Adaptive control of combustion instabilities for combustion systems with right-half plane zeros

Adaptive control offers an efficient means of stabilising combustion instabilities across a range of operating conditions. Self-tuning regulators (STRs) are Lyapunov-based adaptive controllers which are attractive as they do not require detailed prior system characterisation nor on-line system identification. For STRs to be guaranteed to work, the open loop system must not contain any right-half plane (RHP) zeros. This paper shows that many practical combustion systems are likely to contain RHP zeros, caused by wave reflections from boundaries or by the flame transfer function containing RHP zeros. A method of modifying the STR algorithm so that it is able to stabilise systems with RHP zeros is developed. It models the effect of the RHP zeros as a time delay, and utilises a previous STR modification developed for time delays. The method successfully stabilises an experimental Rijke tube with artificially added RHP zeros; its main drawback is that it requires knowledge of the RHP zero locations. When the RHP zeros are caused by reflections from boundaries, this drawback can be overcome. An alternative sensor signal is formed from two pressure readings in such a way as to reduce the relative magnitude of the upstream travelling acoustic wave. This has the effect of shifting any RHP zeros into the LHP. This approach was successfully demonstrated on a numerical model of an unstable combustion system.