The Control Problem of a Three-Link Mechanism with a Flexible Arm Admitting Large Elastic Deflections

• Main Authors: Huang, Bu-Chin, 黃卜慶
• Other Authors: King Yuan
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/77672349474567529458

碩士 === 國立臺灣大學 === 機械工程學系 === 86 === This thesis deals with the dynamic modeling and the control problem of a three-link mechanism. This mechanism consists of an inner rigid link, a flexible forearm connecting to a prismatic joint at the tip of the first link, and a distal rigid link. In order to retain nearly all the intrinsic dynamic properties of the real system, the geometrically exact modelling approach is adopted. Neither large slenderness ratio nor small elastic deflections is assumed in the formulation of equations of motion. Since the interactions between the flexible motion and the rigid motion are taking into account exactly, the dynamic model is best suited for both dynamic analysis and controller design. To examine the feasibility of achieving minimum-phase behavior with noncollocated control, the transfer function matrix of the linearized system is derived. Numerical results indicate that the zeros of the transfer function in the right-half complex plane cannot be removed by changing the parameters of the mechanism. It is therefore concluded that, with the noncollocated control, the system is non-minimum-phase system and the perfect tracking control cannot be achieved theoretically. In this thesis, the position control using a PDS controller is also designed based on the geometrically exact, nonlinear, distributed- parameter model. Global asymptotic stability of the closed-loop system is proved. Numerical simulations demonstrate that a controller with fixed gains can perform equally well, irrespective of the angles of slew and the elastic deflections (small or large). This has merit in practical applications.