Синтез параметрически грубых систем управления с регуляторами и наблюдателями состояния на основе грамианных технологий

Abstract

Automatic control systems based on regulators with state observers are effective means to control linear and linearized objects of a high degree of complexity. One of the key problems in the synthesis of modal systems is the development of parametrically rough (robust) systems that retain their performance, as well as the main quality indicators with possible variations of the parameters of both the control object and the controller itself. The synthesis of a robust system with a state observer is carried out by the modal control method based on the matrix model of the controlled object. To ensure the parametric robustness of the system, the authors have proposed a technique which based on the mathematical apparatus of Gramians of controllability and observability as well as on the similarity transformation of observer matrices. Computer simulation of the system with state controller and observer is carried out by means of the MatLab software. The authors have proposed a method to form an observer state structure that is optimal in the sense of parametric roughness of the system, which is based on the procedure of transforming the similarity of the object model. And the transformation matrix is formed by varying the singular numbers of the controllability and observability gramians. The proposed method allows us to obtain an observer structure with a certain ratio of controllability and observability that ensures the fulfillment of the condition of parametric roughness i.e., the absence of positive feedback in the control device. The results obtained make it possible to clearly demonstrate the high efficiency of using the Gramian method for the synthesis of control systems with state observers with low sensitivity to variations of the controller own parameters.