Improvement of the Qualitative Characteristics of an Automatic Control System with a Fractional-Order PID-Controller

The methods of the theory of fractional-order calculus are used, which extends the possibilities of differentiation and integration to the operators of an arbitrary order during the synthesis of automatic control systems. The expediency of the use of Grunwald-Letnikov equation for the calculation of the fractional-order derivative and integral under the condition of limited signal sampling is demonstrated. It is proved that at certain correlations of the degrees of differential and integral regulation components of the controller the qualitative indices of automatic control systems are better than for conventional integer controller. It justifies the use of the proposed corrective devices. The control system qualitative characteristic regression dependences on the value of the fractional-order degrees of the integral and derivative components are shown. The performed experiment resulted in obtaining the values of the degrees that provide optimal characteristics of the system. The obtained results can be used in the design decisions during the synthesis of high-precision electric drive control systems.