Nonlinear modeling of integrally actuated beams

摘要

A set of nonlinear, intrinsic equations describing the dynamics of beam structures undergoing large deformations is presented. The intrinsic kinematical equations are derived for the general case of a moving beam. Active force/strain terms are added to the equations to take into account active components. The equations are then discretized into finite elements, transformed into state-space form and finally decomposed into modes. Actuation and sensor models are established before implementing a simulation model in Matlab/SIMULINK. The model is validated by comparison with exact, analytical results and then used to analyze the dynamic behavior of an active helicopter blade in vacuum. Beside the analysis of the inherent dynamics of this system in terms of eigenvalues and vectors, the influence of centrifugal stiffening on the modal controllability of the blade is discussed. Finally, the design of a MIMO controller based on full-state optimal control (LQR approach) and optimal state estimation (Kalman filter) is presented with the aim to add vibrational damping to the weakly damped system. The closed loop properties are validated by both analytical methods and simulation runs.