The multi-body system modelling of the Gough–Stewart platform for vibration control

• Published in: Journal of sound and vibration Vol. 271; no. 3; pp. 599 - 614
• Main Authors: Cheng, Yuan, Ren, Gexue, Dai, ShiLiang
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 06.04.2004; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Wind; Motor car; Telescope; Vibration; Stewart mechanism; Reaction force; Cable structure; Parallel mechanism; N body system; PD control; Modeling; Mounting; Linkage mechanism; Vibration control; Feasibility; Root mean square value; Newton method; Flexible cable
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(03)00283-9

This paper studies the dynamics and control of the Gough–Stewart platform for vibration control of a flexible supporting structure. The problem arises from a large radio telescope in which the astronomical equipment is mounted on a platform to be stabilized by a Gough–Stewart platform, while the base platform of the mechanism itself is carried by a vibrating cable-car that moves along flexible cables. As the base platform is not fixed on the ground, the reaction force caused by the motion of the stabilized platform will lead to perturbation on the base platform, and will induce vibration of the whole system. To study the feasibility for vibration control, this paper models the Stewart parallel mechanism as a multi-body systems with an elastically restrained base platform by the Newton–Euler method and proposes a PD control law based on the position prediction of the two platforms. Control simulations are carried out with the simulated wind excitations. The control effects are evaluated by comparing the root-mean-square responses of the stabilized platform.