Fuzzy robust sliding mode control of a class of uncertain systems

Abstract

Aiming at a class of systems under parameter perturbations and unknown external disturbances, a method of fuzzy robust sliding mode control was proposed. Firstly, an integral sliding mode surface containing state feedback item was designed based on robust H_∞ control theory. The robust state feedback control was utilized to substitute for the equivalent control of the traditional sliding mode control. Thus the robustness of systems sliding mode motion was improved even the initial states were unknown. Furthermore, when the upper bound of disturbance was unknown, the switching control logic was difficult to design, and the drawbacks of chattering in sliding mode control should also be considered simultaneously. To solve the above-mentioned problems, the fuzzy nonlinear method was applied to approximate the switching control term. Based on the Lyapunov stability theory, the parameter adaptive law which could guarantee the system stability was devised. The proposed control strategy could reduce the system chattering effectively. And the control input would not switch sharply, which improved the practicality of the sliding mode controller. Finally, simulation was conducted on system with parameter perturbations and unknown external disturbances. The result shows that the proposed method could enhance the approaching motion performance effectively. The chattering phenomenon is weakened, and the system possesses stronger robustness against parameter perturbations and external disturbances.

Keywords

uncertain systems / robust control / fuzzy sliding mode control / chattering

References

[1] SanjoyM, ChitralekhaM. Chattering free adaptive multivariable sliding mode controller for systems with matched and mismatched uncertainty [J]. ISA Transactions, 2013, 52: 335-341

[2] RobertS, DouglasL, PeterW. An adaptive AIMD congestion control protocol for communication networks [J]. Networking, 2004, 3042: 699-711

[3] WuX-l, LiuJ, ZhangJ-h, WangYing. Synchronizing a class of uncertain and variable time-delay fractional-order hyperchaotic systems by adaptive sliding robust mode control [J]. Acta Phys Sin, 2014, 63(16): 160507

[4] ZhangX-x, LiuX-p, ZhuQ-dan. Adaptive chatter free sliding mode control for a class of uncertain chaotic systems [J]. Applied Mathematics and Computation, 2014, 232: 431-435

[5] MehdiR, BijanR S, Tsung-ChihL. Adaptive sliding mode control in a novel class of chaotic systems [J]. Commun Nonlinear Sci Numer Simulat, 2010, 15: 4158-4170

[6] ChenZ-m, MengW-j, ZhangJ-gang. Intelligent anti-swing control for bridge crane [J]. Journal of Central South University, 2012, 19: 2774-2781

[7] MohammadM F, SaeedK. Robust control of electrically driven robots by adaptive fuzzy estimation of uncertainty [J]. Nonlinear Dyn, 2012, 69: 1465-1477

[8] LiuL, WangB-li. Multi objective robust active vibration control for flexure jointed struts of stewart platforms via H∞ and μ synthesis [J]. Chinese Journal of Aeronautics, 2008, 21: 125-133

[9] IanR P, RobertoT. Robust control of uncertain systems: Classical results and recent developments [J]. Automatica, 2014, 50: 1315-1335

[10] NavidN, MehdiR, ZolghadriJ. Adaptive fuzzy sliding mode control scheme for uncertain systems [J]. Commun Nonlinear Sci Numer Simulat, 2009, 14: 3978-3992

[11] LiuS, ChenL-qun. Chaos synchronization of a chain network based on a sliding mode control [J]. Chin Phys B, 2013, 22(10): 100506

[12] LiuJ-k, SunF-chun. Research and development on theory and algorithms of sliding mode control [J]. Control Theory and Applications, 2007, 24(3): 407-418

[13] YaoQ-h, HuangJ-q, WuH-songVariable structure control system [M], 1997ChongqingChongqing University Press7-9

[14] LiuJ-k, SunF-chun. Global sliding mode control with adaptive fuzzy chattering free method for nonlinear system [C]. IMACS Multiconference on Computational Engineering in Systems Applications, 2006541-546

[15] LiuY-f, YangX-g, MiaoD, YuanR-ping. Chaotic synchronization problem of finite-time convergence based on fuzzy sliding mode [J]. Acta Phys Sin, 2007, 56(11): 6250-6257

[16] LiuL-p, HanZ-z, LiW-lin. Global sliding mode control and application in chaotic systems [J]. Nonlinear Dyn, 2009, 56: 193-198

[17] JingY-w, MaoY-e, GeorgiM D, ZhengY, ZhangS-ying. Adaptive global sliding mode control strategy for the vehicle antilock braking systems [C]. 2009 American Control Conference, 2009769-773

[18] LiX-q, JingL, LiuChang. Global sliding mode control for uncertain linear systems with state time-delays [C]. Proceedings of the 29th Chinese Control Conference, 20102234-2239

[19] LiX-q, JingLi. Global sliding mode control for uncertain linear systems with input time-delays [C]. Proceedings of the 8th World Congress on Intelligent Control and Automation, 2010838-842

[20] PangH-p, ChenXia. Global robust optimal sliding mode control for uncertain affine nonlinear systems [J]. Journal of Systems Engineering and Electronics, 2009, 20(4): 838-843

[21] FengY, HanF-l, YuX-huo. Chattering free fullorder sliding-mode control [J]. Automatica, 2014, 50: 1310-1314

[22] WangJ, ZhangT, XuG-kaiTheory and application of robust control [M], 2011Beijing, ChinaPublishing House of Electronics Industry178-191