Robust control of coupled bending and torsional vibrations and contact force of a constrained flexible arm

In this paper, robust control of bending and torsional vibrations and contact force of a one-link flexible arm is discussed. The flexible arm carries a rigid tip body, of which the mass center lies on the center axis of the arm. We derive dynamic equations of the joint angle, the vibrations of the flexible link, and the contact force by using Hamilton´s principle. On the basis of a finite-dimensional modal model of a distributed-parameter system, an optimal controller with low-pass property and a robust H_∞ controller are constructed. A set of simulations has been carried out