Abstract
An approach to the synthesis of automatic control circuits has been proposed, based on a fractional characteristic polynomial, which makes it possible to ensure the desired quality of a transition process under condition for implementing a certain structure of the fractional controller, which depends on the transfer function of a control object. The use of fractional desirable forms extends the range of possible settings of fractional-order controllers in the synthesis of circuits for electrical-mechanical systems, ensures better quality of transients compared to the full-order controllers, and thereby improves the efficiency of synthesized systems. Based on the obtained results of research, it becomes possible to recommend, in order to adjust the circuits for electromechanical systems, using the proposed fractional desirable forms that could meet the desired requirements to the systems of control over electromechanical systems. Construction of electromechanical systems on the principle of control with sequential correction has a significant advantage over other systems, owing to the simplicity of setting each contour, as well as a possibility to implement control coordinate constraints. A procedure for the structural-parametric synthesis of fractional-order controllers has been devised, on condition of their cascading switching in multi-circuit electromechanical systems; the synthesis algorithm of fractional-order controllers for appropriate control circuits has been given. We have synthesized an electromechanical system with cascade switching of controllers by applying the improved method of the generalized characteristic polynomial to choose the structure and parameters of fractional-order controllers and applying the desired form of fractional order. A two-circuit system of subordinate regulation has been considered as an example, in which a control object is the electric drive "thyristor transducer (converter) – engine (motor)". The influence of the synthesized fractional-order controllers on dynamic properties of the electromechanical system "thyristor transducer – engine" has been examined. Our study has shown a possibility to implement the cascading activated controllers for the electromechanical systems where the contours with the transfer full- and fractional-order functions are combined, as well as for systems with fractional-order contours only
Highlights
As regards the electromechanical systems (EMS), one most often faces the structural-parametric methods of synthesis
We have modernized a method for the synthesis of a generalized characteristic polynomial for fractional-order EMS and constructed an algorithm for synthesizing fractional-order controllers for appropriate control circuits
The current and velocity controllers have been synthesized, characterized by a wide range of dynamic properties; it was found that an increase in the value of q entails increasing the magnitude of overshooting when executing the job signal and decreasing the static velocity error in a two-circuit EMS due to the effect of disturbance in the form of a static load momentum
Summary
As regards the electromechanical systems (EMS), one most often faces the structural-parametric methods of synthesis. Such systems implement the principle of consistent correction by the cascading switching of controllers for each regulation coordinate [1, 2] Each circuit within such a system is reduced to a second-order link, which is described by the following characteristic polynomial:. The relevance of research in this field is explained by the need to devise methods to synthesize SSR that are described by fractional-order transfer functions. Such systems emerge if a control object is described by a fractional order, or the desired standard form corresponds to the characteristic polynomial of fractional order [5, 6]
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