超大型天线馈源指向跟踪系统的力学分析及控制研究
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摘要
在国家自然科学基金重点项目的支持下,基于前人的工作,本文主要对新一代超大口径球反射面射电望远镜FAST(Five-hundred Meter Aperture Spherical RadioTelescope)馈源指向跟踪系统的力学分析与控制进行研究。完成的主要工作和取得的研究结论归纳如下:
1.基于柔索的弹性悬链线方程,针对超大型天线的特点,建立了FAST馈源舱柔索支撑系统的非线性静力学模型,导出了系统静态刚度矩阵的解析表达式。由刚度表达式可见,系统刚度与馈源舱的位姿、舱索固接点的位置、柔索数目以及柔索拉力有关。最后,通过数值算例和物理实验验证了分析方法的正确性和有效性。
2.根据馈源舱柔索支撑机构交流伺服驱动系统的等效电路模型,建立了由伺服驱动电机到卷扬机的机电系统的动力学模型。在该模型中不但考虑了摩擦非线性环节的影响,而且还考虑了未建模动态等干扰的影响。在此基础上,针对该交流伺服驱动系统,设计了一种模糊滑模控制方法。这种方法通过分阶段的加入指数趋近控制来加快系统响应,同时利用模糊控制器实时调整滑模控制的趋近律参数。不仅保证了控制系统的快速性和鲁棒性,而且有效地削弱滑模控制的颤动;另外,该控制方案设计简单,便于工程应用。以馈源舱柔索支撑系统交流伺服驱动机构为对象进行数值仿真,结果表明这种控制方法能够获得良好的控制精度和较强的鲁棒性。进一步证明了理论分析的正确性和设计方法的有效性。
3.应用拉格朗日方程建立了馈源舱柔索支撑系统的动力学模型,解决了已知馈源舱运动轨迹,对馈源舱柔索支撑系统的逆运动学、逆动力学问题。同时,在考虑舱体动态运动过程中惯性力影响的前提下,进行馈源舱柔索支撑系统的轨迹规划,进一步可求解特定长度的柔索对处于某一位姿的馈源舱的作用力,并采用具有二次收敛性的Newton-Raphson迭代法进行解算,得到了更快的求解速度以满足控制的要求。数值计算结果表明,舱体中心的运行轨迹与运动要求相吻合;索长、舱体沿各坐标方向的位移、速度和加速度符合周期变化曲线;舱体上作用力的数值合理;从而验证了所建立的馈源舱柔索支撑系统的动力学模型是正确的。同时为进一步实现馈源舱柔索支撑系统的精确控制奠定了基础。
4.通过对馈源舱柔索支撑系统动力学的强非线性、参数不确定性以及受到外界干扰等系统特性的分析,探讨了该类控制系统的控制特点和适用的控制策略。进一步,设计了一种将常规PI控制和Fuzzy控制相结合的Fuzzy-PI混合离散控制策略来实现馈源舱轨迹跟踪控制。这种控制策略不仅能发挥模糊控制鲁棒性强、动态响应快的特点,而且具有常规PI控制器的动态跟踪品质和稳态精度。在此基础上,为了进一步提高Fuzzy-PI混合离散控制系统的适应能力,设计了一种带有自调整因子的模糊控制规则。为了验证该Fuzzy-PI混合离散控制算法的优良控制性能,在相同给定条件和扰动下把Fuzzy-PI混合离散控制算法与常规模糊控制和离散非线性PID控制算法进行了比较研究。数值计算及结果分析表明,该Fuzzy-PI混合离散控制方法可在较大程度上补偿系统的非线性特性,并能提高系统响应的快速性、运动跟踪精度以及抗扰动能力。
5.根据KED(Kineto Elastio Dynamic Analysis)原理建立了柔性支腿Stewart平台的动力学模型。解决了已知动平台运动规划轨迹,求各滑动关节驱动力的动力学逆问题。由于充分考虑了动平台惯性、支腿惯性、支腿弹性和关节摩擦等因素,保证了模型的准确性。这种动力学模型为研究Stewart平台高精度轨迹跟踪控制奠定了基础。针对该机构的非线性、强耦合和多输入多输出等特点,设计了一种PID神经网络控制器(Proportional-Integral-Derivative Neural Network controller)来实现精调Stewart平台的高精度轨迹跟踪。这种PID神经网络控制策略采用基于优化神经网络的PID解耦控制,将PID控制规律融进神经元之中,既具有神经网络自学习、自适应及逼近任意函数的能力,又具有常规PID控制器结构简单、可靠性高等特点。理论分析和数值计算结果表明了该方法的有效性。
This work was supported by Chinese National Natural Science Foundation under Grant No. 10433020. On the basis of the predecessor work, this paper is mainly concerned with the mechanics analysis and control of the feed tracking system for the next generation super antenna, which is the new design project of five-hundred meter aperture spherical radio telescope (FAST ). The main research works can be described as follows.
