Anti-Disturbance Control for Multiple Disturbances

Transcription

1 Workshop a 3 ACC Ani-Disurbance Conrol for Muliple Disurbances Lei Guo (lguo@buaa.edu.cn) Naional Key Laboraory on Science and Technology on Aircraf Conrol, Beihang Universiy, Beijing, 9, P.R. China. Presened by: Peng Yan (pengyan7@gmail.com) 3-6-5

2 Ouline Inroducion Ani-Disurbance Conrol for Muliple Disurbances Applicaions in Spacecrafs Conrol Conclusion 3.6.5

3 Inroducion Ani-disurbance conrol one of he cenral opics of modern conrol heory Disurbance Aenuaion Sochasic Conrol Robus Conrol Exernal Disurbance Adapive Conrol PID Conrol Inernal Model Conrol Sysem wih single disurbance Inernal Disurbance Problem: Mos of he above menioned disurbance aenuaion Disurbance Modeling Oupu Regulaion and Errors Rejecion rejecion mehods are used for sysems wih a single disurbance. Acive Disurbance Objecive: Design Rejecion ani-disurbance Conrol conroller for sysems Equivalen wih muliple disurbances Disurbance (MDs) Observer o improve accuracy and robusness Disurbance of conrol sysems. Based Conrol 3

4 Inroducion In engineering applicaions, complex sysems are ofen described by mahemaical models wih MDs. MDs of space craf modeling error inernal disurbances srucural perurbaion uncerainy unmodeled dynamics sensor measuremen noise conrol acuaor error environmenal graviy gradien orque disurbances sunligh pressure orque Wih he developmen of sensor echnology and daa processing, he MDs exising in pracical processes can be formulaed by differen mahemaical models. Thus, ani-disurbance conrollers for sysems wih MDs can be designed using he informaion 3 年 月 日 (characerisics) of MDs. 4

5 Ani-Disurbance Conrol for MDs Disurbance Modeling and analysis Consan or derivaivebounded disurbance d () σ MDs can be characerized as Disurbance generaed by an exogenous sysem norm-bounded disurbance Random disurbance w () = Ww δ () + B () d() = Vw() d () σ non-gaussian Gaussian Tha is, in engineering applicaions, disurbances originaed from differen sources can be described separaely and formulaed ino a composie form, raher han a single variable. 5

6 Ani-Disurbance Conrol for MDs Disurbance observer (DO) An MIMO sysem wih nonlineariy and MDs Observer of derivaivebounded disurbance x () = Ax() + Ff ( x(),) + B[ u() + d()] + Bd () y() = Cx() + Ff ( x(),) + Dd() ˆ () () () d = v + Lx v = L( v() + Lx()) L Ax + Ff x + Bu ( () ( (),) () ) Observer of disurbance generaed by an exogenous sysem ˆ () () () d = v Lx v = ( W LBV )( v( ) Lx( )) L Ax Ff x Bu ( () ( (),) () ) According o differen characerisics of disurbances, various ypes In. Journal of disurbance of Robus and Nonlinear observers Conrol, can Vol. 5, be pp. consruced: 9-5, 5. such as robus DO, Auomaica, sliding Vol. mode 4, pp , DO, adapive 5. DO and so on IEEE Trans. on Sysems, Man, and Cyberneics-Par B: Cyberneics, Vol. 4, pp ,

7 Ani-Disurbance Conrol for MDs Composie Hierarchical Ani-Disurbance Conrol (CHADC) Reference Signal Base Line Conroller CHADC Conrol Inpu Plan Muliple Disurbances Measuremen Oupu Disurbance Observers Figure : The design diagram of CHADC The inner layer of he CHADC includes a disurbance observer and compensaor. Meanwhile, he ouer layer of he CHADC includes IEEE Trans. on Fuzzy Sysems, Vol. 5, pp , 7. disurbance aenuaion conroller, such ha he hierarchical In. Journal of Robus and Nonlinear Conrol, Vol., pp. 6-8,. srucure can simplify he design mehods, and improve he IEEE Trans. on Auomaic Conrol, Vol. 54, pp. 84-8, 9. accuracy of he conroller. 3 年 月 日 7

8 Ani-Disurbance Conrol for MDs Composie Hierarchical Ani-Disurbance Conrol (CHADC) Closed-loop sysem H Conrol x () = ( A+ B K ) x() + Bd () + Ff ( x( ), ) CHADC (H +DOBC) x () A+ BK BV x() = () () e W+ LBV e B d() F f x B B δ() + + L ( ( ), ) T T ΦF B QC QU BV T T ΦF Q B QC QU ( \ λ ) I T T γ I B R λ T < γ I γ I B P < I C I I I of he Φ Φ = sym( A Q +BR) ΦQ = sym( A +BR ) Φ = sym( PW+RB V ) K = RQ K = RQ L = P R 3 年 月 日 8 Crierion wrien in LMI o es he To sabiliy design conroller using CHADC scheme, he heoreical boleneck and H problem is ha he coupling beween disurbance performance observers/compensaors and disurbance aenuaion conrollers closed-loop increase he complexiy of closed-loop conrol sysems. The sysem sabiliy of he sysem and disurbance aenuaion performance based on a base line conroller no longer hold.

