2015/5/29

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Tielong ShenDepartment of Engineering and Applied Sciences Sophia University, Tokyo, Japan

Applications of Real-time Optimization Algorithm in Modeling and Control of Automotive Powertrains

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On going projects at Sophia

Real-time Optimization (RHC)

> Case Study I: Combustion Engine Control

> Case Study II: Energy Management of HEVs

> Case Study III: Real-time D-Optimization

Future Challenges

Outline

2015/5/29

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Issues and Facility at SOPHIA

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Projects

Advanced control technologies for the next generation of combustion engines,‘05～, Toyota.

Energy management strategy with traffic information ‘11 ～，Nissan

Optimization algorithm for ECU Calibration, ‘12～，Hitachi

Engine efficiency improvement by transient control with dynamical boundary control KAKENHI(B), ‘14 ～

Model-based transient control of combustion engines, KAKENHI(B), No. 23360186）, ‘11-’13

Development of high efficiency engines, JST JKC Project, ’13～

Industrial projects

National projects

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Issues (engine)

-- CPS-based engine management-- Real-time optimization -- Probability-constrained optimal control-- Statistical method for boundary detection-- Stochastic logical control of Residual Gas Fraction-- Knock probability control with likelihood estimation-- Cycle-to-cycle behavior -- Extremal seeking-- D-optimization for calibration

Background: Transient and Hardwar in Loop

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-- Controller model + Real Engine-- ECU + Engine Model

Model

Sensors

Actuators

ECU

-- ECU Calibration based on Engine Model

To get engine physics right, engine-in-the-loop system is effective Real-time operating is always in Transient operation. Controller calibration at static modes does not satisfies real-world.

Engine-in-The-Loop System

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MicroAutoBoX II

dSPACE DS1006AD-Phoenix (A&D)

In Motion/Car Maker

Individual Fuel (P/D), SA, VVTin, VVTex,Throttle

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Real-time Optimization (RHC)

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Model-based Optimal Control Model of system dynamics under control

Cost function along trajectories

Optimization problem with dynamical constraint

Subject to

このイメージは、現在表示できません。

Area: Functional

Control Constraint

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Pontryagin’s Maximum Principle

Cost function

Lev Semenovich Pontryagin1908-1988

Constraint condition

If is the solution, then

Hamiltonian

Real-time Optimization: Receding Horizon control

Reference

Control Period

Output

Area: Functional

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Discretization of the optimality condition (N-steps )

Find:

Numerical Solver: Iterative Algorithm

C/GMRES Algorithm, by T. Ohtsuka

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CASE Study 1:Torque Control of Gasoline Engine

Thanks to M. Kang (Candidate PhD)

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Motivation:Transient Behavior

ThrottleOpening

Rotational Speed

Air flow

Exhaust Gas

Cylinder

Intake valve Ehxaust Valve

Intake Manifold

u y

Input OutputIntake AirDyanmics

RotationalDynamics

ManifoldPressure

t/s12Fuel cut Restarting

14.7

14.7

14.7

Port inj.Direct inj.

0

0

0

t/s12

t/s5

t/s0

0 t/s

throttle opening

engine speed

A/F

5 10 15 20 25 30 35 40

5 10 15 20 25 30 35 40

1500/6

3000/12

13

16

14.7

Fuel Cutting

Fuel Path Switching

Start-up

Throttle Opening

Intake path, fuel path and mechanical dynamics cause transient phenomenon

Transient behavior presents imbalance of mass, thermal energy, etc.

With uncertainties such as nonlinearity, stochastic properties, etc, due to the stochastic characteristics in combustion event.

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Transient Behavior in Combustion Events

−300 −200 −100 0 100 200 3000

10

20

30

40

50

60

Crank angle (degree)

In−cy

linde

r Pre

ssure

(bar

)

Constant Load Mode: Load=76Nm, Average Cycle=3

t=3.0s, 828rpmt=4.0s, 1046rpmt=4.5s, 1337rpmt=5.0s, 1482rpm

0 1 2 3 4 5 6 7

x 10−4

0

10

20

30

40

50

60

Volume of Cylinder (m 3)

In−

cylin

der P

ress

ure

(bar

)

Constant Load Mode: Load=76Nm, Average Cycle=3

t=3.0s, 828rpmt=4.0s, 1046rpmt=4.5s, 1337rpmt=5.0s, 1482rpm

0 5 10 15

5

10

Engi

ne T

hrot

tle

Constant Load Mode: Load=76Nm, Average Cycle=3

0 5 10 1522

23

24

SA

0 5 10 15500

1000

1500

2000

Engi

ne s

peed

(RPM

)

0 5 10 155

10

15

20

Time (s)

CA50

(deg

ree)

Transient response of CA50

Transient response of in-cylinder pressure

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Physics and Control-oriented Model

Air Inlet Path

Dynamics

Fuel Inj. Path

Dynamics

Compr.

