Method and apparatus for tuning a PID controller

A method of tuning a proportional-integral-derivative controller, further referred to as a PID controller, having a transfer function

• W
• c
• ⁡
• (
• s
• )
• =
• K
• c
• (
• 1
• +
• 1
• T
• ic
• ⁢
• s
• +
• T
• dc
• ⁢
• s
• )
• ,
• where s is a Laplace variable and Kc, Tic, and Tdc are tuning parameters, for a process in a feedback control system comprising the steps of:
• (a) selection of a desired gain margin γm of the system for tuning for a gain margin specification or desired phase margin φm, of the system for tuning for a phase margin specification;
• (b) determining the values of the parameters c1, c2, and c3 that define optimal tuning rules of the PID controller from the desired gain margin γm of the system for tuning for a gain margin specification or the desired phase margin φm of the system for tuning for a phase margin specification selected at the previous step;
• (c) bringing the control system into symmetric self-excited oscillations of a frequency at which a phase response of the process is equal to the desired value equal to ψ−180°, where −90°<ψ<90°;
• (d) measurement of a frequency of the oscillations Ω0, and an amplitude of the oscillations α0;
• (e) calculation of the tuning parameters of the PID controller in dependence on the measurements obtained at the previous step.