-
Marcelo MENEZES MORATO Olivier SENAME
Luc DUGARD
Design of a Real-Time LPV MPC Scheme for Semi-Active Suspension
Control of a Full Vehicle
Réunion régulière GT MOSAR, Strasbourg 22 May, 2017
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Marcelo MENEZES MORATOOlivier SENAME
Luc DUGARD
Design of a Real-Time LPV MPC Scheme for Semi-Active Suspension
Control of a Full Vehicle
Réunion régulière GT MOSAR, Strasbourg 22 May, 2017
-
Research’s Framework• Master Project: UFSC & ENSE3
• PERSYVAL LPV4FTC Project
• Internship at gipsa-lab
• Goal: Development of Linear Parameter Varying Approaches
as
Advanced Control Techniques for Vehicle Suspension Systems
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Outline• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
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Outline• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
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Introduction & Motivation
Modern Cars: More Safety and More Comfort!
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Introduction & Motivation
Modern Cars: More Safety and More Comfort!• Controlled
Suspensions: Improve Comfort + Handling
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Introduction & Motivation
Modern Cars: More Safety and More Comfort!• Controlled
Suspensions: Improve Comfort + Handling
• Semi-Active Suspension Systems
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 3/37
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Introduction & Motivation
Modern Cars: More Safety and More Comfort!• Controlled
Suspensions: Improve Comfort + Handling
• Semi-Active Suspension Systems
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Introduction & Motivation
Modern Cars: More Safety and More Comfort!• Controlled
Suspensions: Improve Comfort + Handling
• Semi-Active Suspension Systems
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 3/37
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Introduction & Motivation
Modern Cars: More Safety and More Comfort!• Controlled
Suspensions: Improve Comfort + Handling
• Semi-Active Suspension Systems
Semi-Active Suspension System• High performances achieved
• Moderate Costs
• Problem: Dissipativity Constraints
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Introduction & Motivation
Semi-Active Suspension System• High performances achieved
• Moderate Costs
• Problem: Dissipativity Constraints
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• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
Outline
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Problem Statement & ObjectivesControl of Semi-Active
Suspension Systems
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 6/37
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Problem Statement & ObjectivesControl of Semi-Active
Suspension Systems
Throughout Literature:
- Skyhook, Groundhook Control:
- Clipped Strategies (LQ, H∞):
- ADD, Mixed SH-ADD:
- LPV/H∞ Approaches:
[Karnopp, D. (1974)]
[Tseng, H.E. (1994)], [Sammier, D. (2003)]
[Savaresi, S.M. (2005), (2007)]
[Poussot-Vassal, C. (2008)], [Do, A.L. (2010)], [Nguyen, M. Q.
2015]
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 6/37
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Problem Statement & ObjectivesControl of Semi-Active
Suspension Systems
How to handle dissipativity constraints of dampers?
Throughout Literature:
- Skyhook, Groundhook Control:
- Clipped Strategies (LQ, H∞):
- ADD, Mixed SH-ADD:
- LPV/H∞ Approaches:
[Karnopp, D. (1974)]
[Tseng, H.E. (1994)], [Sammier, D. (2003)]
[Savaresi, S.M. (2005), (2007)]
[Poussot-Vassal, C. (2008)], [Do, A.L. (2010)], [Nguyen, M. Q.
2015]
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 6/37
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Control of Semi-Active Suspension Systems
How to handle dissipativity constraints of dampers?
Natural approach (process + constraints) —> Model Predictive
Control (MPC)
Problem Statement & Objectives
Throughout Literature:
- Skyhook, Groundhook Control:
- Clipped Strategies (LQ, H∞):
- ADD, Mixed SH-ADD:
- LPV/H∞ Approaches:
[Karnopp, D. (1974)]
[Tseng, H.E. (1994)], [Sammier, D. (2003)]
[Savaresi, S.M. (2005), (2007)]
[Poussot-Vassal, C. (2008)], [Do, A.L. (2010)], [Nguyen, M. Q.
2015]
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 6/37
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Control of Semi-Active Suspension Systems
How to handle dissipativity constraints of dampers?
