Implications of noise on the reference signal in feedforward control of harmonic disturbances

The purpose of this Letter is to detail the effect of random (zero-mean) noise on the reference input of an adaptive feedforward filter in the control of single-frequency disturbance inputs. Results from this study indicate that if system identification is required to execute the adaptive algorithm (as is the case with the filtered-x LMS algorithm), then the sample rate should be set at 4 samples per period to minimize the number of finite impulse response filter coefficients needed to compute an accurate estimate of the filtered reference signal for multi-channel control. However, results from this study demonstrate that the sample rate has very little effect on the minimum mean-squared error that can be achieved with the adaptive control filter, owing to the reverberant characteristics of the dynamics system.