Benchmarking Time-Optimal Control Inputs for Flexible Systems

Command shaping techniques adjust the motion commands to e exible systems so that residual vibration is reduced. However, with so many command shaping methods available, benchmarking is necessary so that the contributions and performance of a particular input can be assessed. A closed-form solution for the move plus settling time of a rigid-body input when applied to a e exible system with damping is developed. The move plus settling time ofthe rigid-body solution creates an upper bound on most feasible solutions forsystems with actuator constraints. A lower bound on the point-to-point motion is the pure move time of the rigid-body input. The usefulness and importance of benchmarking using the rigid-body solution, as well as other inputs, is described. Results emphasize the importance of command shaping when the system damping ratio is less than 0.1.