Boundary control of a flexible link electrically driven gantry robot

Gantry robots are used for precision manufacturing and material handling in the electronics, nuclear, and automotive industries. Light flexible links require less power but may vibrate excessively. In this paper, an implementable boundary controller is developed to damp out undesirable vibrations in a flexible link gantry robot driven by a brushed DC motor. Hamilton's principle produces the governing equations of motion and boundary conditions for the flexible link. The electrical subsystem dynamics for a permanent magnet brushed DC motor couple with the link dynamics to form a hybrid ODE-PDE system. Through an embedded desired current control law, an integrator backstepping controller generates the desired control force on the mechanical subsystem. A velocity observer estimates the gantry velocity eliminating one feedback sensor. Numerical simulations using a Galerkin discretized model demonstrate the improved vibration damping characteristics provided by the backstepping boundary control law. Experimental results confirm the theoretical predictions, showing twenty times faster transient decay than PD control with backstepping boundary control.