Wavelets in Control Engineering

This article for control engineering describes new analysis and filter technique: the wavelet transform. The technique presents the signal on both a time as frequency axis, comparable with a windowed Fourier transformation that is shifted along the time axis. In Fourier techniques window width is changed as function of analyzing frequency. Furthermore there is much freedom in choosing the analysis function, which let the wavelet transform do more than only to discover frequency information. Besides as analysis technique the wavelet transform can be used for filtering purposes. With the discrete version of the wavelet transform (DWT) decomposition in frequency-dependent coefficients is possible, from which the original signal can be reconstructed. Since the origins of the DWT lie in the field of signal processing, the available algorithms are efficient but not optimal with respect to the delay times. Therefore a real-time wavelet filter algorithm is derived, which can also be used for analyzing purposes. Two application are worked out ; 1. Wavelet filters for encoder quantization denoising and 2. Online feature detection on a CD-player setup. Wavelets show good results in isolating features (time-patterns in signals), especially short-living events. Building dedicated waveforms can improve the results and the real-time algorithm makes fast detection possible. The experiences are validated on a servo-loop of a CD-player setup, on which external disturbances are presented in the form of shocks and disc-faults. For some disturbances very early detection is possible: the wavelet filter already isolates features where the measurement still moves within the noise level.