Preshaping Command Inputs For Reducing Residual Vibration In Point–To–Point Motion

This paper presents a numerical method in open-loop-control for rapidly moving a flexible mechanical system with no or minimum residual vibration. The theoretical model is particularly concerned with the optimization of the input forcing laws to suppress vibration and to get accurate positioning of the system. This method generates a shaped command input based on a limited number of constant acceleration (forces or torque) laws varying only by steps of equal duration. Kinematical constraints and robustness are taken into account. Simulations are provided and discussed to prove the effectiveness of the control design when objects transported by an overhead crane or flexible manipulators are moved. Simulations show that these preshaped laws provide time-optimal response and strongly reduce the end-point vibration without involving numerical overhead.