Mech523 l19 Fmrlc Casestudy1
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Transcript of Mech523 l19 Fmrlc Casestudy1
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Fall 2008 MECH523 : Intelligent Control 3
Learning mechanism (review)Learning mechanism (review)Tuning of ruleTuning of rule --base of fuzzy controllerbase of fuzzy controller s.ts.t . the. theC.L. system behaves like reference model.C.L. system behaves like reference model.
The learning mechanism consists of:The learning mechanism consists of:Fuzzy inverse modelFuzzy inverse model : Function to map: Function to map yyee (kT(kT ) to) tochanges in the plant inputchanges in the plant input p(kTp(kT ) that are necessary to) that are necessary to
forceforce yyee (kT(kT ) to be zero, or small. (today) to be zero, or small. (today ss lecture)lecture) Similar to fuzzy controller designSimilar to fuzzy controller design
KnowledgeKnowledge --base modifier base modifier : Function to modify fuzzy: Function to modify fuzzycontroller controller s rules rule --base to affect the needed changes inbase to affect the needed changes inthe plant inputs. (last lecture)the plant inputs. (last lecture)
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Fall 2008 MECH523 : Intelligent Control 4
KnowledgeKnowledge --base modifier (review)base modifier (review)
If fuzzy controllerIf fuzzy controller hadhad generated control inputgenerated control input
thenthen yyee (kT(kT )) would have beenwould have been zero.zero.Next time when we have similar value of e andNext time when we have similar value of e andc, plant input will bec, plant input will be u(kTu(kT --T)+p(kTT)+p(kT ).).
FuzzyFuzzycontroller controller Plant
Plant
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Fall 2008 MECH523 : Intelligent Control 5
Modification of outputModification of output MFsMFs (review)(review)Example: Assume fuzzy inverse model producedExample: Assume fuzzy inverse model producedp(kTp(kT )=0.5, for)=0.5, for e(kTe(kT --T)=0.75,T)=0.75, c(kTc(kT --T)=T)= --0.2.0.2.
FuzzyFuzzycontroller controller
Two rulesTwo rules ((RR 11 && RR 22 ))
are active in this case.are active in this case.
Move the correspondingMove the correspondingoutputoutput MFsMFs byby p(kTp(kT ).).
Output MFOutput MFfor Rfor R 11
Output MFOutput MFfor Rfor R 22
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Fall 2008 MECH523 : Intelligent Control 6
Case study: Ship head direction controlCase study: Ship head direction control
Control ship head direction by actuating rudder angle.Control ship head direction by actuating rudder angle.u=5 (u=5 ( m/sm/s ): velocity in x): velocity in x --direction (constant)direction (constant)
An increase in the rudder angle will generally result in a An increase in the rudder angle will generally result in adecrease in the ship heading angle.decrease in the ship heading angle.
InputInputRudder angleRudder angle
OutputOutputShip headingShip heading
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Fall 2008 MECH523 : Intelligent Control 7
FMRLC for direction controlFMRLC for direction control
ShipShip
Fuzzy controller Fuzzy controller
ReferenceReferencemodelmodel
Learning mechanismLearning mechanism
Fuzzy inverse modelFuzzy inverse model
KnowledgeKnowledge --basebasemodifier modifier
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Fall 2008 MECH523 : Intelligent Control 8
Scaling effect onScaling effect on MFsMFs (review)(review)Scaling gains are same as expanding orScaling gains are same as expanding orcontracting input/output membership functions.contracting input/output membership functions.
Scaled FSScaled FS1/31/3 55
FSFS
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Fall 2008 MECH523 : Intelligent Control 9
Input and outputInput and output MFsMFs of FCof FC
(121(121 MFsMFs areareOverlapping.)Overlapping.)
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Fall 2008 MECH523 : Intelligent Control 10
Design of scaling gains of FCDesign of scaling gains of FCgg ee = 1/= 1/ (since the error(since the error e(kTe(kT ) can never be over) can never be over180 deg.)180 deg.)
gg cc = 100= 100 (since ship does not move much faster(since ship does not move much fasterthan 0.01than 0.01 radrad /sec (by simulations).)/sec (by simulations).)gg ee = 8= 8 /18 (since we want to limit/18 (since we want to limit (kT(kT ) between) between80 deg.)80 deg.)
Design of reference modelDesign of reference model
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Fall 2008 MECH523 : Intelligent Control 11
Fuzzy inverse modelFuzzy inverse modelMFsMFs : Same as in the fuzzy controller : Same as in the fuzzy controller Scaling gains: By using Design procedure 1 inScaling gains: By using Design procedure 1 in
Appendix, Appendix,
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Fall 2008 MECH523 : Intelligent Control 12
RuleRule --base of inverse fuzzy modelbase of inverse fuzzy modelCenters of output membership functionsCenters of output membership functions
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Fall 2008 MECH523 : Intelligent Control 13
Rule interpretationsRule interpretationsi=0, j=0i=0, j=0
IfIf ee =0 and=0 and cc=0, then y is tracking=0, then y is tracking yymm perfectly, soperfectly, so
you should not update the fuzzy controller. Therefore,you should not update the fuzzy controller. Therefore,the output of the fuzzy inverse model will be zero.the output of the fuzzy inverse model will be zero.
i=1, j=2i=1, j=2
IfIf ee is positive andis positive and cc is positive, then change theis positive, then change theinput to the fuzzy controller that is generated toinput to the fuzzy controller that is generated toproduce these values ofproduce these values of ee andand cc by decreasing it.by decreasing it.
