Design of continuous-time model reference adaptive and super-twisting sliding mode controller

Abstract

This paper presents a continuous-time Robust Model Reference Adaptive and Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The controller law is composed by two control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main benefit of this novel control algorithm is to present, simultaneously, high robustness and fast dynamic response, which are conflicting with each other in conventional adaptive algorithms. Furthermore, as the STSM Controller is also adaptive, the dynamic response has relevant chattering mitigation without additional efforts on controller design, implementation, or execution. Besides, the union of the STSM with RMRAC also improved sliding accuracy in steady state. Thereby, in steady state, the STSM control contribution is almost zero, which avoids the chattering phenomenon, once it acts only in the transient regimes. The stability and robustness analysis of the control structure are presented, in continuous-time, considering the overall plant, that is, in presence of matched and unmatched dynamics. The continuous-time stability analysis is important in an adaptive system, since it features an intermediary step for control system stability analysis in discrete-time and its application in real plants. In addition, to present the feasibility and benefits of the proposed controller, simulations results of two case studies are presented: one is the controller application in an unstable non-minimum phase plant, and the second is its application for current regulation of a single-phase grid-tied power converter with an LCL filter. Moreover, to corroborate the robustness and tracking performance of the proposed controller a comparison with an adaptive first order Sliding Mode is also presented.