Multivariable PID Control Systems Design by Stable Partial Model Matching on Frequency Domain

Abstract

In this paper, a tuning method of multivariable PID controllers based on partial model matching on frequency domain is proposed. Different from the previous methods which were considered by authors, in this case, determination of multivariable PID controller parameters is defined as a nonlinear optimization problem with inequality constraints. In this procedure, the objective function is constructed so as to minimize the relative frequency model error between the loop transfer function of the control system and that of reference model system at finite frequency points. Inequality constraints are introduced so as to guarantee the stability criteria of multivariable control system given in Rosenbrock's stability theorem. The effectiveness of the method is illustrated through a simulation of 2-input 2-output system.