In this article, the frequency characteristics of a flexible hub-beam system with an attached mass in an arbitrary position are investigated using a first-order approximation coupling (FOAC) model. Three kinds of damping are considered in the model: Damping located at the hub bearing, structural damping caused by the beam material, and damping caused by the air. Cases with both known and unknown large motion of the system are considered. First, the FOAC model is presented with an unknown large motion, using the Hamilton principle and finite element discretization method. Then the dynamic equation for a non-inertial system is presented by neglecting the large motion of the system, and the frequency characteristics of the system are studied using numerical simulations. Simulation results indicate that, for the case with a known large motion, the response frequency of the beam is degressive as the settling position of the mass moves from the fixed end to the free end of the beam. The response frequency of the beam decreases with increasing inertia of the hub. Damping affects only the dynamical equilibrium position of the flexible beam and has little effect on the response frequency of the beam. For the case with an unknown large motion, the response frequency of the beam does not show an obvious degressive trend as the settling position of the mass moves from the fixed end to the mid-point of the beam, but it becomes degressive when the mass moves from the mid-point to the free end of the beam. Damping affects not only the final position of the system, but also the vibration amplitude of the flexible beam. However, the response frequency of the beam is barely affected by the damping.

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.