On the issue of mutually inverse correspondence between the parameters of a digital controller and the coefficients of its transfer function
Abstract
On the issue of mutually inverse correspondence between the parameters of a digital controller and the coefficients of its transfer function
Incoming article date: 10.04.2023The paper considers the types and classification of industrial PID controllers according to various types and groups. A group of linear controllers has been identified, which includes PID controllers, which are most widely used in various technical devices. Some well-known software systems that provide calculations for PID controllers are given. The transition from the mathematical notation of the trapezoidal expansion of the transfer function of the PID controller, used in the PID Tune option of the Matlab environment, to the equivalent transfer function, represented by the symbolic coefficients of the numerator and denominator polynomials, is shown. A theorem is proved that shows a one-to-one correspondence between the parameters P, I, D of the controller and the coefficients of the resulting transfer function. Flowcharts of algorithms for calculating transfer function coefficients (TF) from known values of controller parameters and calculating transfer function coefficients from known values of controller parameters are given. An illustrative example is considered.
Keywords: PID controller, transfer function, block diagram of the algorithm, Matlab environment