Sliding Mode Control for Stabilization and Disturbance Rejection of Uncertain Systems with Output Delays via Predictor and Super-Twisting Observer

Abstract

This paper provides a new stabilization control method for linear time-invariant systems subject to known time-varying measurement delays and matched unknown nonlinear disturbances that may represent actuator faults. Part of the state vector is assumed to be unmeasured in current time. Hence, the proposed method utilizes an open-loop predictor associated with a state observer based on the Super-Twisting Algorithm in order to compensate the delays and estimate the unmeasured state variables. In particular, this nonlinear observer-based structure allows for the reconstruction of the non-modeled fault signals which, unlike the existing literature, are not supposed to be generated by a known exogenous dynamic system, being also robust to parametric uncertainties, whereas the predictor advances in time the delayed output signal. Then, a sliding mode control law is developed to achieve an ideal sliding mode and guarantee global stabilization even in the presence of a more general class of perturbations, non-modeled disturbances, parametric uncertainties and delays due to the inclusion of the Super-Twisting observer. Numerical simulations illustrate the efficiency of the proposed approach.