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Industrial Automatic Control Systems and Controllers

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Design of P and PI-regulators for Nonlinear Systems by Means of Hall and Nichols Diagrams
V.I. Kapalin N.E. Vedyashkina

A simple technique for the design of P and PI-regulators for nonlinear control systems, which is based on the theory of minimax
approximations, is proposed. Unlike the widely known methods of harmonic and statistic linearization, the minimax linearization method
used in the present paper does not require special suppositions concerning the input signal of the nonlinear element. And unlike the
classical method of Taylor series it does not require the small intervals of approximation. The main idea of the proposed method consists
in substitution of the nonlinear element of the system by a family of its linear models obtained by minimax technique. For the design of
the feedback system after this substitution the simple methods of Hall circles for zero kind regulators and Nichols diagram for fi rst kind
regulators is used. This approach may prove out to be preferable for practice than robust control methods which usually give the high
order regulators. For the check of the robust properties as to the nonlinear element all the computations are performed for two kinds
of nonlinear elements – piecewise linear and polynomial. The simulation for the linear models is performed in toolbox Control System
Toolbox of MATLAB. The design of the nonlinear feedback systems is carried out in Simulink. The results of simulation for different levels
of input signals for the nonlinear element corroborated the robustness of the designed nonlinear feedback system concerning the uncertain
nonlinear elements. The simulation was performed for the case of satur ation nonlinear elements but the suggested approach applicable for
every continuous nonlinear elements in the system.
Keywords: P and PI-regulators; minimax approximation; Hall circles; Nichols diagrams; robust control; MATLAB.

Contacts: E-mail: kapalin.v.i@yandex.ru

Pp. 41-47.

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