多输入多输出随机振动试验控制算法及若干问题研究
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摘要
多输入多输出（MIMO）随机振动试验具有比单点振动试验更好的振动环境模拟能力，能够检验出更多的潜在可靠性和安全性问题，对于经济和国防等的发展和进步具有重要意义。多输入多输出随机振动试验已经被写入最新的美军标MIL-STD-810G中，国内外越来越重视多输入多输出随机振动试验。本文以多点线性振动试验控制理论为基础，研究了多输入多输出随机振动试验控制中的相关问题。
基于数字信号处理的全相位谱分析理论，提出了用于改善MIMO随机振动试验控制效果的全相位频响函数估计方法。分析了频响函数估计不准对多输入多输出随机振动试验控制的影响。介绍了全相位谱估计理论并将之引入到频响函数估计中，构成了全相位频响函数估计方法，该方法改善了多输入多输出随机振动试验控制效果。
分析了MIMO频响函数估计中的内存激励信号和实测响应信号之间的关系和不同步原因，提出了用于同步两种信号的二次相关法。对VXI数字信号发送和采集系统的工作流程作了介绍，对信号发送和采集过程中信号之间的同步问题。通过理论分析，根据激励信号和响应信号之间的关系，提出了基于相关函数和随机减量法的二次相关法，计算得到了由计算机生成的内存激励信号和VXI实测的响应信号之间的时间对应关系。
研究了时域随机化过程的“加窗”和“叠加”过程，提出了一种改进的随机驱动信号生成方法。在试验中发现，生成的随机驱动信号的频谱和期望的驱动频谱不一致，从而造成多输入多输出随机振动试验控制结果中总是存在超标谱线。通过对时域随机化过程中的“加窗”和“叠加”两个部分的分析，本文提出了改进的随机驱动信号生成方法，在不改变谱线数的前提下增加伪随机驱动信号长度并采用四帧叠加的方法，改善了随机驱动信号的生成质量，改善了随机振动控制的效果。
分析了影响MIMO随机振动试验控制精度的因素，提出了兼顾快速修正和提高试验控制精度的变参数PID控制算法。将PID控制思想引入到多输入多输出随机振动试验控制中，在对数坐标下引入比例、积分、微分控制环节，然后转变到线性坐标下。根据响应谱和参考谱之间的误差，动态的调整PID控制参数，完成了变参数PID控制算法，实现了在保证快速修正的条件下，提高了随机振动试验控制精度。
对比分析了差分控制算法和比例均方根控制算法，提出了具有稳定收敛的自谱和互谱控制特性的矩阵幂次控制算法。理论推导了矩阵幂次控制算法，并对比分析了差分控制算法、比例均方根控制算法和矩阵幂次控制算法的各自特点，指出了差分控制算法存在“负值问题”的原因及后果。差分控制算法的误差假设和误差修正方法都是基于差分运算的，而矩阵幂次控制算法则采用矩阵乘法的形式进行误差假设、误差计算和误差修正，这种差异是矩阵幂次控制算法避免“负值问题”的原因。最后分别在仿真和试验中验证展示了三种控制算法的控制结果，验证了矩阵幂次控制算法的稳定收敛的自谱和互谱控制能力。
MIMO random vibration test can simulate the real vibration environment better than SISOrandom vibration test, it can find more potential reliability and security problems, and has importantmeaning for the development of economic and national defense. MIMO random vibration test hasbeen required in USA MIL-STD-810G, more attentions has been paid on MIMO random vibrationtest. Based on control theory for MIMO linear vibration test, related issues about MIMO randomvibration test control will be studied in this dissertation.
Base on the all phase spectral estimation theory of digital signal process, all phase frequencyresponse function estimation method is proposed, which can improve the control results of MIMOrandom vibration test. The affect to MIMO random vibration test caused by the inaccurateness offrequency response function estimation is analyzed. Theory of all phase spectral estimation theory isintroduced and is applied into frequency response function estimation, and all phase frequencyresponse function estimation method is formed. This estimation method improved the control resultsof MIMO random vibration test.