Natural approach (process + constraints) —> Model Predictive
Control (MPC)
Not-So-Rich Literature: - Considering Quarter-Car Models:
- Clipped Analytical MPC:
- MPC for Full Car, Road Preview
- MPC for Full Car, Computational Time Issues
Problem Statement & Objectives
Throughout Literature:
- Skyhook, Groundhook Control:
- Clipped Strategies (LQ, H∞):
- ADD, Mixed SH-ADD:
- LPV/H∞ Approaches:
[Karnopp, D. (1974)]
[Tseng, H.E. (1994)], [Sammier, D. (2003)]
[Savaresi, S.M. (2005), (2007)]
[Poussot-Vassal, C. (2008)], [Do, A.L. (2010)], [Nguyen, M. Q.
2015]
[Canale, M. (2006)]
[Giorgetti, N. (2006)]
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 6/37
[Sawodny, O. (2014)]
[Nguyen, M. Q. (2016)
-
Control of Semi-Active Suspension Systems
How to handle dissipativity constraints of dampers?
Natural approach (process + constraints) —> Model Predictive
Control (MPC)
Problem Statement & Objectives
Throughout Literature:
- Skyhook, Groundhook Control:
- Clipped Strategies (LQ, H∞):
- ADD, Mixed SH-ADD:
- LPV/H∞ Approaches:
[Karnopp, D. (1974)]
[Tseng, H.E. (1994)], [Sammier, D. (2003)]
[Savaresi, S.M. (2005), (2007)]
[Poussot-Vassal, C. (2008)], [Do, A.L. (2010)], [Nguyen, M. Q.
2015]
[Canale, M. (2006)],
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 6/37
Not-So-Rich Literature: - Considering Quarter-Car Models:
- Clipped Analytical MPC:
- MPC for Full Car, Road Preview
- MPC for Full Car, Computational Time Issues
[Canale, M. (2006)],
[Giorgetti, N. (2006)]
[Sawodny, O. (2014)
[
Limited Sampling Period for Real-Time Applications
—> 5 ms
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Problem Statement & Objectives
Control Objectives:
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 7/37
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Control Objectives:
Problem Statement & Objectives
• Use a Full Car 7-DOF Vehicle Model
• Take into account the Dissipativity Constraints of all 4
Semi-Active Dampers
• Compute MPC Law in less then 5 ms !
• Prediction of States and Road Disturbances ? —> Extended
Observer
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 7/37
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Control Objectives:
Problem Statement & Objectives
• Use a Full Car 7-DOF Vehicle Model
• Take into account the Dissipativity Constraints of all 4
Semi-Active Dampers
• Compute MPC Law in less then 5 ms !
• Prediction of States and Road Disturbances ? —> Extended
Observer
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 7/37
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Control Objectives:
Problem Statement & Objectives
• Use a Full Car 7-DOF Vehicle Model
• Take into account the Dissipativity Constraints of all 4
Semi-Active Dampers
• Compute MPC control law in less then 5 ms !
• Prediction of States and Road Disturbances ? —> Extended
Observer
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 7/37
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Control Objectives:
Problem Statement & Objectives
• Use a Full Car 7-DOF Vehicle Model
• Take into account the Dissipativity Constraints of all 4
Semi-Active Dampers
• Compute MPC control law in less then 5 ms !
