Tip-contact force control of a single-link flexible arm using feedback and parallel compensation approach

Abstract

SUMMARYIn this paper, the force control of a constrained one-link flexible arm is investigated using a feedback parallel compensation algorithm based on a linear distributed parameter model with internal damping of Kelvin–Voigt type. Generally, the non-collocation of the joint torque input and the tip contact force output comes along with the non-minimum phase in nature. To overcome this inherent limitation, a new input induced by the measurement of root-bending moment and its derivative, and a virtual contact force output generated by a parallel compensator are defined. Therefore, the transfer function from the new input to the virtual contact force output is proved not only strictly minimum phase but also in a stable condition. A PD controller then improves the performance of the overall closed-loop system. Furthermore, the perfect asymptotic tracking of a desired contact force trajectory with internal stability can be achieved accurately. The exact solutions of the infinite-dimensional system are obtained using the infinite product formulation. The proposed system promises stability robustness to parameter uncertainties, also free of spillover problems. Numerical simulations are provided to verify the effectiveness of the proposed approach.