Backstepping boundary control of flexible-link electrically driven gantry robots

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 system of partial and ordinary differential equations. A boundary voltage control law is developed based on Lyapunov theory for distributed parameter systems. Through an embedded desired-current control law, the integrator backstepping controller generates the desired control force on the mechanical subsystem. A velocity observer estimates the gantry velocity, eliminating one feedback sensor. Modal analysis and Galerkin's method generate the closed-loop modal dynamics. Numerical simulations demonstrate the improved vibration damping characteristics provided by the backstepping boundary control law. Experimental results confirm the theoretical predictions, showing the high performance of backstepping boundary control.