An Introduction to System Modeling and Control

10Pole Placement, 2 DOF Controllers, and Internal Stability

Given a transfer function model we first show how to design a controller so that the closed‐loop poles can be placed at any desired location! It turns out to be a quite straightforward procedure. However, the zeros of along with those of often result in significant overshoot in the closed‐loop step response. Consequently, we also show how this overshoot can often be eliminated by passing the step reference input through a filter (transfer function). This use of two transfer functions and is referred to as a two degree of freedom (2 DOF) controller. Finally we present the notion of internal stability, which requires there be no unstable pole–zero cancellations between the controller transfer function and the model transfer ...