Benchmarking time-optimal control inputs for flexible systems

Command shaping techniques adjust the motion commands to flexible 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 flexible system with damping is developed. The move plus settling time of the rigid-body solution creates an upper bound on most feasible solutions for systems 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.