大射电望远镜精调Stewart平台的优化、分析与控制
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摘要
本文依托新一代大射电望远机电光一体化创新设计方案，针对馈源指向跟踪系统高精度轨迹跟踪要求，以精调Stewart平台为研究对象，进行了6自曲度并联机器人的运动学优化设计、动力学分析与奇异性分析，设计了强鲁棒性自抗扰控制器实现高精度轨迹跟踪控制；提出了新一代大射电望远镜馈源指向跟踪系统轨迹跟踪独立控制策略、轨迹规划策略和控制模型；50米缩比模型实验验证了轨迹跟踪控制策略与方法的工程有效姓和可行性。具体内容如下：
1．以并联机器人Jacobian矩阵的条件数为优化设计的目标函数，提出了基于遗传算法的并联机器人最优运动学性能结构参数优化设计方法，采用实值遗传算法，对精调Stewart平台进行了优化设计，得到了最优运动学的精调Stewart平台结构参数，为实现新一代大射电望远镜馈源指向跟踪系统高精度轨迹跟踪控制奠定了坚实的基础。
2．应用虚功原理方法，建立了6自由度并联机器人的动力学分析模型，获得了精调Stewart平台各变位执行器的广义驱动力，为数值仿真分析馈源指向跟踪系统两组成子系统之间的动力学耦合问题奠定了理论基础。
3．提出了基于遗传算法的并联机器人奇异性分析方法，将机器人的奇异性分析转化为在可达工作空间内寻找Jaeobian矩阵行列式平方最小值问题，有效地解决了并联机器人奇异性分析问题。若该最小值不为零，则可以确切地说，该并联机器人不会发生奇异；否则，就会发生奇异。采用实值遗传算法对优化的精调Stewart平台进行了奇异性分析，证明了所设计的精调Stewart平台在工作空间内不会发生奇异。
4．采用分散控制策略实现6自由度精调Stewart平台高精度轨迹跟踪控制，在机器人关节空间设计了强鲁棒性的自抗扰控制器(ADRC)，应用非线性跟踪微分器获得了在测量噪声和未知扰动情况下的高质量微分信号；将影响伺服精度的非线性摩擦视为对被控系统的未知外扰，通过扩张状态观测器实现了不基于任何模型的非线性摩擦补偿；并采用非线性PD合成控制作用，进一步确保了高精度的实现。数值仿真和实验结果验证了所设计的ADRC方法的工程有效性。而且，相关方法可以应用到其它高精度伺服系统的控制中。
5．基于第三章的动力学分析结果，数值仿真分析了新一代大射电望远镜馈源指
一
向跟踪系统两组成子系统之间的动力学耦合问题。提出了新一代大射电望远
镜馈源指向跟踪系统高精度轨迹跟踪独立控制策略，将粗、精调子系统之间
的动力学耦合作用视为对精调子系统的未知外扰，通过强鲁棒性的精调子系
统的自抗扰控制器实现整个大系统的高精度轨迹跟踪控制。提出了相应的简
单易行的轨迹规划策略和跟踪控制模型。通过新一代大射电望远镜馈源指向
跟踪系统50米缩比模型，实验验证了控制策略与方法的工程有效性响行
性。为将来建造500米的新一代大射电望远镜先导模型扫清了关键技格碍
之一。而且，本文所提的独立控制策略、自抗扰控制方法、轨迹规划策略和
运动控制模型，为速度要求较低的其它宏一微机器人系统的眈度轨迹础控
制提供了一个可行的控制方案。
The square kilometre array (SKA) is an ambitious world cooperative project to develop the next generation large radio telescope with the collecting area of one square kilometer. To make full use of the karst formation in Guizhou Province of China, a large spherical radio telescope array of the Arecibo telescope was proposed in China in 1995. Therefore, a completely new design project that integrating mechatronics and optics technologies with several large span cables is proposed to drive the feed-supporting system to realize the high precision positioning.
For the high requirement of trajectory tracking of the feed-supporting system with large span cables, the feasibility of Stewart platform served as a fine-tuning platform and the accomplishment of the high precision tracking are considered in details in this paper.
