The advantages associated with Sliding Mode Control, namely simplicity in design, reduced order dynamics and robustness in sliding mode are often overshadowed by the chattering phenomenon. From the perspective of robotic manipulator control, it is essential that the end effector positions itself at its target set. The Quasi Sliding Mode associated with Discrete-time Sliding Mode Control where the sliding variable crosses the sliding surface in each discrete instant in the sliding phase, attributes an unsettling nature to the positioning of the robot arms. In this context, this paper proposes a new reaching law based Discrete-time Sliding Mode Control for the position control of the manipulator which is capable of reducing the Quasi Sliding Mode Band without slowing down the system response when compared to the well established reaching law proposed in the seminal work of Gao, Homaifa and Wang; these being achieved without the expenditure of extra control effort. The proposed reaching law has been applied to a third order system as well as a two joint rigid robotic manipulator and simulation results are presented and compared with the results obtained with Gao's reaching law to show its efficacy in fulfilling its various attributes.

This paper analyzes the effectiveness of the reaching law approach for sliding mode control of discrete time systems. The method is extended for sliding mode control for multi-input multi-output (MIMO) systems. Modified reaching law for reducing the chattering is proposed. The performance of the proposed controller is analyzed by carrying out simulation studies on MIMO systems. The performance of the controller is also compared with that of the equivalent control.

A variable structure controller design for the tip position control of a flexible one-link manipulator was presented by Thomas et al. (1997). The control torque obtained using this design methodology was subjected to high frequency chattering. This makes it impossible to implement the controller in practice. The absence of a sign(S) function in the control law makes it impossible to implement the boundary layer technique of chatter reduction where the sign(S) function is replaced by a saturation type function to yield a continuous control signal approximation that confines the system trajectory to a small band neighboring the switching surface. This paper presents a new switching law which not only alleviates chattering in the control signal but also ensures ideal sliding mode motion. Simulation results are presented to verify the claims attributed to the proposed method.