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In this paper, an adaptive discrete-time sliding mode control based on reduced-order disturbance observer is proposed for discretized multi-input multi-output systems subjected to unmatching condition. By using the designed discrete reduced-order disturbance observer, a new sliding surface is constructed to counteract the unmatched uncertainties. Then, to guarantee a smaller width of the quasi sliding mode domain, an adaptive reaching law is developed, whose switching gain is adaptively tuned to prevent overestimation of disturbance on the premise of ensuring the reaching condition of sliding surface; meanwhile, the ranges of the quasi sliding mode band and attractiveness region are deduced. The proposed control algorithm has low computational complexity and needs no information about the upper bound of unmatched disturbance. The simulations on the control of a bank-to-turn missile demonstrate that the proposed method can effectively reject unmatched disturbance, and provide higher accuracy in comparison with traditional methods. Keywords Discrete-time sliding mode control • Adaptive reaching law • Reduced-order disturbance observer • Unmatched disturbance • Multi-input multi-output system

In this paper, an implicit discrete‐time fast terminal sliding mode (DFTSM) control with disturbance compensation is designed and analyzed for uncertain high‐order systems. First, a recursive discrete sliding surface is constructed based on implicit Euler technique, which can completely eliminate discretization chattering so as to significantly reduce the boundary layer of sliding mode motion. With the help of a high‐order disturbance compensator, the accuracy limitation of implicit DFTSM control systems is overcome by increasing the order of sliding mode. Then the finite‐time convergence of implicit DFTSM is proved for the first time, and the influence relationship of control parameters on the convergence speed and control accuracy of the algorithm is established. Finally, two numerical examples are provided to demonstrate the effectiveness and superiority of the proposed design approach.

In this article, a novel adaptive reaching law is developed to address discrete‐time sliding mode control systems with mismatched uncertainties. By using the high‐order disturbance compensator, a new reduced‐order sliding surface is constructed to avoid redundancy and decrease superfluous computational expense. Then, an adaptive reaching law with adjustable switching gain is designed to guarantee globally fast convergence of sliding variable. Compared with existing similar works, the proposed reaching law has a main advantage that it can obtain arbitrarily small width of quasi sliding mode domain, leading to suppressed chattering. Based on the analysis of the closed‐loop system, the upper bound of steady states is established. The whole control scheme is able to counteract mismatched uncertainties and achieve high‐precision control at the same time. Finally, a simulated example on bank‐to‐turn missiles is given to verify this research achievement.

In this article, the steady‐state behaviors of discrete‐time nonsingular terminal sliding mode (NTSM) control systems are investigated for the explicit and implicit Euler integration schemes. It is demonstrated that implicit Euler method can guarantee the global convergence of both system states and sliding variable for discrete‐time NTSM control systems, whereas explicit Euler approximation does not. For explicit discrete‐time NTSM, the range of quasi sliding mode band is deduced on the basis of the reachability condition of discrete SM, showing that discretized NTSM can achieve higher control accuracy than the discrete‐time linear sliding mode. By analyzing the distribution features of steady‐state points, the upper bound for steady states is obtained to estimate chattering amplitude, which establishes the influence relationship of sampling time, switching gain and movement characteristics on the bound of steady states. Simulations are presented to validate the theoretical results.