Syteem e Regeltechiek FMT / Mechatroica Deel 4: Blok 9: Stabiliteit va regelyteme De PID regelaar i het frequetie omei Gert va Schothort Philip Cetre for Techical Traiig (CTT) Philip Cetre for Iutrial Techology (CFT) Hogechool va Utrecht - PTGroep Curu Syteem e Regeltechiek Overzicht Deel Wo. 4-4 Deel Wo. -4 Deel 3 Wo. 8-4 Deel 4 Wo. -5 Deel 5 Wo. 9-5 Deel 6 Wo. 6-5 Blok. Ileiig Blok. Baipricipe moelvormig maa-veeryteme Blok 3. De regelaar al veer-emper combiatie Blok 4. Frequetie-omei bechrijvig Blok 5. Baicocepte i e regeltheorie Blok 6. Verere ileiig i e regeltheorie Blok 7. De PD regelaar al veer-emper combiatie Blok 8. Stabiliteit va regelyteme Blok 9. De PID regelaar i het frequetie omei Toepaig: PID regelaarotwerp Blok. Babreete e vertorigoerrukkig Blok. Toepaig: Tue PID regelaar mechatroich yteem Extra regeltechiek Blok. Divere oerwerpe Blok 3. Terugblik
What are the limitatio of PD cotrol?? 3 Limitatio of PD cotroller F x e C() x H() - F Recall k p /k v or PD cotroller: C PD () = (k p k v ) Limitatio PD cotroller: Suppreio of cotat iturbace force F Pure ifferetiatig actio ca ot be realie Suppreio of high-frequet oie i the cotrol loop Suppreio of reoace i the ope loop repoe 4
Limitatio of PD cotroller F x e C() x H() - F Solutio - exte PD cotroller with filter: Itegral actio (PID) Lea-lag filter Seco orer Low Pa filter Notch filter() 5 Itegral Cotrol Pure itegrator: u k i y Time omai repoe: u y time time Frequecy omai repoe: H - H 9 6 3
Proportioal cotroller with I-actio I (PI cotrol) PI cotroller: u C() k i y Trafer fuctio: CI ( ) = ki Frequecy omai repoe: (ee alo Boe plot ext heet) H - H 9 7 Proportioal cotroller with I-actio I (PI cotrol) PI-actio phae -45-5 f i frequecy [Hz] - k i = f i 8 4
PD cotroller with I-actio I (PID cotrol) PI cotroller: C PD C() k i Trafer fuctio: k C() = (k p k v ) ( i ) Frequecy omai repoe:? => Exercie!!! 9 PD cotroller with I-actio I (PID cotrol) PI cotroller: Cloe loop ytem: C PD C() F k i x e C() x H() - F I-actio: Elimiate the teay tate error ue to cotat F!!! 5
PD cotroller with I-actio I (PID cotrol) x m = 5 kg; k i = 6 ra; k p = e6 N/m; k v = 3e3 N/m F? phae - - - Proce Seitivity - mechaic proce eitivity mechaic frequecy [Hz] proce eitivity M F PID cotroller - alterative cofiguratio u Staar cofiguratio C PD y k i k C() = (k p k v ) ( i ) complex zero ot poible Alterative cofiguratio u k p k v k i y( ) C( ) = = k p kv u( ) complex zero poible y ki 6
Differetiatig actio i pure PD cotroller C PD () = (k p k v ) or C PD ( ) = k( ) π f phae 8 k p = 5 N/m; k v = N/m 6 5 frequecy [Hz] 3 Differetiatig actio i pure PD cotroller Realiatio i motio cotroller: velocity etimatio (T =.5e-3) Drawback: phae 5 - frequecy [Hz] 3 3 4 4 High frequet oie i amplifie Limit gai for high frequecie 4 7
r r Cut-off ifferetiatig actio: lea-lag lag filter ( ( ) = k ( ) ) τ Break poit: f C = ll τ / k =; f = Hz; f = 9 Hz f = / phae frequecy [Hz] - 5 Other filter: eco orer low pa C lp ( ) = - ωr βω r ω r / = ; =. -4 phae Frequecy [Hz] - 6 8
C otch ( ) Other filter: otch filter β β ω ω ω ω = ω ω = 8; = 8; =.5 =. phae -5 - -5 frequecy i Hz - 7 Other filter: otch filter - - phae - = 8; = 8; frequecy i Hz =.5; =.5; = 8; = 8; =.5 =.5 8 9
Other filter: kewe otch filter - - phae -4 frequecy [Hz] - = ; =.5; = 6; =.5 9 Overview Filter I-actio - PD Lea-lag orer low pa - Notch
Cotroller tuig - a preview Start with PD, PI, or PID cotroller Lea-lag filter ofte iclue i PD & PID A filter by erie coectio Look at Nyquit curve of ope loop to check tability!!! Stability of cotrol ytem Summary Limitatio of PD cotroller => exteio: Itegral actio: uppre teay tate error Lea lag filter: avoi ifferetiatio oie Low pa: filter high-frequet oie Notch: uppre reoace peak Aemble cotroller by erie coectio