This paper is divided into the following two parts. In the first part, the optimal kinematicaldesign, analysis and control of the fine-tuning Stewart platform for the feed-supporting system are concentrated. In the second parts, the novel independent control strategy is proposed to realize the high precision positioning of the feed-supporting system for the SKA. The main research works can be described as follows.
1. The Jacobian matrix connecting the dexterity performance of parallel platform is first deduced, and then the condition number of Jacobian matrix is employed as the Objective function to implement the optimal kinematical design of the fine-tuning Stewart platform for the SKA. A real-coded genetic methodology for this optimal kinematical design is presented. A niched-penalty approach is used to transform this optimal kinematical design problem to an unconstrained one. A kinematic accuracy comparison of the genetic designed fine-tuning Stewart platform with the quasi-Newtonian designed one is made. The comparison results have shown that the kinematic accuracy of the genetic designed fine-tuning Stewart platform has a much higher accuracy and a compact structure than that of the quasi-Newtonian designed one, which guarantees the accomplishment of high precision trajectory tracking and reduces the disturbance of wind to the feed-supporting system.
2. The dynamic model of 6 DOF parallel manipulator is developed using the principle
of virtual work. The actuating force of each extensible linear actuator is obtained, which has built a solid base for the simulation analysis of the dynamic coupling between the two comprised subsystems of the feed-supporting system for the SKA.
3. The singularity analysis of the general 6 DOF parallel manipulator is transformed into the optimal issue in the reachable workspace, the square of the determinant of Jacobian matrix is selected as the objective function, and the minimal of this objective function is searched by a real-coded genetic algorithm. The singularity of the parallel manipulator depends on this minimal objective function, if this value is zero, the singularity of the parallel manipulator will happen, otherwise, the parallel manipulator is singularity-free. The singularity of the optimal designed fine-tuning Stewart platform is analyzed using this new genetic singularity analysis method. The results have shown that the fine-tuning Stewart platform is singularity-free, which has laid a solid base for the high precision trajectory tracking of the SKA.
4. A robust auto-disturbance rejection controller (ADRC) in linkspace is developed to accomplish the high precision tracking control of the general 6 DOF parallel manipulator. A nonlinear tracking differentiator (TD) in the feedforward patn and an extended-states observer (ESO) in the feedback path are designed to obtain high quality differential signal and the estimate of the states and the real action of the unknown disturbance including the nonlinear friction without any mathematical model, respectively. Moreover, the unmodeled nonlinear friction, being the dominant to degrade the high precision tracking of servo system, is considered as an unknown disturbance, and realized f
1．以并联机器人Jacobian矩阵的条件数为优化设计的目标函数，提出了基于遗传算法的并联机器人最优运动学性能结构参数优化设计方法，采用实值遗传算法，对精调Stewart平台进行了优化设计，得到了最优运动学的精调Stewart平台结构参数，为实现新一代大射电望远镜馈源指向跟踪系统高精度轨迹跟踪控制奠定了坚实的基础。
2．应用虚功原理方法，建立了6自由度并联机器人的动力学分析模型，获得了精调Stewart平台各变位执行器的广义驱动力，为数值仿真分析馈源指向跟踪系统两组成子系统之间的动力学耦合问题奠定了理论基础。
3．提出了基于遗传算法的并联机器人奇异性分析方法，将机器人的奇异性分析转化为在可达工作空间内寻找Jaeobian矩阵行列式平方最小值问题，有效地解决了并联机器人奇异性分析问题。若该最小值不为零，则可以确切地说，该并联机器人不会发生奇异；否则，就会发生奇异。采用实值遗传算法对优化的精调Stewart平台进行了奇异性分析，证明了所设计的精调Stewart平台在工作空间内不会发生奇异。
4．采用分散控制策略实现6自由度精调Stewart平台高精度轨迹跟踪控制，在机器人关节空间设计了强鲁棒性的自抗扰控制器(ADRC)，应用非线性跟踪微分器获得了在测量噪声和未知扰动情况下的高质量微分信号；将影响伺服精度的非线性摩擦视为对被控系统的未知外扰，通过扩张状态观测器实现了不基于任何模型的非线性摩擦补偿；并采用非线性PD合成控制作用，进一步确保了高精度的实现。数值仿真和实验结果验证了所设计的ADRC方法的工程有效性。而且，相关方法可以应用到其它高精度伺服系统的控制中。
5．基于第三章的动力学分析结果，数值仿真分析了新一代大射电望远镜馈源指
一
向跟踪系统两组成子系统之间的动力学耦合问题。提出了新一代大射电望远
镜馈源指向跟踪系统高精度轨迹跟踪独立控制策略，将粗、精调子系统之间
的动力学耦合作用视为对精调子系统的未知外扰，通过强鲁棒性的精调子系
统的自抗扰控制器实现整个大系统的高精度轨迹跟踪控制。提出了相应的简
单易行的轨迹规划策略和跟踪控制模型。通过新一代大射电望远镜馈源指向
跟踪系统50米缩比模型，实验验证了控制策略与方法的工程有效性响行
性。为将来建造500米的新一代大射电望远镜先导模型扫清了关键技格碍
