共振を含む周波数応答計測のための定常発振制御系の安定性解析

抄録

In order to give a theoretical guarantee for frequency response measurement in self-oscillated amplitude estimation problem for thermoacoustic systems, this paper deals with a stability analysis problem of steady-state oscillation control system which automatically maintains the amplitude of plant output at a reference value for frequency response measurement with a resonance in the test frequency range. First, based on a simple second-order oscillation model, it is shown that the stability region on the PI(proportional and integral)-gains plane strongly depends on the excitation frequency in numerical simulation, and almost the same stability region is obtained by numerical analysis of the linear approximation problem of the closed-loop system. Then, the same problem is further analyzed in theoretical way which shows as a result that the stability region on the PI-gains plane is given by a frequency-dependent hyperbolic boundary, and there exists a common PI-gains region for the whole test frequency range to be considered. A setting method of PI-gains is also given.