Force Control of a Distributed-Parameter Flexible Arm via Parallel Compensation

Abstract

In this paper, the force control of a constrained one-link flexible arm is fully studied based on a linear distributed parameter model, including the internal damping of Kelvin-Voight type. A new input induced by the joint angular acceleration and a virtual contact force output generated by a parallel compensator are defined. The inherent limitations due to the non-minimum phase nature of the noncollocation from the joint torque input and the tip contact force output can be thus resolved. Therefore, the transfer function from the new input to the virtual contact force is not only driven to a strictly minimum phase but also stable condition. The integral control is then used to improve the performance of the overall closed loop system. Also, the asymptotic tracking of a desired contact force trajectory can be achieved with the internal stability. On the other hand, the exact solutions in the infinite-dimensional system are reached using the infinite product formulation. Numerical performance results are provided to verify the effectiveness of the proposed approach in term of fast, stable and robust performance.