柔性空间可展开天线的结构与控制集成设计
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摘要
针对空间可展开天线多种因素对展开过程的平稳、准确性影响，本文进行了系统而深入的研究。主要工作如下：
1.应用瑞利-里兹法于柔性构件建模，并从柔性多体系统动力学的角度出发，推导了单元的动能、势能、应变能以及相应的一致质量阵、刚度阵和阻尼阵的表达式，基于拉格朗日第二方程建立了可展开天线系统的展开过程动力学模型。进行了动力响应分析，给出了可展开天线在展开过程中的响应曲线，通过与多刚体动力学模型的仿真试验对比，明确了天线展开过程中的动力学特性及非线性因素对展开过程的影响机理，为展开过程控制系统设计提供了依据。
2.利用Bezier曲线合成驱动索的输入轨迹，通过天线运动学关系式，导出了天线展开过程的运动输出轨迹。研究了通过改变Bezier曲线控制点位置得到不同展开轨迹的可行性，继而通过设置合理的目标函数和约束条件，得到天线最优展开轨迹，既可保证天线角加速度的连续性，又可降低其峰值。最后，研究了展开过程中间匀速段不等式的约束条件，通过数值仿真，得知展开过程保持中间匀速运动会导致天线所受冲击过大，而展开过程应是一个无中间匀速状态的先加速后减速过程，对工程实际有一定指导意义。
3.针对柔性因素带来的展开过程振动问题，提出了一种基于滤波的解耦控制方法。首先，将机构转化为多个瞬时结构进行研究，通过考察瞬时结构基频随展开角度的变化规律，确定了“机构基频”关键位置选取的准则。其次，应用低通滤波器将天线运动反馈分解为纯刚体运动和柔性振动两部分。然后，研究了滤波器截止频率的确定准则，针对不同反馈信号的刚、柔控制器的设计准则，以及两组控制器参数之间的耦合关系及选取准则。
4.探索了天线结构与展开轨迹、天线结构与控制器设计、展开轨迹与控制器设计之间的相互关系，提出了可展开天线结构、展开轨迹及控制系统的集成设计模型。以天线杆件横截面积、Bezier曲线控制点参数及控制器增益参数同时作为设计变量，以减小天线质量、天线在展开过程中所受冲击和展开过程误差累积为目标函数，在满足固有频率、强度、控制系统‘稳准快’等约束条件下，得到最优的综合系统设计方案。
5.设计制作了2m口径的周边桁架索网可展开天线实物模型，进行了模态、形面精度以及展开过程等试验研究。通过试验结果与仿真结果进行比较，验证了本文中结构及展开过程设计方法的合理性与正确性。同时，通过对展开过程中索网形态的测量，分析了索网张力对于天线展开过程的影响规律，提出了对该天线模型的修正方法。
In view of the multi-nonlinear-factor influence to the smoothness and veracity ofdeployment for deployable space antennas, several key technological problems weredealt with in depth. The main works can be described as follows.
1. The deformable bodies are discretized with a hypothesized displacement fieldstructured by the Rayleigh-Ritz method. The kinetic energy, geopotential energy,elasticity potential energy and the corresponding mass matrix, stiffness matrix anddamping matrix are deduced, and then the second type of Lagrange equation is used toestablish the flexible multi-body dynamic model. Via the dynamic analysis, the statevariable responding curves of the deployable antenna can be achieved. The dynamiccharacteristic and the nonlinear influence mechanism of the deployment are obtained,thus providing the foundation for control system design in latter sections.
2. Bezier curves are used to synthesize the input trajectory of the driving cable.Therefore, the corresponding deployment output trajectory can be deduced from theKinetics functions of deployable antennas. The feasibility to obtain differentdeployment trajectories by altering the Bezier control points is investigated. And thenvia setting up reasonable objective function and constraint conditions, the optimaldeployment trajectory can be achieved, which can not only ensure the continuity butalso reduce the peak value of the deployment angular acceleration. Then, the inequalityconstraint, describing the constant deployment mid-period, is discussed. With numericalsimulations and comparisons, it is found that the constant deployment mid-period willlead to large impact on antennas. Therefore, the deployment should be anaccelerated-decelerated curve without constant mid-period, which will give guidance forpractical applications.
