Input command generation for flexible systems with 2nd-order actuators

In this paper, an input shaping command is presented to generate on-off commands where actuator operation is affected by non-linear influence such as electronic dynamics, power transmission inertia and other non-ideal effects. These effects can cause large residual vibration to the flexible systems for rest-to-rest operations. An exact solution with a vector diagram approach is developed by approximating all effects of the control system nonlinearities to the response function of 2nd-order system. The exact commands are analyzed to command design parameters, residual deflection magnitude and sensitivity compared to a conventional input shaper. The input shaped commands are numerically evaluated using a single mode system and experimentally validated with a bridge crane.