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 = α kτ , and, Ti = βτ , which ensures a given prescribed maximum time delay error, dτmax, to time delay, τ , ratio parameter δ = dτmax τ , is presented. The corner stone in this method, is a method product parameter, c̄ = αβ. Analytical relations between the PI controller parameters, Ti, and, Kp, and the time delay error parameter, δ, is presented, and we propose the setting, β = c̄ a (δ + 1), and, α = a δ+1 , which gives, Ti = c̄ a (δ + 1)τ , and, Kp = a (δ+1)kτ , where the parameter, a, is constant in the method product parameter, c̄ = αβ. It also turns out that the integral time, Ti, is linear in, δ, and the proportional gain, Kp, inversely proportional to, δ + 1. For the original Ziegler Nichols (ZN) method this parameter is approximately, c̄ = 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.