"Combustion is essential to the world’s energy generation and transport needs, and will remain so for the foreseeable future. Mitigating its impact on the climate and human health, by reducing its associated emissions, is thus a priority. One significant challenge for gas-turbine combustion is combustion instability, which is currently inhibiting reductions in NOx emissions (these damage human health via a deterioration in air quality). Combustion instability is caused by a two-way coupling between unsteady combustion and acoustic waves - the large pressure oscillations that result can cause substantial mechanical damage. Currently, the lack of fast, accurate modelling tools for combustion instability, and the lack of reliable ways of suppressing it are severely hindering reductions in NOx emissions.This proposal aims to make step improvements in both fast, accurate modelling of combustion instability, and in developing reliable active control strategies for its suppression. It will achieve this by coupling low order combustor models (these are fast, simplified models for simulating combustion instability) with advances in analytical modelling, CFD simulation, reduced order modelling and control theory tools. In particular:* important advances in accurately incorporating the effect of entropy waves (temperature variations resulting from unsteady combustion) and non-linear flame models will be made;* new active control strategies for achieving reliable suppression of combustion instability, including from within limit cycle oscillations, will be developed;* an open-source low order combustor modelling tool will be developed and widely disseminated, opening access to researchers worldwide and improving communications between the fields of thermoacoustics and control theory.Thus the proposal aims to use analytical and computational methods to contribute to achieving low NOx gas-turbine combustion, without the penalty of damaging combustion instability."