Detrimental combustion instability is unwanted in gas turbines, aeroengines and rocket motors. It is typically generated due to the dynamic coupling between unsteady heat release and acoustic pressure. To prevent the onset of combustion instability or dampen large-amplitude oscillations, the coupling must somehow be interrupted. In this work, we design and implement a sliding mode controller and observer to mitigate self-sustained combustion oscillations in an open-ended thermoacoustic system. An acoustically compact heat source is confined and modeled by using a modified form of King’s Law. Coupling the heat source model with a Galerkin series expansion of the acoustic pressure provides an approach to evaluate the performance of the sliding mode control. The thermoacoustic systems with different numbers of eigenmodes and actuators are considered. It is found that self-sustained limit cycle oscillations can be successfully produced from small perturbations in the thermoacoustic systems when the actuators are not actuated. Meanwhile, the system we modeled can be proved to be controllable and observable. In order to gain insight on the thermoacoustic mode selection and triggering, the acoustical energy exchange between neighboring eigenmodes are studied and discussed. As the controller-driven actuators are actuated, the limit cycle oscillations are quickly dampened. And both thermoacoustic systems are stabilized. The successful demonstration indicates that the sliding mode controller can be applied to stabilize unstable thermoacoustic systems, even with multiple eigenmodes.

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