, and T. Kondo, "Modeling of electromagnetic damper

for automobile suspension", Journal of System Design and Dynamics, 1.3,

2007, pp. 524-535.

Y. Kawamoto, Y. Suda, H. Inoue, and T. Kondo, "Electro-mechanical suspension

system considering energy consumption and vehicle manoeuvre", Vehicle

System Dynamics, 46, 2008, pp. 1053-1063.

J. Seo, D. Shin, K. Yi, S. Yim, K. Noh, and H. Choi, "Control of the motorized active

suspension damper for good ride quality", Proceedings of the Institution of

Mechanical Engineers, Part D: Journal of Automobile Engineering , 228.11,

2014, pp. 1344-1358.

D. Shin, G. Lee, K. Yi, and K. Noh, "Motorized vehicle active suspension damper

control with dynamic friction and actuator delay compensation for a better ride

quality", Proceedings of the Institution of Mechanical Engineers, Part D:

Journal of Automobile Engineering , 230.8, 2016, pp. 1074-1089.

International Organization for Standardization, "Mechanical vibration and shock-

evaluation of human exposure to whole body vibration—part 1: general

requirements", ISO 2631-1:1997, 1997.

127

L. Zuo and S. Nayfeh, “Low order continuous-time filters for approximation of

the iso2631-1 human vibration sensitivity weightings,” Journal of

sound and vibration, 265, 2002, pp. 459–465.

128

초 록

전륜 가속도 센서 기반 승차감 향상을

위한 능동 현가 시스템 예측 제어

승용차의 능동 및 반 능동 현가 시스템은 승차감 향상과 핸들링

성능을 개선해 주는 효과 때문에 지난 수십 년간 매우 활발히

연구되어 왔다. 반 능동 현가 시스템에 비해 능동 현가 시스템은 더

향상된 성능과 더 많은 기능을 제공한다는 것은 잘 알려 진

사실이다. 능동 현가 시스템의 주요 기능은 차량 높이 조정, 승차감

향상 및 자세 제어다. 최근 능동 현가 시스템이 장착된 고성능 차량

및 고급 세단이 대량 생산되어 판매되고 있는 추세이다. 예를 들어

Citroen 사의 Hydractive 시스템, Mercedes-Ben 사의 Active Body Control

(ABC) 시스템, BMW 사의 anti-roll control (ARS) 시스템이 개발되어

양산화 되었다. 능동 현가장치의 성능은 전방 도로 정보가 주어지게

되면 크게 향상 될 수 있다. 이러한 전방 도로 정보를 이용한

승차감 향상을 목표로 전세계 다양한 연구 개발이 진행되고 있다.

Mercedes-Benz 사는 세계 최초로 전방 도로 표면을 인식하여 예측

제어하는 능동 현가장치가 장착된 차량을 선 보였다. BMW 는 능동

현가 제어를 위한 비디오 영상 처리 시스템 개발에 노력하고 있다.

129

Volkswagen 사는 레이더 / 레이저 센서를 이용해 전방 도로를

감지하고 현가 시스템을 이에 미리 대비하고 작동시키기 위한

연구를 진행 중에 있다. Honda 사는 적응 형 현가 시스템 및 차량 간

네트워크 시스템에 대한 특허를 보유하고 있다.

다수의 참고 문헌을 심도 있게 검토한 결과, 능동 현가 시스템의

예측 제어 기술은 승객의 안전뿐만 아니라 편의도 증진시킬 수

있을 것으로 기대된다. 하지만 현재 개발되고 있는 최첨단 예측

현가 시스템 기술은 두 가지 주요 문제에 당면해 있다. 첫째, 현재

다수 개발된 현가 시스템 제어 방식에서는 서스펜션 변위 속도

또는 타이어 변위 량과 같이 습득하기 어려운 신호에 대한 정보가

필요하다. 둘째, 전방 도로 정보를 감지하기 위해서는 레이저

스캐너와 같은 정밀하고 비싼 센서가 필요하다. 비록 이러한 센서의

가격이 하락하고 있는 추세이긴 하지만 센서를 자동차에

추가적으로 장착함으로 인해 가격이 상승하고 이는 시스템 양산에

또 다른 장벽이 되고 있다.

따라서 본 논문에서는 현재 양산된 차량용 센서들을 이용하여

낮은 작동 주파수 대역의 능동 현가 시스템 제어를 위한 부분적인

예측 제어 알고리즘을 개발하는 것을 목표로 하고 있다. 알 수 없는

도로 가진 입력에 대처하기 위해, 새로운 수직방향 전 차량 모델이

개발되었다. 이를 통해 쉽게 습득할 수 있는 측정값을 이용한 현가

시스템 상태 변수 추정기를 개발하였다. 전륜에서 발생하는 수직

가속도 정보는 후륜 능동 현가장치의 예측 제어를 위한 제어 량

결정에 사용된다. 차량 신호로부터 현재 주행 모드 판별에 의해

130

현가 시스템 제어 목표는 차고 조절, 자세 제어 및 승차감 향상

제어로 나뉜다.

제안된 능동 현가 시스템 제어 및 상태 변수 추정 알고리즘의

성능은 컴퓨터 시뮬레이션과 차량 테스트를 통해 검증되었다. 그

결과 제안된 제어 및 추정 알고리즘으로 향상된 차량 주행 성능을

확보함을 확인하였다.

주요어: 능동 현가 시스템, 수직방향 전 차량 축소 모델, 칼만 필터,

선형 제차 레귤레이터, 최적 선형 예측 제어 기법, 모델 예측 제어

기법, 전자 기계식 현가 시스템

학 번: 2013-23053