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 fract ional order derivatives. Skaar, Michel, and Miller (''Stability of Vis coelastic Control Systems,'' IEEE Transactions, Vol. AC-33, No. 4, 198 8, pp. 348-357) have proposed a modified root locus scheme for such sy stems and have suggested an approximation method for computation of so lutions which relies on Laplace transformations. We show here, via a c ase study for a slewing beam, how these approximations can be carried out. In Skaar ct al., the focus was on determining stability. In contr ast, this paper shows how time domain performance can be assessed. We show that the necessary inverse Laplace transforms are obtained as sol utions of a weakly singular system of Volterra integral equations. Com parisons are made between the fractional derivative model and a Kelvin -Voight constitutive model.