ABS Control Project Ondrej Ille Pre-bachelor Project.
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Transcript of ABS Control Project Ondrej Ille Pre-bachelor Project.
![Page 1: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/1.jpg)
ABS Control Project
Ondrej IllePre-bachelor Project
![Page 2: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/2.jpg)
• 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
![Page 3: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/3.jpg)
• ABS Laboratory model :
![Page 4: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/4.jpg)
• Angle encoders for measuring wheel positions• Derivations of outputs gives angular velocities• Disc Brake input : • PWM Motor Input• No Dynamometers !!!
1,0u
![Page 5: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/5.jpg)
• Simplified Model Scheme:
![Page 6: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/6.jpg)
• 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
![Page 7: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/7.jpg)
20222222
1110111111
MsxdsrFxJ
MsMsxdsrFxJ
n
n
![Page 8: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/8.jpg)
• 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
![Page 9: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/9.jpg)
• 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
![Page 10: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/10.jpg)
• 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
![Page 11: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/11.jpg)
• Initial condition response without braking:
![Page 12: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/12.jpg)
• Response with the braking:
![Page 13: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/13.jpg)
• 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
![Page 14: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/14.jpg)
• Friction coefficient vs slip in Simulation model:
![Page 15: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/15.jpg)
• Friction coefficient vs Slip in real systems [1]:
![Page 16: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/16.jpg)
• 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
![Page 17: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/17.jpg)
• 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
![Page 18: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/18.jpg)
• 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
![Page 19: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/19.jpg)
• Evaluation parameters tested with simple Relay controller:
![Page 20: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/20.jpg)
• Setting the condition for maximal braking distance and examining Slip Ratio:
![Page 21: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/21.jpg)
• We obtain Setting for Relay controller:16,16115,0205,0 % OFFON SS
![Page 22: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/22.jpg)
• Different controllers:• PID controller – linear control of non-linear
system• Non-linear PID controller :
),,(),,(),,( ufKufKufKC NDNINP
xifx
xifxxsignxfy
1
.),,(
![Page 23: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/23.jpg)
• Non-linear function :
![Page 24: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/24.jpg)
• 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
![Page 25: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/25.jpg)
• Classical PID:
![Page 26: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/26.jpg)
![Page 27: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/27.jpg)
• Non-Linear PID :
![Page 28: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/28.jpg)
• Difference between Linear and Non-linear PID:
![Page 29: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/29.jpg)
• 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
![Page 30: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/30.jpg)
• Smith’s predictor to compensate time delay:
![Page 31: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/31.jpg)
• 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
![Page 32: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/32.jpg)
• Relay without prediction:
![Page 33: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/33.jpg)
• Linear PID for 0.35 reference:
![Page 34: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/34.jpg)
• Non-Linear PID for 0.35 reference:
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• 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
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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
![Page 37: ABS Control Project Ondrej Ille Pre-bachelor Project.](https://reader035.fdocuments.net/reader035/viewer/2022062417/5518a2c6550346b31f8b4932/html5/thumbnails/37.jpg)
• 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??
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