A hybrid robust model reference adaptive controller and proportional integral controller without reference model for partially modeled systems

• Published in: International journal of adaptive control and signal processing 2023-08, Vol.37 (8), p.2113-2132
• Main Authors: Evald, Paulo Jefferson Dias de Oliveira, Hollweg, Guilherme Vieira, Tambara, Rodrigo Varella, Gründling, Hilton Abílio
• Format: Article
• Language: English
• Subjects: Adaptive control; adaptive PI controller; Algorithms; auto‐tuning controller; Control systems design; Controllers; Lyapunov stability analysis; Model reference adaptive control; Perturbation; Proportional integral; Reference signals; Robust control; robustness analysis; Stability analysis
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3628

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.