Process Identification Using Relay Feedback with a Fractional Order Integrator

In this work, a novel relay feedback experiment method is proposed for system identification by connecting a fractional order integrator in front of a basic relay component. With this approach, a linear time invariant process model can be estimated at an arbitrary phase angle in the third or fourth quadrant on the Nyquist curve. Another contribution of this paper is to present a pseudo frequency response concept to generalize the describing function method so as to make it compatible with the frequency response operations. The proposed setup is illustrated through mathematical derivation using the proposed concept. Simulations are provided to verify the effectiveness.