8.2 PID controller design

A proportional-integral-derivative (PID) controller is a cascade compensator that includes proportional, integral, and derivative terms acting on the error. The PID transfer function has the form \[ G_C(s) = K_P + K_I\,\frac{1}{s} + K_D\,s. \tag{8.3}\] where \(K_P\), \(K_I\), and \(K_D\) are the real-valued gains corresponding to each term. The design problem is to select the gains to meet closed-loop performance requirements.

For many systems, a proportional-integral-derivative (PID) controller allows a design that meets requirements for both overshoot and settling time, with zero steady-state error for a step input.

The approach is relatively straightforward, building from the PI controller design technique of section 7.3. In fact, we will simply insert the derivative compensator design between the proportional controller design and the integral compensator design. So, order of our design procedure is proportional, derivative, and then integral. …