含ACLD结构太阳能电池翼动力学建模与振动控制研究
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摘要
大型挠性太阳能电池翼的振动控制是航天器动力学与控制领域的挑战性课题。大挠性太阳能电池翼的大跨度、轻质量、低刚度的结构特点,导致其具有低频率、弱阻尼、模态密集的动力学特性。航天器的轨道和姿态机动以及复杂的空间环境干扰,都可能引发大挠性太阳能电池翼的振动。由于太阳能电池翼结构阻尼弱,空间环境也无大气阻尼,使得太阳能电池翼的振动很难衰减。这些振动将影响航天器的姿态稳定和定位精度,严重时还可能导致航天任务的失败。因此,必须对电池翼进行振动控制,然而,常规的控制方法和经典的控制理论已经难以适应大挠性太阳能电池翼振动控制的需求。本文正是在这样的背景下,展开大挠性太阳能电池翼结构动力学研究,提出了太阳能电池翼的主动约束阻尼(Active Constrained Layer Damping,ACLD)振动控制方式,以及基于LMI的多目标鲁棒振动控制系统设计的理论和方法,并进行了深入的探讨和研究。主要内容如下:
(1)根据太阳能电池翼的结构特点,简化为:单板、单框架板、多板铰接、多框架板铰接和中心刚体+板五种模型。在此基础上,建立了含ACLD结构的太阳能电池翼动力学模型。编制相应的有限元分析程序,并将计算所得特征值和频率响应与Msc.Nastran软件的计算结果进行对比,验证了模型的正确性。
(2)直接从影响粘弹性层剪切变形的角度分析了ACLD结构位置对太阳能电池翼模态阻尼因子的影响,并据此给出了简易地确定ACLD结构位置的方法。
(3)研究了具有主动约束阻尼结构的动力学模型降阶问题。由于粘弹性阻尼材料的存在,使得平衡降阶和动力缩聚两类广泛应用的模型降阶方法不再适用。论文改进了Krylov子空间模型降阶方法,并结合Krylov子空间降阶方法和平衡降阶方法的优点,提出了复合降阶方法。从特征值、频率响应、脉冲响应和正弦响应四个方面说明降阶模型可忠实表征原模型的动力学特点。使用复合降阶方法对动力学模型进行降阶,得到了适合控制系统设计的低阶模型。
(4)引入多通道思想,在LMI框架内研究了电池翼振动控制的多目标综合问题,设计了基于观测器的状态反馈控制器。使用内部反馈回路处理系统的不确定性,引入Lyapunov函数成形的不变椭圆和峰—峰增益使控制输入满足约束限制。得到了具有干扰抑制性能且满足控制输入约束的鲁棒稳定的基于观测器的状态反馈控制器存在的充分条件。以太阳能电池翼为研究对象,通过数值仿真验证了控制器设计方法的可行性和有效性。
(5)开展了基于主动约束阻尼技术的太阳能电池翼振动控制的验证性实验研究。实验结果表明所建理论模型是正确的,采用主动约束阻尼控制技术和鲁棒反馈控制器对抑制电池翼的振动是有效的。
Active vibration control of Large Flexible Solar Array (LFSA) is a challenging subject in the domain of spacecraft dynamics and control. LFSA has structural characters of large span, light mass, low rigidity, which lead to the dynamics characters of low frequency, light damping, dense modes. The vibration of LFSA can be intrigued by orbit or attitude maneuver of the spacecraft, as well as by environment disturbances from the space. Because of the light structural damping of LFSA and absence of atmosphere damping, the harmful vibration doesn't attenuate. The harmful vibration has bad effect on the attitude stability and pointing accuracy of the spacecraft. Conventional control methods and classical control theories are not suited to the control problem of the large flexible system again. Based on the background, this dissertation brings forward the active constrained layer damping control method and multi-objective robust controller design theory and method in the LMI framework, which have been deeply studied and discussed, the main contents and results in the dissertation are as follows:
(1) According to the mechanics characteristics of the LFSA, they are simplified as five kinds of models: one piece of plate, one piece of frame plate, joint multi-plate, joint multi-frame plate and rigid flexible model of the flexible spacecraft. The dynamics model of the above five simplified model with ACLD treatments are developed. The finite element analysis programs are coded in Matlab. The dynamics model are verified through the comparison of eigenvalues and frequency response curves between the model above and one set up by the Msc.Nastran software.
(2) The effect of the ACLD position on the modal damping factors was analyzed from the view of shear deformation of viscoelastic layer, a simple method of the ACLD disposition is given hereby.
(3) Dynamics model reduction is studied for the structures bonded with ACLD treatments. Both the balance reduction method and dynamic reduction method which are widely used, are inapplicable to the model with viscoelastic materials. A new compound model reduction method based on the Krylov subspace method and the balance reduction method is proposed. It demonstrates that the reduced model holds the main dynamics characteristics of the original model including the eigenvalues, the frequency responses, the impulse responses and the sine responses. The lower model available to design the control system is obtained through model reduction using the compound method.
