Phase Magnitude Diagram for Linear Systems With Delay

Abstract

[Abstract] Transfer functions can be viewed as complex functions where the magnitude and the phase of a system depend on complex numbers. In our previous work, we have developed a graphical tool where transfer functions are represented in a four-dimensional space. The magnitude is represented in decibels in the third dimension and a color code is applied to represent the phase in a fourth dimension. Level curves are used to compare points with the same magnitude or phase. This tool, which is called Phase Magnitude diagram, makes it more intuitive to understand complex functions. This representation allows the user to visually obtain the phase and the gain that have to be added to a system to meet some design specifications. After that, any control approach can be employed. The application to systems with delay is discussed in this paper. It is demonstrated that the Phase Magnitude diagram can be efficiently applied to design an ideal PD controller for a system with delay. In addition, it is deduced that this instrument is not limited to this class of system.