Modified Ziegler-Nichols method for fractional PI controllers

The Ziegler-Nichols tuning rules have been very influential and have been used extensively in process industry. This paper presents an extension of the modified Ziegler-Nichols tuning rules for fractional PI controllers. The design method consists on minimizing a frequency objective function subject to a constraint on the maximum sensitivity function M_S. In this paper it is also demonstrated that substantially better performance can be obtained using PI^λ instead of PI controllers. An interpretation of these tuning rules as methods where one point of the Nyquist curve is positioned in a desired point is also given. These tuning rules are compared with other tuning rules and shown to give good results, especially when simplicity, performance and robustness are emphasized.