ABS Control Project

1. ABS Control Project Ondrej Ille Pre-bachelor Project

2. What is ABS in real world? • Advantages of ABS: • - effective braking at different surfaces • - anti block system for car controllability • Disadvantages of ABS: • - longer braking distance

3. ABS Laboratory model :

4. Angle encoders for measuring wheel positions • Derivations of outputs gives angular velocities • Disc Brake input : • PWM Motor Input • No Dynamometers !!!

5. Simplified Model Scheme:

6. System described by equations, based on second Newton’s law: • Sum of the moments applied to wheel is proportional to angular acceleration of the wheel. Coefficient of the proportion is Moment of Inertia

8. Slip – represents relative difference of wheel velocities: • Main controlled parameter, non-linear • When choosing x1,x2 State variables , Slip is inversely proportional to State variables • Different definition according to signs of x1 x2

9. Friction force is function of Slip: • In INTECO model approximated by: • Substitution of parameters and obtaining general model

10. Where c11 to c31 are coefficients of the model, provided by INTECO together with the system • Non-Linear State model • Is the description by cij and b reliable?? • Experiments to compare reality and model described by State equations and coefficients

11. Initial condition response without braking:

12. Response with the braking:

13. Simulated Slip doesn’t respond to real Slip • Incorrect function coefficients: • New identification is not possible due to no dynamometers in model • For control we have to accept the model which is given by INTECO

14. Friction coefficient vs slip in Simulation model:

15. Friction coefficient vs Slip in real systems [1]:

16. ABS control intends to keep Slip at value with maximal friction coefficient ! • Then Friction force is maximal since normal force is given by mass of the car: • Controllability of the car: Lowest possible Slip with maximal friction coefficient • Usual approach: Gain scheduling control

17. Problem in our design due to friction coefficient function • Proposed approach: setting evaluating parameters! • Evaluating parameters: • Braking Distance • Slip Ratio – ideally expresses the car controllability

18. Classical ABS [1]: friction coefficient function has strong affect on braking distance • INTECO simulation model: friction coefficient function has lower affect on braking distance • Braking distance is more affected by amount of time when the Slip is zero. • For this reason we use different reference values

19. Evaluation parameters tested with simple Relay controller:

20. Setting the condition for maximal braking distance and examining Slip Ratio:

21. We obtain Setting for Relay controller:

22. Different controllers: • PID controller – linear control of non-linear system • Non-linear PID controller :

23. Non-linear function :

24. Tuning of controllers (in simulations) : • Ziegler –Nichols method (appropriate for linear systems.) • Trial and Error • Cohen Coons method • Controllers tuned to follow reference value or to achieve best evaluating parameters values

25. Classical PID:

27. Non-Linear PID :

28. Difference between Linear and Non-linear PID:

29. Applying controllers to reality with problems: • Time delay • Non – fitting coefficients of controllers • The difference between the model and reality causes problems in prediction of delay • Solutions: • Retuning with real model • Compensating time delay

30. Smith’s predictor to compensate time delay:

31. Types of tested controllers in reality: • Relay, Linear PID , Non-linear PID • Without delay prediction, With Smiths predictor, With INTECO predictor • Tuning to achieve best Braking distance, Slip Ratio, or follow the reference value

32. Relay without prediction:

33. Linear PID for 0.35 reference:

34. Non-Linear PID for 0.35 reference:

35. Linear vs. Non-Linear PID:

37. Conclusion: • For “optimal” Braking Distance and Slip Ratio the Non-linear PID with Smith’s predictor reached the best result • Is the performance truly so important? What about following the reference? Isn’t simpler controller (Relay) better??