Improved sliding mode controller performance through power rate exponential reaching law

Chattering alleviation is an area of great interest as far as the practicality of sliding mode controllers (SMC) are concerned. Reaching law based SMC design is a well-known chattering alleviation method available in the literature. Among the different conventional reaching law strategies that are available in the literature, power rate reaching law (PRRL) is found to be effective in terms of chattering alleviation and fast reaching. The main disadvantage of PRRL is that it bypasses the major portion of sliding mode motion in order to reduce chattering and to ensure fast reaching. It is well known that the most important advantage of SMC is that it guarantees robustness in the sliding mode phase. Since PRRL reduces the duration of sliding mode phase, the robustness property of SMC is compromised. This limitation of PRRL is being overcome here through an exponential modification so that the attributes of chattering alleviation, fast reaching and robustness in sliding mode phase are guaranteed simultaneously. We propose to call this modified PRRL as Power Rate Exponential Reaching Law (PRERL). The efficacy of the proposed method is validated through simulation studies on a three joint robotic arm set point regulation problem.