Modeling and Vibration Suppression for Fast Moving Linear Robots

This paper deals with vibration suppression for elastic linear robots consisting of elastic beams, bearings and motor gear units. It is of vital importance to use a structured method for deriving the equations of motion for this nonlinear multi body system. The Projection Equation in subsystem form, a synthetical method for calculating the dynamical equations of motion in combination with the Ritz approximation technique, leads to highly nonlinear ordinary differential equations which can be integrated numerically. The control scheme is based on a feedforward part and a feedback loop. A Taylor expansion up to first order leading to a linear time variant system delivers the feedforward torques and a precalculation of the elastic endeffector deflections which can be compensated by a correction of the desired trajectory. Simulation and experimental results are presented.