Constant energy control by time-varying gain for steady-state oscillation of thermoacoustic engines to estimate critical temperature ratio

In order to estimate the critical temperature ratio (CTR) of thermoacoustic engines, a steady-state oscillation control method is proposed. The amplitude of the oscillating pressure is regulated to a reference value by a proportional-integral (PI) controller and a low-pass filter without specifying oscillation frequency. The output signal of the PI controller is used as a time-varying gain in a phase-delay controller so that the plant energy is maintained at a constant that depends on the reference pressure amplitude. A linear relation between the steady-state gain and temperature ratio is empirically observed, which provides an alternative method for estimating the CTR. The closed-loop stability of the proposed control system is analyzed by assuming a second-order resonance model, from which a stability condition on the PI controller's gains and the cut-off frequency of the low-pass filter is derived. The validity of the derived stability condition is shown by experimental results and numerical simulations.