COMPUTATIONAL RESULTS FOR A FEEDBACK-CONTROL FOR A ROTATING VISCOELASTIC BEAM

This paper studies a control system for a one-dimensional, distributed, viscoelastic structure whose constitutive law is modeled using fractional order derivatives. Skaar, Michel, and Miller (''Stability of Viscoelastic Control Systems,'' IEEE Transactions, Vol. AC-33, No. 4, 1988, pp. 348-357) have proposed a modified root locus scheme for such systems and have suggested an approximation method for computation of solutions which relies on Laplace transformations. We show here, via a case study for a slewing beam, how these approximations can be carried out. In Skaar ct al., the focus was on determining stability. In contrast, this paper shows how time domain performance can be assessed. We show that the necessary inverse Laplace transforms are obtained as solutions of a weakly singular system of Volterra integral equations. Comparisons are made between the fractional derivative model and a Kelvin-Voight constitutive model.