Abstract
In this paper, the modeling and optimal control problems are investigated for a class of mechanically flexible cantilevered beams tipped with dynamic actuators on the top. First, considering the mechanism of the tipped dynamic actuator, both dynamics of the beam and the actuator are derived via the Lagrangian formulation. The resultant system is a hybrid system described by an Euler-Bernoulli type partial differential equation and an ordinary differential equation of second-order. Secondly, to suppress the vibration of the beam, based on the derived hybrid system model, we propose the optimal control laws using the dynamic actuators. To obtain the modal expression, a new transformation called the boundary homogenization is introduced. Consequently, the optimal control have a feedback form of the state variables of the beam and the actuator. Finally, several numerical simulation results are presented to demonstrate the good performance of the proposed theory.
