多输入多输出随机振动试验雅克比控制算法

Jacobi control algorithm for MIMO random vibration test

研究了多输入多输出(MIMO,Multiple Input Multiple Output)随机振动试验闭环控制系统中不同元素超标现象,通过分析多输入多输出线性时不变振动系统输入与输出的频域关系,将多路信号的功率谱矩阵分解为自功率谱、相干系数和相位差等元素,推导出能表示输入输出元素微分关系的雅克比控制矩阵,提出了一种全新的MIMO随机振动试验雅克比控制算法。该算法对功率谱矩阵中元素超标现象进行有针对性地控制,其控制收敛速度快、精度高。在多轴振动台上进行两输入两输出振动控制实验,分别设定参考谱的各元素,设置容差带,然后进行频响函数估计,利用新算法对X轴和Y轴的振动进行控制,结果表明利用雅克比控制算法可将自谱、相干系数与相位等均控制在工程标准范围内,控制效果良好。

The question of exceeding or going below the certain limits on close-loop feedback control system of MIMO（Multiple Input Multiple Output）random vibration test is studied,and in the paper the relationship between inputs and outputs of MIMO LTI（Linear Time Invariable）vibration system is deeply analyzed.The PSD（Power Spectral Density）matrix of multiple signals could be expressed by auto-spectral density,coherence and phase which are independent elements,thus the Jacobi control matrix is deduced to express the differential relationship between the input and output signals.In the final a new method called Jacobi control algorithm is proposed to be applied in MIMO random vibration test.The method controls the element values of PSD which exceed or go below certain limits,so the convergence speed is faster and the control precision is higher.A two-input two-output test is conducted on a three-axis electrical vibration table.In the first the reference PSD including auto-spectral density,coherence,and phase should be set,then the tolerance should be set by±3 dB.The FRF（Frequency Response Function）would be estimated by H1 method,and the new algorithm is to be applied to control the X-axis and Y-axis vibration.The results show that the algorithm can update the auto-spectral density,coherence,and phase into the tolerance of reference PSD.