• Prediction of States and Road Disturbances ? —> Extended
Observer
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO - 7/37
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• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
Outline
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System Model & ConstraintsFull Vertical Suspension System
Model
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System Model & ConstraintsFull Vertical Suspension System
Model
Dynamical Equations of Motion
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System Model & ConstraintsFull Vertical Suspension System
Model
Dynamical Equations of Motion
Tire’s Forces
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System Model & ConstraintsFull Vertical Suspension System
Model
Dynamical Equations of Motion
Tire’s Forces
Semi-Active Suspension Forces
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System Model & ConstraintsFull Vertical Suspension System
Model
Dynamical Equations of Motion
Linearization on Small Angles
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System Model & ConstraintsDamper Dissipativity
Constraints
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System Model & ConstraintsDamper Dissipativity
Constraints
Fdij = cij(·).żdefij
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System Model & ConstraintsDamper Dissipativity
Constraints
Fdij = cij(·).żdefij
0 cij cij(·) cij
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System Model & ConstraintsDamper Dissipativity
Constraints
Fdij = cij(·).żdefij
Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
0 cij cij(·) cij
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System Model & ConstraintsDamper Dissipativity
Constraints
Fdij = cij(·).żdefij
Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
0 cij cij(·) cij
�cij �cij �cij
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State-Space Representation
System Model & Constraints
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State-Space Representation
System Model & ConstraintsTs = 5 ms
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• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
Outline
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• MPC —> Need for State and Disturbance Knowledge
• Future Disturbance Estimation —> Enhance CL Performance
• Extended H2 Observer
• Trade-Off: Convergence Speed vs Noise Attenuation
Observer Design + Experimental Validation
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• MPC —> Need for State and Disturbance Knowledge
• Future Disturbance Estimation —> Enhance CL Performance
• Extended H2 Observer
• Trade-Off: Convergence Speed vs Noise Attenuation
Observer Design + Experimental Validation
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[Sawodny, O. (2014)]Disturbance Preview:
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• MPC —> Need for State and Disturbance Knowledge
• Future Disturbance Estimation —> Enhance CL Performance
• Extended H2 Observer
• Trade-Off: Convergence Speed vs Noise Attenuation
Observer Design + Experimental Validation
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Disturbance Model
[Sawodny, O. (2014)]Disturbance Preview:
-
• MPC —> Need for State and Disturbance Knowledge
• Future Disturbance Estimation —> Enhance CL Performance
• Extended H2 Observer
• Trade-Off: Convergence Speed vs Noise Attenuation
Observer Design + Experimental Validation
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[Sawodny, O. (2014)]Disturbance Preview:
Disturbance Model
-
• MPC —> Need for State and Disturbance Knowledge
• Future Disturbance Estimation —> Enhance CL Performance
• Extended H2 Observer
• Trade-Off: Convergence Speed vs Noise Attenuation
Observer Design + Experimental Validation
Pole Placement
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[Sawodny, O. (2014)]Disturbance Preview:
Disturbance Model
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Observer Design + Experimental Validation
H2 Extended Observer Design
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Observer Design + Experimental Validation
H2 Extended Observer Design
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Observer Design + Experimental Validation
H2 Extended Observer Design
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Observer Design + Experimental Validation
H2 Extended Observer Design
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Observer Design + Experimental Validation
H2 Extended Observer Design• Problem Definition:
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Observer Design + Experimental Validation
H2 Extended Observer Design• Problem Definition:
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H2 Norm —> Impulse to Energy Gain! Noise —> Estimation
Error
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Observer Design + Experimental Validation
H2 Extended Observer Design• Problem Solution:
