“…A simple phase-shifting controller with an appropriately chosen phase-shift was typically sufficient for suppression of oscillations, given enough control authority, but the control phase and gain had to be adjusted manually, at every operating condition. The difficulty in determining the optimal phase shift that minimizes pressure oscillations, either by analysis or by experiment, especially in large industrial-scale combustors that operate over a wide range of conditions, has led researchers to call for the use of adaptive schemes (Seume et al, 1997). A direct adaptive scheme (based on extremum-seeking) applicable to control of thermoacoustic modes with large separation in frequencies (and hence essentially decoupled) was recently demonstrated in a 4 MW industrial rig in Banaszuk, Ariyur, Krstic, and Jacobson (2004).…”