proportional error

In the feedback controller design, a proportional controller is used to regulate the output error of piezoelectric actuators.

The PI observer has two feedback loops, a proportional loop and an integral loop of the estimation error; in this way, the PI observer can estimate not only the states but also the unknown inputs.

Then a new controller named proportional resonant (pr) controller was introduced in the current control. It could track the current reference without steady error.