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Observer Design + Experimental Validation
H2 Extended Observer Design• Problem Solution: Pole
Placement
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Observer Design + Experimental ValidationExperimental
Test-bench:
INOVE Soben-Car
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The INOVE Project and Vehicle Test-bench
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Observer Design + Experimental ValidationExperimental
Test-bench:
INOVE Soben-Car
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The INOVE Project and Vehicle Test-bench
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Observer Design + Experimental Validation Validation Results:
Road Estimation
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Observer Design + Experimental Validation
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Validation Results: Roll & Pitch Angles
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Observer Design + Experimental Validation Validation Results:
Roll & Pitch Angles
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0 2 4 6 8 10 12 14 16 18 20−0.05
0
0.05
0.1
0.15
Time (s)
Dis
plac
emen
t (m
)
zs(t)Estimated zs(t)
2.5 3 3.5 4 4.5
−0.02
0
0.02
0.04
Time (s)
Angl
e (ra
d)
θ (t)Estimated θ (t)
4.5 5 5.5 6 6.5 7 7.5 8 8.5−0.02
−0.01
0
0.01
0.02
Time (s)
Angl
e (ra
d)
φ (t)Estimated φ (t)
0 2 4 6 8 10 12 14 16 18 20−2
−1
0
1
Time (s)
Spee
d (m
/s)
\dot{z_s} (t)Estimated \dot{z_s} (t)
0 2 4 6 8 10 12 14 16 18 20−0.05
0
0.05
0.1
0.15
Time (s)
Dis
plac
emen
t (m
)
zs(t)Estimated zs(t)
2.5 3 3.5 4 4.5
−0.02
0
0.02
0.04
Time (s)
Angl
e (ra
d)
θ (t)Estimated θ (t)
12 12.5 13 13.5 14 14.5
−0.01
0
0.01
Time (s)
Angl
e (ra
d)
φ (t)Estimated φ (t)
0 2 4 6 8 10 12 14 16 18 20−2
−1
0
1
Time (s)
Spee
d (m
/s)
\dot{z_s} (t)Estimated \dot{z_s} (t)
-
• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
Outline
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Optimal Solution
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Optimal Solution Proposed Optimal MPC Design
• MPC —> Optimization of Performance Indexes
• Cost Function
• Computational Time Constraints —> Faster Approaches
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Optimal Solution Proposed Optimal MPC Design
• MPC —> Optimization of Performance Indexes
• Cost Function
• Computational Time Constraints —> Faster Approaches
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Optimal Solution Proposed Optimal MPC Design
• MPC —> Optimization of Performance Indexes
• Cost Function
• Computational Time Constraints —> Faster Approaches
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+ Chassis Displacement
-
Optimal Solution Proposed Optimal MPC Design
• MPC —> Optimization of Performance Indexes
• Cost Function
• Computational Time Constraints —> Faster Approaches
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Optimal Solution Proposed Optimal MPC Design
• MPC —> Optimization of Performance Indexes
• Cost Function
• Computational Time Constraints —> Faster Approaches
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Tc >> TsComputationalTime
-
Optimal Solution Proposed Optimal MPC Design
• MPC —> Optimization of Performance Indexes
• Cost Function
• Computational Time Constraints —> Faster Approaches
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Tc >> TsComputationalTime
[Nguyen, M. Q. (2016)]
-
• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
Outline
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Sub-Optimal Pratical Solution
• LPV Representation
• New Control Inputs
• Linear Constraints
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• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
-
• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
Control
-
• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
Control SchedulingParameter
-
• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
Control Inputs
-
• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
Control Inputs
TsX
Full
:=
⇢x[k + 1] = Ad.x[k] + B1d.w[k] + B2d(⇢).�c[k]y[k] = Cd.x[k] +
D1d.w[k] + D2d(⇢).�c[k]
�
-
• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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Fdij = cnomij .żdefij +�cij .żdefij| {z }
uij
Control Inputs
TsX
Full
:=
⇢x[k + 1] = Ad.x[k] + B1d.w[k] + B2d(⇢).�c[k]y[k] = Cd.x[k] +
D1d.w[k] + D2d(⇢).�c[k]
�Affine on p
-
• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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TsX
Full
:=
⇢x[k + 1] = Ad.x[k] + B1d.w[k] + B2d(⇢).�c[k]y[k] = Cd.x[k] +
D1d.w[k] + D2d(⇢).�c[k]
�
�c �c[k] �cx x[k] x
-
• LPV Representation
• New Control Inputs
• Linear Constraints
Sub-Optimal Pratical Solution
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TsX
Full
:=
⇢x[k + 1] = Ad.x[k] + B1d.w[k] + B2d(⇢).�c[k]y[k] = Cd.x[k] +
D1d.w[k] + D2d(⇢).�c[k]
�
�c �c[k] �cx x[k] x
[Nguyen, M. Q. (2016)]Mixed Integer Constraints
-
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Sub-Optimal Pratical Solution
