Determining the settings of PI and PID controllers with a convergent method using computer aided design

The paper presents a new method applicable in determining the settings of PI and PID controllers for models of controlled systems given by the following transfer functions [wzór] and [wzór]. Using the capabilities of computer operations with symbolic variables, the closed system transfer function is expanded into a chain-type fraction, type V (Bultheel, 1978; Khovanskii, 1956; Halawa and Trzmielak-Stanislawska, 1986; Wall, 1973) and the second order convergent method is used as a simplified model. Denominator of this convergent M(s), is the following polynomial [wzór] with coefficients being the functions of controlled system parameters and unknown controller settings. Diagrams of step responses for systems given by second-order transfer functions are well known. Assuming the values of [wzór] and [wzór], we get a set of non-linear equations used to determine controller settings. The set of equations has been determined and resolved by means of Mathematica language which allows calculations with symbolic variables.