The relationship between memory excitation signals and measured response signals and thereason of their asynchronism are analyzed, a double correlation method to synchronize these twosignals is proposed. After the introduction of working process of VXI digital signal transmission andacquisition instrument, the synchronization problem between sending signals and sampling signals ispresented. Base on the relationship between exciting signals and response signals, a doublecorrelation method is proposed, in which the correlation function calculation and random decrementmethod are used. Double correlation method can get the time history relationship between excitingsignals in computer memory and response signals measured by VXI.
The “window” and “overlap” process of the time domain randomization process are analyzed; animproved generation method of random exciting signal is proposed. It is found in tests that thefrequency spectrums of generated signals are not the same with the expected drive spectrums, whichwill result in the over range spectrum in control result of MIMO random vibration test. After theanalyses of “window” and “overlapping” of time domain randomization process, a four frameoverlapping method is proposed. Under the circumstance of not changing the number of spectrumlines, this method improves the exciting signals and the random test control results.
Factors that affect the control accuracy of MIMO random vibration test are analyzed; PID controlalgorithm with variable arguments is proposed to make rapid correction and to improve control accuracy. The idea of PID control is applied into MIMO random vibration test control. Theproportional control, integral control and differential control is introduced in test control under thelogarithmic coordinates, and then been transformed into forms under linear coordinates. The valuesof arguments of PID control are adjusted according to the errors between response spectrums andreference spectrums. The PID control algorithm can make the rapid correction of response spectrums,and also improve the random vibration test control accuracy.
Compare analsis among control algorithms are made, Matrix power control algorithm (MPCA) isproposed, which can steadily and convergently control the auto spectrum and cross spectrum. Thetheory of matrix power control algorithm is deduced. A compare analysis among difference controlalgorithm (DCA), proportional root mean square control algorithm (PRMSCA) and MPCA is made.The error assumption and error correction of DCA is based on difference operation, while the errorassumption, error calculation and error correction is base on matrix multiplication operation. Thisdifference forms is why MPCA can avoid the “negative value problems”. At last simulations andtests are made, the results proved the auto spectrum and cross spectrum control ability of MPCA.
基于数字信号处理的全相位谱分析理论，提出了用于改善MIMO随机振动试验控制效果的全相位频响函数估计方法。分析了频响函数估计不准对多输入多输出随机振动试验控制的影响。介绍了全相位谱估计理论并将之引入到频响函数估计中，构成了全相位频响函数估计方法，该方法改善了多输入多输出随机振动试验控制效果。
分析了MIMO频响函数估计中的内存激励信号和实测响应信号之间的关系和不同步原因，提出了用于同步两种信号的二次相关法。对VXI数字信号发送和采集系统的工作流程作了介绍，对信号发送和采集过程中信号之间的同步问题。通过理论分析，根据激励信号和响应信号之间的关系，提出了基于相关函数和随机减量法的二次相关法，计算得到了由计算机生成的内存激励信号和VXI实测的响应信号之间的时间对应关系。
研究了时域随机化过程的“加窗”和“叠加”过程，提出了一种改进的随机驱动信号生成方法。在试验中发现，生成的随机驱动信号的频谱和期望的驱动频谱不一致，从而造成多输入多输出随机振动试验控制结果中总是存在超标谱线。通过对时域随机化过程中的“加窗”和“叠加”两个部分的分析，本文提出了改进的随机驱动信号生成方法，在不改变谱线数的前提下增加伪随机驱动信号长度并采用四帧叠加的方法，改善了随机驱动信号的生成质量，改善了随机振动控制的效果。
分析了影响MIMO随机振动试验控制精度的因素，提出了兼顾快速修正和提高试验控制精度的变参数PID控制算法。将PID控制思想引入到多输入多输出随机振动试验控制中，在对数坐标下引入比例、积分、微分控制环节，然后转变到线性坐标下。根据响应谱和参考谱之间的误差，动态的调整PID控制参数，完成了变参数PID控制算法，实现了在保证快速修正的条件下，提高了随机振动试验控制精度。
对比分析了差分控制算法和比例均方根控制算法，提出了具有稳定收敛的自谱和互谱控制特性的矩阵幂次控制算法。理论推导了矩阵幂次控制算法，并对比分析了差分控制算法、比例均方根控制算法和矩阵幂次控制算法的各自特点，指出了差分控制算法存在“负值问题”的原因及后果。差分控制算法的误差假设和误差修正方法都是基于差分运算的，而矩阵幂次控制算法则采用矩阵乘法的形式进行误差假设、误差计算和误差修正，这种差异是矩阵幂次控制算法避免“负值问题”的原因。最后分别在仿真和试验中验证展示了三种控制算法的控制结果，验证了矩阵幂次控制算法的稳定收敛的自谱和互谱控制能力。
