Optimisation of digitally adjustable analogue biquad filters in feedback active control

In active cancellation of sound radiation from structures, feedback control is applied if no suitable reference is available. In feedback active control, analogue filters are typically used due to their short latency time. The filters have traditionally been simple compensators with fixed coefficients. Such compensators can be implemented as second-order biquad filters. This paper concerns the use of biquad filters with digitally adjustable parameters as analogue feedback compensators. The biquad filters can be implemented using a Field Programmable Analogue Array (FPAA) circuit. The benefit of the FPAA implementation is that the parameters are set digitally, and the zeros and poles as well as the corresponding quality factors can be easily modified. An optimisation method based on random search is proposed for optimising the coefficients of the biquad blocks. The optimisation objective is to minimise the magnitude of the transfer function from the disturbance to the error while the maximum amplification of the error is a constraint. For the design of the compensator, only the complex frequency response of the plant is required. The performance of the optimiser is evaluated with an optimiser provided in MATLAB. Using both optimisers, an optimal compensator is designed for a test plant. In this paper, the random search optimiser is described and the optimisation results are shown.