Novel use of relays in identifying frequency response points

Relays with hysteresis are used to determine points on the frequency response curve of a plant with a specified gain or phase. On-line algorithms are developed to adjust the parameters of a relay in such a way that the limit cycling conditions correspond to the operating point of interest. When the objective is to find the point with a specified gain, the amplitude of the relay is tuned iteratively. When the objective is to find the point with a specified phase, then the width of the hysteresis is tuned. The plant and its gain cross-over frequency are assumed unknown. The only assumption is that stable limit cycling conditions exist for the plant under relay feedback control. Simulation results show that our algorithms can give accurate identification of the frequency response points. We show further how these tunings can lead to on-line tuning of phase lead and phase lag compensators