Nonlinear PD Control of a Long-Span Cable-Supporting Manipulator in Quasi-Static Motion

This paper addresses modeling and control of a cable-supporting manipulator serving as the feed supporting structure of a large radio telescope. The manipulator consists of six long cables so that their curves must be considered. The end-effector is prone to vibration due to the long-span cables even if cable lengths can change perfectly just as they are expected. To deal with this problem, a feedback controller in the workspace is devised, in which the effects of both the cable length error and the pose error of the end-effector are taken into account. A controller is first devised for the resultant cable wrench exerted on the end-effector. Then the incremental relationship between the cable end force and the cable length together with the displacements of the end-effector is deduced. Combining this relationship, we convert the controller into a nonlinear one with cable length increment as the control output, which can be readily utilized in the manipulator. Numerical examples and experiments carried out on a field model of dimension 50 m validate the positioning precision of the manipulator and we can conclude the feasibility of the proposed feed supporting system.