Analytical and Graphical Design of PID Compensators on the Nyquist plane

This paper focuses on the design of PID compensator to exactly satisfy the gain margin, the phase margin and the gain or phase crossover frequency specifications. The design problem is numerically solved using the so called PID inversion formulae method. A graphical interpretation of the solution on the Nyquist plane is presented. This could be suitable on education environment to deeply understand the design of PID compensators. Simulations results show the effectiveness of the presented method.