A novel composite fixed-time sliding mode control scheme for second-order systems with mismatched disturbances: application to Buck converter

In this paper, a composite fixed-time sliding mode controller is proposed to address the problems of finite-time escape and large initial error inherent in disturbance observer (DOB) based controllers. The proposed hybrid control strategy utilizes a fixed-time DOB and is designed to stabilize a class of second-order systems in the presence of both matched and mismatched disturbances, while ensuring fixed-time convergence. First, a fixed-time DOB is developed to estimate both types of disturbances. Second, a robust sliding mode variable with variable exponent coefficient and a former finite-time sliding mode controller are proposed to guarantee state convergence without using DOB estimation, thereby preventing the state from diverging due to the unknown large initial error caused by DOB and ensuring convergence prior to switching. Third, a latter robust fixed-time DOB-based controller is designed after exact estimation of disturbances is achieved and an estimation of the overall convergence time is provided. Furthermore, strict Lyapunov analysis is employed to prove that the disturbed system under the fixed-time DOB and composite sliding mode controller is fixed-time stable. Simulation results for a standard planar uncertain system and Buck converter with mismatched disturbance demonstrate the effectiveness of the proposed controller.