Devising a combined method for setting PI/PID controller parameters for oil and gas facilities - Horbiichuk, Mykhailo; Vasylenchuk, Mykhailo; Yednak, Ihor; Lahoida, Andrii (Eastern-European Journal of Enterprise Technologies, 2025)
The object of this study is automatic control systems of the first, second, and third orders. The principal task was to ensure the stability of control systems while minimizing overshot and regulation time. A combined method for determining the tuning parameters of PI/PID controllers has been devised, which combines the s-plane method and the generalized quadratic criterion. The s-plane method is based on the Vieta theorem, which relates the roots of the characteristic equation of a closed-loop control system to its parameters. They are functions of the tuning parameters of PI/PID controllers. By choosing the left roots of the characteristic equation of a closed-loop system on the s-plane, the desired quality indicators of the control system can be achieved. The roots of the equation are functionally related to the parameters of PI/PID controllers. From the system of algebraic equations that follow from the Vieta theorem, the tuning parameters for PI/PID controllers are found as a solution to such a system. At the second stage of solving the problem, the roots of the characteristic equation are chosen so that the generalized quadratic criterion is a function only of real part of one of the characteristic equation’s roots. As a result, we obtain a one-dimensional minimization problem, the local minimum of which was sought within a predetermined search interval. This interval was chosen on the condition that the parameters for PI/PID controllers would be strictly positive. The roots of the characteristic equation of the closed-loop system would belong to the left half-plane of the s-plane. Such a choice of the search interval guarantees the stability of the closed-loop automatic control system. It was found that compared to the s-plane method, the overshot and regulation time were reduced by an average of 73.5 % and 66.5 %. This could increase the speed of industrial controllers