MIMO random vibration test can simulate the real vibration environment better than SISOrandom vibration test, it can find more potential reliability and security problems, and has importantmeaning for the development of economic and national defense. MIMO random vibration test hasbeen required in USA MIL-STD-810G, more attentions has been paid on MIMO random vibrationtest. Based on control theory for MIMO linear vibration test, related issues about MIMO randomvibration test control will be studied in this dissertation.
Base on the all phase spectral estimation theory of digital signal process, all phase frequencyresponse function estimation method is proposed, which can improve the control results of MIMOrandom vibration test. The affect to MIMO random vibration test caused by the inaccurateness offrequency response function estimation is analyzed. Theory of all phase spectral estimation theory isintroduced and is applied into frequency response function estimation, and all phase frequencyresponse function estimation method is formed. This estimation method improved the control resultsof MIMO random vibration test.
The relationship between memory excitation signals and measured response signals and thereason of their asynchronism are analyzed, a double correlation method to synchronize these twosignals is proposed. After the introduction of working process of VXI digital signal transmission andacquisition instrument, the synchronization problem between sending signals and sampling signals ispresented. Base on the relationship between exciting signals and response signals, a doublecorrelation method is proposed, in which the correlation function calculation and random decrementmethod are used. Double correlation method can get the time history relationship between excitingsignals in computer memory and response signals measured by VXI.
The “window” and “overlap” process of the time domain randomization process are analyzed; animproved generation method of random exciting signal is proposed. It is found in tests that thefrequency spectrums of generated signals are not the same with the expected drive spectrums, whichwill result in the over range spectrum in control result of MIMO random vibration test. After theanalyses of “window” and “overlapping” of time domain randomization process, a four frameoverlapping method is proposed. Under the circumstance of not changing the number of spectrumlines, this method improves the exciting signals and the random test control results.
Factors that affect the control accuracy of MIMO random vibration test are analyzed; PID controlalgorithm with variable arguments is proposed to make rapid correction and to improve control accuracy. The idea of PID control is applied into MIMO random vibration test control. Theproportional control, integral control and differential control is introduced in test control under thelogarithmic coordinates, and then been transformed into forms under linear coordinates. The valuesof arguments of PID control are adjusted according to the errors between response spectrums andreference spectrums. The PID control algorithm can make the rapid correction of response spectrums,and also improve the random vibration test control accuracy.
Compare analsis among control algorithms are made, Matrix power control algorithm (MPCA) isproposed, which can steadily and convergently control the auto spectrum and cross spectrum. Thetheory of matrix power control algorithm is deduced. A compare analysis among difference controlalgorithm (DCA), proportional root mean square control algorithm (PRMSCA) and MPCA is made.The error assumption and error correction of DCA is based on difference operation, while the errorassumption, error calculation and error correction is base on matrix multiplication operation. Thisdifference forms is why MPCA can avoid the “negative value problems”. At last simulations andtests are made, the results proved the auto spectrum and cross spectrum control ability of MPCA.
引文
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