- The FMPC Method, Proposed by [Boyd, 2008]
Computation of LPV MPC Law
- LPV Matrices fixed through prediction horizon
-
Sub-Optimal Pratical Solution
- The FMPC Method, Proposed by [Boyd, 2008]- LPV Matrices fixed
through prediction horizon
Computation of LPV MPC Law
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-
Sub-Optimal Pratical Solution
- The FMPC Method, Proposed by [Boyd, 2008]- LPV Matrices fixed
through prediction horizon
Computation of LPV MPC Law
- LPV —> fixed at instant k
- Primal-Barrier Interior-Point Method
- Infeasible Start Newton Method
- Warm Start Techniques
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-
Sub-Optimal Pratical Solution
- The FMPC Method, Proposed by [Boyd, 2008]- LPV Matrices fixed
through prediction horizon
Computation of LPV MPC Law
- LPV —> fixed at instant k
- Primal-Barrier Interior-Point Method
- Infeasible Start Newton Method
- Warm Start Techniques
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Approximate J,Primal-Barrier Term
instead of linear inequality constraints
-
Sub-Optimal Pratical Solution
- The FMPC Method, Proposed by [Boyd, 2008]- LPV Matrices fixed
through prediction horizon
Computation of LPV MPC Law
- LPV —> fixed at instant k
- Primal-Barrier Interior-Point Method
- Infeasible Start Newton Method
- Warm Start Techniques
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Solving the approximate QPwith infeasible
StartNewton Method,
use of dual variables,
primal and dual residual search
-
Sub-Optimal Pratical Solution
- The FMPC Method, Proposed by [Boyd, 2008]- LPV Matrices fixed
through prediction horizon
Computation of LPV MPC Law
- LPV —> fixed at instant k
- Primal-Barrier Interior-Point Method
- Infeasible Start Newton Method
- Warm Start Techniques
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Last array of control steps U shifted (z-1)
as start for nextcomputation
-
Objective:Control all 4 Semi-Active ER Dampers
Provide Suitable Trade-Off Handling vs Comfort Performances
Abide to all Dissipativity Constraints
Computational Time < 5 ms
Sub-Optimal Pratical Solution Simulation Results:
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Objective:Control all 4 Semi-Active ER Dampers
Provide Suitable Trade-Off Handling vs Comfort Performances
Abide to all Dissipativity Constraints
Computational Time < 5 ms
Simulation Scenario:Straight Road, Constant Speed
Frontal and Lateral Bumps Comparison with Analytical Clipped
MPC, [Giorgetti, N. (2006)]
Sub-Optimal Pratical Solution Simulation Results:
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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Objective:Control all 4 Semi-Active ER Dampers
Provide Suitable Trade-Off Handling vs Comfort Performances
Abide to all Dissipativity Constraints
Computational Time < 5 ms
Simulation Scenario:Straight Road, Constant Speed
Frontal and Lateral Bumps Comparison with Analytical Clipped
MPC, [Giorgetti, N. (2006)]
Sub-Optimal Pratical Solution Simulation Results:
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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Nc = Np = 10
-
Sub-Optimal Pratical Solution Simulation Results: Computation of
Control Law
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Sub-Optimal Pratical Solution Simulation Results: Road Profile +
Estimation
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Sub-Optimal Pratical Solution Simulation Results: Road Profile +
Estimation
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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Bump on all WheelsExcite Chassis Acceleration
-
Sub-Optimal Pratical Solution Simulation Results: Road Profile +
Estimation
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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Bump only on Left sideExcite Roll Motion
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Sub-Optimal Pratical Solution
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Simulation Results: Chassis Displacement
-
Sub-Optimal Pratical Solution Simulation Results: Chassis
Acceleration
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Sub-Optimal Pratical Solution Simulation Results: Chassis
Acceleration
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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Sub-Optimal Pratical Solution
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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Simulation Results: Roll Angle
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Sub-Optimal Pratical Solution
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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Simulation Results: Roll Angle
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AMPC —> Clipping ActionNo guarantees of CL Performances
-
−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
−30
−20
−10
0
10
20
30
Suspension Deflection Speed (m/s)
Susp
ensi
on F
orce
(N)
Force vs. Susp. Deflection Speed at Rear Right Corner
