Novel Discrete Reaching Law for Sliding Mode Control of Robotic Manipulators to Reduce Quasi Sliding Mode Band with Improved Reaching

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.