Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems Sanjoy Mondal ⇑ , Chitralekha Mahanta Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India article info Article history: Received 9 May 2011 Accepted 3 August 2011 Available online 12 August 2011 Keywords: Discrete control Integral sliding mode control Composite nonlinear feedback Nonlinear function abstract In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlin- ear feedback (CNF) method is proposed. The aim of the controller is to improve the tran- sient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feed- back control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction The concept of sliding mode control (SMC) has received considerable attention in the past few decades. In SMC, the sys- tem trajectory is forced to move along a chosen manifold in the state space by the use of an appropriate variable structure control signal. SMC was developed by Emelyanov [1] and Utkin and Young [2] who showed that sliding mode could be achieved by changing the controller structure. The use of digital computers in controller design in recent years has made the use of discrete-time representation more suitable than continuous time representation [3–9]. In the case of discrete-time sliding mode control, the control signal is applied only at regular intervals of time and the signal is held constant in between these instants. Sliding mode control strat- egy is one of the robust control techniques, which is invariant against the matched parameter variations and disturbance [10]. However, before the sliding surface is reached, the system does not possess the property of being insensitive to noise and matched uncertainty [10]. In 1996, Utkin and Shi [11] proposed integral sliding mode (ISM) control. In this controller, the order of the motion equation was equal to that of the original system, rather than being reduced by the dimension of the control input. Thus, a smooth control law could be obtained which guaranteed robustness throughout the entire response of the system starting from any initial position. Integral sliding mode controller received a lot of attention for the above reason. In 1996 Wang et al. [12] introduced new methods for designing integral sliding mode controller. In 2000 Su et al. [13] showed that by choosing a proper sampling strategy in discrete sliding mode control design, the thickness of the boundary layer could be reduced. In 2005 Basin et al. [14] showed an application of integral sliding mode control for uncertain systems with time delay. Integral sliding mode control was also developed for matched and unmatched uncertainties [15,16]. In 2007 Abidi et al. [17] designed a 1007-5704/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2011.08.010 ⇑ Corresponding author. Tel.: +91 361 258 2507; fax: +91 361 2582542. E-mail addresses: m.sanjoy@iitg.ernet.in (S. Mondal), chitra@iitg.ernet.in (C. Mahanta). Commun Nonlinear Sci Numer Simulat 17 (2012) 1320–1331 Contents lists available at SciVerse ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns