The structure of the control system is shown in the schematic picture below. It consists of an input signal, a sensor, a feedback loop, and a regulator. The physical system consists of the gear and axis system described in DC Motor and Weak Axis. Since the physical system has negative static gain the PI gain also has to be negative.

By varying the controller gain k we can study how the system response is affected. In this case we vary the gain from 1 (StiffServoMechanism 1) to 2 (StiffServoMechanism 5) in steps of 0.25. The plot below shows the result:

For a step by step tutorial see Multidomain—A Servo Mechanism.