3. A decoupling control method is presented for the controlled deployment offlexible deployable space antennas. In order to define the concept of the ‘mechanismeigenfrequency’, mechanism is transformed to several instantaneous structures. Viafinding the variational rules of instantaneous structure eigenfrequency with the changeof the deployment angle, the guideline for ‘critical position’, where the ‘mechanismeigenfrequency’is obtained, is proposed. A low-pass filter is used to decouple themovement feedback signal into two separate parts: the rigid movement and the vibrationcaused by flex factors. The cut-off frequency of the low-pass filter is discussed. Therigid and flex controllers are designed according to the characteristics of the decoupledfeedback respectively. And then the coupling relationship of the gain parameters between the two controllers is discussed and a guideline for the proper parameterselection is proposed based on an energy correlation analysis.
4. The coupled relationship of the antenna structure, deployment trajectory, andcontrol system is discussed, and then the integrated design model is proposed. Amulti-objective function is set to simultaneously minimize the antenna mass, the impacton antenna, and the error accumulation for control system. The link cross-section areasof the antenna, the Bezier control points, and the controller gain parameters are selectedas the design variables. And with the eigenfrequency, stiffness, stability, rapidity andaccuracy constraints, the optimal integrated system design is achieved.
5. A2-meter-diameter model for Astromesh cable-net deployable antenna isdesigned and built. Experimental investigation is carried out, such as structural modalanalysis, reflector surface precision, and deployment test. Based on the comparing withthe simulation and test results, the rationality of the structure and deployment analysismethod in this paper is validated. Meanwhile, based on the measurements of thecable-state in the deployment, the influence of the cable tension to the deployment isdiscussed, and then the revised deployment dynamic model is proposed.
1.应用瑞利-里兹法于柔性构件建模，并从柔性多体系统动力学的角度出发，推导了单元的动能、势能、应变能以及相应的一致质量阵、刚度阵和阻尼阵的表达式，基于拉格朗日第二方程建立了可展开天线系统的展开过程动力学模型。进行了动力响应分析，给出了可展开天线在展开过程中的响应曲线，通过与多刚体动力学模型的仿真试验对比，明确了天线展开过程中的动力学特性及非线性因素对展开过程的影响机理，为展开过程控制系统设计提供了依据。
2.利用Bezier曲线合成驱动索的输入轨迹，通过天线运动学关系式，导出了天线展开过程的运动输出轨迹。研究了通过改变Bezier曲线控制点位置得到不同展开轨迹的可行性，继而通过设置合理的目标函数和约束条件，得到天线最优展开轨迹，既可保证天线角加速度的连续性，又可降低其峰值。最后，研究了展开过程中间匀速段不等式的约束条件，通过数值仿真，得知展开过程保持中间匀速运动会导致天线所受冲击过大，而展开过程应是一个无中间匀速状态的先加速后减速过程，对工程实际有一定指导意义。
3.针对柔性因素带来的展开过程振动问题，提出了一种基于滤波的解耦控制方法。首先，将机构转化为多个瞬时结构进行研究，通过考察瞬时结构基频随展开角度的变化规律，确定了“机构基频”关键位置选取的准则。其次，应用低通滤波器将天线运动反馈分解为纯刚体运动和柔性振动两部分。然后，研究了滤波器截止频率的确定准则，针对不同反馈信号的刚、柔控制器的设计准则，以及两组控制器参数之间的耦合关系及选取准则。
4.探索了天线结构与展开轨迹、天线结构与控制器设计、展开轨迹与控制器设计之间的相互关系，提出了可展开天线结构、展开轨迹及控制系统的集成设计模型。以天线杆件横截面积、Bezier曲线控制点参数及控制器增益参数同时作为设计变量，以减小天线质量、天线在展开过程中所受冲击和展开过程误差累积为目标函数，在满足固有频率、强度、控制系统‘稳准快’等约束条件下，得到最优的综合系统设计方案。
5.设计制作了2m口径的周边桁架索网可展开天线实物模型，进行了模态、形面精度以及展开过程等试验研究。通过试验结果与仿真结果进行比较，验证了本文中结构及展开过程设计方法的合理性与正确性。同时，通过对展开过程中索网形态的测量，分析了索网张力对于天线展开过程的影响规律，提出了对该天线模型的修正方法。
In view of the multi-nonlinear-factor influence to the smoothness and veracity ofdeployment for deployable space antennas, several key technological problems weredealt with in depth. The main works can be described as follows.
