Sufficient conditions for the stability of a locally admissible dynamic system with constraints on phase coordinates and controls
Keywords:
sufficient conditions for stability, dynamical systems, projection operators, optimization, stabilization of program motions, locally admissible controls, restrictions on phase coordinates and controls, synchronous generator, mathematical model, SimInTechAbstract
Introduction: The synthesis of systems for the stabilization of program motions of objects is an urgent task of control theory. Projection operator methods of mathematical programming are adequate methods of control synthesis for this class of problems. Purpose: To develop the methods for synthesizing locally admissible controls for stabilizing programmed motions of linear and nonlinear dynamic objects with restrictions. Results: The linear stationary control object is specified in the form of a difference operator controlled according to Kalman criterion. For the specified control object, transformations of the projection operator for solving problems of stabilization of program movements with restrictions have been carried out and equations for the transition and stationary states of the system under study have been synthesized. The compression condition is obtained from an estimate of the norm of deviation of the phase coordinates of the system from the stationary state. Based on the principle of compressive mappings, a sufficient condition for the stability of a projection-operator dynamic system with restrictions on phase coordinates and controls is obtained. The derivation of a sufficient stability condition made it possible to determine the projection operator feedback parameter and ensure the stability of the projection operator of the dynamic system obtained earlier. As a control object, a vector-matrix model of a synchronous generator in the Cauchy form was used for the computational experiment. A computational experiment confirmed the theoretical generalizations obtained in the study. Practical relevance: The fulfillment of the inequality condition to determine the feedback parameter guarantees the stability of the projection operator dynamic system.