Robustné PID-regulátory s obmedzeniami Robust Constrained PID Control DC0: Robust I 0 and FI 0 controller design - PDF

Description
Robutné PID-regulátory obmedzeniami Robut Contrained PID Control DC0: Robut I 0 and FI 0 controller deign rof. Ing. Mikuláš Huba, Ph.D. Ing. Peter Ťaák, Ph.D. Tato rezentace je olufinancována Evrokým ociálním

Please download to get full document.

View again

of 38
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Information
Category:

News & Politics

Publish on:

Views: 69 | Pages: 38

Extension: PDF | Download: 0

Share
Transcript
Robutné PID-regulátory obmedzeniami Robut Contrained PID Control DC0: Robut I 0 and FI 0 controller deign rof. Ing. Mikuláš Huba, Ph.D. Ing. Peter Ťaák, Ph.D. Tato rezentace je olufinancována Evrokým ociálním fondem a tátním rozočtem Čeké reubliky. Content : I 0 and FI 0 controller Introduction Static feedforward control, FI 0 and I 0 controller Generic and equivalent tructure for comenation of inut and outut diturbance Nonmodelled dynamic Performance Portrait and Robutne Characteritic Hitory 2 Inut Diturbance Comenation Static feedforward control w / v u u a y 3 Inut Diturbance (ID) Comenation Static feedforward control with comenation of the inut diturbance w u / - v u a y v 4 Outut Diturbance (OD) Comenation Static feedforward control w / 0 u y a v o y 5 Outut Diturbance Comenation Static feedforward control with comenation of the outut diturbance w - / 0 u y a v o y v o 6 I 0 -ID controller generic tructure w Static feedforward control with comenation of inut diturbance u / 0 - v u a y v f T f - u f (Filtered) Invere lant model u af 0 T f y m 7 I 0 -OD controller generic tructure w Static feedforward control with comenation of outut diturbance u / 0 - y a v o y v of 0 T f - u f (Filtered) Parallel lant model u af T f y m 8 I 0 -ID controller - equivalent tructure exlicit integrator Omitting refilter = I-controller = FI 0 controller w v u y X T f - T f v f 9 FI 0 controller = I controller Filtered reone continuou for t = 0 w - T f u v y v f 0 Exlicit integrator Involved in hydraulic & electromechanical actuator mechanical contraint for integration w FI 0 -ID-controller - generic fundamental tructure Omitting ideal refilter in the equivalent cheme = Introducing low-a refilter into generic cheme = filtered reone continuou for t = 0 / 0 T f - u v u a y v f T f - u f u af 0 T f y m 2 FI 0 -controller (generic fundamental tructure) Two baic modification for inut and outut diturbance 3 Influence of Nonmodelled Dynamic Aroximation for the non-modeled dynamic (not conidered in deriving controller equation/tructure) F nd Td e T a ; T ar T d T a Several method for identification of T ar available T ar = time, at which the normed te reone reache 63% of the teady tate value 4 FI 0 controllerdead time T d The dominant dynamic (memoryle lant) determine the controller tructure Uability limit and control quality of thi tructure deend on the nonmodelled dynamic Dead time Td frequently ued aroximation of the nonmodelled dynamic Dead time influence for the lant outut y 0 and y may be evaluated analytically or uing the erformance ortrait method 5 / / ; / / 0 w w e F e e F Cloed loo tranfer function Normalized variable Normalized tranfer function e W Y F T e e W Y F I T I w f I I T T I w d d d ; ; ; ; 0 f d d T T T FI 0 controllerdead time T d 6 FI 0 controllerdead time T d Charakteritic olynomial A e / Condition of the double real ole 0 Solution A A ; A 0 q / Otimal (analytical) tuning e 0 ex ; / q ex( e) ; / ; T d / Tf ex 0 7 FI 0 controllerdead time T d Characteritic olynomial Stability border A A Stability border condition j 0 j co in / Critical tuning A j e je / j / 0 / 2 Critical ole crit q / / 2 / / T / f, crit 0 T 2 d 8 FI 0 controllerdead time T d Performance Portrait tolerated deviation of MO & NO ε: 0 (red) (darkblue) uncertainty boxe with reect to κ and T d /T f IAE contour outut y 9 FI 0 controllerdead time T d 0 5 Weakened and trict MO Exerimentally determined MO border different from the aeriodicity border 0 ex / ; ;dotted 0 T d / T f 00 y [%] / q / IAE 0 / T d IAE / T d FI 0 controllertime contant T a T A B T T W Y F A B T T T T W Y F f