Adaptive Fuzzy Control of State-Feedback Time-Delay Systems With Uncertain Parameters

Abstract This paper describes an effective and relatively simple design method for an adaptive multi-input single-output (MISO) fuThis work is financed by the Polish MinistInitiative of Excellence” program from 2019 – 2022. Project number 027/RID/2018/19, funding amount 11 999 900 PLN.zzy controller for a linear plant with partially known parameters including transport delay. The model reference adaptive control idea was applied, incorporating a reference model that defines the desired closed-loop performance. The reference model containing the fuzzy controller and the plant provides control system performances that are not inferior to those attainable with linear state feedback. The frequency-domain stability conditions for nonlinear state feedback are formulated. They are crucial for the proposed approach and guarantee stability and convergence of the adaptation process. Unlike in other works, the number of MISO fuzzy controller inputs has no restrictions. In this way, the design procedure generalizes the results reported thus far. The idea of automatic fuzzy controller tuning to obtain quasi-optimal system behavior is proposed. The adaptive fuzzy controller design procedure is exemplified for third- and fourth-order systems with delayed feedback.