A Sliding Mode Approach to Asymptotic Recovery of Nominal Performance for Uncertain Linear Systems

This article presents a new structure of a sliding mode disturbance observer (SM-DOB) for handling model uncertainty and unmodeled disturbances. The proposed SM-DOB is composed of two key components. First, a Levant’s differentiator is used to estimate the high-order time derivatives of the output. To satisfy the conditions required for the effective operation of Levant’s differentiator, we employ an integral SM technique so that on the sliding surface, the real plant’s dynamics are substituted with the nominal dynamics. With this structure, the proposed SM-DOB can achieve robust disturbance rejection and recover nominal performance in finite time. The stability and the finite time convergence of the proposed SM-DOB are rigorously proved by the Lyapunov stability method. Finally, to show the superiority and verify the validity of the proposed SM-DOB, we conduct both numerical simulations and laboratory experiments with brushless dc (BLDC) motor drives. It is observed that the proposed SM-DOB guarantees satisfactory performance in rejecting both input disturbance and plant uncertainty while remaining robust in the presence of noisy measurement.