Proposed Control Approach Quasi-Sliding Mode Control

International Journal of Computer Trends and Technology (IJCTT)          
© 2018 by IJCTT Journal
Volume-55 Number-1
Year of Publication : 2018
Authors : Lodhi Sadam Sadiq Khan, Du Bao Zhu, Naveed Ahmed Qureshi, Ibrajimov Shokhzod
DOI :  10.14445/22312803/IJCTT-V55P103


Lodhi Sadam Sadiq Khan, Du Bao Zhu, Naveed Ahmed Qureshi, Ibrajimov Shokhzod "Proposed Control Approach Quasi-Sliding Mode Control". International Journal of Computer Trends and Technology (IJCTT) V55(1):7-16, January 2018. ISSN:2231-2803. Published by Seventh Sense Research Group.

Abstract -
Time delays and external disturbances are unavoidable in many practical control applications, e.g., in robotics, manufacturing, and process control and it is often a source of instability or oscillations, see, e.g., [1,2] and the references therein. Therefore, the design of control and observation schemes has been an interesting problem for dynamical systems to compensate for time delays [3] and to estimate external disturbances [4]. To enhance robustness, the sliding mode control methodology has been recognised as an effective strategy for uncertain systems, see, e.g., and references therein. In this context, there have been considerable efforts devoted to the problem of sliding mode control design for uncertain systems with matched disturbances, see, e.g., [5,6] and references therein. However, when the matching conditions for disturbances are not satisfied, their effects can be only partially rejected in the sliding mode. Therefore, the control design for this case remains a challenging problem. For a class of linear systems with time-varying delay and unmatched disturbances, a sliding-mode control strategy was developed in and sufficient conditions were derived in terms of linear matrix inequalities (LMIs) to guarantee that the state trajectories of the system converge towards a ball with a pre-specified convergence rate. By using the invariant ellipsoid method, another sliding mode control design algorithm was proposed for a class of linear quasi-Lipschitz disturbed system to minimise the effects of unmatched disturbances to system motions in the sliding mode . Later, by combining the predictor-based sliding mode control with the invariant ellipsoid method, an improved result was reported to take into account also time delay in the control input [10]. Recently, a disturbance observer-based sliding mode control was presented in where mismatched uncertainties were considered.

[1] Richard J.P. Time-delay systems: an overview of some recent advances and open problems. Automatica, 39[10]:1667–1694, 2003.
[2] Kharitonov V. L. Time-Delay Systems: Lyapunov Functionals and Matrices. Birkhau¨ser, New York, 2013.
[3] Natori K., Tsuji T., Ohnishi K., and Hace A. Time-delay compensation by communication disturbance observer for bilateral Teleoperation under timevarying delay. IEEE Transactions on Industrial Electronics, 57[3]:1050–1062.
[4] Trinh H. and Ha Q.P. State and input simultaneous estimation for a class of time-delay systems with uncertainties. IEEE Transactions on Circuits and Systems II, 54[6]:527–531, 2007.
[5] Xia Y. and Jia Y. Robust sliding-mode control for uncertain time-delay systems: An LMI approach. IEEE Transactions on Automatic Control, 48:1086– 1092, 2003.
[6] Han X., Fridman E., Spurgeon S.K., and Edwards C. On the design of sliding mode static output feedback controllers for systems with state delay. IEEE Transactions on Industrial Electronics, 56[9]:3656–3664, 2009.
[7] Xia Y., Fu M., Si P., and Wang M. Robust sliding mode control for uncertain discrete-time systems with time delay. IET Control Theory and Applications, 4[4]:613–624, 2010.
[8] Xi Z. and Hesketh T. Discrete time integral sliding mode control for systems with matched and unmatched uncertainties. IET Control Theory and Applications, 4[4]:889–896, 2010.
[9] Zhu F. Estimation and unknown input reconstruction via both reduced-order and high-order sliding mode observers. Journal of Process Control, 22[1]:296– 302, 2011.
[10] Polyakov A. Minimization of disturbances effects in time delay predictorbased sliding mode control systems. Journal of the Franklin Institute, 39:1380–1396, 2012.
[11] Bartoszewicz A. Discrete-time quasi-sliding-mode control strategies. IEEE Transactions on Industrial Electronics, 45[4]:633–637, 1998.
[12] Gao W., Wang Y., and Homaifa A. Discrete-time variable structurecontrol systems. IEEE Transactions on Industrial Electronics, 42[2]:117–122,1996.
[13] Cheng C.C., Lin M.H., and Hsiao J.H.Sliding mode controllers design for linear discrete-time systems with matching perturbations. Automatica, 36[8]:1205–1211, 2000.

Quasi-Sliding, Model Control, Time-Delay Systems, Lyapunov Functionals.