1. Vehicle Dynamics Modeling and Control
Xingchen Fan
2/14/2017

2. Inspiration 1: LQR control of active suspension (2013)
Modeling
LQR controller design
Half-car model with LQR control

3. Inspiration 2: passive damper modeling (2016)
Change picture

4. Motivation My passion for cars, dynamics and control
As part of process for learning vehicle dynamics
Learn how to model, analyze and control complicated dynamical systems
Why MATLAB/Simulink
No black box
Benefits from the control design capabilities of MATLAB
Easy to be modular and have various levels of details

5. Overview

6. Dynamics modeling workflow
Understand dynamics (Gillespie, Rajamani, Milliken, Harty, Bosch, etc.)
Separate into modules
Define states, inputs and outputs
Represent dynamics in Simulink
Clean up signal routing (create new modules if necessary)
Test and debug: steady-state response, frequency response, etc.
Integrate modules
Increase complexity (e.g. add nonlinearity)

7. Example 1: linear quarter-car ride model
Simplest standalone model
Features:
Masks for modules
Each mask has its state bus for analysis and debugging

8. Example 1: linear quarter-car model
Use frequency response to debug the model

9. Example 2: linear full-car ride model
Kinematics
Anti-roll bars
Unsprung masses
Sprung mass

10. Example 3: anti-roll bar
Essentially a proportional feedback controller!
Credit: Blundell & Harty

11. Example 3: anti-roll bar
Roll rock (only “P control” with an anti-roll bar, needs more roll damping  active damping)

12. Example 4: nonlinear bicycle handling model
Lateral dynamics
Kinematics
Tires
Yaw dynamics
Current nonlinearity: Fiala tire model, steering saturation

13. Example 4: nonlinear bicycle handling model
Step steering input

14. Example 5: full vehicle model
Global coordinates
Full-car ride model
Four-wheel handling model
Accelerations
Tire loads

15. Model debugging techniques
Incremental development
Modular design
Use symmetry
Physical intuition: first principles
Steady-state analysis
Frequency analysis
Comparison to real driving data

16. Control design workflow
Make sure the model is as accurate as it should be
Understand the plant: stability, damping ratio, frequency response
Controller design:
- SISO: root locus/phase margin  compensator
MIMO: LQR
Nonlinear: phase portrait  bang-bang, sliding mode
Compare open-loop and closed-loop responses
Tune parameters

17. Example 1: ride control (skyhook damping)
Plant
Controller
Feedback on sprung mass position is not necessary

18. Example 2: path tracking
Global coordinates
Controller
Error coordinates
Plant
𝛿=− 𝑘 𝑝 𝑒+ 𝑥 𝐿𝐴 Δ𝜓
𝑒 = 𝑈 𝑦 + 𝑈 𝑥 Δ𝜓

19. Example 2: path tracking
Root locus design: add a zero to “attract” the loci of two poles at origin

20. Example 2: path tracking (root locus)
Root locus design
 Good performance but unreasonable steering input

21. Example 2: path tracking (LQR)
LQR design: smaller proportional gain, longer lookahead distance
 Reasonable steering, worse but acceptable performance (could be tuned more aggressively)

22. Example 3: path tracking + cruise control
Global Coordinates
Lateral Controller
Error Coordinates
Plant
Longitudinal Controller

23. ABS is essentially a feedback controller on tire slip ratio
Example 4: ABS
Control strategies
Actuator limitations
Compute slip ratio
ABS is essentially a feedback controller on tire slip ratio
Control strategies:
Proportional control
PD control: require wheel acceleration
Bang-bang control: hold, dump, pump (more practical for actuators)

24. Example 4: ABS Slip ratio is maintained for peak longitudinal force
Minimal difference between effective wheel speed and vehicle speed
Directional stability, steerability, shorter braking distance on low-friction surface

25. Future work
Dynamics:
Camber, load-dependent friction, nonlinear bushing
Suspension kinematics
More understeer effects: compliance, roll steer, aligning torque, etc.
Motor in powertrain
Teach myself MSC Adams
Control:
Anti-pitch/anti-roll
ESC
Platoon control
Nonlinear control for nonlinear models

26. Questions?

27. Thanks!
Portfolio: xingchenfan.weebly.com LinkedIn: linkedin.com/in/xingchen-fan