高柔结构AMD振动控制系统实施的相关方法研究
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摘要
国民经济的发展促使我国高柔结构的蓬勃发展。为使强风作用下高柔结构的加速度和层间位移满足相关规范要求，一般需要提高结构的刚度，较大幅度地增加结构的造价。主动质量阻尼器（Active Mass Damper/Driver, AMD）是一种通过增加结构阻尼来满足规范要求的有效途径，其控制效果好、控制频带宽，且性价比相比较高。目前，有关AMD控制系统的研究较多，但实际工程应用却并不多见，这主要是由于工程应用仍有较多问题，如被控结构数值模型的建立、全状态反馈控制系统基于部分楼层加速度的状态观测器设计、系统时滞的影响情况及有效补偿控制器设计等。本文针对上述问题主要开展了如下研究工作：
基于几种常用模型减维方法的对比分析，结合高柔结构的特点选择其中较适用的减维方法进行改进，并将从结构时域响应、频率响应和系统极点分布等方面对比分析改进方法获得的低维模型与原模型，最后基于上述低维模型设计低维AMD控制器，并以某实际高柔结构AMD控制系统数值模型和四层框架实验模型为例进行验证。
针对全状态反馈AMD控制系统，基于系统状态方程及模糊神经网络分别设计以部分楼层加速度为输入的系统全状态观测器，同样以实际AMD控制系统数值模型及实验模型进行验证。最后以基于状态方程的观测器误差为指标，通过数值模拟确定了某实际高柔结构中加速度传感器的布置方案。
为减小反馈信号中噪声对控制系统的影响及满足AMD控制的实时性要求，基于Kalman滤波原理及线性矩阵不等式（LMI）理论设计基于LMI的Kalman实时滤波器，最后将以实际高柔结构数值模型及四层框架AMD实验模型为例验证该滤波器的有效性。
理论分析时滞对单自由度控制系统和多自由度控制系统极点位置、稳定性的影响，并给出保证系统稳定的最大时滞计算公式，基于该公式分析控制增益和被控结构参数对系统稳定性的影响。基于AMD控制时滞对系统极点位置的影响情况及极点配置算法设计时滞补偿控制器，并以某实际高柔结构AMD控制系统的数值模型及实验系统为例进行验证。
基于伺服电机输入输出关系式，建立AMD控制系统不计CSI效应、计低阶CSI效应和计高阶CSI效应时的数学模型，分析了CSI效应的影响机理及受结构参数的影响情况。针对CSI效应导致的系统时变时滞，设计H∞控制器以减小该效应对控制系统的影响。
基于期望惯性质量相对速度与行程间的函数关系式，推导由AMD行程实时计算反馈增益的公式，并以实际工程为例分析反馈增益离散时变或连续时变时AMD行程的受控情况。另外，以某四层框架AMD控制系统为例，简要介绍实际AMD控制系统设计与实施的步骤与方法。
Flexible buildings are developing rapidly with the development of the national economy. However, the structural responses under strong wind, such as accelerations of high-rise buildings and inter-story displacement angle, are too large to meet comfort requirements in relevant codes, so stiffness of the structure need to be increased generally, which results in a substantial increase in the cost. Active Mass Damper （or Active Mass Driver, AMD） is a potential solution to the above questions because of its good control effect, great control bandwidth in frequency and high performance-to-price ratio. Although AMD control system has been widely studied, while its applications in civil engineering are fewer than the other control devices, such as Tuned Mass Damper （TMD）. There are still many questions should be solved in engineering applications, including establishment of accurate numerical model to the structure, observer design of full state feedback control system based on partial floor’s accelerations, influence of time delays of AMD control system on the system performances, effective compensator design to compensate time delays and other issues. In response to those problems, the following work has been done.
The order of a control system is reduced based on comparative analysis of several commonly used methods. The optimal method will be improved combined with characteristics of high-rise buildings. Comparative analysis of original model and reduced model are obtained using the improved method, which includes structural responses in time domain and frequency domain, pole distribution of the two systems, etc. A reduced-order controller is designed based on the low-order model. Lastly, numerical analysis of a high-rise building with an AMD control system and experimental analysis of a four-layer frame with an AMD control system are carried out to verify the accuracy and validity of low-order model and controller.
For an AMD control system with full state feedback, two observers with partial floor’s accelerations as input are designed, where the system state equations and fuzzy neural network are used for two observers separately. To proof the accuracy and validity of the proposed method, numerical analysis of a high-rise building with an AMD control system and experimental analysis of a four-layer frame with an AMD control system are both given. Finally, to take the average observation error as objectives, the locations of accelerometers in high-rise buildings are determined by the minimum value of average observation error.
To reduce the influence of noise in feedback signal in control system and to meet the requirements of real-time control of AMD control system, a LMI-Kalman filter is designed based on Kalman filtering theory and linear inequalities （LMI） theory. Furthermore, the effectiveness of the filter is certified based on a numerical model of a high-rise building and experimental four-layer frame model with an AMD control system.
Influence of time delay on pole position and stability for AMD control systems with single degree or multi-degree of freedom is analyzed in theory. According to the analysis results, the maximum time delay to ensure stability of the system is calculated, as following, the influence of control gain and structural parameters on system stability is analyzed. Then a time-delay compensation controller is designed based on the pole assignment algorithm to an actual high-rise building with an AMD system.
Based on the input-output formula of servo motor, numerical model of an AMD control system is established, which includes the model without CSI effect, the model with low-order CSI effect and the model with high-order CSI effect, respectively. Based on these three models, mechanism of CSI effect and the influence of structural parameters on CSI effect are analyzed, while the result shows that essence of CSI is equal to a time-varying time lag. To reduce the influence of this effect on the control system, a H∞controller is designed. At last, effectiveness of compensator is verified.