MaximalMinimalAMPCFMPC
Sub-Optimal Pratical Solution Simulation Results: Semi-Active
Damper Force
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
−30
−20
−10
0
10
20
30
Suspension Deflection Speed (m/s)
Susp
ensi
on F
orce
(N)
Force vs. Susp. Deflection Speed at Rear Right Corner
MaximalMinimalAMPCFMPC
Sub-Optimal Pratical Solution Simulation Results: Semi-Active
Damper Force
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AchievableControlled
Damper ForceSet
-
Sub-Optimal Pratical Solution Simulation Results: Semi-Active
Damper Force
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−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
−30
−20
−10
0
10
20
30
Suspension Deflection Speed (m/s)
Susp
ensi
on F
orce
(N)
Force vs. Susp. Deflection Speed at Rear Right Corner
MaximalMinimalAMPCFMPC
-
Sub-Optimal Pratical Solution Simulation Results: Semi-Active
Damper Force
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
−30
−20
−10
0
10
20
30
Suspension Deflection Speed (m/s)
Susp
ensi
on F
orce
(N)
Force vs. Susp. Deflection Speed at Rear Right Corner
MaximalMinimalAMPCFMPC AMPC —> ADD
-
−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
−30
−20
−10
0
10
20
30
Suspension Deflection Speed (m/s)
Susp
ensi
on F
orce
(N)
Force vs. Susp. Deflection Speed at Rear Right Corner
MaximalMinimalAMPCFMPC
Sub-Optimal Pratical Solution Simulation Results: Semi-Active
Damper Force
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
33/37
-
−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
−30
−20
−10
0
10
20
30
Suspension Deflection Speed (m/s)
Susp
ensi
on F
orce
(N)
Force vs. Susp. Deflection Speed at Rear Right Corner
MaximalMinimalAMPCFMPC
Sub-Optimal Pratical Solution Simulation Results: Semi-Active
Damper Force
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FMPC —> Wide Range of Force
-
• Introduction & Motivation
• Problem Statement & Objectives
• System Model & Constraints
• Observer Design + Experimental Validation
• Optimal Solution
• Sub-Optimal Practical Solution
• Conclusions
Outline
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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• LPV FMPC Technique —> Efficient Results!
• Time Constraints Respected + Good Trade-Off Handling vs
Comfort
• AMPC —> Two State Control (Max Min)
• FMPC —> Wide Use of Damper Force
• Dissipativity Constraints of Dampers are Respected!
• Full 7-DOF Vehicle Semi-Active Suspension Control
• Good for Practical Implementation!
Conclusions
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• LPV FMPC Technique —> Efficient Results!
• Time Constraints Respected + Good Trade-Off Handling vs
Comfort
• AMPC —> Two State Control (Max Min)
• FMPC —> Wide Use of Damper Force
• Dissipativity Constraints of Dampers are Respected!
• Full 7-DOF Vehicle Semi-Active Suspension Control
• Good for Practical Implementation!
Conclusions
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• LPV FMPC Technique —> Efficient Results!
• Time Constraints Respected + Good Trade-Off Handling vs
Comfort
• AMPC —> Two State Control (Max Min)
• FMPC —> Wide Use of Damper Force
• Dissipativity Constraints of Dampers are Respected!
• Full 7-DOF Vehicle Semi-Active Suspension Control
• Good for Practical Implementation!
Conclusions
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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• LPV FMPC Technique —> Efficient Results!
• Time Constraints Respected + Good Trade-Off Handling vs
Comfort
• AMPC —> Two State Control (Max Min)
• FMPC —> Wide Use of Damper Force
• Dissipativity Constraints of Dampers are Respected!
• Full 7-DOF Vehicle Semi-Active Suspension Control
• Good for Practical Implementation!
Conclusions
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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• LPV FMPC Technique —> Efficient Results!
• Time Constraints Respected + Good Trade-Off Handling vs
Comfort
• AMPC —> Two State Control (Max Min)
• FMPC —> Wide Use of Damper Force
• Dissipativity Constraints of Dampers are Respected!
• Full 7-DOF Vehicle Semi-Active Suspension Control
• Good for Practical Implementation!
Conclusions
RT MPC Semi-Active Full Veh. - Marcelo MENEZES MORATO -
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• LPV FMPC Technique —> Efficient Results!
• Time Constraints Respected + Good Trade-Off Handling vs
Comfort
• AMPC —> Two State Control (Max Min)
• FMPC —> Wide Use of Damper Force
• Dissipativity Constraints of Dampers are Respected!
• Full 7-DOF Vehicle Semi-Active Suspension Control
• Suitable for Practical Implementation!
Conclusions
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• Application to real vehicle Test-Bench
• Compare with [Nguyen, M. Q. (2016)]
• Couple FMPC and Mixed-Integer Programming Techniques ?
Conclusions
Future Work
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Merci!!!
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Questions ?
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