An event-based adaptation of the relay feedback experiment for frequency response identification of stable processes

Abstract

An event-based modification of the classical relay feedback experiment without the inclusion of additional elements (integrator, time delay, …) for identification of the spectrum of stable processes between zero and the phase cross-over frequency is presented. By inserting an event-based sampler in the control loop, the natural behaviour of a classical relay is simulated and the system is forced to work in two modes. The event-based sampler activates the first mode by sending control actions to the process every time the error signal crosses zero; this mode is to discover the approximated value of the cross-over frequency ω180∘. During the second mode, the event-based sampler sends samples to the process simulating that the error signal crosses zero at ω180∘/N where N is the number of points to identify in the range 0≤ω≤ω180∘. One advantage of this procedure is that the logic used in an already existing relay feedback experiment to fit a transfer function model or tune a controller could be maintained just replacing the relay block by the event-based sampler block presented in the paper. Simulations and experiments with different processes and in presence of noise demonstrate the effectivity of the procedure.