Based on the relationship between auxiliary mass stroke and its relative speed, a calculation formula of feedback gain based on auxiliary mass stroke is established to achieve computing time-varying feedback gain step by step or continuously. Analysis on how AMD strokes change with gains step by step or continuously is carried out using an actual project. In addition, procedures and methods of design and implementation of AMD control systems is introduced briefly based on a four-layer frame with an AMD control system.
基于几种常用模型减维方法的对比分析，结合高柔结构的特点选择其中较适用的减维方法进行改进，并将从结构时域响应、频率响应和系统极点分布等方面对比分析改进方法获得的低维模型与原模型，最后基于上述低维模型设计低维AMD控制器，并以某实际高柔结构AMD控制系统数值模型和四层框架实验模型为例进行验证。
针对全状态反馈AMD控制系统，基于系统状态方程及模糊神经网络分别设计以部分楼层加速度为输入的系统全状态观测器，同样以实际AMD控制系统数值模型及实验模型进行验证。最后以基于状态方程的观测器误差为指标，通过数值模拟确定了某实际高柔结构中加速度传感器的布置方案。
为减小反馈信号中噪声对控制系统的影响及满足AMD控制的实时性要求，基于Kalman滤波原理及线性矩阵不等式（LMI）理论设计基于LMI的Kalman实时滤波器，最后将以实际高柔结构数值模型及四层框架AMD实验模型为例验证该滤波器的有效性。
理论分析时滞对单自由度控制系统和多自由度控制系统极点位置、稳定性的影响，并给出保证系统稳定的最大时滞计算公式，基于该公式分析控制增益和被控结构参数对系统稳定性的影响。基于AMD控制时滞对系统极点位置的影响情况及极点配置算法设计时滞补偿控制器，并以某实际高柔结构AMD控制系统的数值模型及实验系统为例进行验证。
基于伺服电机输入输出关系式，建立AMD控制系统不计CSI效应、计低阶CSI效应和计高阶CSI效应时的数学模型，分析了CSI效应的影响机理及受结构参数的影响情况。针对CSI效应导致的系统时变时滞，设计H∞控制器以减小该效应对控制系统的影响。
基于期望惯性质量相对速度与行程间的函数关系式，推导由AMD行程实时计算反馈增益的公式，并以实际工程为例分析反馈增益离散时变或连续时变时AMD行程的受控情况。另外，以某四层框架AMD控制系统为例，简要介绍实际AMD控制系统设计与实施的步骤与方法。
Flexible buildings are developing rapidly with the development of the national economy. However, the structural responses under strong wind, such as accelerations of high-rise buildings and inter-story displacement angle, are too large to meet comfort requirements in relevant codes, so stiffness of the structure need to be increased generally, which results in a substantial increase in the cost. Active Mass Damper （or Active Mass Driver, AMD） is a potential solution to the above questions because of its good control effect, great control bandwidth in frequency and high performance-to-price ratio. Although AMD control system has been widely studied, while its applications in civil engineering are fewer than the other control devices, such as Tuned Mass Damper （TMD）. There are still many questions should be solved in engineering applications, including establishment of accurate numerical model to the structure, observer design of full state feedback control system based on partial floor’s accelerations, influence of time delays of AMD control system on the system performances, effective compensator design to compensate time delays and other issues. In response to those problems, the following work has been done.
The order of a control system is reduced based on comparative analysis of several commonly used methods. The optimal method will be improved combined with characteristics of high-rise buildings. Comparative analysis of original model and reduced model are obtained using the improved method, which includes structural responses in time domain and frequency domain, pole distribution of the two systems, etc. A reduced-order controller is designed based on the low-order model. Lastly, numerical analysis of a high-rise building with an AMD control system and experimental analysis of a four-layer frame with an AMD control system are carried out to verify the accuracy and validity of low-order model and controller.
For an AMD control system with full state feedback, two observers with partial floor’s accelerations as input are designed, where the system state equations and fuzzy neural network are used for two observers separately. To proof the accuracy and validity of the proposed method, numerical analysis of a high-rise building with an AMD control system and experimental analysis of a four-layer frame with an AMD control system are both given. Finally, to take the average observation error as objectives, the locations of accelerometers in high-rise buildings are determined by the minimum value of average observation error.
To reduce the influence of noise in feedback signal in control system and to meet the requirements of real-time control of AMD control system, a LMI-Kalman filter is designed based on Kalman filtering theory and linear inequalities （LMI） theory. Furthermore, the effectiveness of the filter is certified based on a numerical model of a high-rise building and experimental four-layer frame model with an AMD control system.
Influence of time delay on pole position and stability for AMD control systems with single degree or multi-degree of freedom is analyzed in theory. According to the analysis results, the maximum time delay to ensure stability of the system is calculated, as following, the influence of control gain and structural parameters on system stability is analyzed. Then a time-delay compensation controller is designed based on the pole assignment algorithm to an actual high-rise building with an AMD system.
Based on the input-output formula of servo motor, numerical model of an AMD control system is established, which includes the model without CSI effect, the model with low-order CSI effect and the model with high-order CSI effect, respectively. Based on these three models, mechanism of CSI effect and the influence of structural parameters on CSI effect are analyzed, while the result shows that essence of CSI is equal to a time-varying time lag. To reduce the influence of this effect on the control system, a H∞controller is designed. At last, effectiveness of compensator is verified.
Based on the relationship between auxiliary mass stroke and its relative speed, a calculation formula of feedback gain based on auxiliary mass stroke is established to achieve computing time-varying feedback gain step by step or continuously. Analysis on how AMD strokes change with gains step by step or continuously is carried out using an actual project. In addition, procedures and methods of design and implementation of AMD control systems is introduced briefly based on a four-layer frame with an AMD control system.
引文
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