Stability Analysis for a Constrained Single-Link Flexible Arm using Linear Distributed Parameter Approach

The passivity-based PD force control of a constrained one-link flexible arm is investigated using a linear distributed parameter model. In order 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 new input induced by the measurement of root bending moment and a virtual contact force output generated by a parallel compensator are defined. The transfer function from the new input to the virtual contact force output is passive. 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 infinite-dimensional system are obtained successfully. This closed loop system has stability robustness to parameter uncertainties and is free spillover problems. Numerical simulations are provided to verify the effectiveness of the proposed approach.