Guaranteed Cost Control of State-Delay System Based on the Equivalent-Input-Disturbance Approach
Fang Gao*, Min Wu **, †, Jinhua She**,***, and Pan Yu*
*School of Information Science and Engineering, Central South University
Changsha 410083, China
**School of Automation, China University of Geosciences
Wuhan 430074, China
***School of Engineering, Tokyo University of Technology
Hachioji 192-0987, Japan
This paper considers a guaranteed cost control problem for state-delay systems with exogenous disturbances for a proper plant. The equivalent-input-disturbance (EID) approach is extended to be able to handle a state-delay system. A new control law is constructed that incorporates an EID estimate in order to ensure a satisfactory control performance. A stability condition for the closed-loop system is provided in terms of a linear matrix inequality, using the Lyapunov function method. Furthermore, a guaranteed cost control state feedback control law and a state observer are designed, based on the linear matrix inequality (LMI). Two numerical examples are provided to demonstrate the validity of the method.
-  L. Xie, E. Fridman, and U. Shaked, “Robust Η∞ control of distributed delay systmes with application to combustion control,” IEEE Trans. on Automatic Control, Vol.46, pp. 1930-1935, 2001.
-  G. Gu, V. Kharitonov, and J. Chen, “Stability of time-delay systems,” Boston: Birkhauser, 2003.
-  S. Niculescu, “Delay effects on stability: a robust control approach,” Springer-Verlag, New York, 2001.
-  J. Hale and L. Verduyn“Introduction to functional differential equations,” Springer-Verlag, New York, 1993.
-  O. J. M. Smith, “Closed control of loops with dead time,” Chemical Engineering Progress, Vol.53, pp. 217-219, 1957.
-  K. Watanabe and M. Ito, “A process-model control for linear systems with delay,” IEEE Trans. on Automatic Control, Vol.26, No.6, pp. 1261-1269, 1981.
-  K. J. Astrom, C. C. Hang, and B. C. Lim, “A new smith predictor for controlling a process with an integrator and long dead-time,” IEEE Trans. on Automatic Control, Vol.39, No.2, pp. 343-345, 1994.
-  W. D. Zhang and Y. X. Sun, “Modified smith predictor for controlling integrator/time delay processes,” Industrial Engineering Chemistry Research, Vol.35, No.8, pp. 2769-2772, 1996.
-  T. Takehara, T. Kunitake, H. Hashimoto, and F. Harashima, “The control for the disturbance in the system with time delay,” Proc. of the 4th Int. Workshop on Advanced Motion Control, Vol.1, pp. 349-353, 1996.
-  Y. Tian and F. Gao, “Control of integrator processes with dominant time delay,” Industrial Engineering Chemistry Research, Vol.38, No.8, pp. 2979-2983, 1999.
-  O. Camacho and F. D. Cruz, “Smith predictor based-sliding mode controller for integrating processes with elevated deadtime,” ISA Trans., Vol.43, pp. 257-270, 2004.
-  O. Camacho, R. Rojas, and W. Garcia-Gabin, “Some long time delay sliding mode control approaches,” ISA Trans., Vol.46, No.1, pp. 95-101, 2007.
-  T. Umeno and Y. Hori, “Robust servo system design with two degrees of freedom and its application to novel motion control of robot manipulators,” IEEE Trans. on Industrial Electronics, Vol.40, No.5, pp. 473-485, 1993.
-  H. S. Lee and M. Tomizuka, “Robust motion controller design for high-accuracy positioning systems,” IEEE Trans. on Industrial Electronics, Vol.43, pp. 48-55, 1996.
-  Y. Choi, K. Yang, W. K. Chung, H. R. Kim, and I. H. Suh, “On the robustness and performance of disturbance observers for second-order systems,” IEEE Trans. on Automatic Control, Vol.48, pp.315-320, 2003.
-  P. Mattavelli, “An improved deadbeat control for ups using disturbance observer,” IEEE Trans. on Industrial Electronics, Vol.52, No.1, pp. 206-212, 2005.
-  O. Camacho and F. D. Lacruz, “Smith predictor based-sliding mode controller for integrating processes with elevated deadtime,” ISA Trans., Vol.235, No.43, pp. 257-270, 2004.
-  O. Camacho and F. D. Lacru, “Some long time delay sliding mode control approaches,” ISA Trans., Vol.46, pp. 95-101, 2007.
-  J. L. Chang, “Applying discrete-time proportional integral observers for state and disturbance estimations,” IEEE Trans. on Automatic Control, Vol.51, No.5, pp. 814-818, 2006.
-  F. J. Lin and P. H. Shen, “Robust fuzzy neural network sliding-mode control for two-axis motion control system,” IEEE Trans. on Industrial Electronics, Vol.53, No.4, pp. 1209-1225, 2006.
-  X. Chen, T. Fukuda, and K. D. Young, “A new nonlinear robust disturbance observer,” Systems Control Letter, Vol.41, No.3, pp. 189-199, 2000.
-  R. J. Liu, M. Wu, G. P. Liu, J. H. She, and C. Thomas, “Active disturbance rejection control based on an improved equivalent-input-disturbance approach,” IEEE/ASME Trans. on Mechatronics, Vol.18, No.4, pp. 1410-1413, 2013.
-  M. Wu, K. P. Lou, F. Xiao, R. J. Liu, Y. He, and J. H. She, “Design of equivalent-input-disturbance estimator using a generalized state observer,” J. of Control Theory and Applications, Vol.11, No.1, pp. 74-79, 2013.
-  R.J. Liu, G.P. Liu, M. Wu, et al. “Disturbance rejection for time-delay systems based on the equivalent-input-disturbance approach,” J. of the Franklin Institute, Vol.351, No.6, pp. 3364-3377, 2014.
-  W. J. Chen, J. D. Wu, and J. H. She, “Design of compensator for input dead zone of actuator nonlinearities,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.17, No.6, pp. 805-812, 2013.
-  J. Yang, W. H. Chen, and S. Li, “Nonlinear disturbance observer based robust control for systems with mismatching disturbances/ uncertainties,” IET Control Theory & Applications, Vol.5, No.18, pp. 2053-2062, 2011.
-  S. Li, J. Yang, and W. H. Chen, “Generalized extended state observer based control for systems with mismatched uncertainties,” IEEE Trans. on Industrial Electronics, Vol.59, No.12, pp. 4792-4802, 2012.
-  J. Yang, S. Li, and W. H. Chen, “Nonlinear disturbance observer based control for multi-input multi-output nonlinear systems subject to mismatching condition,” Int. J. of Control, Vol.85, No.8, pp. 1071-1082, 2012.
-  J. Leyva-Ramos and A. E. Rearson, “An asymptotic modal observer for linear aubnomms time lag systems,” IEEE Trans. on Automatic Control, Vol.40, No.7, pp. 1291-1294, 1995.
-  P. P. Khargonek, I. R. Petersen, and K. Zhou, “Robust stabilization of uncertain linear systems: quadratic stabilizability and Η∞ control theory,” IEEE Trans. on Automatic Control, Vol.35, pp. 356-361, 1990.
-  L. Xie, “Output feedback Η∞ control of systems with parameter uncertainty,” Int. J. of Control, Vol.63, No.4, pp. 741-750, 1996.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.