Youla Parameterized Control Against Line Spectrum Vibration with an Adaptive Forgetting Factor Improved by a Genetic Algorithm

Line spectrum vibration produced by rotating machinery exists widely in mechanical systems, which leads to a decrease in equipment machining measurement accuracy. The adaptive
$\mathbf{Q}$
parametric controller is an effective line spectrum control method, that uses the RLS (recursive least squares) algorithm to adjust
$\mathbf{Q}$
parameters online to adapt to external excitation. However, the fixed forgetting factor has an inherent contradiction between the steady-state error and the tracking speed. In this paper, the optimal combination of forgetting factors at every moment is selected through genetic algorithm (GA) training and the adaptive law between residual error and the forgetting factor is summarized. Simulation results show that the improved controller can track and suppress the spectra of five changing lines. Moreover, compared with other adaptive laws, this method not only reduces the steady-state error, but also improves the tracking speed, which demonstrates the advantage of this optimization method.