Active Control of Viscoelastic Systems by the Method of Receptance

Viscoelastic materials have frequency and temperature-dependent properties and they can be used as passive controlling devices in wide range of vibration applications. In order to design active control for viscoelastic systems, an accurate mathematical modeling is needed. In practice, various material models and approximation techniques are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state-space models, which introduces several challenges such as introduction of nonphysical internal state variables and requirement of observer/state estimator design. In this paper, it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available receptance transfer functions (RTF) and hence eliminating the need for state-space modeling for control design. By using the recently developed receptance method, it is shown that active control for poles and zeros assignment of the viscoelastic systems can be achieved. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of RTF and solution of the set of linear system of equations.