This paper presents a discrete-time Robust Adaptive Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The control law is composed by two different control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main advantage of the control structure is its robust performance and high adaptability in face of unmodelled dynamics, presenting a fast reference tracking without chattering, since it uses a second-order Sliding Mode action into adaptive control structure. The stability and robustness analysis of the control structure are presented in discrete time, considering the overall plant, that is, in presence of matched and unmatched dynamics. In addition, the control structure performance is corroborated with simulation results, considering a non-minimum phase unstable plant. Moreover, the presented results are compared with an adaptive first-order SM control-based RMRAC, which can be clearly seen that proposed controller has better performance, mainly by means of chattering mitigation.

Grid-connected converters are uncertain time-varying systems, whose controllers must deal with the relevant inductive content and high harmonic distortion of the sampled voltages. Adaptive controllers are feasible control strategies for these applications, because their gains are continuously adjusted in response to system perturbations, and they are also robust to unmodeled dynamics and exogenous disturbances. However, adaptive controllers are not necessarily capable of rejecting all harmonic components on grids with high harmonic distortion. Therefore, this work presents a robust model reference adaptive control-based with an adaptive super-twisting sliding mode, which is improved with a harmonic compensation strategy in which additional control actions to deal with the harmonic contents of the $5{\text{th}}$ , $7{\text{th}}$ , $11{\text{th}}$ , and $13{\text{th}}$ of the fundamental component of the electrical grid are incorporated into the control structure. Experimental results are provided of a 7.5-kW converter connected to a distorted and unbalanced grid with an LCL filter, where the developed control structure presents a total harmonic distortion (THD) of 2%, while the controller without harmonic compensation obtains a 2.5% THD.