An implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems

In conventional reaching law approaches, the disturbance suppression is achieved at the cost of high-frequency chattering or increasing the complexity of algorithm such as adding a high-order disturbance compensator. This paper presents the design and analysis of a novel implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems. First, the implicit Euler technique is introduced into the design of discrete reaching laws, and it is proved to be able to eliminate numerical chattering completely. By using a self-adaptive power term, the newly designed reaching law can obtain an arbitrarily small boundary layer of sliding surface, and at the different phases of sliding mode motion, the adaptive power parameter can automatically regulate its value to guarantee globally fast convergence without destroying the accuracy of sliding variable. Then, based on a predefined trajectory of sliding variable, the discrete-time sliding mode control law is developed to realize high control accuracy without additional design. Compared with previous methods, the main contribution of proposed reaching law lies in that it can acquire high-precision sliding mode motion and simultaneously eliminate numerical chattering in spite of complex uncertainties only by adjusting the adaptive power parameter. Finally, a simulation example on the piezomotor-driven linear stage is provided to verify the theoretical results.