精密柔性抛物壳智能结构系统及其主动控制研究
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摘要
随着空间技术的飞速发展,各类航天器及其有效载荷结构的智能化、一体化要求不断提高,基于智能材料的结构电子学系统及其主动控制问题已经成为各交叉学科研究的重点。尽管近20年来国内外关于压电层合板壳智能结构控制方面的研究已经逐渐展开,但是针对具有典型空间应用背景的柔性旋转抛物壳智能结构的系统研究还处于起步阶段,还有很多关键技术亟待突破。本研究在国家自然科学基金项目“薄壁回转结构动力学建模及形状智能控制研究”和“光致伸缩耦合柔性回转结构的非接触精密控制研究”的共同支持下,以精密光学仪器和空间天线系统中薄壁曲面构件的振动控制为背景,采用理论分析、数值仿真和系统模型试验相结合的方法开展压电层合精密柔性抛物壳智能结构系统及其振动主动控制研究,为此类智能结构的具体应用提供理论依据和技术支持。
本文从微分几何与弹性板壳理论出发,基于Love-Kirchhoff薄壳假设和一阶剪切变形理论分析了弹性旋转抛物壳单元的力学模型;依据多功能混合板壳理论和压电本构方程,讨论了压电-弹性层合壳体结构所涉及的力、电能场转换及耦合作用关系,得出压电层合壳体单元的合成力和力矩基本表达式;基于Hamilton原理、线性压电理论和薄壳理论基本假设推导出具有一般性的压电层合双曲率壳智能结构系统动力学方程。
考虑到双曲率弹性壳的振动特性在数学上很难求解,在分析了三种常见的振动简化理论的基础上,本文对压电层合抛物壳智能结构系统动力学方程和应变表达式进行了无矩简化;同时,针对旋转抛物壳在空间天线系统中所处的自由边界条件,提出一组基于无矩简化的自由柔性抛物壳振动模态形状函数;通过弹性壳模型的理论振型仿真和实验模态测试结果的对比,研究了自由边界柔性抛物壳连续体的低阶模态振动特性。
基于正压电效应、Gauss理论、开环假设和Maxwell方程,推导出具有一般性的层合壳分布传感信号方程;利用自由边界旋转抛物的模态形状函数,得出模态传感信号表达式,并确定由不同子午线、圆周方向薄膜应变构成的分布传感信号分量;结合典型的旋转抛物壳参数,仿真分析了不同传感信号分量的作用和模态敏感性,参数评价了传感器布局对传感信号幅值的影响.
在压电层合壳力-电耦合模型的基础上,本文给出了无矩简化的旋转抛物壳智能结构系统控制方程,并应用模态正交性和模态展开方法将系统控制方程转换到模态域;引入Love控制算子和单位阶跃函数,推导出分布式作动器模态控制力表达式,以横向振动为主探讨了作动器子午线/圆周方向上薄膜和弯曲控制分量的作用;通过数值仿真,分析了柔性抛物壳上空间分布的压电作动器的微控行为、有效面积和规格化控制效应,进而为分布式作动器布局和构型提出了设计参考。
根据压电薄膜传感/作动器的基本性能和工作特点,设计了用于微弱传感信号调理和作动器高压激励的集成电路模块,基于VC开发出多路信号采集、分析、处理与主动控制的系统软件,建立起压电层合柔性抛物壳智能结构的系统实验平台;通过对试验模型分布传感与激励的开环测试,验证了系统的有效性和可靠性,试验数据也证实了传感与激励信号理论分析中的规律性结论。
通过对硬件系统的参数辨识,建立了各环节的传递函数,然后按照极点配置方法和正位置反馈方法设计系统控制器,并分别对压电层合抛物壳的低阶独立模态和耦合模态进行振动控制实验,实验结果表明控制算法增大了系统阻尼,抑制了振动幅值,实现了对结构振动的主动控制。最后,针对空间抛物壳智能结构系统受外界扰动的随机性和控制能量有限性,提出了一种自适应模态控制模式,实验证明该方法可以在随机激励条件下准确地判定最佳激励位置并有效地施加主动控制。
With the rapid development of space technologies, the requirement for integrated and intelligent structures applied to various space vehicles, structures and their payloads has been continuously raised. Therefore, the structronic system and active control, based on smart materials and intelligent control systems, have been becoming one of the mainstream research and development activities. Although the research on active control of piezoelectric laminated smart shell structures has been carried out in the last two decades precision control of smart flexible paraboloidal shells of revolution, especially applied to space structures, has just begun and needs to strive to make a technological breakthrough. Supported by the National Science Fund of China projects“Research on Dynamic Modeling and Smart Shape Control of Thin Structure of Revolution”and“Research on Non-contact Precise Control of Flexible Photostrictive Coupled Shells of Revolution,”with the background of vibration control of thin shell components in the precision optical apparatus and space antenna systems, this research focuses on developing precision smart flexible paraboloidal shell and its active vibration control system, by way of theoretical analysis, numerical simulation, and laboratory demonstration. This research provides theoretical fundamentals, practical implementation, for design applications of this class of smart paraboloidal shell structures.
