Abstract
The responses of the controlled inverted pendulum to vertical oscillation are discussed. The authors investigate the responses of the inverted pendulum, which is stabilized by the optimal controller, to the vertical vibrations. With theoretical analysis, numerical simulations and experiments using the large scale vibration exciter, the stability to the vertical vibration is examined. The results show the system dynamics is governed by the Mathieu equation, thus the frequency response reaches its peak when the frequency of the forced vibration is twice as high as the natural frequency of the controlled inverted pendulum system.
