Input Shaping Control of a Flexible Structure for Rest-to-Rest and Non-Rest-to-Rest Maneuvers

Minimizing the vibrations of flexible structures during maneuvering is a challenging problem. Input shaping control is an effective way to reduce vibration, but in some cases, it does not guarantee a final rest state. In particular, if the initial state is not at rest, then it is difficult to bring the final state to rest at the end of a maneuver. This article proposes the use of a single-switch reference control combined with an optimized Zero Vibration Derivative-Derivative (ZVDD) shaper. The ZVDD-shaped torque profile is defined by a small number of parameters, which can be optimized by a standard numerical optimization algorithm. The resulting control is effective in reducing vibration and bringing the final state to rest, regardless of the starting conditions. Two examples related to rest-to-rest control and non-rest-to-rest control are presented.