Application of an active pendulum-type vibration absorber for Duffing systems

This paper deals with the passive/active vibration control problem for damped Duffing systems, using a nonlinear pendulum-type vibration absorber. The primary system is a damped Duffing system affected by exogenous forces with excitation frequencies close to the principal parametric resonance. The design of the (passive) autoparametric vibration absorber is obtained by using an approximation of the nonlinear frequency response, computed via the multiple scales method. Then, in order to improve the overall system performance against variations on the amplitude and excitation frequency in the external force, it is incorporated a servomechanism to manipulate the pendulum length and, therefore, the autoparametric pendulum-type absorber can be automatically tuned into a given frequency bandwidth, by means of the application of a nonlinear control law combining feedback and feedforward compensation terms. The design of the autoparametric absorber, frequency analysis, control algorithm, stability analysis and closed-loop system performance are discussed. Finally, some simulations results are included to illustrate the dynamic performance of the overall system.