Multi-input multi-output random vibration control using Tikhonov filter

Noises always disturb the control effect of an environment test especially in multi-input multi-output (MIMO) systems. If the frequency response function matrices are ill-conditioned, the noises in the driving forces will be amplified and the response spectral lines may awfully exceed their tolerances. Most of the major biases between the response spectra and the reference spectra are produced by the amplified noises. However, ordinary control algorithms can hardly reduce the level of noises. The influences of the noises on both the auto- and cross-power spectra are analyzed in this paper. As a conventional frequency domain method on the inverse problem, the Tikhonov filter is adopted in the environment test to suppress the exceeding spectral lines. By altering regularization parameters gradually, the auto-power spectra can be improved in a closed control loop. Instead of using the traditional way of selecting regularization parameters, we observe the coherence change to estimate noise eliminations. Incidentally, the requirement of coherence control can be realized. The errors of the phase are then studied and a phase control algorithm is introduced at the end as a supplement of cross-power spectra control. The Tikhonov filter and the proposed phase control algorithm are tested numerically and experimentally. The results show that the noises in the vicinity of lightly damped resonant peaks are more stubborn. The response spectra are able to be greatly improved by the combination of these two methods.