Designing the behavior of controllers is an important task for many applications. Every application needs its own requirements fulfilled. For example a CNC machine needs a controller with a strict asymptotic convergence to the set value. An overshooting behavior can’t be tolerated due to the fact that once removed material can’t be replaced by the same tool. Other examples for devastating results with an overshooting controller behavior are autopilots landing an aircraft or shuttles docking the ISS.
Are there any real applications where a controller with an overshooting behavior can not only be tolerated but leads to an overall suitable performance for the system? I am looking for a specific example not just field of tasks where it might be the case.
Thoughts of my own
There are systems where an overshooting control behavior can be tolerated. Like if a robot needs to stay on a specific path on the way to its destination with a given tolerance. A controller that controls the distance to this given path can let the robot wiggle a little around the given trajectory as long as it keeps it inside the tolerance. But if you can design a controller with an asymptotic converge to its trajectory you would prefer it to get rid of this wiggle. I can’t think of any real application where you would prefer an overshooting controller over an asymptotic one if you had the choice.