Matrix Power Control Algorithm for Multi-input Multi-output Random Vibration Test

 Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output (MIMO) random vibration test. During the control process with the difference control algorithm (DCA), a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix (DELTM) may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm (PRMSCA) provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm (MPCA) is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.