Optimization of PID control parameters using the pole-placement approach

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.This paper presents an analytical method of determining optimum PID parameters using the pole placement approach followed by the closed-loop analysis of Pebble-Bed Modular Reactor (PBMR) reactor temperature control employing thermo-fluid simulation software. The proposed method is a reliable alternative to the Ziegler Nichols, Cohen-and-Coon and other approaches that normally suggest initial controller parameters that would require further optimization. The pole placement approach forces the positions of the poles of the closed-loop characteristic equation to the stable region in the z-domain. In this approach the plant model is represented by an Auto-Regressive Moving Average (ARMA) black box model and the parameters of the model are determined by employing the Batch Least Squares approach. The pole-placement method reduces the determination of PID parameters to the setting of only a single parameter referred to as the tailoring coefficient of a first order tailoring polynomial. The controller settings can be selected with the value of the tailoring coefficient migrating from zero towards the unit circle at -1 in the z-domain. This progression results in closed loop responses that range from underdamped ( t1 = 0 ) to overdamped as 1 t approaches -1. Although the mathematics behind the approach is quite involved, in this work the methodology has been transformed into a user-friendly MATLAB© based calculation. The above method is applied to the control of pebble-bed modular nuclear reactor (PBMR) temperature by manipulating the reactor activity. The closed loop transients are generated from a Flownex© thermal-hydraulics modelling/simulation environment.