Minimum variance and LQG control for active noise cancellation - a comparison

Some active noise cancellation (ANC) researchers have proposed generalized minimum variance control as a viable scheme for active noise cancellation. Other early minimum variance researchers have proposed a variant of minimum variance for non-minimum-phase systems which guarantees closed-loop stability. This paper demonstrates that closed-loop stability is an insufficient condition for stable minimum-variance control. Using a well-known, experimentally-verified model of an acoustic duct, it is demonstrated that feedback signals can become unbounded with the minimum variance approach even if the closed-loop stability condition is satisfied by the modified minimum variance control for non-minimum-phase systems. Usage of the generalized minimum variance control version leads to an essentially open-loop control system due to the large Q needed to stabilize the system. Usage of the control-weighted minimum variance control strategy for non-minimum-phase systems, while theoretically feasible, is non-trivial to implement in real-time. This motivates the use of LQG control. We present the use of polynomial LQG feedback control with a disturbance feedforward structure.