Robust force control of a flexible arm with a nonsymmetric rigid tip body

In this article, we discuss modeling and robust control of bending and torsional vibrations and contact force of a flexible arm with a nonsymmetric rigid tip body. By using Hamilton's principle and the Lagrange multiplier method, dynamic equations of the constrained flexible arm are derived. Since the flexible arm has the nonsymmetric tip body, the bending and torsional vibrations are coupled. As the obtained boundary conditions of the distributed parameter system are nonhomogeneous, we introduce a change of variables to derive homogeneous boundary conditions. By using the eigenvalues and the correpsonding eigenfunctions related to the distributed parameter system, we derive a finite-dimensional modal model. To compensate for the spillover instability, we construct robust controllers of an optimal controller with a low-pass property and an H∞ controller. Some experiments have been carried out to show the effectiveness of the proposed robust controllers. © 2001 John Wiley & Sons, Inc.