Active Control of thermoacoustic instabilities in continuous premixed combustion processes is being increasingly investigated for operating at lean low NOx conditions. Recently, we have developed a model-based approach for active control design which accounts for the underlying acoustics, heat release dynamics, and sensor and actuator dynamics. While this model captures a number of the dominant dynamic features of a premixed laminar combustor, there are a number of uncertainties associated with it as well. In this paper, we study the sensitivity of this model with respect to parametric uncertainties, and the efficacy of a fixed control design for suppressing pressure oscillations. We show that under certain conditions, the fixed controller is inadequate and present a self-tuning controller which is capable of delivering the desired performance in the presence of these uncertainties. The controller proposed is based on a rigorous analytical foundation, and is shown through simulation results to lead to better performance than corresponding fixed controllers. Adaptive algorithms based on the LMS-filter are shown to result in numerical instabilities.