The Sine Wave Tuning method: Robust PID controller design in the frequency domain

The paper presents a novel robust PID controller design method for nominal performance specified in terms of maximum overshoot and settling time. The PID controller design provides guaranteed gain margin GM. The parameter of the tuning rules is a suitably chosen point of the plant frequency response obtained by a sine-wave signal with excitation frequency ωn. Then, the designed controller moves this point into the phase crossover with the required gain margin GM. The couple (ωn;GM) is specified with respect to closed-loop performance requirements in terms of ηmax (maximum overshoot) and ts (settling time) according to developed parabolic dependences. The new approach has been verified on a vast batch of benchmark examples; subsequently, the developed algorithm has been extended to robust PID controller design for plants with unstable zero and unstructured uncertainties.