A New Discrete Reaching Law for Discrete-time Sliding Mode Control

In this paper, a novel reaching law for discrete time sliding mode control is proposed. The law aims at reducing the width of quasi sliding mode band as well as fast reaching of the sliding variable to the sliding surface. While there are many existing reaching laws that give rise to an accelerated reaching phase, they often engender an initial spike in the control effort. This problem is addressed in the paper by defining a reaching law that regulates the rate of change of the sliding variable in such a way as to curtail the control effort. The proposed reaching law, when compared to the well established reaching law proposed first by Gao, Homaifa and Wang, leads to faster reaching with smaller Quasi Sliding Mode Band while maintaining the same control effort. The efficacy of the proposed reaching law has been verified through simulations and compared with the simulation results obtained for Gao's reaching law to illustrate its various advantages.