An optimisation-based design method for analogue feedback controllers for active noise control

Feedback control is used in active noise control (ANC) systems in which a suitable reference signal is not available or cannot be economically obtained [1], [2], [3]. For feedback control, optimal design techniques such as LQG (linear quadratic Gaussian) and H2/H∞ have been developed. LQG control has been very successful in solving problems, in which simple statespace models can accurately represent the dynamics of the system under control. In many practical applications, accurate plant models are not available, however. In H2/H∞ optimal feedback control, the mean-square value of the error signal, an H2 norm, is minimised while robust stability, an H∞ constraint, is maintained. Using H2/H∞ control, stability of a closed-loop system is guaranteed under changing operation conditions. [2] Both LQG and H2/H∞ control require a priori information such as a plant model or knowledge about the plant uncertainty. Therefore, design of a feedback controller based on these methods is typically a complex task. In [4], a method for designing a control filter using a constrained optimisation algorithm is presented. The control filter is expressed in a general polynomial form and the algorithm is not limited to any category of filters. The resulting control filter is essentially a phase-lag compensator [5].