Model Reduction for PID Design

Abstract Generally, Internal Model Control (IMC) results in a controller of the same order as the model; that is, a second order model will yield a PID controller and a first order model yields a PI controller. Therefore, within the IMC paradigm, PID control of higher than second order plants is associated with a model reduction problem. Solutions to this problem have previously been formulated as criterion optimisation. In this paper we outline a computationally very convenient alternative, in which the model is calculated as the average of the model obtained by retaining the slowest pole(s) and the one obtained by retaining the low order coefficients. Advantages of this technique include simplicity, preservation of physical parameters and a closed loop performance that is comparable to, or better than existing methods in most cases.