Abstract
Active vibration control (AVC) based on adaptive finite impulse response (FIR) filters inhere delays in conditional signal dispersion. Reasons for these delays are geometrical arrangements, and computational time in analog digital converters (ADCs) and in digital analog converters (DACs). The delays represent a phase shift in periodic signals. These delays avoid instant feedback of the signals through the least mean square (LMS) algorithm. This can lead to instability and even divergence. This study presents a modification of the LMS algorithm by adjusting the underlying gradient descent algorithm. Using analytic considerations, it shows the conditions of convergence for the stepsize as well as the gradient. The result is that all delays occurring can be compensated entirely. Unlike the delayed LMS algorithm, the introduced method considers possible delays analytically and furnishes the possibility for a perfect delay compensation. Modifications are easy to put into practice and were researched and verified using various simulations. Measurements on a duct in a range from 100 Hz to 1000 Hz confirm the success of adjustment and show an excellent convergence over the whole tested frequency range. Signal manipulation, for example, with a low-pass filter, which allows reverse phase shifts between – π and π, results only in a small frequency range and may be omitted by using the delay compensated LMS algorithm. The analytic mathematical derivation of the required modification can be implemented easily.