Boundary Feedback Stabilization of a Nonlinear Flexible Gantry Manipulator Using Disturbance Observer

This paper aims to develop a boundary control solution for a single-link gantry robot manipulator with one axis of rotation. The control procedure is considered with link’s transverse vibrations while system undergoes rigid body nonlinear large rotation and translation. Initially, based on Hamilton principle, governing equations of hybrid motions as a set of partial differential equations (PDE) and ordinary differential equations (ODE) will be derived. The control objectives which are sought for include: moving the system to a desired position, regulating large angular position and finally suppressing the flexible link transverse vibrations simultaneously. By considering novel Lyapunov functions and avoiding any simplifications, In the presence of external boundary disturbance, proper control feedback signals and boundary disturbance observer are introduced in order to reach mentioned control objectives and compensate external boundary disturbance effect simultaneously. At last uniform ultimate boundedness of the closed loop system is proven in which by choosing proper design parameters, system states and position error converge exponentially to a small neighborhood of zero.  In order to illustrate the performance of the proposed control method, numerical simulation results are provided.