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 G M . 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 ω n . Then, the designed controller moves this point into the phase crossover with the required gain margin G M . The couple ( ω n ; G M ) is specified with respect to closed-loop performance requirements in terms of η max (maximum overshoot) and t s (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.