Cluster-based control of quasiperiodic thermoacoustic oscillations*

We demonstrate the application of cluster-based control to suppress two-frequency quasiperiodic oscillations in a prototypical thermoacoustic oscillator. This approach involves discretizing sensor measurements of pressure and heat-release-rate fluctuations into multiple clusters within a low-dimensional feature space. To determine the optimal closed-loop control laws, we use a Nelder-Mead simplex search on a cost function that balances the thermoacoustic amplitude (state cost) against the actuator power consumption (input cost). Our results show that this data-driven control strategy can effectively suppress various two-frequency quasiperiodic oscillations while minimizing actuator power usage. This study underscores the potential of cluster-based control in enhancing the stability of aperiodic thermoacoustic systems, paving the way for applications in energy conversion and combustion devices.