Limited-state commands for systems with two flexible modes

This paper generates command profiles to reduce residual vibration for rest-to-rest motion of flexible systems with two-modes. The commands are limited-state, in that they contain only two positive and two negative valves. This allows them to be utilized with simple on–off, or limited-state actuators. A great advantage of the command profiles is that they are described by closed-form functions. The commands are designed by first canceling the two-modes of flexible vibration and then satisfying a secondary constraint to arrive at the desired target location as quickly as possible. The performance of the control method is evaluated as a function of move distance, actuator effort, maximum transient deflection, and robustness to modeling errors. The control method is illustrated with a numerical simulation of a two-mode system. It is also experimentally validated on a portable bridge crane with double-pendulum dynamics.