ABS Control Project

Ondrej IllePre-bachelor Project

• 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

• ABS Laboratory model :

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

1,0u

• Simplified Model Scheme:

• 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

JMi

i

20222222

1110111111

MsxdsrFxJ

MsMsxdsrFxJ

n

n

• 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

0,0,; 21112222

1122

xxxrxrxr

xrxr

• Friction force is function of Slip:• In INTECO model approximated by:

• Substitution of parameters and obtaining general model

)(NF FF

)11.2()(

)10.2()cos)((sin

)()(

12

23

34

wwwa

w

sL

sS

P

P

• 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

)9.2())((31

)8.2()())((2

)7.2())(())((

11

11252422322121

11161514113121111

MubcM

MsSccxccxcSx

MscSccxccxcSx

• Initial condition response without braking:

• Response with the braking:

• 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

12

23

34)(

)cos)((sin

)()(

wwwa

w

sL

sS

P

P

• Friction coefficient vs slip in Simulation model:

• Friction coefficient vs Slip in real systems [1]:

• 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

)(..)( gmFF NF

• 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

• 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

• Evaluation parameters tested with simple Relay controller:

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

• We obtain Setting for Relay controller:16,16115,0205,0 % OFFON SS

• Different controllers:• PID controller – linear control of non-linear

system• Non-linear PID controller :

),,(),,(),,( ufKufKufKC NDNINP

xifx

xifxxsignxfy

1

.),,(

• Non-linear function :

• 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

• Classical PID:

• Non-Linear PID :

• Difference between Linear and Non-linear PID:

• 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

• Smith’s predictor to compensate time delay:

• 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

• Relay without prediction:

• Linear PID for 0.35 reference:

• Non-Linear PID for 0.35 reference:

• Linear vs. Non-Linear PID:

Controller

Reference value used 0.197 0.35 0.5 0.197 0.35 0.5

Average Braking Distance 42,58 38,90 39,08 43,07 38,72 35,78Average Slip Ratio 35,31 46,97 54,39 22,09 37,1 50,2

Linear PID Non-linear PID

NameReference value

used

Average Braking distance

Average Slip Ratio

ON =0.5 OFF=0.5 42,7 57,87ON=0.20 OFF=0.11 47,3 32,23

Rellay with INTECO predictor

Reference = 0.540,82 35,97

Reference = 0.5 39,08 54,39Reference = 0.35 38,9 46,97Reference=0.197 42,58 35,31

Reference=0.5 35,78 50,2Reference=0.35 38,72 37,1Reference=0.197 43,07 22,09Reference = 0.5 38,13 44,37

Reference = 0.35 34,78 45,28Referene =0.197 38,76 34,32Reference = 0.5 32,46 48,46

Reference = 0.35 44,31 22,22Referene =0.197 35,49 35,7

PID Smiths predictor

NLPID Smiths predictor

Rellay without predictor

PID without predictor

NLPID without predictor

• 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??