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 = k , and, Ti = , which ensures a given prescribed maximum time delay error, d max, to time delay, , ratio parameter = d max , is presented. The corner stone in this method, is a method product parameter, c = . Analytical relations between the PI controller parameters, Ti, and, Kp, and the time delay error parameter, , is presented, and we propose the setting, = c a ( + 1), and, = a +1, which gives, Ti = c a ( + 1) , and, Kp = a ( +1)k , where the parameter, a, is constant in the method product parameter, c = . It also turns out that the integral time, Ti, is linear in, , and the proportional gain, Kp, inversely proportional to, + 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