Modern design of classical controllers: Digital PID controllers

This paper presents a new approach to the design of digital Proportional-Integral-Derivative (PID) controllers. The objective is to determine the PID gains to satisfy a desired crossover frequency and closed-loop stability margins. The design procedure is based on a simple parametrization consisting of ellipses and straight lines which represent constant magnitude and constant phase loci in the space of controller gains. The intersection of these figures give us the PID gains that satisfy the desired performance. It must be ensured that the selected design point is contained in the stabilizing set of controllers, which can be computed using recent methods. A numerical example and a power electronics application of a voltage source inverter are given to illustrate and validate the proposed approach.