Control of slew maneuver of a flexible beam mounted non-radially on a rigid hub: a geometrically exact modelling approach. (English) Zbl 1235.74204
Summary: The positioning control using a joint torque is studied for a hub-beam system with a tip payload. In order to make the axial vibration of the beam accessible to the joint torque, the flexible beam mounted non-radially on the rigid hub is considered. Neither model truncation nor small deflection assumption is employed throughout the process of dynamic modelling and controller design. A joint PD controller with additional feedback of joint acceleration and root strain of the beam is derived using a Lyapunov-type method. Global asymptotic stability of the desired equilibrium position is proved rigorously. The geometrically exact formulation presented in this work can be viewed as a generalization of the related work based on the small deflection assumption investigated in the existing literature.
MSC:
74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
70B15 | Kinematics of mechanisms and robots |
93C85 | Automated systems (robots, etc.) in control theory |
93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |