In this paper,a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method.In the proposed model,the coupling deformation of any element of the beam is only related with the nodal coordinates of this element.So this model is suitable to the rotating beam in an arbitrary shape.Numerical examples of slender beams in straight and irregular shapes are carried out to demonstrate the validation of the proposed model.Simulation results indicate that the proposed model can be used valid for dynamic description of flexible rotating beam in irregular shape, and for both low and high rotation speeds.
The first-order approximation coupling （FOAC） model was proposed recently for dynamics and control of flexible hub-beam systems. This model may deal with system dynamics for both low and high rotation speed, while the classical zeroth-order approximation coupling （ZOAC） model is only available for low rotation speed. This paper assumes the FOAC model to present experimental study of active positioning control of a flexible hub-beam system. Linearization and nonlinear control strategies are both considered. An experiment system based on a DSP TMS320F2812 board is introduced. The difference between linearization and nonlinear control strategies are studied both numerically and experimentally. Simulation and experimental results indicate that, linearized controller can make the system reach an expected position with suppressed vibration of flexible beam, but the time taken to position is longer than expected, whereas nonlinear controller works well with precise positioning, suppression of vibration and time control.