&

Comb.

Torque

Gener.

Proc.

Crankshaft

Rotational

Dynamics

Speed

Throtle

Fuel Inj.

Air

Fuel Torque

Σ

Spark

Air Inlet Path

Dynamics

Fuel Inj. Path

Dynamics

Compr.

&

Comb.

Torque

Gener.

Proc.

Crankshaft

Rotational

Dynamics

Speed

Throtle

Fuel Inj.

Air

Fuel Torque

Σ

Spark

Air path dynamics(MVM)

Rotation speed dynamics

Torque Generation Model (Static)

Mean-value Transient Model

Mean value : 0.0047 g/s Variance : 0.6935

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subject toa) Dynamic equations

b) Torque output equation

c) Necessary constraints

Control objective

Real-time Optimization: Torque Tracking

Torque Tracking

0

50

100

150

Eng

ine

Tor

que[

Nm

]

0

5

10

15

Thr

ottl

e[de

g]

0

1000

2000

3000

Eng

ine

Spe

ed[r

pm]

0 10 20 30 40 50 60 70 80 90 100

-20

0

20

40

Time[s]

Tra

ckin

g E

rror

[Nm

]

SetPointOriginalImproved

Original Improved

neActl

Original Improved

40

60

80

Original RHC parameters:

Predictive time: 0.3sControl period: 0.01sPredictive period: 0.01sPredictive steps: 30

Improved RHC parameters:

Predictive time: 1sControl period: 0.01sPredictive period: 0.01sPredictive steps: 30Integral Gain: 0.6

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1000

1500

2000

2500

Eng

ine

Spe

ed[r

pm]

0

5

10

15

Thr

ottl

e[de

g]

40

60

80

100

Loa

d[N

m]

0 20 40 60 80 100 120 140 160 180 200-300

-200

-100

0

100

200

300

Time [s]

Tra

ckin

g E

rror

[rpm

]

SetPoint ne(PID) ne(MPC)

(PID) (MPC)

l

PID MPC

Tracking error Mean value variance

PID 0.21543 1460.6545

MPC 0.045444 1038.7143

Experiment (Speed Tracking)

Comparison between PID control and RHC control (Enlarged figure)

1500

1600

1700

1800

1900

Eng

ine

Spe

ed [rp

m]

5

6

7

Thr

ottle[

deg]

30

40

50

60

Loa

d[N

m]

45 50 55 60-100

-50

0

50

Time [s]

Tra

ckin

g Err

or[r

pm]

1200

1400

1600

1800

2000

Eng

ine

Spe

ed [rp

m]

0

5

10

15

Thr

ottle[

deg]

40

60

80

100

Loa

d[N

m]

120 125 130 135 140 145

-200

-100

0

100

200

Time [s]

Tra

ckin

g Err

or[r

pm]

SetPoint

ne(PID)

ne(MPC)

(PID)

(MPC)

l

PID

MPC

SetPoint

ne(PID)

ne(MPC)

(PID)

(MPC)

l

PID

MPC

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Driving cycle tests

0

50

100

150

Veh

icle

Spe

ed

Veh.Spd.Ref [Km/h]

Veh.Spd.Actl [Km/h]

0

100

200

300

Eng

ine

Tor

que

d [Nm]

e Actl [Nm]

1000

2000

3000

Eng

ine

Spe

ed

n

e Actl [rpm]

0

20

40

60

80

Drive

r.In

puts &

Thr

ottle

Acc [deg]

Brk [%]

Thr.Actl[deg]

0 50 100 150 200 250 300 350 400 450 500-40

-20

0

20

40

Time [s]

Tra

ckin

g Err

or

Error[Nm]

0

100

200

0

10

20

Tracking error Mean value:

-0.0783 Nm Variance:

23.9715

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CASE Study II:Energy Management for HEVs

Thanks to Dr. J. Zhang, Shunichi Hara(M.S.)

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Energy Management Problem

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VehiclePowertrainEnergy Manag.

SpeedWheels TorqueRequest

Environment

Demand Decision

Energy Management Problem

Off-line (Here-and-Now)

Goal of Energy Management: Minimizing Consumption

Total power must satisfies the demanded power by driver

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VPower-train

Energy Manage

ment

速度

Power Demand

Slope

--Off-line optimization--Fuel or Equivalent Consumption--Prior Route Information

Rule-based and Optimization

Rule-based approachHigh efficiency operating point of each power deviceunder the constraint of total power demand

Optimization-based Approach

Prior Information

Brief Review

Rule-based Approach

Optimization-based Approach[A] Dynamical Programming

Off‐line optimization (DP, Stochastic DP, Pontriyagin’s Principle)Global optimal solution regarding to a priori known driving cycle

Ref. O. Sundstrom, et al,Oil&Gas ST, V65,2010; S. Moura, et al., IEEE CST, V19,2011

Based on efficiency property of the devicesRef. L. Serrao, S. Onori, G. Rizzoni, ASME JDSMC, Vol133, 2011

[B] ECMS（ Equivalent Consumption Minimization Strategy）Ref. G. Rizzoni, IFAC Workshop EPCSM, 2012, C.Musardo et al., EJC, V11, 2005

[C] Real-time Optimization

Look‐ahead optimal control, Receding Horizon ControlRef. H.Borhan et al., IEEE CST, V20,2012

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Modeling

Input

engine torque

motor torque

発 generator torque

braking torque

Output

Speed

バッ

燃料 Fuel Consumption

power balancing

state Variable:control input:

external constraint:

Dynamical Model in Nonlinear State Equation Form

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Real-time Optimization

Constraint of power split by driver-demand has been embedded

Simulations Validation with GT‐Simulator provided by JSAE‐SICE benchmark problem

Standard city driving cycle

Driving cycle with part of highway driving

Regular Driving

Jam Driving

slope θ=0;ωemax=4000[rpm], ωgmin=2000[rpm];SoC(0)=0.9;

T=5[s], δτ=0.01[s];

(δτ:Control Period)

Thanks to IDAJ for supporting GT-SUIT

*Parameter from Y. Yasui, JSAE‐SICE Benchmark Problem 2

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Engine-in-The-Loop HEV

Motor-Battery-Driveline-V

Standard city driving cycle (regular driving) 

Acceleration performance is weak due to the limitation of the engine power when the emergency mode is activated

Alpha‐speed

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Standard city driving cycle (Jam driving) 

Comparisons (regular driving) 

by the proposed control scheme by the benchmark example control scheme

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Receding Horizon Control Algorithm

Example Algorithm

FinalSoC[‐]

Fuel Consumption[g]

Sd[%]FinalSoC[‐]

FuelConsumption[g]

Sd[%]

Standard CityDriving

Regular 0.4942 398.95 92.7 0.5203 570.5

100Jam 0.4858 496.78 96.5 0.5066 909.6

Driving with Highway 0.4709 567.7 91.8 0.5087 764.8

Testing Results on GT‐SUIT

Realtimeness Testing on dSPACE

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CASE Study III:Real-time D-Optimization

Thanks to Mitsuru Toyoda (Mater Course)

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Model: linearity

Parameter Identification

Solution

Model Identification: Least-Squares Estimation

Plant

Model

LSE

With the estimation

Experiment Design: D-Optimization

Statistical property

Expectation

Variance

D-Optimality

Wald(1943), Kiefer, Wolfowita (1959).

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Fisher information matrix

D-Optimization: Find optimal input for identification

D-Optimalityto reject covariance of estimated parameter, design optimal input signal in the

sense of

Plant

Discretization

Real-time D-optinization)

Example: Linear Second-order System

With constraint

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2015/5/29 日立報告資料 43

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

t(k)

a1(k)

a1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2

-1.5

-1

-0.5

0

t(k)

a2(k)

a2(k)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5x 10

-4

b2(k)

b1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-50

0

50

t(k)u(k)

u(k)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

t(k)

y(k)

y(k)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.2

-0.1

0

0.1

0.2

t(k)

y(k)−y(k)

y(k) − y(k)

Concluding Remarks

Stochastic property

Model-free control strategy

Real-time Optimization with constraint

Multi-core ECU

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Palazzo Imperiale

Tokyo Bay, Pacifico

Sophia University

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