abs control project
DESCRIPTION
ABS Control Project. Ondrej Ille Pre-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 :. - PowerPoint PPT PresentationTRANSCRIPT
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
MsxdsrFxJMsMsxdsrFxJ
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
xxxrxrxrxrxr
• 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
wwwaw
sLsS
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
MubcMMsSccxccxcSxMscSccxccxcSx
• 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)()(
wwwaw
sLsS
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
xifxxifxxsign
xfy1
.),,(
• 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 0.5Average Braking Distance 42,58 38,90 39,08 43,07 38,72 35,78
Average 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??