Simple method of calculating set point weighting parameter for unstable systems with a zero

Abstract

A simple method is proposed for the calculation of the set point weighting parameter in PI/PID controllers for unstable systems with a zero. Unstable second order systems with a positive or negative zero are considered. The method consists of equating the coefficients of s both in numerator and in denominator of the closed loop transfer function model for a servo problem. This method gives a simple equation for the set point weighting parameter ( β). Simulation results are given for the improved performance for the systems with a positive or a negative zero with one stable and one unstable pole. The performance of the set point weighted controller using the value of β by the simple method is compared with that obtained by minimizing the ISE value by a numerical optimization method.