(4) In the multichannel spirit, the multi-objective synthesis of vibration control of the grid solar arrays is discussed. The observer-based states feedback controller is designed in the LMI framework. The model uncertainties are dealt with by introducing an internal feedback loop. The input saturation constraint is addressed by the peak-peak gain and the invariant ellipsoid shaped by the Lyapunov function. A sufficient condition is derived for disturbance rejection performance, and the control input constraints. Taking the rigid solar array as the research object, the controller method is shown to be feasible and effective through the numerical simulation.
(5) Validating vibration control experiment of the imitational foldaway solar array with ACLD treatments is done. The experiment results show that the ACLD control strategy and the robust controller can suppress the vibration of the solar array effectively.
(1)根据太阳能电池翼的结构特点,简化为:单板、单框架板、多板铰接、多框架板铰接和中心刚体+板五种模型。在此基础上,建立了含ACLD结构的太阳能电池翼动力学模型。编制相应的有限元分析程序,并将计算所得特征值和频率响应与Msc.Nastran软件的计算结果进行对比,验证了模型的正确性。
(2)直接从影响粘弹性层剪切变形的角度分析了ACLD结构位置对太阳能电池翼模态阻尼因子的影响,并据此给出了简易地确定ACLD结构位置的方法。
(3)研究了具有主动约束阻尼结构的动力学模型降阶问题。由于粘弹性阻尼材料的存在,使得平衡降阶和动力缩聚两类广泛应用的模型降阶方法不再适用。论文改进了Krylov子空间模型降阶方法,并结合Krylov子空间降阶方法和平衡降阶方法的优点,提出了复合降阶方法。从特征值、频率响应、脉冲响应和正弦响应四个方面说明降阶模型可忠实表征原模型的动力学特点。使用复合降阶方法对动力学模型进行降阶,得到了适合控制系统设计的低阶模型。
(4)引入多通道思想,在LMI框架内研究了电池翼振动控制的多目标综合问题,设计了基于观测器的状态反馈控制器。使用内部反馈回路处理系统的不确定性,引入Lyapunov函数成形的不变椭圆和峰—峰增益使控制输入满足约束限制。得到了具有干扰抑制性能且满足控制输入约束的鲁棒稳定的基于观测器的状态反馈控制器存在的充分条件。以太阳能电池翼为研究对象,通过数值仿真验证了控制器设计方法的可行性和有效性。
(5)开展了基于主动约束阻尼技术的太阳能电池翼振动控制的验证性实验研究。实验结果表明所建理论模型是正确的,采用主动约束阻尼控制技术和鲁棒反馈控制器对抑制电池翼的振动是有效的。
Active vibration control of Large Flexible Solar Array (LFSA) is a challenging subject in the domain of spacecraft dynamics and control. LFSA has structural characters of large span, light mass, low rigidity, which lead to the dynamics characters of low frequency, light damping, dense modes. The vibration of LFSA can be intrigued by orbit or attitude maneuver of the spacecraft, as well as by environment disturbances from the space. Because of the light structural damping of LFSA and absence of atmosphere damping, the harmful vibration doesn't attenuate. The harmful vibration has bad effect on the attitude stability and pointing accuracy of the spacecraft. Conventional control methods and classical control theories are not suited to the control problem of the large flexible system again. Based on the background, this dissertation brings forward the active constrained layer damping control method and multi-objective robust controller design theory and method in the LMI framework, which have been deeply studied and discussed, the main contents and results in the dissertation are as follows:
(1) According to the mechanics characteristics of the LFSA, they are simplified as five kinds of models: one piece of plate, one piece of frame plate, joint multi-plate, joint multi-frame plate and rigid flexible model of the flexible spacecraft. The dynamics model of the above five simplified model with ACLD treatments are developed. The finite element analysis programs are coded in Matlab. The dynamics model are verified through the comparison of eigenvalues and frequency response curves between the model above and one set up by the Msc.Nastran software.
(2) The effect of the ACLD position on the modal damping factors was analyzed from the view of shear deformation of viscoelastic layer, a simple method of the ACLD disposition is given hereby.
(3) Dynamics model reduction is studied for the structures bonded with ACLD treatments. Both the balance reduction method and dynamic reduction method which are widely used, are inapplicable to the model with viscoelastic materials. A new compound model reduction method based on the Krylov subspace method and the balance reduction method is proposed. It demonstrates that the reduced model holds the main dynamics characteristics of the original model including the eigenvalues, the frequency responses, the impulse responses and the sine responses. The lower model available to design the control system is obtained through model reduction using the compound method.
(4) In the multichannel spirit, the multi-objective synthesis of vibration control of the grid solar arrays is discussed. The observer-based states feedback controller is designed in the LMI framework. The model uncertainties are dealt with by introducing an internal feedback loop. The input saturation constraint is addressed by the peak-peak gain and the invariant ellipsoid shaped by the Lyapunov function. A sufficient condition is derived for disturbance rejection performance, and the control input constraints. Taking the rigid solar array as the research object, the controller method is shown to be feasible and effective through the numerical simulation.
(5) Validating vibration control experiment of the imitational foldaway solar array with ACLD treatments is done. The experiment results show that the ACLD control strategy and the robust controller can suppress the vibration of the solar array effectively.
引文
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