Lead, Lag, and PID Controllers

In this chapter first-order lead and lag controller design principles will be outlined. Then, PID controllers will be designed from the same principles. The basic idea behind lead controller design is to increase the phase of G ₁, to increase the phase margin. The basic idea in lag controller design is to reduce the magnitude of G ₁ to bring the crossover frequency to a desired location. Thus, lag controller design procedure does not involve any trial and error type of iterations. PID controllers can be seen as extreme cases of lead-lag controllers. General form of a PID controller is Let e(t) be the input to the controller C _PID(s). Thus, the people can design PD controllers using lead controller design principles. By cascading a PI controller with a PD controller, they obtain a PID controller. Therefore, PID controllers can be designed by combining lead and lag controller design principles, like lead-lag controllers.