A hybrid robust model reference adaptive controller and proportional integral controller without reference model for partially modeled systems
Paulo Jefferson Dias de Oliveira Evald, Guilherme Vieira Hollweg, Rodrigo Varella Tambara, H.A. Gründling
Abstract
Summary This work presents the discrete‐time stability analysis of a hybrid robust model reference adaptive controller and proportional‐integral controller (MRAC‐PI) controller using Lyapunov criterion. The control structure merges the classical PI controller with a robust model reference adaptive control, resulting in an adaptive and robust control strategy, where the gains unite both control techniques in a unique structure and it does not require the design of a reference model, being able to track straightforwardly the reference signal. The adaptive gains are updated continuously by a modified gradient algorithm regarding control action, regulation error, and the system output. The stability analysis provides the controller design constraints, while also demonstrate the tendency of regulation error to a residual set, and proves the boundedness of all closed‐loop signals. Furthermore, as the controller is robust to unmodeled dynamics, it is feasible to control partially modeled systems. Simulation results in a real‐world engineering application are presented to corroborate the robustness of this controller and show its fast response in the face of critical exogenous system perturbations.