Deflection-limiting commands to slew flexible systems with velocity limits

A new method to generate deflection-limiting commands for flexible systems with actuator velocity limits is presented and evaluated. In addition to limiting transient deflection, the command profiles reduce residual vibration for rest-to-rest motion of oscillatory systems with one dominant mode. A beneficial advantage of the command profiles is that they are described by closed-form functions of the system frequency, deflection-limiting ratio, velocity limit, actuator force-to-mass ratio, and desired move distance. The performance of the commands is evaluated with respect to move duration, transient oscillation energy, maximum transient deflection, and robustness to modeling errors. The proposed approach is illustrated with a numerical simulation of a benchmark system.