9 Ani-Disurbance Conrol for MDs The following problems deserve furher sudies based on he exising resuls. Analyze he mechanisms of disurbance characerisics and disurbance modeling for various sources. Relax he resricions on he disurbance model maching condiions when consrucing he disurbance observer. Reduce he conservaiveness of disurbance and uncerain parameer esimaion. Exend he exising CHADC schemes o he cases of disurbance aenuaion and rejecion for sysems wih unknown parameers and uncerain disurbances

10 3 Applicaions in Spacecrafs Conrol CHADC design for aiude conrol of flexible spacecrafs r PD Conroller Space environmenal disurbances ŵ u w w Vibraion Disurbance Vibraion Observer Spacecraf Plan Figure : The design diagram of CHADC for flexible spacecrafs The coupling dynamics beween flexible and rigid-body pars of spacecrafs are reaed as a disurbance erm. Nonlinear Dynamics, Vol. 67, pp. 8-88,. Make use of he characerisics of vibraion disurbance o design CHADC o improve he accuracy of aiude conrol sysem

11 3 Applicaions in Spacecrafs Conrol CHADC design for aiude conrol of flexible spacecrafs Spacecraf plan: Flexible paddle J θ() + F η() = u () + d() η() + C η() +Λ η() + F T θ() = d Hub T ( J FF ) θ () = FC ( η() +Λη( ) ) + u () + d() Sae equaion: d Sae: x () θ () = θ () x () = Ax() + B[ u() + d ()] + Bd () Disurbance descripion: d() = FC ( η() +Λη()) d Conrol law: u () = dˆ () + Kpθ + K dθ

12 3 Applicaions in Spacecrafs Conrol CHADC design for aiude conrol of flexible spacecrafs Sep: Disurbance modeling and analysis Spacecraf plan: η = Λ η + η + + d() = FC ( dη() + Λη( )) T () M [ () Cd () F J ( u () d()) ] Disurbance model: d() = Vw() w () = Ww () + Hu() + Hd() η () I T w() =, V [ F FCd ], W, H, M I F J F T η() = Λ = = = M Λ M C d M F J Sep: Consruc disurbance observer dˆ ˆˆ () = Vw (), w () = v () Lx () v () = ( W+ LBV)( v () Lx ()) + L( Ax ()+ Bu ()) + Hu() 3.6.5

13 3 Applicaions in Spacecrafs Conrol CHADC design for aiude conrol of flexible spacecrafs Sep3: Design CHADC Augmening sae equaion: x () A + BK BV x() B d() e() = + W + LBV e() LB + H H reference oupu: z() = Cx() + C e() + Dd () CHADC: u () = dˆ () +Kx() Sep4: Observer gain L and conrol gain K can be obained by he following LMI: T Φ BV B C T sympw ( + RBV ) RB + PH C K=R X T < γ I D L=P R I

14 3 Applicaions in Spacecrafs Conrol Simulaion resuls.5 Acual Esimaed Error.5 Acual Esimaed Error Disurbance(Nm) Disurbance(Nm) Aiude angle(deg) Time(s) Figure 3: The esimae of disurbance using modeled observer 5 x -3 modeled DOBC + H unmodeled DOBC + H H Time(s) Figure 5: The simulaion resuls of Aiude angle Time(s) Figure 4: The esimae of disurbance using un-modeled observer Noaion: The simulaion resuls of disurbance esimae and Aiude angle for spacecrafs wih small effecs produced by high order elasic modes shown in Figure

15 3 Applicaions in Spacecrafs Conrol Simulaion resuls.5 Acual Esimaed Error.5 Acual Esimaed Error Disurbance(Nm) Disurbance(Nm) Aiude angle(deg) Time(s) Figure 6: The esimae of disurbance using modeled observer 5 x -3 modeled DOBC + H unmodeled DOBC + H H Time(s) Figure 8: The simulaion resuls of Aiude angle Time(s) Figure 7: The esimae of disurbance using un-modeled observer Noaion: The simulaion resuls of disurbance esimae and Aiude angle for spacecrafs wih large effecs produced by high order elasic modes shown in Figure

16 3 Applicaions in Spacecrafs Conrol Semi-physical simulaion Figure 9: Hardware es for DOBC

17 3 Applicaions in Spacecrafs Conrol Semi-physical simulaion resuls Figure : semi-physical simulaion resuls of pich angle using H and H +DOBC

18 4 Conclusion The core of he ani-disurbance conrol for MDs is o research he CHADC schemes. The hierarchical srucure can simplify he design mehods and improve he accuracy of he conroller. Is main feaure is o make full use of disurbance characerisics, and classify he models of various disurbances. Besides he applicaion in spacecraf conrol, he idea of CHADC has been applied o he problems of filering, faul deecion and diagnosis, where muliple disurbances exis. There are many remaining open problems ha deserves more sudies in his general area

19 Workshop a 3 ACC Thanks! 3 年 月 日 9