A Hybrid Robust Adaptive Sliding Mode Controller for partially modelled systems: Discrete-time Lyapunov stability analysis and application

• Published in: Nonlinear analysis. Hybrid systems 2023-05, Vol.48, p.101333, Article 101333
• Main Authors: Milbradt, Deise Maria Cirolini, Evald, Paulo Jefferson Dias de Oliveira, Hollweg, Guilherme Vieira, Gründling, Hilton Abílio
• Format: Article
• Language: English
• Subjects: Robust Model Reference Adaptive Control; Sliding Mode Controller; Stability proofs
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2023.101333

This work presents a new discrete-time Hybrid Robust Adaptive Sliding Mode Controller, developed from the union of a Robust Model Reference Adaptive Controller, an Adaptive Sliding Mode Controller, and an Adaptive One Sample Ahead Preview Controller in an unique control structure. Robust Model Reference Adaptive Controller is an adequate direct adaptive control strategy to control partially known plants, but can present slow closed-loop response to ensure global stability. Therefore, an adaptive One Sample Ahead Preview controller is incorporated to accelerate transient regimes, once it tries to track reference signal in one sample. Furthermore, an adaptive Sliding Mode Controller is also merged in the controller structure to help controller performance in transient regime and it also improves relevantly the steady state response in a scenario of several unmodelled dynamics Stability analysis of this controller using Lyapunov criterion and its robustness proof are provided, considering the plant subjected to unmodelled dynamics, which provides controller design constraints. These proofs show the controller is globally stable, and the tracking error tends to a residual set in steady state, even in the presence of matched and unmatched dynamics. Numerical simulations of the Hybrid Robust Adaptive Sliding Mode Controller applied on an unstable nonminimum-phase plant are presented, where only part of the overall plant is take into consideration for controller design. Results corroborate the feasibility and robustness of the developed control strategy and the performance superiority when compared to an adaptive One Sample Ahead Preview controller, with a 75% tracking error reduction in a scenario of several unmodelled dynamics.