Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

Lan Zhou ; Jinhua She ; Chaoyi Li ; Changzhong Pan

International Journal of Applied Mathematics and Computer Science, Tome 26 (2016), p. 285-295 / Harvested from The Polish Digital Mathematics Library

Résumé

This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

Détail

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:280117

Bibliographie

[000] Chen, X., Fukuda, T. and Young, K.D. (2000). A new nonlinear robust disturbance observer, Systems and Control Letters 41(3): 189-199. | Zbl 0986.93045

[001] Chung, C.H. and Chen, M.S. (2012). A robust adaptive feedforward control in repetitive control design for linear systems, Automatica 48(1): 183-190. | Zbl 1244.93041

[002] 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

[003] Ho, D.W.C. and Lu, G. (2003). Robust stabilization for a class of discrete-time nonlinear system via output feedback: The unified LMI approach, International Journal of Control 76(7): 105-115. | Zbl 1026.93048

[004] Hu, C.X., Yao, B., Chen, Z. and Wang, Q.F. (2011). Adaptive robust repetitive control of an industrial biaxial precision gantry for contouring tasks, IEEE Transactions on Control Systems Technology 19(6): 1559-1568.

[005] 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.

[006] 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(37): 356-361.

[007] Liu, J.Q., Chen, W.J., Wu, M., She, J. and He, Y. (2014a). Compensation in repetitive control system for aperiodic disturbances and input dead zone, 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, pp. 2752-2757.

[008] Liu, R.J., Liu, G.P., Wu, M., She, J. and Nie, Z.Y. (2014b). Robust disturbance rejection in modified repetitive control system, Systems and Control Letters 70: 100-108. | Zbl 1290.93055

[009] Miyazaki, T., Ohishi, K., Shibutani, I., Koide, D. and Tokumaru, H. (2006). Robust tracking control of optical disk recording system based on sudden disturbance observer, 32nd Annual Conference of the IEEE Industrial Electronics Society, Paris, France, pp. 5215-5220.

[010] Pipeleers, G., Demeulenaere, B., Schutter, J.D. and Swevers, J. (2009). Generalised repetitive control: Relaxing the period-delay-based structure, IET Control Theory and Applications 3(11): 1528-1536.

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

[012] She, J., Wu, M., Lan, Y.H. and He, Y. (2010). Simultaneous optimisation of the low-pass filter and state-feedback controller in a robust repetitive-control system, IET Control Theory and Applications 4(8): 1366-1376.

[013] She, J., Xin, X. and Pan, P. (2011). Equivalent-input-disturbance approach-analysis and application to disturbance rejection in dual-stage feed drive control system, IEEE Transactions on Mechatronics 16(2): 330-340.

[014] 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

[015] Wu, M., Xu, B.G., Cao, W.H. and She, J. (2014). Aperiodic disturbance rejection in repetitive-control systems, IEEE Transactions on Control Systems Technology 22(3): 1044-1051.

[016] 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

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

[018] 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.

[019] Zhou, L., She, J., Wu, M. and He, Y. (2013). Design of a robust observer-based modified repetitive-control system, ASME Journal of Dynamic Systems, Measurement, and Control 52(3): 375-382.

[020] Zhou, L., She, J., Wu, M., He, Y. and Zhou, S.W. (2014a). Estimation and rejection of aperiodic disturbance in a modified repetitive-control system, IET Control Theory and Applications 8(10): 882-889.

[021] Zhou, L., She, J. and Zhou, S. (2014b). A 2D system approach to the design of a robust modified repetitive-control system with dynamic output-feedback controller, International Journal of Applied Mathematics and Computer Science 24(2): 325-334, DOI: 10.2478/amcs-2014-0024. | Zbl 1293.93262