A nonlinear observer-based adaptive robust control approach for a class of uncertain asymmetric hysteretic systems

Abstract

This article presents a robust control scheme for a class of asymmetric hysteretic systems with both parametric uncertainties and external disturbances, where an asymmetric Bouc–Wen model is adopted to represent the hysteretic behavior. A novel adaptive non-singular terminal sliding mode control methodology with hysteretic state estimation is proposed to achieve finite-time stabilization of such systems for vibration suppressions. In the proposed control framework, a hysteresis observer is constructed to capture the unmeasurable hysteretic force, and the adaptive control technique is used to accommodate the hysteretic uncertainties and unknown system parameters. Moreover, a fast terminal sliding mode controller without the singularity problem is designed to improve the robustness and dynamic performance of such systems, where the terminal sliding mode function is proposed to guarantee the finite-time convergence of the system states, and the reaching law with fractional power is constructed to accelerate the occurrence of the corresponding terminal sliding mode surface. Meanwhile, the finite-time stability of the whole closed-loop system is also analyzed. Finally, numerical simulation results deployed on a magnetorheological elastomer vibration isolation system are provided to validate the effectiveness of the proposed control algorithm.

Keywords

Nonlinear observer hysteresis Bouc–Wen model adaptive robust control

Get full access to this article

View all access options for this article.

References

Yang

Niu

Spline adaptive filter with fractional-order adaptive strategy for nonlinear model identification of magnetostrictive actuator. Nonlinear Dyn 2017; 90(3): 1647–1659.

Zhang

Yan

Disturbance observer-based prescribed adaptive control for rate-dependent hysteretic systems. Int J Robust Nonlinear Control 2018; 28(6): 2298–2317.

Tang

Sun

, et al. Takagi-Sugeno fuzzy control for semi-active vehicle suspension with a magnetorheological damper and experimental validation. IEEE/ASME Trans Mechatron 2017; 22(1): 291–300.

Tjahjowidodo

Lau

MWS

, et al. Position control of asymmetric nonlinearities for a cable-conduit mechanism. IEEE Trans Autom Sci Eng 2017; 14(3): 1515–1523.

, et al. A state-of-the-art review on magnetorheological elastomer devices. Smart Mater Struct 2014; 23(12): 1–24.

Chai

Compensation of hysteresis nonlinearity in magnetostrictive actuators with inverse multiplicative structure for Preisach model. IEEE Trans Autom Sci Eng 2014; 11(2): 613–619.

Chen

CY.

Adaptive control for ionic polymer-metal composite actuators. IEEE Trans Syst Man Cybern Syst 2016; 46(10): 1468–1477.

Dong

Tan

Janschek

Nonsmooth predictive control for Wiener systems with backlash-like hysteresis. IEEE/ASME Trans Mechatron 2016; 21(1): 17–28.

Baradaran-nia

Alizadeh

Khanmohammadi

, et al. Optimal sliding mode control of single degree-of-freedom hysteretic structural system. Commun Nonlinear Sci Numer Simul 2012; 17(11): 4455–4466.

10.

Xiao

Dynamic compensation and H∞ control for piezoelectric actuators based on the inverse Bouc-Wen model. Rob Comput Integr Manuf 2014; 30(1): 47–54.

11.

Weber

Bouc-Wen model-based real-time force tracking scheme for MR dampers. Smart Mater Struct 2013; 22(4): 045012.

12.

Zhu

Wang

Non-symmetrical Bouc-Wen model for piezoelectric ceramic actuators. Sens Actuat A 2012; 181: 51–60.

13.

Song

Der Kiureghian

Generalized Bouc-Wen model for highly asymmetric hysteresis. J Eng Mech 2006; 132(6): 610–618.

14.

Kwok

Nguyen

, et al. Bouc-Wen model parameter identification for a MR fluid damper using computationally efficient GA. ISA Trans 2007; 46(2): 167–179.

15.

Tjahjowidodo

Lau

MWS

, et al. Hysteresis modeling and position control of tendon-sheath mechanism in flexible endoscopic systems. Mechatron 2014; 24(1): 12–22.

16.

A novel piezoactuated XY stage with parallel, decoupled, and stacked flexure structure for micro-/nanopositioning. IEEE Trans Ind Electron 2011; 58(8): 3601–3615.

17.

Ikhouane

Manosa

Rodellar

Adaptive control of a hysteretic structural system. Automatica 2005; 41(2): 225–231.

18.

Zhang

Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity. IEEE Trans Autom Control 2014; 59(5): 1336–1341.

19.

Koo

Yoo

, et al. Precise tracking control of piezoelectric actuators based on a hysteresis observer. Nonlinear Dyn 2012; 70(3): 1969–1976.

20.

Ikhouane

Dyke

SJ.

Modeling and identification of a shear mode magnetorheological damper. Smart Mater Struct 2007; 16(3): 605–616.

21.

Low

Guo

Modeling of a three-layer piezoelectric bimorph beam with hysteresis. J Microelectromech Syst 1995; 4(4): 230–237.

22.

Shirinzadeh

, et al. Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 2005; 41(11): 1957–1964.

23.

Zheng

Robust finite-time output feedback control of perturbed double integrator. Automatica 2015; 60: 86–91.

24.

Feng

Man

Non-singular terminal sliding mode control of rigid manipulators. Automatica 2002; 38(12): 2159–2167.

25.

Yang

CJ.

Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros. Commun Nonlinear Sci Numer Simul 2013; 18(3): 682–691.

26.

Zhang

Krause

Fast terminal sliding-mode finite-time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems. Int J Robust Nonlinear Control 2018; 28(2): 625–639.

27.

Bhat

Bernstein

. Finite-time stability of homogeneous systems. In: Proceedings of the American control conference, Albuquerque, NM, 6 June 1997, pp.2513–2514. New York: IEEE.

28.

Nguyen

Komatsuzaki

Iwata

, et al. Robust adaptive controller for semi-active control of uncertain structures using a magnetorheological elastomer-based isolator. J Sound Vib 2018; 434: 192–212.

29.

Jung

Eem

Jang

, et al. Seismic performance analysis of a smart base-isolation system considering dynamics of MR elastomers. J Intell Mater Syst Struct 2011; 22(13): 1439–1450.