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Background and Objectives: Nowadays, because of accuracy, speed, cost, and flexibility of digital control laws, control systems are implemented by computers, microprocessors or DSP chips. Therefore, many investigators have recently focused on the design of discrete-time controllers and computer-based control. Methods: 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 discretetime system. Results: 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. Conclusion: In this paper, a sliding mode controller based on the disturbance estimator was designed for a discrete-time nonlinear affine system. Due to the effectiveness of disturbance estimators in the performance of controllers, two kinds of disturbance estimators were considered.

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