The Performance Of Adaptive Feedforward And Optimal Feedback Active Control Systems

Abstract

L Active control systems are often implemented as feedforward controllers, using a reference signal correlated ‘with the disturbance which is to be controlled. In many cases the disturbance is periodic. If the field to be controlled were perfectly stationary, a fixed, timeinvariant, feedforward controller could be implemented, which could be designed beforehand to give optimal reductions. In most practical situations, however, the primary disturbance is changing either in magnitude, phase, or frequency and the controller has to be made adaptive in order to track these changes. Such adaptive controllers have transient convergence propemes which, in general, it is difficult to analyse. This is because of the interaction between the dynamic behaviour of the controller and the dynamic behaviour of the physical system under control. The block diagram of a single channel adaptive feedforward controller is shown in Figure 1. Typically, the controller is implemented as an FIR digital filter and the algorithm used to adjust the filter coefficients is the fdtered-x LMS algorithm widrow and Steams, 19851, for which there is a multichannel generation known as the Multiple Error LMS algorithm Flliott et al., 19871. If it is assumed that the controller is adapting slowly compared with the delays and time coristants of the system under control, fairly conventimal methods can be used to analyse this algorithm, which are similar to those used in the analysis of the electrical LMS algorithm PVidrow and Stems, 19851. It has been observed, however, that in practice the filtered-x LMS irlgorithm is able to adapt much faster than this.