Rapid phase selection method for MIMO closed-loop vibration control with non-Gaussian signal shaping

This article investigates a closed-loop control method for multi-input multi-output (MIMO) non-Gaussian random vibration testing. Unlike Gaussian vibration scenarios, the challenge lies in rapidly generating non-Gaussian random signals with specified power spectral density (PSD), skewness, and kurtosis. Although the original phase selection method (OPSM) can perfectly achieve such requirement, its high computational complexity and limited real-time performance hinder the application in the MIMO vibration testing, due to numerous parameters. To deal with this, a rapid phase selection method (RPSM) is proposed, based on the OPSM. The RPSM simplifies the parameters into two core variables. Specifically, for PSD with 400 spectral lines, RPSM can reduce the parameters from 400 variables to 2, corresponding to 99.5% dimensionality reduction. Based on the RPSM, a closed-loop control method is formulated according to the deviations between the responses and references. It can control the PSD profiles, skewness, and kurtosis of all control channels within the specified tolerances. Experimental results from biaxial vibration testing demonstrate the effectiveness of the proposed methodology.