Control theory basics
The control output (what you are calling the system input) and the system output are not necessarily proportional.  In your example, the system is in part a integrator.  This sort of thing is common.  The extra pole in the system does have to be taken into account in the controller, else it can easily lead to instability.

The less directly related the control output and the system output are, the more complicated the control algorithm has to be.  In the real world, you often get systems that are non-linear, partially integrate the input, etc.  This is why control theory is a discipline onto itself.