Design of a Discrete-time Sliding Mode Controller for Nonlinear Affine Systems based on Disturbance Estimation

In this paper, a sliding mode controller based on the disturbance estimation is designed for a class of discrete-time nonlinear affine systems. Based on two disturbance compensator schemes, static and dynamic, procedures of sliding mode controller design are proposed for the discrete-time system. In the case of measurable state variables, the instantaneous value of disturbances can be estimated based on the value of states and control signals. In two proposed control laws, there is no switching expression to induce the problem of chattering. Moreover, based on the necessary and sufficient quasi-sliding mode condition proposed by Sarpturk, boundedness and robustness of the proposed controllers is evaluated. In the case of constant or slowly time-varying disturbances, the quasi-sliding mode band converges asymptotically to zero and in this case, the proposed method is converted to the ideal sliding mode. Finally, two examples are provided to verify the proposed control laws and to compare the performance of the proposed controllers.