Synthesis of Controllers for the Servo Systems on the Basis of the Isomorphism Principle

Abstract

The aim of the research is to develop a practically implementable formalized method for synthesis of conrollers for the general form systems based on the common isomorphism principle formerly offered in the theory of the systems. The research results are rigorous substantiation of the new type controllers structure - isomorphic controllers - and the formalized procedure of their synthesis. It was demonstrated that a feedback in the form of isomorphic controller is necessary and sufficient for controllability of the system in contrast to the well-known methods, first postulated the necessity of a feedback and then offered application of the procedure for controller synthesis. The feasibility of presenting a model (transfer function) of an object as a combination of an isomorphic controller and a reference model was proved, which allowed to localize the ensuring of controllability in the controller, which represents a controlling mean, and the required quality of the transient processes - in the reference model realizing a control objective. Such a localiztion provides a possibility to obtain extremely high quality of the transient processes in the control loop. The use of a mathematical apparatus of the modern algebra based on morphisms has provided significantly high level of generality of the proven statements about the general form systems and linear systems controllability. The advantages of isomorphic controllers, reference models and the high gains method combination for the linear systems were shown. Such a combination ensures a high control quality as well as increase of the loop robustness in respect of the parametric disturbances and noise impact. Application examples of the isomorphic controller synthesis for the linear systems, which demonstrated their features, are provided. The advantages of the isomorphic controllers were substantiated and generalized.