On Tuning PI Controllers for Integrating Plus Time Delay Systems

Some analytical results concerning PI controller tuning based on integrator plus time delay models are worked out and presented. A method for obtaining PI controller parameters, Kp=alpha/(k*tau), and, Ti=beta*tau, which ensures a given prescribed maximum time delay error, dtau_max, to time delay, tau, ratio parameter delta=d au_max/tau, is presented. The corner stone in this method, is a method product parameter, c=alpha*beta. Analytical relations between the PI controller parameters, Ti, and, Kp, and the time delay error parameter, delta, is presented, and we propose the setting, beta=c/a*(delta+1), and, alpha=a/(delta+1), which gives, Ti=c/a*(delta+1)*tau, and Kp=a/((delta+1)*k*tau), where the parameter, a, is constant in the method product parameter, c=alpha*beta. It also turns out that the integral time, Ti, is linear in, delta, and the proportional gain, Kp, inversely proportional to, delta+1. For the original Ziegler Nichols (ZN) method this parameter is approximately, c=2.38, and the presented method may e.g., be used to obtain new modified ZN parameters with increased robustness margins, also documented in the paper.