Robust R-S-T Digital Control and Open Loop System Identification A Brief Review

Transcription

1 IEEE dvanced Process Conrol Workshop, Vancouver, pril 29-Ma, 2002 Robus R-S-T Digial Conrol and Open Loop Ssem Idenificaion rief Review I.D. Landau Laboraoire d uomaiue de GrenobleINPG/CNRS, France landau@lag.ensieg.inpg.fr DPTECH, 4 Rue du Tour de l Eau, S. Marin d Hères38, France info@adapech.com I.D.Landau :Digial Conrol/Ssem Idenificaion

2 Peugeo PS pplicaions of R-S-T Conrollers Double Twis Machine Pourier Sollac Florange Ho Dip Galvanizing I.D.Landau :Digial Conrol/Ssem Idenificaion 360 Flexible rm LG 2

3 Implemenaion of R-S-T Digial Conrollers PLC Lero implemens R-S-T digial conrollers and Daa acuisiion modules LSP 320 LSP 320 implemens R-S-T digial conrollers and Daa acuisiion modules I.D.Landau :Digial Conrol/Ssem Idenificaion 3

4 Conroller Design and Validaion Performance specs. Robusness specs. DESIGN METHOD MODELS IDENTIFICTION Ref. CONTROLLER u PLNT Idenificaion of he dnamic model 2 Performance and robusness specificaions 3 Compaible conroller design mehod 4 Conroller implemenaion 5 Real-ime conroller validaion and on sie re-uning 6 Conroller mainenance same as 5 I.D.Landau :Digial Conrol/Ssem Idenificaion 4

5 Ouline Robus digial conrol -The R-S-T digial conroller -asic design -Robusness issues -n example Open loop ssem idenificaion -Daa acuisiion -Model complexi -Parameer esimaion -Validaion I.D.Landau :Digial Conrol/Ssem Idenificaion 5

6 Robus Digial Conrol I.D.Landau :Digial Conrol/Ssem Idenificaion 6

7 The R-S-T Digial Conroller CLOCK r Compuer conroller u D/ ZOH PLNT /D Discreized Plan r m m Conroller T - S R u d Plan Model = I.D.Landau :Digial Conrol/Ssem Idenificaion 7

8 I.D.Landau :Digial Conrol/Ssem Idenificaion 8 r m m T S d R u Conroller Plan Model - The R-S-T Digial Conroller Plan Model: * = = G d d n a n a =... *... = = b b n n R-S-T Conroller: * R d T u S = Characerisic polnomial closed loop poles: = R S P d

9 Pole Placemen wih R-S-T Conroller r m m * d T - S u -d R -d -d - -d - m * - m P - * - * - Conroller : R = H R' ; S H S' H H : R = S R, S fixed pars Regulaion: R and S soluions of: d H S' H R' = P = S R P D P F Tracking : T = P / Reference rajecor: * compuer file * = m / m r I.D.Landau :Digial Conrol/Ssem Idenificaion dominan poles auxiliar poles 9

10 Connecions wih oher Conrol Sraegies - Digial PID : n R = n = 2; H = S S -Tracking and regulaion wih independen objecivesmrc: P = * P D P F Hp.: * has sable damped zeros - Minimum variance racking and regulaion MVC: P = * C noise model - Inernal Model Conrol IMC: P = P F Hp.: * has sable damped zeros Hp.: has sable damped poles I.D.Landau :Digial Conrol/Ssem Idenificaion 0

11 r u T The Sensiivi Funcions Oupu sensiivi funcion p -> S p - S = S -d R = S P Inpu sensiivi funcion p -> u S up - = - R S -d R = - R P Noise sensiivi funcion b -> S b - = - - disurbance p -d S R -d R S -d R = - -d R P Plan Model b measuremen noise I.D.Landau :Digial Conrol/Ssem Idenificaion S p - S b =

12 Robusness Margins z = e jω - G Im H Re H Tpical values: M 0.5-6d, τ > Ts Μ Φ 2 ω CR ω CR crossover freuenc H OL = 3 ω CR M 0.5 G 2 ; Φ > 29 The inverse is no necessaril rue! Modulus Margin: M = H OL z - min = S p z max = S p Dela Margin: τ = min Φi i i ω CR I.D.Landau :Digial Conrol/Ssem Idenificaion 2

13 δ W uncerain disk ω = 0 Im G ω = π a relaed sensiivi funcion defines he size of he oleraed uncerain Robus Sabili Re G -j G e ω Famil of plan models: G' F G, δ, W G nominal model; δ z W x z Robus sabili condiion: S W x x S x W < x < x - size of uncerain a pe of uncerain defines an upper emplae for he modulus of he sensiivi funcion There also lower emplaes because of he relaionship beween various sensiivi fc. I.D.Landau :Digial Conrol/Ssem Idenificaion 3

14 Templaes for he Sensiivi Funcions nominal perform. 0 Sp d Sp max = - M dela margin 0.5f s Oupu Sensiivi Funcion Sup d 0 acuaor effor 0.5f s Inpu Sensiivi Funcion S up - size of he oleraed addiive uncerain W a G = G δw a I.D.Landau :Digial Conrol/Ssem Idenificaion 4

15 P = R S Robus Conroller Design Pole placemen wih sensiivi funcions shaping Nominal performance: P D P F = R' = S' H R H S P D and par of H R and llow o shape he sensiivi funcions Several approaches o design : -Ieraive Choosing and using band sop filers H Ri / PFi, H Sj / PFj P F -Convex opimizaion see Langer, Landau, uomaica, June99, Opreg dapech H S I.D.Landau :Digial Conrol/Ssem Idenificaion 5

