Passivity-based Integral Control and Stability Analysis of a Constrained Single-link Flexible Arm

The design of flexible manipulator is complicated due to inherently infinite dimension in nature. The sequential challenge is the problem such a non-minimum phase that is the cause of system instability. In this paper, a constrained single-link flexible arm is fully investigated using a linear distributed parameter model. In order to overcome the inherent limitations, a new input induced by the joint angular acceleration and an output generated using the contact force and root shear force are defined. A necessary and sufficient condition is thus derived so that all poles and zeros of the new transfer function lie on the imaginary axis. Also, the passive integral control is designed to accomplish the regulation of the contact force. The excellent performance of the passive integral controller is verified through numerical simulations.