Analytical tuning of PIλ controllers with phase margin and robustness

An analytical parameters tuning method of PI
^λ
controllers is discussed with exact phase margin and robustness against the gain variations of the controlled plants. According to the definitions of phase margin and the robustness to the gain changes of the controlled plant at gain cross over frequency, three nonlinear equations containing the three tuning parameters of PI
^λ
controller are obtained and an algorithm for analytically solving the nonlinear equations is proposed. The well-known Ziegler-Nichols tuning rule for classical PI Controller is used for the purpose of comparison. It is shown via simulation that the desired phase margin and robustness can be achieved by the proposed tuning rule of PI
^λ
controllers.