Синтез P и PI-регуляторов для нелинейных систем с использованием окружностей Холла и диаграмм Никольса

Промышленные АСУ и контроллеры. 2015. № 6. С. 41–47.

Kapalin V. I., Ведяшкина Наталья Евгеньевна

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 order regulators and Nichols diagram for fi rst order 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: робастное управление, система MATLAB, MATLAB, P and PI-regulators, minimax approximation, Hall circles, Nichols diagrams, robust control, P и PI-регуляторы, минимаксные аппроксимации, круги Холла и диаграммы Никольса