f f a f I a I w f a f a I a I a w / ; / ; / / ; / / Cloed loo tranfer function 2 FI 0 controllertime contant T a Cloed loo tranfer function F F w0 w T a / T f f ; Double real cloed loo ole / / / / 0 / B B A 0 A ; ; Critical tuning / 4 / 0 22 FI 0 controllertime contant T a Weakened and trict monotonicity Exerimentally determined monotonicity border different form the aeriodicity border baed on the DRDP 4 00 y [%] y : : / q / IAE / T a / q / y IAE / T a FI 0 controller: comaring loo with dead time T d or with time contant T a IAE veru tolerated overhooting For T d it hold IAE =IAE 0 For T a thi hold jut for ε 0 24 FI 0 controller - robutne characteritic Influence of uncertainty c a or c d on IAE for different tolerated overhooting c a = T amax /T amin, c d = T dmax /T dmin 25 Hitory Aeriodicity border double real dominant ole Oldenbourg, R.C. and H. Sartoriu: Dynamik elbttätiger Regelungen. R.Oldenbourg-Verlag, München, 944 Newer reference imle formula with τ=2 for overhooting 4.04% Skogetad, S.: Simle analytic rule for model reduction and PID controller tuning. Journal of Proce Control Volume 3, Iue 4, 2003, Oldenbourg a Sartoriu, 944 T d for overhooting 0 % given a Hitória / Skogetad, 2003 T d for overhooting 4.04% given a - / 2 00 y [%] / e q / IAE 0 / T d IAE / T d I 0 controllerdead time T d Characteritic olynomial & Critical tuning remain the ame a for the FI 0 controller Difference with reect to FI 0 control are in the: Performance Portrait Achievable dynamic and Otimal tuning rule 28 I 0 controllerdead time T d / / / / / / 0 0 w w e W Y F e e W Y F ; ; ; 0 f d d T T T Cloed loo tranfer function for normalized variable 29 I 0 controllerdead time T d Performance Portrait tolerated deviation of MO & NO ε: 0 (red) (darkblue) with reect to κ and T d /T f IAE contour outut y 30 FI 0 veru I 0 controllerdead time T d For I 0 minimal IAE value earate the area of trictly NO&MO tranient from thoe with a tolerable overhooting = much more convenient localization of the oerating oint 0 and T f may now be tuned earately (for FI 0 in a roduct) FI 0 I 0 3 I 0 controllerdead time T d Performance Portrait tolerated deviation of MO & NO ε: (red) (darkblue) ε-mo v. TV 0 contour For = the TV 0 contour are equal to thoe of MO area with 2ε that indicate jut one ule deviating from trictly MO reone 32 FI 0 : Concluion Structure of FI 0 (I controller) = tatic feedforward control DOB with the firt order filter the firt order refilter with the time contant equal to that of the DOB A reliable controller tuning require aroximation of the nonmodelled dynamic by time contant, or more frequently by dead time 33 FI 0 : Concluion To guarantee a tolerated overhooting, robut controller tuning mut reect the maximal lant gain max and the maximal value of the nonmodelled dynamic (T amax, or T dmax ) Senitivity to fluctuation of the time arameter i the ame a enitivity to lant gain change 34 FI 0 : Concluion Higher requirement on control quality (lower tolerated overhooting) lead to increaed enitivity to model uncertainty For the time contant and lower tolerated overhooting thi enitivity i higher than for the dead time and converely, for higher tolerated overhooting the enitivity i higher in the cae of dead time than for a time contant 35 I 0 : Concluion Structure of I 0 controller = tatic feedforward control DOB with the firt order filter In comaring with FI 0, the etoint reone may be reaonably imroved A reliable controller tuning require aroximation of the nonmodelled dynamic (by a time contant, or more frequently by a dead time). 36 I 0 : Concluion To guarantee a tolerated overhooting, robut controller tuning mut reect the maximal lant gain max and the maximal value of the nonmodeled dynamic (T amax, or T dmax ) Senitivity to fluctuation of the time arameter i different from the enitivity to lant gain change. 37 I 0 : Concluion Requirement to kee the diturbance reone (i.e. T f 0 =cont) lead finally to dynamic comarable with thoe achieved by reaonably imler FI 0 Therefore, we will deal motly jut with the imler FI 0 = I-controller 38
Related Search
Similar documents
View more...
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks