Perspectives on linear compensator designs for active combustion control

Abstract

Some of the earliest research in active combustion control (ACC) showed that the use of simple phase-shifter circuits feeding back acoustic pressure to voice-coil actuators was sufficient to achieve some reduction of the acoustic pressure caused by thermoacoustic instabilities in atmospheric combustors. Since that time, many researchers have continued to use phase-shifter controllers to suppress pressure fluctuations for a variety of combustion testbeds. In addition, other researchers have proposed the use of somewhat more’ sophisticated linear controllers and demonstrated their capabilities in reducing peak pressures. All of the ACC results motivate a series of interesting questions from a linear systems theory perspective: Why does a simple phase inverter controller generally ‘work’ for this problem? What is the effective Gequency response function for the phase-shifter compensator and how does it impact the controlled response? Can critical performance characteristics of the controlled system (magnitude of suppression and occurrence of controller-induced instabilities) be predicted a priori? Are there common features between the simple phase shift controller and other linear controllers that have been successful? Are there ‘untried’ linear controller designs that are motivated by these analyses and existing results for suppression of instabilities in combustors? This paper focuses on a subset of these perspectives, relying on the use of relevant linear control theory concepts to provide some answers and illuminate the need for more extensive nonlinear analyses (the subject of future publications) for predicting certain information. Specifically, this paper Copyright 63 1999 by t+ American Institute of Aeronautics and Astronautics provides a detailed discussion of the phase-shifter control method that has been so popular for active combustion control. Analytical and experimeutal considerations demonstrate how to predict frequencies and approximate amplitudes of controller-induced instabilities (also referred to as ‘spillover’ or ‘secondary peaks’) when using acoustic control and a phase-shifter compensator. This investigation also illustrates the intluence of the phase-shifter controller on the degree of controllability achieved for acoustic control of thermoacoustic insrabilities in a simple tube combustor.