Predefined-time sliding mode control based on exact time disturbance observer for second-order systems with matched and mismatched disturbances

This paper's primary motivation is to present a globally predefined-time sliding mode control (PtSMC) strategy to stabilize a class of second-order systems subjected to matched and mismatched disturbances. To achieve this, the paper proposes a new exact time disturbance observer (DOB) based on a terminal time regulator, which accurately estimates the disturbances within a prescribed time, effectively preventing the system state from escaping to infinity due to high gains and overestimation. In addition, a new predefined-time sliding mode variable with the estimation of DOB is developed to ensure a predefined-time convergence on the sliding mode phase against mismatched disturbances. The proposed DOB-based technique can alleviate the chattering resulting from the use of an overestimated gain, in contrast to the controller without employing a DOB. Furthermore, a predefined-time reaching law is introduced to guarantee a global predefined-time convergence. This paper establishes the stability of the disturbed second-order system under the proposed controller through strict Lyapunov analysis. The novelty of the proposed method lies in its global predefined-time convergence, chattering-reduced properties and robustness against matched and mismatched disturbances. Finally, numerical simulations and application examples validate the proposed methodology's effectiveness.