Synthesis and implementation of fractional-order controllers in a current curcuit of the motor with series excitation

Abstract

We have synthesized and investigated fractional-order regulators, which provide for a series of technological processes the best indicators for the quality of transient process, specifically DC motors with series excitation. Given the dependence of magnetic flux on the armature current and saturation of the magnetic system, a motor armature circuit turns into a system with significant nonlinear properties under static and dynamic modes. However, it can be described with high accuracy by the transfer function of fractional order. Owing to the appropriate fractional integral-differentiating regulators, it becomes possible to obtain the quality of transient processes that is better than when using classic methods.

We have considered standard methods to synthesize the coefficients of regulators and established that such settings result in deterioration of transients due to the saturation of regulators, caused by power supply voltage limitation. Therefore, it has been proposed, for a closed circuit with different structures of fractional regulators, to use a genetic algorithm for determining the optimal values of the coefficients of regulators based on the criterion for the shortest time of first harmonization and minimum overshoot.

Experimental study into different structures of regulators has been performed conducted for settings on the module optimum and a fractional order of astatism from 0.35 to 1.5. Based on the results obtained, it can be argued that the best indicators are demonstrated by regulators at astatism 1+μco, 1.5. The overshoot is then actually less than 2 %. It has been also shown that astatism 1+μco ensures high-quality of transient processes in the unsaturated zone of magnetic system as well. The research results could be used primarily in the systems of closed control in DC motors with series excitation, as well as with objects in which power laws are observed