Outline. Fuzzy Control: Background. Parameterization of Nonlinear Controllers. Process. Controller. Knowledge-Based Control Systems (SC42050)

Transcription

1 phi.5.5 x.5 Knowldg-Basd Control Systms (SC425) Otlin Lctr 3: Knowldg basd fzzy control. Dirct fzzy control. Alfrdo Núñz Sction of Railway Enginring CiTG, Dlft Univrsity of Tchnology Th Nthrlands tl: Robrt Babška Dlft Cntr for Systms and Control 3mE, Dlft Univrsity of Tchnology Th Nthrlands tl: Sprvisory fzzy control. 3. Softwar tools for fzzy control. 4. Ovrviw of applications. Fzzy Control: Backgrond controllr dsignd by sing If Thn rls instad of mathmatical formlas (knowldg-basd control), Paramtrization of Nonlinar Controllrs Controllr arly motivation: mimic xprincd oprators, fzzy rasoning: intrpolation btwn discrt otpts, thta crrntly: also controllrs dsignd on th basis of a fzzy modl (modl-basd fzzy control), Paramtrizations PL PS Z PS Z NS a fzzy controllr rprsnts a nonlinar mapping (bt compltly dtrministic!). Sigmoidal Nral Ntworks Z NS NL Fzzy Systms Radial Basis Fnctions Wavlts Splins

2 Fzzy Systm is a Nonlinar Mapping Basic Fzzy Control Schms Dirct (low-lvl, Mamdani) fzzy control Fzzy sprvisory (high-lvl, Takagi Sgno) control Fzzy modl-basd control Controlld by Oprators Knowldg Acqisition Goal (rfrnc) Distrbancs Goal (rfrnc) Distrbancs Hman oprator y Hman oprator y Knowldg acqisition Fzzy if-thn rls

3 Dirct Fzzy Control Exampl of Oprator Knowldg Goal (rfrnc) Distrbancs Cas Condition Action to b takn Rason Fzzy controllr y BZ OK a. Dcras fl rat slightly To rais prcntag of oxygn OX low BE OK 2 BZ OK a. Rdc fl rat To incras prcntag of oxygn for action b OX low b. Rdc fan spd To lowr back-nd tmpratr and BE high maintain brning zon tmpratr Implmntation Fzzy if-thn rls 3 BZ OK a. Incras fan spd To rais back-nd tmpratr OX OK b. Incras fl rat To maintain brning zon tmpratr BE low Extract from Pray s txtbook for kiln oprators (Ostrgaard, 999) FLC Analog to PID Control PID Control: Intrnal Viw d (t) = P(t)+I t (τ)dτ +D d(t) dt r - PID y P I + d dt D

4 PID Control: Intrnal Viw (t) = P(t)+I t (τ)dτ +D d(t) dt Fzzy PID Control (t) = f ( (t), t (τ)dτ, d(t) ) dt d dt P I + D d dt Fzzy knowldg-basd systm dynamic filtr static mapping dynamic filtr Fzzy PID Control Exampl: Proportional Control r - Fzzy Controllr y d Dynamic Pr-filtr Static map Dynamic Post-filtr r - P y Fzzifir Knowldg bas Infrnc Dfzzifir

5 Controllr s Inpt Otpt Mapping Fzzy Proportional Control: Rls = P If rror is Ngativ Big thn control inpt is Ngativ Big If rror is Positiv Big thn control inpt is Positiv Big If rror is Zro thn control inpt is Zro Controllr s Inpt Otpt Mapping Exampl: Friction Compnsation. DC motor with static friction. PB 2. Fzzy rls to rprsnt normal proportional control. ZE 3. Additional rls to prvnt ndsirabl stats. NB NB ZE PB

6 DC Motor: Modl Proportional Controllr voltag Armatr K(s) L.s+R Load J.s+b Friction s angl P Motor Mx Control K Angl Linar Control Fzzy Control Rl Bas shaft angl [rad] If rror is Positiv Big thn control inpt is Positiv Big; If rror is Ngativ Big thn control inpt is Ngativ Big; If rror is Zro thn control inpt is Zro;.5 control inpt [V]

7 Mmbrship Fnctions for Error Additional Rls Ngativ Big Zro Positiv Big If rror is Positiv Big thn control inpt is Positiv Big; If rror is Ngativ Big thn control inpt is Ngativ Big; If rror is Zro thn control inpt is Zro; If rror is Ngativ Small thn control inpt is not Ngativ Small; If rror is Positiv Small thn control inpt is not Positiv Small; Mmbrship Fnctions for Error Fzzy Control Ngativ Big Ngativ Small Zro Positiv Big Positiv Small shaft angl [rad] control inpt [V]

8 Inpt Otpt Mapping of th Controllr Anothr Soltion: Sliding Mod Control local nonlinarity.5 shaft angl [rad] control inpt [V] Exprimntal Rslts - Proportional Control Exprimntal Rslts - Fzzy Control.2.2 position [rad].. position [rad] control inpt [V] 5 5 control inpt [V]

9 Mmbrship Fnctions Fzzy PD Controllr: Rl Tabl mmbrship dgr Control rror rror rror rat NB ZE PB NB NB NB ZE ZE NB ZE PB PB ZE PB PB mmbrship dgr Control rror R 2 : If rror is NB and rror rat is ZE thn control is NB Fzzy PD Controllr cont d Sprvisory Fzzy Control.5.5 control.5 control.5.5 rror rat.5.5 rror.5.5 rror rat.5.5 rror.5 control.5 Classical controllr y.5.5 rror rat.5.5 rror.5

10 Sprvisory Fzzy Control Sprvisory Control Rls: Exampl xtrnal signals If procss otpt is High Fzzy Sprvisor thn rdc proportional gain Slightly and incras drivativ gain Modratly. Classical controllr y (Sprvisd PD controllr) Exampl: Invrtd Pndlm Cascad Control Schm α Rfrnc Position controllr Angl controllr Invrtd pndlm (forc) x

11 Convntional PD controllr Fzzy Sprvisd PD controllr.5.5 cart position [m] cart position [m] angl [rad].. angl [rad] control inpt [ ] control inpt [ ] Takagi Sgno Control Takagi Sgno Control Takagi Sgno PD controllr: Takagi Sgno PD controllr: R : If r is Low thn L = P L +D L ė R 2 : If r is High thn H = P H +D H ė R : If r is Low thn L = P L +D L ė R 2 : If r is High thn H = P H +D H ė = µ L(r) L +µ H (r) H µ L (r)+µ H (r) = γ L (r) L +γ H (r) H = µ L(r) L +µ H (r) H µ L (r)+µ H (r) = γ L (r) L +γ H (r) H = {γ L (r)p L +γ H (r)p H }+{γ L (r)d L +γ H (r)d H }ė = {γ L (r)p L +γ H (r)p H }+{γ L (r)d L +γ H (r)d H }ė

12 Takagi Sgno Control Takagi Sgno Control Takagi Sgno PD controllr: Takagi Sgno PD controllr: R : If r is Low thn L = P L +D L ė R 2 : If r is High thn H = P H +D H ė R : If r is Low thn L = P L +D L ė R 2 : If r is High thn H = P H +D H ė = µ L(r) L +µ H (r) H µ L (r)+µ H (r) = γ L (r) L +γ H (r) H = µ L(r) L +µ H (r) H µ L (r)+µ H (r) = γ L (r) L +γ H (r) H = {γ L (r)p L +γ H (r)p H }+{γ L (r)d L +γ H (r)d H }ė = {γ L (r)p L +γ H (r)p H }+{γ L (r)d L +γ H (r)d H }ė = P(r)+D(r)ė, = P(r)+D(r)ė, P(r) conv(p L,P H ),... Takagi Sgno Control is Gain Schdling TS Control: Inpt Otpt Mapping fzzy schdling Controllr K Inpts Controllr 2 Otpts Controllr

13 TS Control: Exampl. Strongly nonlinar procss (otpt-dpndnt gain). 2. Fzzy sprvisor to adjst th gain of a proportional controllr. 3. Comparison with linar (fixd-gain) proportional control. Nonlinar procss: TS Control: Exampl d 3 y(t) dt 3 + d2 y(t) dt 2 + dy(t) = y 2 (t)(t) dt Problms with linar control: stability and prformanc dpnd on procss otpt r-tning th controllr dos not hlp nonlinar control is th only soltion TS Control: Exampl Comparison of Prformanc Goal: Dsign a controllr to stabiliz th procss for a wid rang of oprating points (y > ): TS (proportional) control rls: If y is Small thn (k) = P Small (k) If y is Mdim thn (k) = P Mdim (k) If y is Larg thn (k) = P Larg (k)

14 Typical Applications Typical Applications Tn paramtrs of low-lvl controllrs (ato-tning). Improv prformanc of classical control (rspons-assistd PID). Adaptation, gain schdling (aircraft control). Tn paramtrs of low-lvl controllrs (ato-tning). Improv prformanc of classical control (rspons-assistd PID). Adaptation, gain schdling (aircraft control). + Enhancmnt of classical controllrs. + Intrfac btwn low-lvl and high-lvl control. Ad hoc approach, difficlt analysis. Fzzy Control: Dsign Stps Paramtrs in a Fzzy Controllr control nginring approachs + hristic knowldg Fzzification modl Dfzzification modl. Dtrmin inpts and otpts. Scaling Fzzifir Infrnc ngin Dfzzifir Scaling 2. Dfin mmbrship fnctions. 3. Dsign rl bas. Scaling factors Mmbrship fnctions Rl bas Mmbrship fnctions Scaling factors 4. Tst (compltnss, stability, prformanc). Data bas Knowldg bas Data bas 5. Fin-tn th controllr.

15 Softwar for Fzzy Control Hardwar for Fzzy Control Sifzzy (Simns) FzzyTch (Inform) AB-Flx (Alln Bradly) TDC-3 (Honywll) Fzzy logic-assistd PID controllrs (Omron, Yokogawa, Wst Instrmnts). PLC coprocssors (Omron, Alln Bradly). Ddicatd hardwar (fzzy logic chips). many othrs... Ddicatd Hardwar Applications of Fzzy Control procss control (cmnt, chmical, glass)

16 Oprator Spport in Control Fzzy Dcision Spport Systm Prodction of dtrgnts Control Actions Ingrdints Viscosity Viscosity M Prssr No. of nozzls Plvrization towr Qality: - litr wight - moist contnt Fzzy dcision spport systm Hman oprator Prssr Nozzls Tmpratr Blnd air Whirl air DCS comptr Excl Blnd air Hatr Whirl air Tmpratr Convyor δ m δ w Prodct Information PC SiFzzy Fzzy Rl Bas Implmntation Distribtd Control Systm Moist Dry Ok Wt R R 2 R 3 R 4 No Actions R 5 R 6 R 7 R 8 Light Ok Havy Wight R 6 R R 6 n 6 R 7 R R 7 n 7 stat (Constraints) - Partitioning into rror rgions - Each rgion has an ordrd st of control rls Laboratory rport Stord data Prodct sampl Evry 5-3 min. Evry min. PC DCS comptr Excl SiFzzy Evry sc. Evry 3 sc. Evry 6 sc. or on rqst Hman oprator

17 Evalation: Rslts Applications of Fzzy Control Improvmnt [%] Improvmnt in moistr contnt man std man std man std procss control (cmnt, chmical, glass) sprvision (scrity of powr distribtion ntworks) Improvmnt [%] Class A Class B Class C Improvmnt in litr-wight man std man std man std Scrity Assssmnt of a Powr Ntwork Fzzy Dcision PEN/EBA DIEMEN 3 EDON 2 2 ENS HGL µ µ VS NS SI VI EZH EZH 3 KRIMPEN 2 2 EINDH CRAY MAASV GEERT BORSS A DltaN PNEM MEGA BELGIUM SUBSYSTEM NUON DOET DODEW MAASB 3 GERMANY µ µ µ VS NS SI VI VS NS SI VI

18 Applications of Fzzy Control Traffic Managmnt procss control (cmnt, chmical, glass) sprvision (scrity of powr distribtion ntworks) traffic managmnt and control Forcasting (Simns) Knowldg-Basd Systm Parking garag Day of Wk Tim of Day Sason Holiday Tmporal Nd Rl bas Wathr Traffic Dnsity Tmporal Nd # cars driving in # cars driving ot Main Rl bas Parking Garag Marinplatz FULL Parking Garag Stachs FREE Tmpratr Rainfall Snshin Wathr Rl bas Capacity Spcial Sitations Forcast

19 Applications of Fzzy Control Intllignt Thrmostat procss control (cmnt, chmical, glass) sprvision (scrity of powr distribtion ntworks) traffic managmnt and control (prdiction) consmr goods (camcodrs, hos appliancs) Applications of Fzzy Control procss control (cmnt, chmical, glass) sprvision (scrity of powr distribtion ntworks) traffic managmnt and control (prdiction) consmr goods (camcodrs, hos appliancs) cars (ngin managmnt, atomatic transmission)