Closed-form deflection-limiting commands

Command signals that can move a flexible system without residual vibration and also limit the transient deflection are very useful. Unfortunately, these types of commands can be difficult to generate and have historically required intense numerical optimization. A new method for creating deflection-limiting commands is described and evaluated. The major advancement is that the problem is solvable in closed form, rather than via numerical optimization. Simulations of a mass-spring-mass system are presented as a function of deflection limit and move distance. The results compare favorably to previously presented optimized solutions.