A Novel Monitoring Function Based Boundary Force Controller Design for PDE Modeling Flexible Manipulator With Uncertain Control Directions

A contact force control and vibration suppression problem for a one-link flexible manipulator with uncertain control directions and input constraints is discussed in this paper. The flexible manipulator is described by a PDE (Partial Differential Equation) model. Nussbaum function is a widely used method to address the challenge of uncertain control directions. However, the Nussbaum function has notable drawbacks such as uncontrollable amplitude increase, frequent controller gain direction changes, and an indeterminate final gain value. To overcome these drawbacks, we propose a novel boundary controller design that integrates a monitoring function to evaluate the current gain direction and a switching scheme to determine if and when the gain direction should change. This allows us to achieve the force control and vibration suppression with uncertain control directions. Importantly, our proposed controller offers several advantages: (1) it enables simultaneous satisfaction of input constraints, (2) ensures a maximum of one change in controller gain direction before convergence to the correct direction, and (3) allows for the specification of a definitive final value for the controller gain. The effectiveness of the proposed controller is verified by numerical simulation.