Abstract
This paper deals with the self-tuning control problem of linear systems described by autoregressive exogenous (ARX) mathematical models in the presence of unmodelled dynamics. An explicit scheme of control is described, which we use a recursive algorithm on the basis of the robustnessσ-modification approach to estimate the parameters of the system, to solve the problem of regulation tracking of the system. This approach was designed with the assumptions that the norm of the vector of the parameters is well-known. A new quadratic criterion is proposed to develop a modified recursive least squares (M-RLS) algorithm withσ-modification. The stability condition of the proposed estimation scheme is proved using the concepts of the small gain theorem. The effectiveness and reliability of the proposed M-RLS algorithm are shown by an illustrative simulation example. The effectiveness of the described explicit self-tuning control scheme is demonstrated by simulation results of the cruise control system for a vehicle.
Highlights
Adaptive control has been known since 1950 by Caldwell [1]
This paper deals with the self-tuning control problem of linear systems described by autoregressive exogenous (ARX) mathematical models in the presence of unmodelled dynamics
Different robust adaptive control of monovariable systems have been developed on the basis of the modified recursive least squares algorithm M-RLS with approach robustness dead zone [33,34,35,36]
Summary
Adaptive control has been known since 1950 by Caldwell [1]. Different types of adaptive controls were discussed and used to design adaptive laws of the proposed control schemes. Different robust adaptive control schemes have been developed and applied to the class of linear systems described by a mathematical model ARX in the presence of unmodelled dynamics [30,31,32]. The M-RLS algorithm was extended to a multivariable system, where the stability condition of estimation scheme has been shown and a robust self-tuning control has been developed [38]. This paper focuses on the regulation-tracking problem for the stochastic systems described by the ARX mathematical model, in the presence of unknown unmodelled dynamics in the parameters of the system This problem consists of developing a control law (called the corrector) allowing the output of the system to follow a time-varying reference signal while reducing the effects of disturbances acting at different locations of the system to be controlled.
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