This paper begins with the theories of differential geometry and elastic plate and shell, and analyzes component mechanical model of elastic paraboloidal shell of revolution, based on Love-Kirchhoff’s shell assumption and the theory of first order shear deformation; According to the theory of multifunctional hybrid shells and piezoelectric constitutive equation, the switch between force and electricity field and their coupling relations in the piezo-elastic laminated shell structure are fully discussed, thus coming to a basic resultant force and moment expression of piezoelectric laminated shell component; Based on the Hamilton’s principle, the linear piezoelectric theory and basic assumption of thin shell theory, the systemematic dynamic equations of generic piezoelectric laminated smart double curvature shell structure is deduced.
In consideration of the difficulty in finding a solution to the vibration feature of double curvature elastic shell in the filed of mathematics, the systematic dynamic equations of the piezoelectric laminated shell smart structure and the strain expressions are simplified by Membrane approximation in this paper, after the analysis of the three common vibration approximation theories. Meanwhile, concerning the free boundary condition of the paraboloidal shell of revolution in space antenna, a series of vibration mode shape functions of free flexible paraboloidal shell is proposed based on the membrane approximation theory. By comparing the results among the theoretical modal shape simulation and experiment modal test of the elastic shell model, the characteristics of the low modal shapes of membrane paraboloidal shell continuum with free boundary condition are investigated.
Based on positive piezoelectric effect, Gauss theory, open loop assumption and Maxwell equation, the distributed sensing signal equation of the general laminated shell is derived; using the mode shape function of paraboloidal shell with free boundary condition, the modal sensing signal is formulated, and distributed sensing signal components consist of different membrane strains in the meridianal and circumferential direction are defined. In combination with the typical parameters of paraboloidal shell of revolution, the effects of various sensing signal components and their mode sensitivity are analyzed; the magnitude of the sensing signal influenced by the layout of sensors is evaluated.
On the basis of piezoelectric laminated shell mechanical-electrical coupling modeling, this paper raises the system governing equations of membrane paraboloidal shell of revolution smart structure, and transfers the equations to modal domain by applying modal orthogonality and modal expansion method. By introducing Love control operator and unit step function, the modal control force expression of distributed actuator is deduced, and mainly grounded on transverse vibration, the membrane and bending control components in meridianal and circumferential direction are discussed. Through the numerical simulation, this paper has respectively analyzed the micro-control action, effective area and normalized control action of distributed piezoelectric actuator laminated on the flexible paraboloidal shells, thereby making a guidelines to distributed actuator layout and configuration design.
According to the basic function and characteristics of PVDF film sensor/actuator, the circuit modules are devised to be applied to the adjustment of microscopic sensing signal and to the high voltage actuation. In consequence of the system software that is developed by VC and aims at collection, analysis and processing of the multiplex signals, as well as the active control, the system experiment platform of piezoelectric laminated flexible paraboloidal shell smart structure is built. Through the open loop test on the distributed sensing and actuation of the experimental model, the availability and reliability of the system are verified, and the experimental data also prove the regular conclusions in the theoretical analysis of sensing and actuation signal.
