Non-collocated boundary control for contact-force control of a one-link flexible arm

This paper deals with contact-force control of a one-link flexible arm whose tip is constrained to a rigid environment. To realize the contact-force control, a boundary controller is proposed based on a dynamic model represented by an infinite dimensional model. In particular, the proposed controller does not need the physical parameters in its implementation, and this results in the non-collocated boundary controller. The closed-loop system is analyzed in an appropriate Hilbert space, and it is shown that the exponential stability of the closed-loop system is obtained by setting the feedback gains to locate the eigenvalues of the closed-loop system on the complex left half-plane. In addition, in an attempt to realize the better control performance, another controller which is a modified version of our controller is proposed. Finally, the stability, robustness to the uncertainty in physical parameters, and disturbance response of the closed-loop system are investigated by numerical simulations.