Active vibration absorption of multi-frequency harmonic forces on mass-spring-damper systems

In this article an active vibration absorption scheme for linear mass-spring-damper mechanical systems subject to exogenous multi-frequency harmonic excitations is presented. The proposed scheme considers an active vibration absorber as a dynamic controller, which can simultaneously be used for vibration attenuation and desired position reference trajectory tracking tasks. The differential flatness property exhibited by the mechanical system is employed to design a control law to extend the vibrating energy dissipation capacity of a dynamic vibration absorber for multi-frequency vibration. The disturbance input signal affecting the differentially flat linear system dynamics and time derivatives up to third order of the flat output, which are required for the controller implementation, are estimated by using a flat output-based high-gain dynamic observer. Some simulation results are provided to show the robust and efficient performance of the proposed active vibration absorption scheme when the primary system is submitted to resonant frequency harmonic excitations.