毕业生知识库

500米口径球面射电望远镜FAST（Five-hundred-meter Aperture Spherical radio Telescope）是我国自主设计并建造的全球最大的射电望远镜。FAST要实现对外太空射电源的精确观测，要求馈源接收机的位姿精度满足设计指标。实现FAST接收机对信号聚焦点的精确跟踪主要依靠馈源支撑系统，该系统由包含索驱动、AB转轴的粗调机构和Stewart精调平台构成。由于FAST的舱-索系统存在大柔性和低阻尼的特点，若运动规划不当则可能引起系统振动，从而影响接收机位姿精度甚至破坏机械机构。对此，本文围绕馈源支撑系统的建模、换源和圆弧运动的抑振规划方法以及接收机终端的位置误差补偿算法等方面进行研究。以FAST馈源支撑整体控制系统为工程背景，本文主要的研究内容如下。
1. 从整体上介绍FAST及其馈源支撑系统的工作原理，根据抑振运动规划的研究需要，通过对FAST舱-索系统的固有频率和阻尼比等参数的分析，建立FAST舱-索系统的简化模型。同时推导了Stewart平台的正逆运动学模型，为基于AB轴调节的误差补偿的研究做铺垫。
2. 提出基于最优双S曲线规划和ZVD输入整形法的串级抑振运动规划方法，将两者结合起来应用于FAST舱-索系统运动规划的设计。本文给出了串级抑振运动规划中的输入整形不改变最优双S曲线规划中的最优时间比的数学证明，同时展示了对应的算法流程。仿真与现场实验表明算法能抑制馈源舱在换源和圆弧运动中产生振动，验证了所提方法有效性，同时仿真实验表明该方法对于固有频率变化具有鲁棒性。
3. 提出基于AB轴调节的误差补偿方案，旨在减少Stewart快速补偿的反作用力可能造成的舱-索系统的振动并补偿接收机终端的位置误差。通过建立相关的坐标系，推导出接收机终端的位置关于AB轴角的雅克比矩阵。在此基础上分别以最小化平方误差（MSE）和正则化的MSE为目标，进行误差补偿。通过相关的数值分析，对比了两者的位置误差补偿效果和约束AB轴角微调量大小方面的性能差别。
最后，在FAST馈源支撑整体控制系统中实现本文提出的串级抑振运动规划算法。现场实验结果表明：本文所提算法能抑制馈源舱运动过程中的振动，提高系统运行的平稳性。

FAST (short for Five-hundred-meter Aperture Spherical radio Telescope), which was designed and built by China independently, is the largest radio telescope in the world. In order to detect radio from the outer space precisely, it is crucial that the pose accuracy satisfy the expected performance index. Actually, tracking the focus of radio precisely depends heavily on the Feed Support System (FSS), which consists of the coarse adjustment mechanical structure (including the cable-driven parallel robot and the A-B rotator) and Stewart manipulator for fine adjustment. Due to the flexibility and low damping ratio, the cable-cabin system of FAST may suffer vibration without proper trajectory planning, which can cause pose deviation and even destroy the mechanical structure. To solve this, this thesis is focused on the modeling of FSS, the vibration-free trajectory planning for the slewing and circling task, and the research on compensation for the position error of the receiver terminal. Based on the Whole Control System of FSS (WCSFSS) project, the main contributions of this thesis are listed as follows.
1. The basic operation mechanism of FAST including FSS is introduced. According to the requirement of research on vibration-free trajectory planning, a simplified cable-cabin model is established based on the analysis of the natural frequency and damping ratio of the cable-cabin system. Meanwhile, the forward and inverse kinematics equations of Stewart manipulator are derived to pave the way for the research of error compensation based on the adjustment of the A-B rotator.
2. Combining the Optimal Double S-curve Planning with ZVD input shaping, Cascade Vibration-free Trajectory Planning (CVTP) is proposed and applied to the motion planning of the cable-cabin system. In this thesis, it is proved that the input shaping procedure will not shift the optimal ratio of the ramping-up time to the total acceleration time for the Optimal Double S-curve Planning as a sub process in Cascade Vibration-free Trajectory Planning. At the same time, the corresponding procedure of the algorithm is shown. The results of simulation and experiment at the site of FAST demonstrate that the proposed planning method is effective and robust to the change of natural frequency in the slewing and circling task.
3. An algorithm framework for position error compensation based on the adjustment of the A-B rotator is proposed to alleviate the vibration of the cable-cabin system caused by the counterforce from the rapid acting of Stewart manipulator and to compensate for the position error of the receiver terminal. With the involved coordinate frames established, the Jacobian Matrix, which relating the change of angles of the A-B rotator to the position deviation of the receiver terminal, is derived. Based on the Jacobian Matrix, two proposals for error compensation conforming to the principle of Minimum Square Error (MSE) and Regularized MSE respectively are discussed and compared with each other in their capability of error compensation and limitation of angle adjustment of the A-B rotator through numerical analysis.
Finally, the proposed Cascade Vibration-free Trajectory Planning is implemented in the software of the WCSFSS project. The experiment at the site of FAST proves that the proposed CVTP is effective for suppressing vibration of the Feed Cabin and contributes to stability of the system during operation.