1. The deformable bodies are discretized with a hypothesized displacement fieldstructured by the Rayleigh-Ritz method. The kinetic energy, geopotential energy,elasticity potential energy and the corresponding mass matrix, stiffness matrix anddamping matrix are deduced, and then the second type of Lagrange equation is used toestablish the flexible multi-body dynamic model. Via the dynamic analysis, the statevariable responding curves of the deployable antenna can be achieved. The dynamiccharacteristic and the nonlinear influence mechanism of the deployment are obtained,thus providing the foundation for control system design in latter sections.
2. Bezier curves are used to synthesize the input trajectory of the driving cable.Therefore, the corresponding deployment output trajectory can be deduced from theKinetics functions of deployable antennas. The feasibility to obtain differentdeployment trajectories by altering the Bezier control points is investigated. And thenvia setting up reasonable objective function and constraint conditions, the optimaldeployment trajectory can be achieved, which can not only ensure the continuity butalso reduce the peak value of the deployment angular acceleration. Then, the inequalityconstraint, describing the constant deployment mid-period, is discussed. With numericalsimulations and comparisons, it is found that the constant deployment mid-period willlead to large impact on antennas. Therefore, the deployment should be anaccelerated-decelerated curve without constant mid-period, which will give guidance forpractical applications.
3. A decoupling control method is presented for the controlled deployment offlexible deployable space antennas. In order to define the concept of the ‘mechanismeigenfrequency’, mechanism is transformed to several instantaneous structures. Viafinding the variational rules of instantaneous structure eigenfrequency with the changeof the deployment angle, the guideline for ‘critical position’, where the ‘mechanismeigenfrequency’is obtained, is proposed. A low-pass filter is used to decouple themovement feedback signal into two separate parts: the rigid movement and the vibrationcaused by flex factors. The cut-off frequency of the low-pass filter is discussed. Therigid and flex controllers are designed according to the characteristics of the decoupledfeedback respectively. And then the coupling relationship of the gain parameters between the two controllers is discussed and a guideline for the proper parameterselection is proposed based on an energy correlation analysis.
4. The coupled relationship of the antenna structure, deployment trajectory, andcontrol system is discussed, and then the integrated design model is proposed. Amulti-objective function is set to simultaneously minimize the antenna mass, the impacton antenna, and the error accumulation for control system. The link cross-section areasof the antenna, the Bezier control points, and the controller gain parameters are selectedas the design variables. And with the eigenfrequency, stiffness, stability, rapidity andaccuracy constraints, the optimal integrated system design is achieved.
5. A2-meter-diameter model for Astromesh cable-net deployable antenna isdesigned and built. Experimental investigation is carried out, such as structural modalanalysis, reflector surface precision, and deployment test. Based on the comparing withthe simulation and test results, the rationality of the structure and deployment analysismethod in this paper is validated. Meanwhile, based on the measurements of thecable-state in the deployment, the influence of the cable tension to the deployment isdiscussed, and then the revised deployment dynamic model is proposed.
引文
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