Systeem en Regeltechniek FMT / Mechatronica

Transcription

1 Systm n Rgltchnik FMT / Mchatronica Dl 6: Blok 4: Etra rgltchnik Trugblik / Evaluati Grt van Schothorst Philips Cntr for Tchnical Training (CTT) Philips Cntr for Industrial Tchnology (CFT) Hogschool van Utrcht - PTGrop Cursus Systm n Rgltchnik Ovrzicht Dl Wo. 4-4 Dl Wo. -4 Dl 3 Wo. 8-4 Dl 4 Wo. -5 Dl 5 Wo. 9-5 Dl 6 Wo. 6-5 Blok. Inliding Blok. Basisprincips modlvorming massa-vrsystmn Blok 3. D rglaar als vr-dmpr combinati Blok 4. Frqunti-domin bschrijving Blok 5. Basisconcptn in d rglthori Blok 6. Vrdr inliding in d rglthori Blok 7. D PD rglaar als vr-dmpr combinati Blok 8. Stabilitit van rglsystmn Blok 9. D PID rglaar in ht frqunti domin Blok. Bandbrdt n vrstoringsondrdrukking Blok. Topassing: Tunn PID rglaar mchatronisch systm Blok. St-points n fdforward tuning Blok 3. Digital implmntati ffctn Blok 4. Trugblik / Evaluati

2 Mchatronics: Combining disciplins provids bttr solutions Mchanical Elctronic / Elctrical Pnumatic Hydraulic Chmical Thrmal Optical Acoustical Softwar Know all modrn tchnologis and thir applications B abl to work out systm solutions 3 Introduction Mchanics & Dynamics F m m F F 4

3 Introduction Th rol of control Output Systm Mchanics & Dynamics Output Driv Control Actuators Snsors Fdback Mchatronic Systm Approach: Activ lmnts, control of stiffnss and damping 5 Basic principls modlling mass-spring-systms Fr motion (translation) m d c c m d d c m m m d c c β βω ω ω ω 6 3

4 4 7 c d m Rsonanc frquncy & damping Rsonanc frquncy & damping Basic principls modlling mass-spring-systms ω π c m f c m, Rsonanc frquncy: m d m c d ω β Rlativ damping: ω β ω c d c m 8 Stp rspons of mass Stp rspons of mass-spring spring-systm systm Basic principls modlling mass-spring-systms h(t) c d m ) cos( t t β ω βω

5 Th controllr as spring-dampr combination Controlling th position of a mass F disturb F? M Control Objctivs: Gtting thr Staying thr 9 Th controllr as spring-dampr combination Scond control objctiv gtting thr : h d k F srvo M F disturb F k( h ) d( h Controllr: F k ( ) srvo p s kv( s ) ( s : stpoint) Spring-dampr forc F: ) 5

6 Frquncy Domain Dscription Frquncy Domain solution for quation of motion F M ) Choos a sinusoidal input: F Fˆ sin( ω t) ) Thn for a linar systm: ˆ sin( ω t ϕ) ω ˆ cos( ω t ϕ) ω ˆsin( ω t ϕ) F M ˆ?; ϕ? Frquncy Domain Dscription Frquncy Domain solution for quation of motion F M 3) Solution: ˆ Fsin( ω t) Mω ˆ sin( ωt ϕ) ϕ H 8 ˆ ˆ H Fˆ M F ω F M H F Mω Frquncy Rspons Function! 6

7 Basic concpts in control thory Transfr Function So w hav: ( Ms ds k) ( F( This lads to th Transfr Function : ( F( Ms Not that in Laplac domain: ds k ( F( So: output systm input!!! In block rprsntation: F Ms ds k 3 Basic concpts in control thory Th Bod plot of a mass-spring spring-systmsystm Transfr Function: ( F( Ms ds k d k M F s / M βω os ωo Rcall: ω o β k M d Mk Eignfrquncy Rlativ damping 4 7

8 Basic concpts in control thory Th Bod plot of a mass-spring spring-systmsystm Transfr Function: ( F( Ms ds k Asymptots in Bod plot: s H /k H /k H º s H /Ms H /Mω Brak point: H H /k H 8º log(/k) log (/Mω ) log (/M) - log(ω) - 8 ω ω ο k M 5 Furthr introduction in control thory Why fdback? Fdback with disturbancs: s - C( d d Rcall: ( H c ( s ( C( C( So: s if: C( >> 6 8

9 Furthr introduction in control thory Why fdback? Th aim of fdback is... Disturbanc Supprssion 7 Furthr introduction in control thory Four important transfr functions s F s F d C( - Opn Loop: Closd Loop: Snsitivity: Procss Snsitivity: H o ( C( H ( ) c s C( ( s C( S( ( ) s s C( H ( ( F ps d C( 8 9

10 Th PD controllr as spring-dampr combination Th Bod plot of a PD controllr Transfr Function: C C( F ( ( k p kv Asymptots in Bod plot: C Amplitud: C k p k v ω k p c 9 s C k p C k p C º s C k v s C k v C 9º Brak point: log k p logk logω v ω c k k p v 9 Th PD controllr as spring-dampr combination Intrmzzo: Multiplication of Bod plots C( ( C( ( C k p º k p k v 9º H M - CH º -8º -9º

