Modelling and robust Model Predictive Control of an unstable thermoacoustic system with constraints

This paper investigates the modelling of a thermoacoustically unstable Rijke tube and the robust Model Predictive Control of a derived polytopic linear model with constraints. For guaranteed stability a linear state feedback controller is designed using linear matrix inequalities and used within a feedback formulation of a Model Predictive Controller. It is shown in simulation that the robust Model Predictive Controller ensures robust stability of the polytopic linear model under constraints.