16 360 Flexible rm LIGHT SOURCE RIGID FRMES MIRROR LUMINIUM DETECTOR TCH. POT. ENCODER LOCL POSITION SERVO. COMPUTER I.D.Landau :Digial Conrol/Ssem Idenificaion 6

17 360 Flexible rm Freuenc characerisics Poles-Zeros Idenified Model I.D.Landau :Digial Conrol/Ssem Idenificaion 7

18 Shaping he Sensiivi Funcions Oupu Sensiivi Funcion - Sp Inpu Sensiivi Funcion - Sup 25 Sp - Sensibilié perurbaion-sorie 60 Sup - Sensibilié perurbaion-enrée gabari Module [d] D C Module [d] gabari D C Freuence [Hz] wihou auxiliar poles - wih auxiliar poles C- wih sop band filer D- wih sop band filer Freuence [Hz] H S P H R P / F 2 / F 2 I.D.Landau :Digial Conrol/Ssem Idenificaion 8

19 Open Loop Ssem Idenificaion I.D.Landau :Digial Conrol/Ssem Idenificaion 9

20 Ssem Idenificaion Mehodolog I/0 Daa cuisiion under anexperimenal Proocol Model Complexi Esimaion or Selecion Choice of he Noise Model Parameer Esimaion Model Validaion No Yes Conrol Design I.D.Landau :Digial Conrol/Ssem Idenificaion 20

21 I/O Daa cusiion Signal : a P.R..S seuence Magniude : few % of he inpu operaing poin Clock freuenc : fclock = / p fs ; p =, 2,3 f s = sampling freuenc N Lengh : 2 pt ; N = number of cells, T = / f s s s Larges pulse : NpT s Lengh : < allowed duraion of he experimen Larges pulse : R rise ime P.R..S. NpT s r I.D.Landau :Digial Conrol/Ssem Idenificaion 2

22 n I/O File ineria d.c. moor. u power amplifier filer M acho generaor TG I.D.Landau :Digial Conrol/Ssem Idenificaion 22

23 n Complexi Esimaion from I/O Daa Objecive : To ge a good esimaion of he model complexi direcl from nois daa = max n, n d nˆ = min CJ = min op minimum nˆ nˆ n, n, d [ J nˆ S nˆ, N ] J n 0 n n op CJn Sn,N I.D.Landau :Digial Conrol/Ssem Idenificaion complexi penal erm error erm should be unbiased To ge a good order esimaion, J should end o he value for nois free daa when N use of insrumenal variables 23

24 Parameer Esimaion Discreized plan u DC ZOH Plan DC ε djusable discree-ime model - Esimaed model θˆ parameers Parameer adapaion algorihm I.D.Landau :Digial Conrol/Ssem Idenificaion 24

25 I.D.Landau :Digial Conrol/Ssem Idenificaion 25 u -d e : e u S d = Recursive Leas Suares u -d w 2: w u S d = Oupu ErrorO.E. Insrumenal Variable u -d e C [ ] / 4: e C u S d = Generalized Leas Suares u -d e C 3: e C u S d = Exended Leas Suares O.E. wih Exended Predicion Model Recursive Maximum Likelihood «Plan Noise» Models ~ 33% ~ 64% ~ % ~ 2%

26 I.D.Landau :Digial Conrol/Ssem Idenificaion 26 Parameer Esimaion Mehods * * d u =θ T ψ = vecor measuremen vecor parameer ψ θ ; Plan Model ˆ ˆ T φ =θ Esimaed model observaion vecor vecor parameer esimaed φ θ ; ˆ ˆ ˆ 0 0 = Φ = T θ ε Predicion error Parameer adapaion algorihm 2 0 ; 0 ˆ ˆ < < Φ Φ = Φ = F F F T λ λ λ λ ε θ θ [ ] f φ = Φ

27 Parameer Esimaion Mehods I- ased on he asmpoic whiening of he predicion error Recursive Leas Suares, Exended Leas Suares, Recursive Max. Likelihood, O.E. wih Exended Predicion Model II- ased on he asmpoic decorrelaion beween he predicion error and he observaion vecor Oupu Error, Insrumenal Variable I.D.Landau :Digial Conrol/Ssem Idenificaion 27

28 Validaion of Idenified Models Saisical Validaion u Plan - Model - RMX RRX predicor u Plan - Model Oupu Error Predicor - - ε ε Whieness Tes Decorrelaion Tes 2.7 RN i ; i N normalized crosscorelaion N 97% number of daa N 2.7 N = 256 RN i praical value : RN i I.D.Landau :Digial Conrol/Ssem Idenificaion 28

29 Sofware Tools for Implemening he Mehodolog Ssem Idenificaion -Winpim dapech idenificaion in open loop and closed loop operaion -CLID dapech idenificaion in closed loop Malab Toolbox Conroller Design -Winreg dapech design and opimisaion of R-S-T digial conrollers -Opreg dapech auomaed design of robus digial conrollers under Malab Real-ime implemenaion -Winrac dapech: cascade digial conrol I.D.Landau :Digial Conrol/Ssem Idenificaion 29

30 «Personal» References Landau.I.D.,990 Ssem Idenificaion and Conrol Design, Prenice Hall, N.J.,US Landau I.D., 995 : «Robus digial conrol of ssems wih ime dela he Smih predicor revisied», In. J. of Conrol, vol. 62, pp Landau I.D., Lozano R., M Saad M., 997 : dapive Conrol, Springer, London,U.K. Landau I.D., 993 Idenificaion e Commande des Ssèmes, 2nd ediion, Hermes, Paris June Landau I.D., 2002 Commande des Ssèmes Concepion, idenificaion e mise en œuvre, Hermes, Paris June I.D.Landau :Digial Conrol/Ssem Idenificaion 30