11 Th PD controllr as spring-dampr combination Th Bandwidth Concpt - Scond ordr systm amplitud [db] Opn Loop phas [dg] - - frquncy [Hz] - Th PD controllr as spring-dampr combination Th Bandwidth Concpt - Dfinition PHILIPS: Bandwidth: db crossing opn loop

12 Stability of control systms Intrmzzo: pols and zros (s - z ( ) ) (s - z ) (s - z m ) H s K (s - p ) (s - p ) (s - p n ) zros pols Zros ar roots of th numrator polynomial (valus of s for which numrator bcoms zro) Pols ar roots of th dnominator polynomial (valus of s for which dnominator bcoms zro) n: numbr of pols ordr of th systm 3 Stability of control systms Stability of pols in s-plans (t)p(st) Im( LHP RHP R( 4

13 Stability of control systms Nyquist stability critrion Graphical valuation of stability For incrasing frquncy along th curv of j ) in th compl plan, th point (-,) should stay at th lft hand sid of th curv with srj s plan w plan Im(H) r> - r w r> R(H) 5 Stability of control systms Im(Ho).5.5 Stability margins Nyquist plot of opn loop rticl stag /GM -.5 PM R(Ho) 6 3

14 Th PID controllr in th frquncy domain Limitations of PD controllr s F d C( - F s Rcall k p /k v or PD controllr: C PD ( (k p k v Limitations PD controllr: Supprssion of constant disturbanc forcs F d Pur diffrntiating action can not b ralisd Supprssion of high-frqunt nois in th control loop Supprssion of rsonancs in th opn loop rspons 7 Th PID controllr in th frquncy domain Limitations of PD controllr s F d C( - F s Solutions - tnd PD controllr with filtrs: Intgral action (PID) Lad-lag filtr Scond ordr Low Pass filtr Notch filtr( 8 4

15 Th PID controllr in th frquncy domain Ovrviw Filtrs I-action - PD Lad-lag nd ordr low pass - Notch 9 Bandwidth and disturbanc supprssion Disturbanc supprssion No control: Closd-loop: y o Hd yc S y H y o CH c d CH Bnfit of fdback Snsitivity function Eampl: H.; CH 4 ; d y o.. y c 4-6 S

16 Bandwidth and disturbanc supprssion Opn-loop: y o khcr Rlativ chang: y o y o khcr HCr k yo HCr kch Closd-loop: y c r kch y c y Rlativ chang: y y c y yc y o y y o c o c Robustnss k S k kch kch c kch r CH r kch CH CH r CH k kch Bnfit of fdback Snsitivity function 3 Bandwidth and disturbanc supprssion Dsign for prformanc Bod Snsitivity Intgral amplitud 5 [db] f b frquncy [Hz] 3 6

17 Bandwidth and disturbanc supprssion Loop Shaping Procdur. Stabiliz th plant: Add lad/lag with zro BW/3 and pol BW*3, adjust gain to st stability or add a pur PD with brakpoint at th BW.. Add low-pass filtr: Choos pols BW*6. 3. Add notch, if ncssary, or apply any othr kind of first or scond ordr filtr and shap th loop. 4. Add intgral action: Choos zro BW/5. 5. Incras BW: Incras gain and adapt zros/pols of intgral action, lad/lag and othr filtrs. During stps -5: chck all rlvant transfr functions and rlat to disturbanc spctrum. 33 Ercis Moving targt: 3 Hz, 3mm Allowd tracking rror: 4µm 34 7

18 Stpoints and fdforward tuning Fdback plus fdforward s ^ H - ( s - C( F fb F ff ( if: ^ 35 Stpoints and fdforward tuning Friction fdforward - Implmntation s s sign ( ) s k fc k fa k fv s - C( 36 8

19 Stpoints and fdforward tuning acclration [m/s ] Third ordr stpoint Jrk rctangular instad of acclration -6 acclration 8 third ordr 6 4 scond ordr tim [msc] Digital implmntation ffcts Ercis: building blocks in digitally controlld systm [ ] [ ] [V] [A] [N] [m]? Digital controllr? () - ()? (3)? (4) /(ms ) [ ]? (6) [V]? (5) What lmnts do th qustion marks rprsnt? 38 9

20 Digital implmntation ffcts Caus and ffcts of dlay Dlay in digital systm causd by: Tim ndd to calculat nw actions (forc) as rspons to nw inputs (position rror, calld T c Lag ffct in th DA convrsion (ZOH) So, in total dlay complis to: T dlay T c.5 T s Rmark: Transfr function of dlay with tim T: H dlay ( -Ts FRF of dlay with tim T: H dlay (ω) -jωt 39 Digital implmntation ffcts Caus and ffcts of dlay At what sampl rat would th phas margin b 5 dgrs largr? 4

21 Rviw and valuation Evaluati Rlvanti voor daglijks praktijk? Aansluiting op andr vakkn? Nivau / moilijkhidsgraad? Snlhid van bhandln? Balans thori / praktijk / ofningn? Ondrwrpn gmist? Ondrwrpn ovrbodig? 4