Force Control of a Constrained One-link Flexible Arm : a Distributed-parameter Modeling Approach

The force control of a constrained one-link flexible arm is considered based on a linear distributed parameter model. To overcome the inherent limitations caused by the non-minimum phase nature of the noncollocation of the joint torque input and the tip contact force output, a passive transfer function is obtained by using the methods of feedback and output redefinition. A passivity-based PD controller is then designed to accomplish the regulation of the contact force. With the infinite product representations of transcendental functions, exact solutions of the noncollocated infinite-dimensional closed-loop force control system are obtained. This closed loop system has stability robustness to parameter uncertainties and is free from spillover problems. Numerical simulations are provided to verify the effectiveness of the proposed approach.