Sliding Mode Control With Perturbation Estimation (SMCPE) and Frequency Shaped Sliding Surfaces

Abstract

Sliding Mode Control with Perturbation Estimation (SMCPE) is a recent control routine which steers uncertain dynamic systems with disturbances to follow a desired trajectory. It eliminates the conventional requirement for the knowledge of uncertainty upper bound. A perturbation estimation scheme provides a tool for robustness. This text offers an additional robustizing mechanism: selection of time-varying sliding functions utilizing frequency shaping techniques. Frequency shaping together with sliding mode control introduces a behavior for selectively penalizing tracking errors at certain frequency ranges. This combination provides two advantages concurrently: (a) It filters out certain frequency components of the perturbations therefore eliminating the possible excitation on the unmodelled dynamics, and (b) it drives the state to the desired trajectory despite perturbations. The crucial point is that a priori knowledge of the perturbation upper bound is not necessary to eliminate the perturbation effects at the designated frequencies. Numerical examples prove the effectiveness of this novel scheme.