Active control of a flexible hub-beam system using optimal tracking control method

In this paper, active control of a flexible hub-beam system is investigated using optimal tracking control method and a first-order approximation coupling (FOAC) model. Using the Hamilton theory and assumed mode method (AMM) for discretization, the FOAC model considering second-order coupling quantity of axial displacement caused by transverse displacement of beam is first investigated. Subsequently a simplified FOAC model (or the SFOAC model) which neglects the effect of axial deformation of beam is presented in this paper. Active position control for the system is then studied by optimal tracking control theory. Since the controller obtained is a function of mode coordinate, an extraction method of modal coordinate from actual physical measurements is developed. Numerical simulations are carried out to demonstrate effectiveness of the proposed method. Simulation results indicate that the SFOAC model is valid for dynamic description of flexible hub-beam system and thus is available for control design. Modal filter proposed is effective in extracting modal coordinate from physical measurements. Desired position of system may be achieved by the proposed controller. Residual vibration of beam may be suppressed by this controller as well.