Through the parameter identification on the hardware system, the transfer functions of all links are established, and in terms of the pole placement and positive position feedback method, two kinds of controllers were designed, which have been put into use to the vibration control experiments, focusing on the low independent mode and coupled modes in piezoelectric laminated paraboloidal shell respectively. The experiment data show that these control methods enlarge the system damping and restrain the amplitude of vibration, making the active control come true. Finally, in accordance with random of the environment excitation of the space paraboloidal shell structure system and the limitation of the control energy, this paper proposes a self-adaptive modal control method. The experiment proves that, in the case of random excitation, the method can accurately judge the prefect actuator position, and effectively exert the active control on the smart structure.
本文从微分几何与弹性板壳理论出发,基于Love-Kirchhoff薄壳假设和一阶剪切变形理论分析了弹性旋转抛物壳单元的力学模型;依据多功能混合板壳理论和压电本构方程,讨论了压电-弹性层合壳体结构所涉及的力、电能场转换及耦合作用关系,得出压电层合壳体单元的合成力和力矩基本表达式;基于Hamilton原理、线性压电理论和薄壳理论基本假设推导出具有一般性的压电层合双曲率壳智能结构系统动力学方程。
考虑到双曲率弹性壳的振动特性在数学上很难求解,在分析了三种常见的振动简化理论的基础上,本文对压电层合抛物壳智能结构系统动力学方程和应变表达式进行了无矩简化;同时,针对旋转抛物壳在空间天线系统中所处的自由边界条件,提出一组基于无矩简化的自由柔性抛物壳振动模态形状函数;通过弹性壳模型的理论振型仿真和实验模态测试结果的对比,研究了自由边界柔性抛物壳连续体的低阶模态振动特性。
基于正压电效应、Gauss理论、开环假设和Maxwell方程,推导出具有一般性的层合壳分布传感信号方程;利用自由边界旋转抛物的模态形状函数,得出模态传感信号表达式,并确定由不同子午线、圆周方向薄膜应变构成的分布传感信号分量;结合典型的旋转抛物壳参数,仿真分析了不同传感信号分量的作用和模态敏感性,参数评价了传感器布局对传感信号幅值的影响.
在压电层合壳力-电耦合模型的基础上,本文给出了无矩简化的旋转抛物壳智能结构系统控制方程,并应用模态正交性和模态展开方法将系统控制方程转换到模态域;引入Love控制算子和单位阶跃函数,推导出分布式作动器模态控制力表达式,以横向振动为主探讨了作动器子午线/圆周方向上薄膜和弯曲控制分量的作用;通过数值仿真,分析了柔性抛物壳上空间分布的压电作动器的微控行为、有效面积和规格化控制效应,进而为分布式作动器布局和构型提出了设计参考。
根据压电薄膜传感/作动器的基本性能和工作特点,设计了用于微弱传感信号调理和作动器高压激励的集成电路模块,基于VC开发出多路信号采集、分析、处理与主动控制的系统软件,建立起压电层合柔性抛物壳智能结构的系统实验平台;通过对试验模型分布传感与激励的开环测试,验证了系统的有效性和可靠性,试验数据也证实了传感与激励信号理论分析中的规律性结论。
通过对硬件系统的参数辨识,建立了各环节的传递函数,然后按照极点配置方法和正位置反馈方法设计系统控制器,并分别对压电层合抛物壳的低阶独立模态和耦合模态进行振动控制实验,实验结果表明控制算法增大了系统阻尼,抑制了振动幅值,实现了对结构振动的主动控制。最后,针对空间抛物壳智能结构系统受外界扰动的随机性和控制能量有限性,提出了一种自适应模态控制模式,实验证明该方法可以在随机激励条件下准确地判定最佳激励位置并有效地施加主动控制。
With the rapid development of space technologies, the requirement for integrated and intelligent structures applied to various space vehicles, structures and their payloads has been continuously raised. Therefore, the structronic system and active control, based on smart materials and intelligent control systems, have been becoming one of the mainstream research and development activities. Although the research on active control of piezoelectric laminated smart shell structures has been carried out in the last two decades precision control of smart flexible paraboloidal shells of revolution, especially applied to space structures, has just begun and needs to strive to make a technological breakthrough. Supported by the National Science Fund of China projects“Research on Dynamic Modeling and Smart Shape Control of Thin Structure of Revolution”and“Research on Non-contact Precise Control of Flexible Photostrictive Coupled Shells of Revolution,”with the background of vibration control of thin shell components in the precision optical apparatus and space antenna systems, this research focuses on developing precision smart flexible paraboloidal shell and its active vibration control system, by way of theoretical analysis, numerical simulation, and laboratory demonstration. This research provides theoretical fundamentals, practical implementation, for design applications of this class of smart paraboloidal shell structures.
This paper begins with the theories of differential geometry and elastic plate and shell, and analyzes component mechanical model of elastic paraboloidal shell of revolution, based on Love-Kirchhoff’s shell assumption and the theory of first order shear deformation; According to the theory of multifunctional hybrid shells and piezoelectric constitutive equation, the switch between force and electricity field and their coupling relations in the piezo-elastic laminated shell structure are fully discussed, thus coming to a basic resultant force and moment expression of piezoelectric laminated shell component; Based on the Hamilton’s principle, the linear piezoelectric theory and basic assumption of thin shell theory, the systemematic dynamic equations of generic piezoelectric laminated smart double curvature shell structure is deduced.
In consideration of the difficulty in finding a solution to the vibration feature of double curvature elastic shell in the filed of mathematics, the systematic dynamic equations of the piezoelectric laminated shell smart structure and the strain expressions are simplified by Membrane approximation in this paper, after the analysis of the three common vibration approximation theories. Meanwhile, concerning the free boundary condition of the paraboloidal shell of revolution in space antenna, a series of vibration mode shape functions of free flexible paraboloidal shell is proposed based on the membrane approximation theory. By comparing the results among the theoretical modal shape simulation and experiment modal test of the elastic shell model, the characteristics of the low modal shapes of membrane paraboloidal shell continuum with free boundary condition are investigated.
Based on positive piezoelectric effect, Gauss theory, open loop assumption and Maxwell equation, the distributed sensing signal equation of the general laminated shell is derived; using the mode shape function of paraboloidal shell with free boundary condition, the modal sensing signal is formulated, and distributed sensing signal components consist of different membrane strains in the meridianal and circumferential direction are defined. In combination with the typical parameters of paraboloidal shell of revolution, the effects of various sensing signal components and their mode sensitivity are analyzed; the magnitude of the sensing signal influenced by the layout of sensors is evaluated.
On the basis of piezoelectric laminated shell mechanical-electrical coupling modeling, this paper raises the system governing equations of membrane paraboloidal shell of revolution smart structure, and transfers the equations to modal domain by applying modal orthogonality and modal expansion method. By introducing Love control operator and unit step function, the modal control force expression of distributed actuator is deduced, and mainly grounded on transverse vibration, the membrane and bending control components in meridianal and circumferential direction are discussed. Through the numerical simulation, this paper has respectively analyzed the micro-control action, effective area and normalized control action of distributed piezoelectric actuator laminated on the flexible paraboloidal shells, thereby making a guidelines to distributed actuator layout and configuration design.
According to the basic function and characteristics of PVDF film sensor/actuator, the circuit modules are devised to be applied to the adjustment of microscopic sensing signal and to the high voltage actuation. In consequence of the system software that is developed by VC and aims at collection, analysis and processing of the multiplex signals, as well as the active control, the system experiment platform of piezoelectric laminated flexible paraboloidal shell smart structure is built. Through the open loop test on the distributed sensing and actuation of the experimental model, the availability and reliability of the system are verified, and the experimental data also prove the regular conclusions in the theoretical analysis of sensing and actuation signal.
Through the parameter identification on the hardware system, the transfer functions of all links are established, and in terms of the pole placement and positive position feedback method, two kinds of controllers were designed, which have been put into use to the vibration control experiments, focusing on the low independent mode and coupled modes in piezoelectric laminated paraboloidal shell respectively. The experiment data show that these control methods enlarge the system damping and restrain the amplitude of vibration, making the active control come true. Finally, in accordance with random of the environment excitation of the space paraboloidal shell structure system and the limitation of the control energy, this paper proposes a self-adaptive modal control method. The experiment proves that, in the case of random excitation, the method can accurately judge the prefect actuator position, and effectively exert the active control on the smart structure.
引文
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