Abstract. 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.Keywords: sliding mode control (SMC), switching function, linear quadratic regulator (LQR).
IntroductionThe origin of a sliding mode control (SMC) has been proposed by Utkin [1] and Itkis [2]. Advanced technologies of the SMC have been proposed by several researchers [3,4,5,6,7,8]. The control system requires a stability of the system, a quick response, a steady-state characteristic and a robustness for the parameter uncertainty in industrial applications. The goal of the SMC is to obtain a desired response under the assumption that the system has a plant parameter uncertainty, and that an unknown disturbance is added to a control system. At the SMC, the behavior of the closed-loop system is determined by the switching function. The SMC is a nonlinear robust control, and attempts to stabilize the system by limiting the state to a switching hyperplane. One of the features is to have the excellent robustness for disturbances and the plant parameter uncertainty, so that the SMC servo system fulfills the matching condition [8].In this paper, we propose a controller design approach based on the multi-variable SMC. The purpose of this research is to design the system in which the actual plant follows the reference model by suppressing the error between the trajectory of the plant and that of the reference model. In particular, we design a reference model in the