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柔性支撑Stewart平台的分析、优化与控制研究
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摘要
本文依托国家自然科学基金“巨型射电天文望远镜(FAST)总体设计与关键技术研究”重点项目,针对超大型柔索驱动并联机器人难以满足馈源跟踪精度要求的难题,探讨了六自由度Stewart平台作为二级精调稳定机构、实现FAST馈源支撑与指向跟踪系统空间高精度动态定位、指向和轨迹跟踪的关键性问题。对Stewart平台的机电综合伺服带宽、构型优化设计、软硬件实现、机构标定和运动控制进行了深入研究,通过FAST50m缩尺现场模型进行了实验验证。主要工作及创造性成果如下:
     1.定义了具有明确物理意义的机电综合伺服带宽,给出了对Stewart平台机电一体化系统响应快速性的评价方法。从Stewart平台机构的运动学和动力学角度,分析了决定其伺服带宽的机械和控制因素,得出了在选定Stewart平台构型参数、驱动支腿的动力学性能和虎克铰、球铰的负载能力的情况下,求解伺服带宽的通用方法,并进行了算例分析。
     2.建立了综合衡量机构运动学、动力学性能和动力学耦合程度的Stewart平台构型设计多目标优化模型,采用实值编码的自适应遗传算法,对Stewart平台的优化问题进行了求解。得到了在满足灵活工作空间和机电综合伺服带宽的前提下,具有更高灵巧度和更弱动力学耦合作用的设计参数。
     3.构建了基于SynqNet同步多轴网络控制器的Stewart平台软、硬件控制系统,实现了馈源平台的典型轨迹动态跟踪控制。采用具有运动平滑作用的梯形速度模式进行了固定基座Stewart平台的典型轨迹规划与实现,针对建造的Stewart平台,进行了工作空间、静态定位精度、动态轨迹跟踪精度和机电综合伺服带宽的实验研究,验证了Stewart平台优化设计结果的有效性。
     4.提出了基于并联机构学原理的三维机动目标解耦跟踪预测算法,为克服馈源舱在外部扰动(风荷和动力学耦合)和内部摄动(柔索系统的柔性、滞后和铰链的摩擦等)作用下的位移响应对馈源平台定位指向的影响奠定了基础。该算法构造了具有良性条件数的虚拟Stewart平台,采用非线性跟踪微分器在其解耦的关节空间进行支腿长度的跟踪预测,进而通过虚拟Stewart平台的位置正解实现了对馈源舱运动位姿的跟踪预测,算例分析证实了所提出算法的高精度和实时性。
     5.设计了自适应交互PID监督控制器,解决了柔性支撑Stewart平台的控制难题。引入自适应交互算法解决了PID参数的实时调整,用以产生柔性支撑Stewart平台的规划级控制量,在电动缸执行级采用带前馈的数字PID伺服滤波器完成电动缸的高精度轨迹跟踪,改善了馈源舱和Stewart平台耦合系统控制过程的动态性能。FAST50m模型现场实验表明,结合解耦预测算法对馈源舱的运动预测,自适应交互PID监督控制器效果明显,确保了馈源支撑与指向跟踪系统在以期望的跟踪速度运行时,定位和指向精度完全满足控制要求。
The research works of this dissertation are based on a major project of Chinese National Science Foundation, entitled by“Overall design and key technogies research of the five hundred meters aperture shperical radio telescope (FAST)”. In view of the difficulty to realize the tracking precision of the feed source for the huge flexible wire driven parallel manipulator (WDPR), several key technological problems in the application of the six-degrees-of-freedom Stewart platform, which was used as a secondary stabilizing and tuning mechanism for achieving the specification of the feed source in FAST, were delt with. The mechatronic servo bandwidth, design optimization, software and hardware implementation, calibration and motion control were developed, which were validated by the experiments of the 50m scaled model of FAST. The main works can be described as follows.
     1. The definition of mechatronic servo bandwidth of the six-degrees-of-freedom Stewart platform was made in the beginning, which has the straightforward physical meaning and can be used to estimate the moving ripidity of the mechatronic system of the Stewart platform. The mechanical and control factors determining the mechatronic servo bandwidth were discussed in the kinematics and dynamics points of view. Given the configuration parameters, dynamical performace of the legs and load capacity of the universal and spherical joints, the general solution to the servo bandwidth is proposed. Besides, a case study was carried out.
     2. The multi-objective configuration optimization model of the Stewart platform was established, which integrated the kinematic, dynamic peformance and dynamical compliance degree with the flexbile base. The real-coded adaptive genetic algorithm was employed to solve the optimization problem. Under the conditioin of satisfying the dexterous and mechatronic servo bandwidth, the design parameters of the Stewart platform for higher dexterity and weaker dynamical compliance were obtained.
     3. Based on the SynqNet sychronized multi-axis network controller, the hardware and software control system of the Stewart platform were developed, and the following control of the typical trajectory was implemented. The smoothly moving trapezoidal mode was adopted to plan and realize the typical trajectory. Aiming at the constructed Stewart platform, experiments on the workspace, static positioning accuracy, and dynamical trajectory tracking accurcy and mechatronic servo bandwidth were carried out. Consequently, the optimized result was validated by experiments.
     4. A decoupled tracking and prediction algorithm was presented, which laid a base for overcoming the effect of displacement response of the feed cabin by the external disturbance (wind load and dynamical compliance) and internal perturbation (the flexibility and lag of the flexible cables, the friction of the joints) on the feed platform. In this algorithm the three dimensional object was treated as the end-effector of a suppositional six degrees-of-freedom fully parallel manipulator. The lengths of actuating links are predicted in the decouled joint space, and then the future position of the object is obtained with forward kinematics of the suppositional parallel manipulator. Taking the two stage compound control model of FAST feed supporting and orienting system as an example, the numerical simulation shows the algorithm has the advantages of high predication accuracy and real time computation.
     5. In order to overcome the control difficulty of the flexible supported Stewart platform, the adaptive interactive PID controller, which utilized the adaptive interactive algorithm to adjust the parameters of conventional PID controller, was devised as the supervisory controller in the joint space of the Stewart platform. The supervisory controller was used to generate the control commands in the upper level of the electrical cylinders and improve the dynmical performance of the control process. Besides, in the lower level of the the electrical cylinders, the digital servo filters with feedforward were employed to track the desired trajectory accurately. The experiments of the FAST50m field model validate the effectiveness of the adaptive PID supervisory controller, accompanied with the motion predication of the feed cabin. The feed supporting, pointing and tracking system could meet the demands of positioning and orientating precision with the desired tracking velocity.
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