Controllers gone unstable

In order to obtain asymptotic tracking, we need $S(0)=0$, which means we’d need one of the poles of $G K$ to be zero. If $G$ has no poles at zero, then $K$ must be the transfer-function to have the pole at zero. But in order to be asymptotically stable, we need the real parts of the poles to be less than zero, correct? So does it matter if our controller is not asymptotically stable? Is there a way to design a controller that is both asymptotically stable AND provides asymptotic tracking?

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The challenges of position control

On our daily lives we interact with devices (some engineered) that can steer toward a desired position. That could be a linear position, in a cart, in a valve or lock, angular position, in a motor or rotary system, or some more complicated 3D task, such as a robot or human arm. For their ubiquity, some may believe that position control is a simple, almost trivial task. They are up for surprises.

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