Active control of synchronous machine vibrations: an adaptive optimal MIMO controller

This paper deals with a new multiple input multiple output active control algorithm applied to reduce synchronous machine vibrations. Usually, this kind of algorithm has good performance on linear time-invariant, or slowly timevarying systems. The present system has been developped taking into account the presence of a linear periodically time-varying transfer function. Signals are first shown periodic with the same fundamental frequency. Next, Fourier coefficients of the signals measured by sensors are linked to the inputs ones thanks to a linear matrix equation. Classical least mean square minimization can then be used to find the optimal input Fourier coefficients. Finally, a simple adaptive algorithm updating these coefficients is elaborated, in order to converge to the optimal solution and to follow the disturbances fluctuations. Results on real vibration signals show good attenuation performance with one or several sensors.