Method of synthesis of locally permissible limited controls for stabilization of program motions of dynamic objects
Keywords:
dynamical systems, projection operators, optimization, stabilization of program motions, nonlinear difference operator, 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: development of methods for the synthesis of locally admissible controls for the stabilization of program motions of nonlinear dynamic objects under restrictions on the phase coordinates and controls. Results: A projection control operator for stabilization systems of program motions or equilibrium positions is proposed, using the boundary values of a pair of Lagrange multipliers to limit the type of inequality, a countable number of finite-dimensional mathematical programming problems. For nonlinear locally controlled difference operators, admissible controls are synthesized that stabilize program motions under restrictions on phase coordinates and controls. As a result, an operator of a dynamical system with projection-operator feedback is obtained for the problems of stabilization of program motions with restrictions on the vectors of phase coordinates and controls. As a dynamic object, for a computational experiment with a synthesized operator, a mathematical model of a synchronous generator was used, consisting of a system of bilinear differential equations with parameters corresponding to equations in the form of V.A. Venikova. The computational experiment confirmed the theoretical generalizations obtained in the work. Practical relevance: The developed methods generalize the formulations of control synthesis problems for stabilizing program motions or equilibrium positions of nonlinear control systems with restrictions on phase coordinates and controls. The development of the projection-operator method of finite-dimensional optimization is of great practical importance for the synthesis of controls for complex dynamic systems, including the control of the joint dynamics of electromechanical and electromagnetic processes in large energy associations such as the Unified Electric Power System of the Russian Federation.