1. Based on the elastic analytical equation of catenary of a cable with two endpoints fixed and considering the special characteristics of super antenna, a nonlinear static mechanical model of the cable-suspended system is derived. According to the highly nonlinear relationship between end force of a cable and cabin displacement, the incremental expression of forces on cabin exerted by the cable-suspended system, in terms of cabin displacement, is formulated based on the static mechanical model, and then the analytical expression of the static stiffness matrix is obtained. It can be noted from the expression that the static stiffness of cable-suspended system has relations with position and posture of the cabin, position of connection point between the cabin and the cable, and the number and drag force of the cable. In the end, the correctness and effectiveness of the analysis method is verified by the combination of numerical simulation and experimental research. Results between simulation and experiment can be matched fairly well.
2. According to the equivalent circuit of the servomechanism, the dynamic model of the electromechanical coupling system for the cable-suspended mechanism is developed in the presence of internal model uncertainties in both nonlinear friction and servomechanism dynamics and external disturbances. Due to the inherent characteristics of the nonlinearity structure, a novel control method combining sliding mode control with fuzzy logic control is designed for the sake of realizing the trajectory tracking of the object. The approach applies fuzzy controller to adjust the parameters of reach law of sliding mode timely. At the same time the exponent approximating control is added by grading. This approach not only ensures the speediness and robustness of the control system, but also can weaken chattering, and the design of the control system is simple and it can be easily applied in the engineering. Taking the servomechanism model for the cable-suspended system as example, the simulation study on the algorithm is carried out, and its effectiveness and higher robustness are confirmed.
3. Aiming at the cable-suspended system, on the basis of the inverse kinematics analysis the inverse dynamic formulation of the cable-cabin system with non-negligible cable mass was established by means of Lagrange's Equations. At the same time, considering the inertia force of the cabin in motion, trajectory planning of the cable-cabin system is conducted. So the actuating forces on the cabin locating at a certain position and pose can be solved with the given driving cable lengths. The equations can be solved by using Newton-Raphson method possessing the quadratic convergence property, which can guarantee a faster computation speed to meet the requirement of real time control algorithm. Simulation results illustrate that the center of the cabin tracks the planned trajectory relatively well; the length of cable varies symmetricly; the forces actuating on the cabin in the direction of X and Y are equal to the centripetal forces in the direction of X and 7 as the cabin moves along the path, respectively; on the other hand, the force actuating on the cabin in the direction of Z equals the gravity of the cabin. From the aforementioned results, it may be concluded that we justify the dynamic modeling for control.
4. Taking account of the model uncertainties and external disturbances for the cable-suspended system, control strategy of the flexible system is discussed. In addition, considering the characteristics of nonlinearity, slow time-varying, and multivariable coupling of the system, a fuzzy control plus proportional-integral hybrid discrete-time control method combining PI control with fuzzy logic control, which can enhance the control performance for steady state errors, is developed for more effective and robust performance. The scheme with proportional-integral-tuning unit, which optimizes the control rules by adjusting factors, is utilized to carry out the trajectory tracking of the cabin. For comparison, a discrete-time nonlinear PID control arithmetic and a conventional fuzzy logic controller are also used for the motion control for the cable-suspended system. The system is simulated with expected signal input via the controller based on the established dynamic equation. The results show that the control system achieves a better tracking performance and the control system has strong robustness.
5. On the basis of the principle of KED ( Kineto Elastio Dynamic Analysis ), an inverse dynamic formulation for a flexible Stewart platform with elastic legs is derived through Newton-Euler method, which involves the inertias of the platform and six legs, the elasticity of the legs and frictions at joints. So this establishes a basis for realizing the tracking control of the Stewart platform. In view of the characteristics of nonlinearity, strong coupling, and MIMO ( Multi-Input and Multi-Output ) system, a proportional-integral-derivative neural network controller is designed to carry out the high-precision trajectory tracking of the platform. The PID neural network is a kind of feedforward multilayer network. Its hidden layer neurons are proportional neuron ( P ), integral neuron ( I ), and derivative neuron ( D ). The numbers of the neurons, the connective forms and primary value of the weights are based on the rules of the PID control. The PID neural network controller can effectively incorporate neural network and PID control into its basic design, and has very good dynamic and static properties. The results of theoretical analysis and simulation verify that the proposed control strategy is effective and reasonable, and can realize dynamic trajectory following under the condition of external disturbances.
