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Research Papers

# Design of Repetitive-Control System With Input Dead Zone Based on Generalized Extended-State Observer

[+] Author and Article Information
Min Wu

Professor
School of Automation,
China University of Geosciences;
Hubei Key Laboratory of Advanced Control and
Intelligent Automation for Complex Systems,
Wuhan 430074, Hubei, China
e-mail: wumin@cug.edu.cn

Pan Yu

School of Information Science and Engineering,
Central South University,
Changsha 410083, Hunan, China;
Hubei Key Laboratory of Advanced Control and
Intelligent Automation for Complex Systems,
Wuhan 430074, Hubei, China

Xin Chen

Professor
School of Automation,
China University of Geosciences;
Hubei Key Laboratory of Advanced Control and
Intelligent Automation for Complex Systems,
Wuhan 430074, Hubei, China

Jinhua She

Professor
School of Automation,
China University of Geosciences;
Hubei Key Laboratory of Advanced Control and
Intelligent Automation for Complex Systems,
Wuhan 430074, Hubei, China;
School of Engineering,
Tokyo University of Technology,
Hachioji 192-0982, Tokyo, Japan

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 27, 2016; final manuscript received December 22, 2016; published online May 10, 2017. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 139(7), 071008 (May 10, 2017) (9 pages) Paper No: DS-16-1212; doi: 10.1115/1.4035615 History: Received April 27, 2016; Revised December 22, 2016

## Abstract

This paper concerns a repetitive-control system with an input-dead-zone (IDZ) nonlinearity. First, the expression for the IDZ is decomposed into a linear term and a disturbance-like one that depends on the parameters of the dead zone. A function of the system-state error is used to approximate the combination of the disturbancelike term and an exogenous disturbance. The estimate is used to compensate for the overall effect of the IDZ and the exogenous disturbance. Next, the state-feedback gains are obtained from a linear matrix inequality that contains two tuning parameters for adjusting control performance; and the pole assignment method is employed to design the gain of a state observer. Then, two stability criteria are used to test the stability of the closed-loop system. The method is simple, employing neither an inverse model of the plant nor an adaptive control technique. It is also robust with regard to the different parameters of the IDZ, uncertainties in the plant, and the exogenous disturbance. Finally, two numerical examples demonstrate the effectiveness of this method and its advantages over others.

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## References

Inoue, T. , Iwai, S. , and Nakano, M. , 1981, “ High Accuracy Control of a Proton Synchrotron Magnet Power Supply,” 8th IFAC World Congress, pp. 3137–3142.
Hara, S. , Yamamoto, Y. , Omata, T. , and Nakano, M. , 1988, “ Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals,” IEEE Trans. Autom. Control, 33(7), pp. 659–668.
He, L. Q. , Zhang, K. , Xiong, J. , and Fan, S. F. , 2015, “ A Repetitive Control Scheme for Harmonic Suppression of Circulating Current in Modular Multilevel Converters,” IEEE Trans. Ind. Electron, 30(1), pp. 471–481.
Wu, M. , Xu, B. G. , Cao, W. H. , and She, J.-H. , 2014, “ Aperiodic Disturbance Rejection in Repetitive-Control Systems,” IEEE Trans. Control Syst. Technol., 22(3), pp. 1044–1051.
Zhou, L. , She, J.-H. , Wu, M. , and Zhang, J. , 2011, “ Design of Robust Modified Repetitive-Control System for Linear Periodic Plants,” ASME J. Dyn. Syst., Meas., Control, 134(1), p. 011023.
Mayergoyz, I . D. , 1986, “ Mathematical Models of Hysteresis,” IEEE Trans. Mag., 22(5), pp. 603–608.
Yi, J. , Chang, S. , and Shen, Y. , 2009, “ Disturbance-Observer-Based Hysteresis Compensation for Piezoelectric Actuators,” IEEE/ASME Trans. Mechatronics, 14(4), pp. 456–464.
Wang, X. S. , Su, C. Y. , and Hong, H. , 2004, “ Robust Adaptive Control of a Class of Nonlinear Systems With Unknown Dead-Zone,” Automatica, 40(3), pp. 407–413.
Zhang, T. P. , and Ge, S. S. , 2008, “ Adaptive Dynamic Surface Control of Nonlinear Systems With Unknown Dead Zone in Pure Feedback Form,” Automatica, 44(7), pp. 1895–1903.
Recker, D. , Kokotovic, P. , Rhode, D. , and Winkelman, J. , 1991, “ Adaptive Nonlinear Control of Systems Containing a Deadzone,” 30th IEEE Conference on Decision Control, Brighton, UK, Dec. 11–13, pp. 2111–2115.
Zhou, J. , Wen, C. , and Zhang, Y. , 2006, “ Adaptive Output Control of Nonlinear Systems With Uncertain Dead-Zone Nonlinearity,” IEEE Trans. Autom. Control, 51(3), pp. 504–511.
Li, Z. , Li, T. , and Feng, G. , 2016, “ Adaptive Neural Control for a Class of Stochastic Nonlinear Time-Delay Systems With Unknown Dead Zone Using Dynamic Surface Technique,” Int. J. Robust Nonlinear Control, 26(4), pp. 759–781.
Wu, L. B. , Yang, G. H. , Wang, H. , and Wang, F. , 2016, “ Adaptive Fuzzy Asymptotic Tracking Control of Uncertain Nonaffine Nonlinear Systems With Non-Symmetric Dead-Zone Nonlinearities,” Inform. Sci., 348, pp. 1–14.
Corradini, M. L. , and Orlando, G. , 2002, “ Robust Stabilization of Nonlinear Uncertain Plants With Backlash or Dead-Zone in the Actuator,” IEEE Trans. Control Syst. Technol., 10(1), pp. 158–166.
Li, S. , Yang, J. , Chen, W. H. , and Chen, X. , 2012, “ Generalized Extended State Observer Based on Control for Systems With Mismatched Uncertainties,” IEEE Trans. Ind. Electron., 59(12), pp. 4792–4802.
Levine, W. S. , 1996, The Control Handbook, CRC Press, Boca Raton, FL.
Khargonekar, P. P. , Petersen, I. R. , and Zhou, K. , 1990, “ Robust Stabilization of Uncertain Linear Systems: Quadratic Stabilizability and H Control Theory,” IEEE Trans. Autom. Control, 35(3), pp. 356–361.
Gao, Z. , 2006, “ Active Disturbance Rejection Control: A Paradigm Shift in Feedback Control System Design,” American Control Conference, Minneapolis, MN, June 14–16, pp. 2399–2405.
Wu, S. , and Ren, G. , 2004, “ Delay-Independent Stability Criteria for a Class of Retarded Dynamical Systems With Two Delays,” J. Sound Vib., 270(4–5), pp. 625–638.
Hu, S. S. , 2007, “Automatic Control Principle,” 5th ed., Science Press, Beijing, China, pp. 95–97.

## Figures

Fig. 1

GESO-based MRCS with an IDZ

Fig. 2

IDZ

Fig. 8

Simulation results for MRCS with and without GESO of Plant (44) with IDZ (45)

Fig. 3

Reference input and exogenous disturbance

Fig. 4

Simulation results for GESO-based MRCS of Plant (35) with IDZ (37)

Fig. 5

Simulation results for method in Ref. [8] of Plant (35) with ΔA=0, ΔB=0, d0(t)=0, and IDZ (37)

Fig. 6

Simulation results for GESO-based MRCS of Plant (35) with ΔA=0, ΔB=0, d0(t)=0, and IDZ (37)

Fig. 7

Simulation results for GESO-based MRCS of Plant (35) with IDZ (43)

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