Force Transmission Through a Structurally Flexible Beam: Dynamic Modeling and Feedback Control

This paper studies the control of end-point force in a constrained flexible beam actuated at the hub. To this end, transfer functions are obtained from the torque input at the hub to shear-force outputs along the link in a pinned-pinned configuration. The force output is selected to vary continuously on the beam from hub to tip. It is shown that these outputs exhibit strictly nonminimum-phase behavior. Formulas are derived for dominant zeros which yield upper limits on achievable closed-loop control bandwidths for force control at the end point of the link. A parameterized force output which exhibits marginally minimum phase behavior is obtained, and its control bandwidth is investigated. The performance of a redefined output force controller is further studied using numerical simulations and experiments.