Design of observer-based discrete repetitive-control system based on 2D model

Abstract

A discrete observer-based repetitive control (RC) design method for a linear system with uncertainties was presented based on two-dimensional (2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality (LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.

Keywords

state observer / two-dimensional discrete system / repetitive control / linear matrix inequality

References

[1] NakanoM, YamamotoY, InoueT, HaraS. Repetitive control [M]. Tokyo, Japan: Auto Control Press, 199019-26

[2] LinY H, ChungC C, HungT H. On robust stability of nonlinear repetitive control system: factorization approach [C]. American Control Conference. Boston, USA, 19912646-2647

[3] PawelD, KrzysztofG, OlivierB, EricR. Control of discrete linear repetitive processes using strong practical stability and H^∞ disturbance attenuation [J]. Systems & Control Letters, 2012, 61: 1138-1144

[4] HuC-x, YaoB, ChenZ, WangQ-feng. Adaptive robust repetitive control of an industrial biaxial precision gantry for contouring tasks [J]. IEEE Transactions on Control Systems Technology, 2011, 19(6): 1559-1568

[5] TomasH, ZhongQ-chang. A current-control strategy for voltage-source inverters in microgrids based on H_∞ and repetitive control [J]. IEEE Transactions on Power Electronics, 2011, 26(3): 943-952

[6] TomasH, ZhongQ-chang. H_∞ repetitive voltage control of grid-connected inverters with a frequency adaptive mechanism [J]. IET Power Electron, 2010, 3(6): 925-935

[7] WuM, ZhouL, SheJ-hua. Design of observer-based H^∞ robust repetitive-control system [J]. IEEE Transactions on Automatic Control, 2011, 56(6): 1452-1457

[8] ZhouL, WuM, SheJ-h, HeYong. Design of robust repetitive control system with a state observer [J]. Control Theory & Applications, 2009, 26(9): 942-948

[9] FuC-h, WuM, HeY, YuanS-gui. Guaranteed cost discrete repetitive control system design based on two dimensional model [J]. Systems Engineering and Electronics, 2012, 34(8): 1685-1690

[10] LanY-h, WuM, SheJ-hua. Stability analysis and controller design for repetitive control systems [J]. Acta Automatica Sinica, 2009, 35(8): 1122-1127

[11] GalkowskiK, RogersE, XuS, LamJ, OwensD. LMIs—a fundamental tool in analysis and controller design for discrete linear repetitive processes [J]. IEEE Transaction on Circuits and Systems I: Fundamental Theory and Applications, 2002, 49(6): 768-778

[12] KhargonekP P, PetersenI R, ZhouK. Robust stabilization of uncertain linear systems: quadratic stabilizability and H_∞ control theory [J]. IEEE Transactions on Automatic Control, 1990, 35(3): 356-361

[13] XieL-hua. Output feedback H_∞ control of systems with parameter uncertainty [J]. International Journal of Control, 1996, 63(4): 741-750

[14] MacduffeeC CThe theory of matrices [M], 2004, New York, Dover Publications: 81-89

[15] LanY-h, HuangH-x, ZhouYong. Observer-based robust control of a (1<α<2) fractional-order uncertain systems: A linear matrix inequality approach [J]. IET Control Theory and Application, 2012, 6: 229-234

[16] LaiX-z, PanC-z, WuM, SheJ-h, YangS X. Robust stabilization and disturbance attenuation for a class of underactuated mechanical systems [J]. Journal of Central South University, 2012, 19: 2488-2495