A Two-surface Discrete Sliding Mode Control based on Approach Angle Reaching Law Rinu Alice Koshy, Susy Thomas Abstract-- Sliding mode controllers are known to be robust to parameter changes, disturbances and uncertainties. In this paper a novel discrete time sliding mode controller with two surfaces is proposed to improve the speed of response. Here, approach angle reaching law is used to take the trajectory to the surfaces. The advantage is that the system trajectory is bought to the first surface with maximum velocity thereby shortening the reaching phase. The scheme assures robustness, asymptotic stability and fast transients with minimum chattering. Index Terms-- Discrete Sliding mode control, two surface sliding mode control, Approach angle, Chattering, Asymptotic Stability I.INTRODUCTION HE core of variable structure control system is its sliding mode. Variable structure control, which provides the robust stability, is an area that has attracted much research interest. With the computer technology being widely applied in control field, the discrete variable structure control has attained wide popularity. It is well known that Discrete-time VSC has properties that are quite different from the continuous-time VSC, because of the finite sampling time. In discrete-time systems, the control input is updated at a sampling instant, and is unchanged until the next sampling instant. Therefore, the control input cannot be changed at the very instant when the system motion crosses the sliding surface. For this reason, it is not easy to maintain ideal sliding mode motion. Since the invariance and robustness properties of VSC are satisfied only in sliding mode, these desirable properties may not be maintained in DVSC. Furuta proposed a variable structure algorithm which drives the system state to an appropriately determined sector in state space [3]. Manuscript received on December 08, 2011 1.Rinu Alice Koshy, Research scholar, Electrical Engineering Department, National Institute of Technology Calicut, India/Assistant Professor ,Rajagiri School of Engineering ,Cochin, India(phone no.09895055233,e.mail: rakoshy@gmail.com ) 2. Dr. Susy Thomas, Professor, Electrical Engineering Department, National Institute of Technology Calicut, Kerala, India(e.mail: susy@nitc.ac.in ) In 1990 GAO had presented the reaching law method to design the controller, and extended the same to discrete time counter part [1], [2]. In the reaching law approach, switching function dynamics satisfying the reaching condition is chosen, and then the control input is derived from the inverse dynamics. Therefore, in this approach, the determination of the control law is simple. Also, the control input derived has a property to make the switching function stable by choosing the design parameters to satisfy the reaching condition. But there exist deficiencies like, the reaching law cannot finally keep the system stable at the origin, and the chattering character of the system is one of the major drawbacks due to the discontinuous switching control which excites the unmodelled high frequency dynamics of the system [2],[4]. In this paper, an improved two surface discrete sliding mode control using approach angle reaching law is presented. In Approach angle methodology the trajectory is forced on to the chosen switching surface by the reaching control law for which the reaching angle is generally small. The direct implication of this constraint is that reaching phase is increased. This in turn affects the robustness of the control system. In the proposed method we define two surfaces where, the first surface is a virtual surface that aids the fast motion of the trajectory on to its final destination. The motion from this to the second one is then effected by the approach angle reaching law with small approach angle to avoid chattering. This sliding mode motion then guarantees that the system state is bounded under the existence of time varying disturbance and uncertainty. The paper is organized as follows. In section II, the some concepts of reaching law is revealed. In section III, the approach angle reaching law is explained in detail. In section IV a simulation example is given to compare the performance of approach angle based two surface sliding mode controllers with that of single surface sliding mode controllers. In section V, conclusion is given. II .CONCEPTS Comparing with continuous-time control system, the properties, the existence conditions and the reaching conditions of the sliding mode in discrete-time variable structure control will be changed because of the existence of sampling process [1]. Theoretically, DSMC systems cannot be obtained from their continuous counterpart by means of simple equivalence [11]. T Proceedings of the International MultiConference of Engineers and Computer Scientists 2012 Vol II, IMECS 2012, March 14 - 16, 2012, Hong Kong ISBN: 978-988-19251-9-0 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) IMECS 2012