Optimization, Analysis And Control Of The Stewart Platform For The SKA

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 principleof 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...