RATIONAL APPROXIMATION OF THE TRANSFER-FUNCTION OF A VISCOELASTIC ROD

The transfer function P for a viscoelastic rod, excited by a torque at one end and observed at the same end, is studied. This function can be expressed as P(s) = s-2g(beta2(s)), where g is an infinite product of fractional linear transformations and beta is a (generally transcendental) function that characterizes a particular viscoelastic material. First a partial product approximation g(N) for g is developed, and it is shown that the corresponding P(N)(s) = s-2g(N)(beta2(s)) approximates P in a way that is appropriate for use in the construction of suboptimal rational stabilizing compensators for the rod. The next step is to approximate each linear fractional transformation of beta2 that appears in the finite product g(N)(beta2(s)) by a rational function. When the damping is weak it is possible to do this by separating the dynamic modes from the static ''creep'' modes, and subsequently ignoring the creep modes. Some numerical data illustrating the process are presented.