TUNING THE CONTROLLER FOR OBJECT MODELS WITH ONE TO FOUR POLES USING THE POLINOMIAL METHOD

Abstract

The paper describes the procedure for tuning the controller for control object models with one to four poles using the polynomial method, by imposing the damping ratio and the settling time of the synthesized system. The numerator and denominator polynomials of the object's transfer function are decomposed into components containing zeros in the left and right halves of the complex plane. Based on the order of the object model and the conditions for solving the system of algebraic equations, the physical feasibility of the control algorithm, and the robustness of the system, the desired polynomial of the synthesized system is constructed. This polynomial consists of two sub-polynomials with unknown coefficients, and the degrees and unknown polynomials as well as the degree of the desired polynomial are calculated. From the damping ratio and settling time, the dominant poles of the synthesized system are determined. Based on these poles, the characteristic polynomial of the closed-loop system is constructed, and, if necessary, additional real poles are added as far away as possible from the dominant poles to meet the system's performance requirements. From the resulting equality, by equating the coefficients of the same powers of the variable s on the left and right sides of the equality, a system of algebraic equations is obtained, from which the unknown coefficients and polynomials are determined. Using the stable components of the object model and the unknown polynomials, the transfer function of the control algorithm is constructed. Examples of controller tuning for first-fourth order object models using the polynomial method have been analyzed. The synthesized systems have high performance and good robustness.