On the impact of model accuracy for active damping of a viscoelastic beam

How much do model errors influence the closed loop performance? This question is investigated for the control problem of designing active damping of vibrations in a viscoelastic cantilever beam. The beam is physically modeled using Fourier transformed Euler-Bernoulli beam equations. For control design the standard LQG technique is employed, and two different finite order models are used. One is based on truncated modal analysis of the system, and the other model is numerically fitted with respect to the frequency response of the physically theoretical model. The so obtained controllers are evaluated on the physical model with respect to disturbance attenuation and robustness for stability. It is found that all controllers stabilizes the system and attenuates the vibrations, but the controllers based on the numerically fitted model perform notably better than those based on truncated modal analysis.