The influence of nonlinear dynamics on linear controller design for instability suppression in a premixed tube combustor

Self-excited oscillations in combustion systems occur as a result of linear instabilities that originate whenever the fluctuating heat release and the acoustic pressure satisfy the Rayleigh criterion. The limit cycle amplitude is determined by specific nonlinearities in the system. As a rule, nonlinear systems that can support limit cycles exhibit a coupling phenomenon when excited at subharmonic and superharmonic frequencies. It is of interest to examine the effects of such nonlinearities on active control strategies that attempt to alleviate the self-excited oscillations. A simple premixed tube combustor arrangement has been constructed to serve as a testbed for controller design studies. This paper discusses how linear controllers affect the observed tube response. The closed-loop performance of a nonlinear control law is also contrasted with the linear controller's influence on the coupled system's harmonic response.