Sliding mode controller design for MIMO nonlinear systems: A novel power rate reaching law approach for improved performance

This paper proposes a novel approach to the design of reaching law based on Sliding Mode Controller (SMC) for multi input multi output (MIMO) non-linear systems so as to overcome the drawbacks associated with conventional reaching law based SMC design strategies. The modification is proposed with an aim to completely eliminate chattering, to ensure control inputs within admissible limits and to guarantee fast response when SMC is used. Modification to conventional power rate reaching law is the point of interest here in order to ensure complete elimination of chattering. Two different modifications to power rate reaching law are presented which incorporate control constraints during controller design so that admissible control input limits are not exceeded. The first modified method ensures limited control effort as well as complete chattering free response, but does not improve the reaching characteristics. So a second adaptive modification to power rate reaching law is also presented here. This method ensures fast reaching to the sliding surface along with properties of complete elimination of chattering and bounded control inputs. However, as in power rate reaching law these modified methods retain the limitation of not possessing robustness properties. The method is applied to a three degree of freedom robotic arm which is typically a non-linear MIMO system. The ability of the presented method to satisfy attributes, viz., chattering free operation, bounded control inputs and fast response is compared with the performance of various reaching law methods available in the literature. The performance of the proposed method is validated through simulation studies on the robotic arm example.