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.
The robust self-tuning regulator of a class of linear systems, which can be described by the input-output Auto-Regressive Moving Average with exogenous (ARMAX) mathematical model with unknown and time-varying parameters, at bounded external disturbances is developed. A scheme of polynomial approximation has been applied to approximate the unknown and time-varying parameters of systems. The modified recursive extended least squares RELS estimation algorithm with a relative dead zone is proposed and applied to estimate the unknown and time-varying parameters intervening in the ARMAX mathematical model. The formulation of the explicit schemes of self-tuning regulation problem is resolved by using the minimum variance output or the generalized minimum variance output. The obtained control law, which is an optimal solution of minimizing a correspondent criterion, permit to reduce the effect of noise upon the output of system. An example of numerical simulation illustrates the effectiveness of the explicit schemes of self-tuning regulator and presents the performances by using the modified recursive extended least squares estimation algorithm with a relative dead zone in a step of the parametric estimation of a linear time-varying systems.
General termsModified recursive extended least squares estimation algorithm RELS with a relative dead zone, explicit schemes of minimum variance self-tuning regulator, explicit schemes of generalized minimum variance self-tuning regulator.
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