PM diagram of the transfer function and its use in the design of controllers

This paper presents the graphical chromatic representation of the phase and the magnitude of the transfer function G(s) of a system and its educational use in the design of the most typical controllers. The magnitude is represented in decibels and the phase is represented by colours. This representation permits to put a face to the transfer functions, deepening our intuitive understanding of transfer functions. An important characteristic of this diagram is that permits to read the phase and the gain margins directly and the imaginary axis cut represents the Bode diagram. It permits to see intuitively the connexions among the different diagrams. It is also possible to put the grid with damping ratio ζ and frequency ω_n. In summary, this PM diagram can be useful, especially in Control Education because improves the intuition about transfer functions, and it can be used in a Classical Control Course to complement the design of controllers using the Root Locus diagram.