Three-dimensional display of phase space diagrams

Phase plane analysis of linear and nonlinear systems has been widely in recent years. These graphical displays give considerable insight into system response. A serious short coming of this procedure is the limitation to two dimensions. A third-order system must be studied on two, two-dimensional graphs or represented by a second-order mathematical approximation for the third-order system. For nonlinear systems employing relays, saturation, etc., the approximations must be made with care.

In an effort to reduce discrepancies and improve the visualization of system response, this paper presents a method to obtain three-dimensional displays of system graphs. Third-order phase graphs of nonlinear and linear systems can be graphed directly without approximations. A discussion of the principles involved will be presented first. Then, analog and digital programs will be given. Finally, example problems will be discussed.