A generalized reaching-law-based discrete-time integral sliding-mode controller with matched/mismatched disturbance attenuation

A generalized reaching-law-based (RL-based) discrete-time integral sliding-mode controller, which is versatile for either matched or mismatched disturbances, is designed in this paper to obtain high output tracking accuracy and avoid tremendous control efforts. Specifically, a disturbance decomposition-based discrete-time integral sliding surface is designed, and a generalized discrete-time reaching law is established. Different from the existing integral sliding surfaces, the proposed sliding surface synthesizes a disturbance-related integral term that is defined based on disturbance decomposition; this is crucial to the disturbance attenuation. Moreover, different from the available discrete-time reaching laws, the proposed reaching law introduces an adaptive exponential term into the control gains, and hence, the conventional RL-based discrete-time integral sliding-mode control (DISMC) and the equivalent-control-based (EC-based) DISMC can be integrated. Rigorous analysis shows that the closed-loop system is stable, the control effort can be satisfactory, and the steady-state output tracking accuracy is of order O(T2)$$ O\left({T}<^>2\right) $$ for both matched and mismatched disturbances. The proposed method is proven effective through numerical simulations.

Automated summary

In this paper, a generalized reaching-law-based discrete-time integral sliding-mode controller is designed to achieve high output tracking accuracy and avoid significant control efforts for both matched and mismatched disturbances. By synthesizing a disturbance-related integral term based on disturbance decomposition, the proposed sliding surface differs from existing integral sliding surfaces and is crucial for disturbance attenuation. The proposed reaching law introduces an adaptive exponential term into the control gains, which allows for the integration of conventional RL-based DISMC and EC-based DISMC.