1.基于柔索的弹性悬链线方程,针对超大型天线的特点,建立了FAST馈源舱柔索支撑系统的非线性静力学模型,导出了系统静态刚度矩阵的解析表达式。由刚度表达式可见,系统刚度与馈源舱的位姿、舱索固接点的位置、柔索数目以及柔索拉力有关。最后,通过数值算例和物理实验验证了分析方法的正确性和有效性。
2.根据馈源舱柔索支撑机构交流伺服驱动系统的等效电路模型,建立了由伺服驱动电机到卷扬机的机电系统的动力学模型。在该模型中不但考虑了摩擦非线性环节的影响,而且还考虑了未建模动态等干扰的影响。在此基础上,针对该交流伺服驱动系统,设计了一种模糊滑模控制方法。这种方法通过分阶段的加入指数趋近控制来加快系统响应,同时利用模糊控制器实时调整滑模控制的趋近律参数。不仅保证了控制系统的快速性和鲁棒性,而且有效地削弱滑模控制的颤动;另外,该控制方案设计简单,便于工程应用。以馈源舱柔索支撑系统交流伺服驱动机构为对象进行数值仿真,结果表明这种控制方法能够获得良好的控制精度和较强的鲁棒性。进一步证明了理论分析的正确性和设计方法的有效性。
3.应用拉格朗日方程建立了馈源舱柔索支撑系统的动力学模型,解决了已知馈源舱运动轨迹,对馈源舱柔索支撑系统的逆运动学、逆动力学问题。同时,在考虑舱体动态运动过程中惯性力影响的前提下,进行馈源舱柔索支撑系统的轨迹规划,进一步可求解特定长度的柔索对处于某一位姿的馈源舱的作用力,并采用具有二次收敛性的Newton-Raphson迭代法进行解算,得到了更快的求解速度以满足控制的要求。数值计算结果表明,舱体中心的运行轨迹与运动要求相吻合;索长、舱体沿各坐标方向的位移、速度和加速度符合周期变化曲线;舱体上作用力的数值合理;从而验证了所建立的馈源舱柔索支撑系统的动力学模型是正确的。同时为进一步实现馈源舱柔索支撑系统的精确控制奠定了基础。
4.通过对馈源舱柔索支撑系统动力学的强非线性、参数不确定性以及受到外界干扰等系统特性的分析,探讨了该类控制系统的控制特点和适用的控制策略。进一步,设计了一种将常规PI控制和Fuzzy控制相结合的Fuzzy-PI混合离散控制策略来实现馈源舱轨迹跟踪控制。这种控制策略不仅能发挥模糊控制鲁棒性强、动态响应快的特点,而且具有常规PI控制器的动态跟踪品质和稳态精度。在此基础上,为了进一步提高Fuzzy-PI混合离散控制系统的适应能力,设计了一种带有自调整因子的模糊控制规则。为了验证该Fuzzy-PI混合离散控制算法的优良控制性能,在相同给定条件和扰动下把Fuzzy-PI混合离散控制算法与常规模糊控制和离散非线性PID控制算法进行了比较研究。数值计算及结果分析表明,该Fuzzy-PI混合离散控制方法可在较大程度上补偿系统的非线性特性,并能提高系统响应的快速性、运动跟踪精度以及抗扰动能力。
5.根据KED(Kineto Elastio Dynamic Analysis)原理建立了柔性支腿Stewart平台的动力学模型。解决了已知动平台运动规划轨迹,求各滑动关节驱动力的动力学逆问题。由于充分考虑了动平台惯性、支腿惯性、支腿弹性和关节摩擦等因素,保证了模型的准确性。这种动力学模型为研究Stewart平台高精度轨迹跟踪控制奠定了基础。针对该机构的非线性、强耦合和多输入多输出等特点,设计了一种PID神经网络控制器(Proportional-Integral-Derivative Neural Network controller)来实现精调Stewart平台的高精度轨迹跟踪。这种PID神经网络控制策略采用基于优化神经网络的PID解耦控制,将PID控制规律融进神经元之中,既具有神经网络自学习、自适应及逼近任意函数的能力,又具有常规PID控制器结构简单、可靠性高等特点。理论分析和数值计算结果表明了该方法的有效性。
This work was supported by Chinese National Natural Science Foundation under Grant No. 10433020. On the basis of the predecessor work, this paper is mainly concerned with the mechanics analysis and control of the feed tracking system for the next generation super antenna, which is the new design project of five-hundred meter aperture spherical radio telescope (FAST ). The main research works can be described as follows.
