A graphical approach to design PI controller for integrator plus dead-time processes

The proportional-integral (PI) and proportional integral-derivative (PID) controllers are widely used in lots of industrial control systems for many years since Ziegler and Nichols proposed their first PID tuning scheme. This is because the PI/PID controller structure is simple and its principle is easier to understand than most other advanced controllers. The aim and the contribution of this paper is to develop a novel graphical method to design the PI controller for industrial processes which are modeled by an integrator plus dead time (IPDT) transfer function. For this purpose, a set of loci is developed and plotted in the controller parameters plane, which one of the quantities consists of gain and phase margins, gain and phase crossover frequencies and Smith's vector margin is constant on each locus. Next, the desired closed loop system characteristics are stated in the form of two loci. By sketching these two loci and obtaining their intersection point the controllers parameters are determined. Finally some examples are given to demonstrate the effectiveness of the proposed method.