Control algorithm update for multi-input multi-output random environment test

When conducting multi-input multi-output (MIMO) random vibration environment test, response spectral lines of under test article may exceed their tolerances and some of them can hardly be controlled by control algorithms. The cause of this phenomenon is the high level noises in the input forces, which are induced by the inverse of the ill-conditioned frequency response function matrices. These spectral lines may even trigger the instability of control algorithms and eventually result in an accidental test shutoff. The classical control algorithm for MIMO random vibration environment test contributed by Smallwood is analyzed theoretically and experimentally in the paper to reveal its weakness on dealing with this kind of error. An updated algorithm is proposed on the basis of inverse theory to overcome the difficulty of controlling these stubborn spectral lines. The main idea of the work is to reduce the level of noise components in input forces by regularizing singular values of ill-conditioned frequency response function matrices. An adjusting rule is set up according to the auto-power spectra tolerances. A simulation and an experiment are supplied in the paper to verify the effectiveness of the updated algorithm, the results are satisfactory.