| 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.
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