When are overshooting controllers preferred over asymptotic ones?

Question

Disclaimer

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.

Question

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.

Answer 1

For some systems, the salient criterion is settling time to within some error band. Sometimes you can get faster settling by allowing earlier overshoot.

If you need a system to get to within some minimum error of before starting a process, you probably don't care what the system is doing before the process is started, only that it gets there as quickly as possible since you're waiting until then. It's not hard to come up with scenarios where settling time is important, and overshoot before settling largely irrelevant.

For example, let's say some process has to occur at a nominal 200 °C, ±10 °C. When you're powering on the oven, you care that it settles to the 190-210 °C range quickly. It's going to get there faster than a asymptotic controller if allowed to overshoot to 210 °C, then oscillate with ever-decreasing amplitude around 200 °C. The same holds true if you change the set point, and you can't do anything useful until it gets to within some tolerance of the new setpoint.