We want to increaseWe want to increase , and thus we want to decrease, and thus we want to decrease to achieve this.to achieve this.
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Fall 2008 MECH523 : Intelligent Control 15
Simulation result: GradientSimulation result: Gradient --basedbased
Model Reference Adaptive ControlModel Reference Adaptive Control
H e a
d d i r e c
t i o n
( d e g )
H e a
d d i r e c
t i o n
( d e g )
Time (sec)Time (sec)
Slow convergence!Slow convergence!
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Fall 2008 MECH523 : Intelligent Control 16
Simulation result:Simulation result: LyapunovLyapunov --basedbased
Model Reference Adaptive ControlModel Reference Adaptive Control
H e a
d d i r e c
t i o n
( d e g )
H e a
d d i r e c
t i o n
( d e g )
Time (sec)Time (sec)
Slow convergence!Slow convergence!
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Fall 2008 MECH523 : Intelligent Control 17
Disturbance rejectionDisturbance rejection
Disturbance at rudder (deg)Disturbance at rudder (deg)
Head direction (deg)Head direction (deg)(FMRLC)(FMRLC)
Head direction (deg)Head direction (deg)(Gradient(Gradient --based MRAC)based MRAC)
Head direction (deg)Head direction (deg)((LyapunovLyapunov --based MRAC)based MRAC)
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Fall 2008 MECH523 : Intelligent Control 18
DiscussionDiscussionIn this example, FMRLC gives:In this example, FMRLC gives:
Fast convergence compared toFast convergence compared to MRACsMRACs
Good disturbance rejection compared toGood disturbance rejection compared to MRACsMRACsHowever, in general:However, in general:
No guarantee that FMRLC is always better thanNo guarantee that FMRLC is always better thanMRACsMRACsNo guarantee of closedNo guarantee of closed --loop stabilityloop stability
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Fall 2008 MECH523 : Intelligent Control 19
SummarySummaryFuzzy Model Reference Learning ControlFuzzy Model Reference Learning ControlHow to select fuzzy inverse modelHow to select fuzzy inverse model
Scaling gains (Two design procedures in Appendix)Scaling gains (Two design procedures in Appendix)Fuzzy system (Application dependent)Fuzzy system (Application dependent)
Ship direction control by FMRLCShip direction control by FMRLCEx: Read until p.346.Ex: Read until p.346.
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Fall 2008 MECH523 : Intelligent Control 20
Fuzzy inverse model designFuzzy inverse model designDesign procedure 1Design procedure 1 for scaling gainsfor scaling gains
(Assume normalized I/O universe of discourse.)(Assume normalized I/O universe of discourse.)
1.1. Select as follows.Select as follows.
2.2. Apply step Apply step r(kTr(kT ) with typical magnitude. See) with typical magnitude. Seea)a) If there is unacceptable oscillations inIf there is unacceptable oscillations in y(kTy(kT ))
aroundaround yymm (kT(kT ), increase derivative gain), increase derivative gainb)b) IfIf y(kTy(kT ) is unable to) is unable to keep upkeep up withwith yymm (kT(kT ),),
decrease derivative gaindecrease derivative gainc)c) IfIf y(kTy(kT ) is acceptable) is acceptable w.r.tw.r.t .. yymm (kT(kT ), done!), done!
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Fall 2008 MECH523 : Intelligent Control 21
Fuzzy inverse model designFuzzy inverse model designDesign procedure 2Design procedure 2 for scaling gainsfor scaling gains
(Assume normalized I/O universe of discourse.)(Assume normalized I/O universe of discourse.)
SetSet gg pp =0. (Begin without learning mechanism.)=0. (Begin without learning mechanism.)If it works fine, FC is already wellIf it works fine, FC is already well --designed.designed.
2.2. Choose gains by maximal magnitudes.Choose gains by maximal magnitudes.
3.3. Turn on learning mechanism by increasingTurn on learning mechanism by increasing gg pp slightly.slightly.(Slow update of output(Slow update of output MFsMFs in fuzzy controller.) Tunein fuzzy controller.) Tunethe inverse model if necessary.the inverse model if necessary.
4.4. Continue to increaseContinue to increase gg pp , and tune the inverse model if, and tune the inverse model ifnecessary. (Increased adaptation speed, possibility ofnecessary. (Increased adaptation speed, possibility ofoscillations and instability.)oscillations and instability.)