1. Based on the elastic analytical equation of catenary of a cable with two endpoints fixed and considering the special characteristics of super antenna, a nonlinear static mechanical model of the cable-suspended system is derived. According to the highly nonlinear relationship between end force of a cable and cabin displacement, the incremental expression of forces on cabin exerted by the cable-suspended system, in terms of cabin displacement, is formulated based on the static mechanical model, and then the analytical expression of the static stiffness matrix is obtained. It can be noted from the expression that the static stiffness of cable-suspended system has relations with position and posture of the cabin, position of connection point between the cabin and the cable, and the number and drag force of the cable. In the end, the correctness and effectiveness of the analysis method is verified by the combination of numerical simulation and experimental research. Results between simulation and experiment can be matched fairly well.
2. According to the equivalent circuit of the servomechanism, the dynamic model of the electromechanical coupling system for the cable-suspended mechanism is developed in the presence of internal model uncertainties in both nonlinear friction and servomechanism dynamics and external disturbances. Due to the inherent characteristics of the nonlinearity structure, a novel control method combining sliding mode control with fuzzy logic control is designed for the sake of realizing the trajectory tracking of the object. The approach applies fuzzy controller to adjust the parameters of reach law of sliding mode timely. At the same time the exponent approximating control is added by grading. This approach not only ensures the speediness and robustness of the control system, but also can weaken chattering, and the design of the control system is simple and it can be easily applied in the engineering. Taking the servomechanism model for the cable-suspended system as example, the simulation study on the algorithm is carried out, and its effectiveness and higher robustness are confirmed.
3. Aiming at the cable-suspended system, on the basis of the inverse kinematics analysis the inverse dynamic formulation of the cable-cabin system with non-negligible cable mass was established by means of Lagrange's Equations. At the same time, considering the inertia force of the cabin in motion, trajectory planning of the cable-cabin system is conducted. So the actuating forces on the cabin locating at a certain position and pose can be solved with the given driving cable lengths. The equations can be solved by using Newton-Raphson method possessing the quadratic convergence property, which can guarantee a faster computation speed to meet the requirement of real time control algorithm. Simulation results illustrate that the center of the cabin tracks the planned trajectory relatively well; the length of cable varies symmetricly; the forces actuating on the cabin in the direction of X and Y are equal to the centripetal forces in the direction of X and 7 as the cabin moves along the path, respectively; on the other hand, the force actuating on the cabin in the direction of Z equals the gravity of the cabin. From the aforementioned results, it may be concluded that we justify the dynamic modeling for control.
4. Taking account of the model uncertainties and external disturbances for the cable-suspended system, control strategy of the flexible system is discussed. In addition, considering the characteristics of nonlinearity, slow time-varying, and multivariable coupling of the system, a fuzzy control plus proportional-integral hybrid discrete-time control method combining PI control with fuzzy logic control, which can enhance the control performance for steady state errors, is developed for more effective and robust performance. The scheme with proportional-integral-tuning unit, which optimizes the control rules by adjusting factors, is utilized to carry out the trajectory tracking of the cabin. For comparison, a discrete-time nonlinear PID control arithmetic and a conventional fuzzy logic controller are also used for the motion control for the cable-suspended system. The system is simulated with expected signal input via the controller based on the established dynamic equation. The results show that the control system achieves a better tracking performance and the control system has strong robustness.
5. On the basis of the principle of KED ( Kineto Elastio Dynamic Analysis ), an inverse dynamic formulation for a flexible Stewart platform with elastic legs is derived through Newton-Euler method, which involves the inertias of the platform and six legs, the elasticity of the legs and frictions at joints. So this establishes a basis for realizing the tracking control of the Stewart platform. In view of the characteristics of nonlinearity, strong coupling, and MIMO ( Multi-Input and Multi-Output ) system, a proportional-integral-derivative neural network controller is designed to carry out the high-precision trajectory tracking of the platform. The PID neural network is a kind of feedforward multilayer network. Its hidden layer neurons are proportional neuron ( P ), integral neuron ( I ), and derivative neuron ( D ). The numbers of the neurons, the connective forms and primary value of the weights are based on the rules of the PID control. The PID neural network controller can effectively incorporate neural network and PID control into its basic design, and has very good dynamic and static properties. The results of theoretical analysis and simulation verify that the proposed control strategy is effective and reasonable, and can realize dynamic trajectory following under the condition of external disturbances.
引文
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