On the Ishlinsky rule and the control of electromechanical high order systems

Abstract

Introduction. The article considers the problem associated with oscillations in electromechanical systems.  Attention is drawn to the complication of their mathematical models used to describe oscillatory processes in systems, which are usually differential equations (ordinary or in partial derivatives), as a rule, of high orders. The well-known methods of simplification and use of mathematical models have been mentioned.

Methods and results. The statement is formulated as follows: control of a high-order system state as a second-order system can in some cases provide an acceptable quality of control of a high-order system. It is concluded that it is possible to improve the state of complex systems by synthesizing their control systems based on simple motion models.  The problem of optimal control of a second-order plant has been considered in order to determine the simplified structure of the control system. The possibility of using the structure of the second-order object control system has been determined for real systems of a higher order (induction motors). The article analyzes the results of introducing the control of electric drives with induction motors of various capacities with mathematical models up to the 29th order.

Conclusion. It is noted that the control of a high-order system as a second-order system can in some cases provide an acceptable quality of control of a high-order system.