Phase Margin of Frequency Response Measurement Control System Based on Steady-state Oscillation Control

Abstract

In order to obtain the nonlinear characteristic of an unknown control target, a method based on the steady-state oscillation control has been proposed in which the amplitude of the output signal is kept constant at a target value while frequency response measurements are performed, and this method has been used to estimate the pressure amplitude during self-oscillation of a thermoacoustic system. Stability analysis of the control system has also been reported revealing that the stability region of PI(proportional integral) compensator's gains, however, there has been insufficient comparison with conventional reference tracking control, which uses a sinusoidal reference signal for the output signal. In this paper, the two methods are quantitatively compared in the case of a second-order vibration system as the control target, and it is shown that the proposed method has the advantage of having a larger phase margin than the conventional method. Specifically, it is theoretically shown that (i) the conventional method does not allow phase inversion of the control target, but the proposed method does, and (ii) the conventional method allows only a dead time of at most half the period of the test frequency, but the proposed method allows an arbitrarily long dead time, which are further verified by numerical simulation.