Fundamental Limits of Performance in Minimum-Time Motion Control due to Structural Flexibility

Abstract

This paper considers the problem of producing time-optimal rest-to-rest motion of a mechanical system subject to limits of actuation effort. Linear dynamic models of a single-mode vibratory structure are considered for two different cases of velocity-limited and force-limited actuation. Minimum-time solutions for rest-to-rest motion with zero residual vibration are obtained by considering geometric constraints for state variables trajectories. This set of equations is reduced and then solved by a root-finding procedure to obtain switching times for the control input signal. The overall speed of motion obtained using the optimal input solution can be considered as a fundamental limit for the achievable performance of a given system. The set of time-optimal solution are therefore presented to show how the speed of motion varies with actuator capacity. These results provide useful information and guidance for matching actuator capacity with flexible structure characteristics of a system under control.