Controller Design Approach Based on Multi-variable Sliding Mode Control

This paper explains and demonstrates the controller design approach based on the multi-variable sliding mode control (SMC). Many conventional SMCs are constructed as a servo system. Herein, we design a reference model in the SMC servo system, so that the plant output follows the reference model output. The switching function, including the model state variables, is determined, before calculating a linear plant input, in order to keep the state trajectory on the switching surface. A nonlinear plant input is determined in order to allow the state variable to reach and remain on the switching surface, so that the matching condition is satisfied. The plant state variables are estimated by an observer, and the optimal feedback gain and the integral gain are determined by the linear quadratic regulator (LQR). We confirmed the effectiveness of the proposed method by performing simulations for several plants.