之一。而且，本文所提的独立控制策略、自抗扰控制方法、轨迹规划策略和
运动控制模型，为速度要求较低的其它宏一微机器人系统的眈度轨迹础控
制提供了一个可行的控制方案。
The square kilometre array (SKA) is an ambitious world cooperative project to develop the next generation large radio telescope with the collecting area of one square kilometer. To make full use of the karst formation in Guizhou Province of China, a large spherical radio telescope array of the Arecibo telescope was proposed in China in 1995. Therefore, a completely new design project that integrating mechatronics and optics technologies with several large span cables is proposed to drive the feed-supporting system to realize the high precision positioning.
For the high requirement of trajectory tracking of the feed-supporting system with large span cables, the feasibility of Stewart platform served as a fine-tuning platform and the accomplishment of the high precision tracking are considered in details in this paper.
This paper is divided into the following two parts. In the first part, the optimal kinematicaldesign, analysis and control of the fine-tuning Stewart platform for the feed-supporting system are concentrated. In the second parts, the novel independent control strategy is proposed to realize the high precision positioning of the feed-supporting system for the SKA. The main research works can be described as follows.
1. The Jacobian matrix connecting the dexterity performance of parallel platform is first deduced, and then the condition number of Jacobian matrix is employed as the Objective function to implement the optimal kinematical design of the fine-tuning Stewart platform for the SKA. A real-coded genetic methodology for this optimal kinematical design is presented. A niched-penalty approach is used to transform this optimal kinematical design problem to an unconstrained one. A kinematic accuracy comparison of the genetic designed fine-tuning Stewart platform with the quasi-Newtonian designed one is made. The comparison results have shown that the kinematic accuracy of the genetic designed fine-tuning Stewart platform has a much higher accuracy and a compact structure than that of the quasi-Newtonian designed one, which guarantees the accomplishment of high precision trajectory tracking and reduces the disturbance of wind to the feed-supporting system.
2. The dynamic model of 6 DOF parallel manipulator is developed using the principle
of virtual work. The actuating force of each extensible linear actuator is obtained, which has built a solid base for the simulation analysis of the dynamic coupling between the two comprised subsystems of the feed-supporting system for the SKA.
3. The singularity analysis of the general 6 DOF parallel manipulator is transformed into the optimal issue in the reachable workspace, the square of the determinant of Jacobian matrix is selected as the objective function, and the minimal of this objective function is searched by a real-coded genetic algorithm. The singularity of the parallel manipulator depends on this minimal objective function, if this value is zero, the singularity of the parallel manipulator will happen, otherwise, the parallel manipulator is singularity-free. The singularity of the optimal designed fine-tuning Stewart platform is analyzed using this new genetic singularity analysis method. The results have shown that the fine-tuning Stewart platform is singularity-free, which has laid a solid base for the high precision trajectory tracking of the SKA.
4. A robust auto-disturbance rejection controller (ADRC) in linkspace is developed to accomplish the high precision tracking control of the general 6 DOF parallel manipulator. A nonlinear tracking differentiator (TD) in the feedforward patn and an extended-states observer (ESO) in the feedback path are designed to obtain high quality differential signal and the estimate of the states and the real action of the unknown disturbance including the nonlinear friction without any mathematical model, respectively. Moreover, the unmodeled nonlinear friction, being the dominant to degrade the high precision tracking of servo system, is considered as an unknown disturbance, and realized f
引文
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