A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

Lan Zhou ; Jinhua She ; Shaowu Zhou

International Journal of Applied Mathematics and Computer Science, Tome 24 (2014), p. 325-334 / Harvested from The Polish Digital Mathematics Library

Résumé

This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic outputfeedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value decomposition of the output matrix and Lyapunov stability theory are used to derive an asymptotic stability condition based on a Linear Matrix Inequality (LMI). Two tuning parameters in the LMI manipulate the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.

Détail

Publié le : 2014-01-01

Zbl 1293.93262

EUDML-ID : urn:eudml:doc:271885

Bibliographie

[000] Bristow, D.A., Tharayil, M. and Alleyne, A.G. (2006). A survey of iterative learning control, IEEE Control Systems Magazine 26(3): 96-114.

[001] Doi, M., Masuko, M., Ito, Y. and Tezuka, A. (1985). A study on parametric-vibration in chuck work, Bulletin of the Japan Society of Mechanical Engineers 28(245): 2774-2780.

[002] Galkowski, K., Paszke, W., Rogers, E., Xu, S., Lam, J. and Owens, D.H. (2003). Stability and control of differential linear repetitive processes using an LMI setting, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 50(9): 662-666.

[003] Hara, S., Yamamoto, Y. and Omata, T. (1988). Repetitive control system: A new type servo system for periodic exogenous signals, IEEE Transactions on Automatic Control 33(7): 659-668. | Zbl 0662.93027

[004] Hladowski, L., Galkowski, K., Rogers, E., Zhou, L., He, Y. and Kummert, A. (2012). Repetitive process based iterative learning control for a two motors system, IEEE International Conference on Control Applications, CCA 2012, Dubrovnik, Croatia, pp. 154-159.

[005] Ho, D.W.C. and Lu, G. (2003). Robust stabilization for a class of discrete-time non-linear system via output feedback: The unified LMI approach, International Journal of Control 76(2): 105-115. | Zbl 1026.93048

[006] Inoue, T., Nakano, M. and Iwai, S. (1981). High accuracy control of a proton synchrotron magnet power supply, Proceedings of the 8th IFAC World Congress, Kyoto, Japan, pp. 216-221.

[007] Jarzebowska, E.M. (2008). Advanced programmed motion tracking control of nonholonomic mechanical systems, IEEE Transactions on Robotics 24(6): 1315-1328.

[008] Khargonek, P.P., Petersen, I.R. and Zhou, K. (1990). Robust stabilization of uncertain linear systems: Quadratic stability and $H_∞$ control theory, IEEE Transactions on Automatic Control 35(3): 356-361.

[009] Li, Z.D. and Yang, W.D. (2011). $H_∞$ robust repetitive control with output feedback for roll eccentricity compensation, Control Theory and Applications 28(3): 381-388.

[010] Omata, T., Hara, T. and Nakano, M. (1985). Repetitive control for linear periodic systems, Electrical Engineering in Japan 105(3): 131-138.

[011] Petersen, I.R. and Hollot, C.V. (1986). A Riccati equation approach to the stabilization of uncertain linear systems, Automatica 22(4): 397-411. | Zbl 0602.93055

[012] Rogers, E., Galkowski, K. and Owens, D.H. (2007). Control Systems Theory and Applications for Linear Repetitive Processes, Lecture Notes in Control and Information Sciences, Vol. 349, Springer-Verlag, Berlin. | Zbl 1116.93005

[013] Roncero-Sanchez, P., Acha, E. and Ortega-Calderon, J.E. (2009). A versatile control scheme for a dynamic voltage restorer for power-quality improvement, IEEE Transactions on Power Delivery 24(1): 277-284.

[014] She, J., Fang, M. and Ohyama, Y. (2008). Improving disturbance-rejection performance based on an equivalentinput-disturbance approach, IEEE Transactions on Industrial Electronics 55(1): 380-389.

[015] She, J., Zhou, L. and Wu, M. (2012). Design of a modified repetitive-control system based on a continuous-discrete 2D model, Automatica 48(5): 844-850. | Zbl 1246.93049

[016] Songschon, S. and Longman, R.W. (2003). Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control, International Journal of Applied Mathematics and Computer Science 13(2): 169-177. | Zbl 1071.93019

[017] Verdult, V., Lovera, M. and Verhaegen, M. (2007). Identification of linear parameter-varying state space models with application to helicopter rotor, International Journal of Control 77(13): 1149-1159. | Zbl 1077.93506

[018] Wu, L.G., Shi, P., Gao, H.J. and Wang, C.H. (2008). $H_∞$ filtering for 2D Markovian jump systems, Electric Machines and Control 44(7): 1849-1858. | Zbl 1149.93346

[019] Wu, M., Zhou, L., She, J. and He, Y. (2010). Design of robust output-feedback repetitive controller for class of linear systems with uncertainties, Science China: Information Sciences 53(5): 1006-1015.

[020] Wu, L.G., Gao, H.J. and Wang, C.H. (2011). Quasi sliding mode control of differential linear repetitive process with unknown input disturbance, IEEE Transactions on Industrial Electronics (7): 3059-3068.

[021] Wu, M., Zhou, L. and She, J. (2011b). Design of observer-based $H_∞$ robust repetitive-control system, IEEE Transactions on Automatic Control 56(6): 1452-1457.

[022] Wu, L.G., Yao, X.M. and Zheng, W. X. (2012). Generalized H2 fault detection for Markovian jumping two-dimensional systems, Automatica 48(8): 1741-1750. | Zbl 1268.93096

[023] Xie, L.H. and Du, C.L. (2002). $H_∞$ Control and Filter of TwoDimensional System, Springer, Berlin.

[024] Yamamoto, Y. (1994). A function space approach to sampled data control systems and tracking problems, IEEE Transactions on Automatic Control 39(4): 703-713. | Zbl 0807.93038

[025] Zhou, K., Doyle, J.C. and Glover, K. (1996). Robust and Optimal Control, Prentice Hall, Upper Saddle River, NJ. | Zbl 0999.49500

[026] Zhou, L., She, J. and Wu, M. (2012). Design of a robust modified repetitive-control system for a periodic plant, ASME Journal of Dynamic Systems, Measurement, and Control 134(1): 011023-1-7.