Analysis of a Class of Third Order Non-linear Systems Using Phase Plane Techniques

Abstract

In the method of analysis presented, phase plane techniques have been successfully modified to cater to a class of third order non-linear systems. This method is applicable to control systems having non-linearities in the feedback loops.

The technique involves plotting an (x₁, x₃) master plane having all possible trajectories for any non-zero value of x₂. The variation and initial conditions of variable x₂ are incorporated by adding a set of x₃-scales, and an origin shift scale, for various values of x₂, to the (x₁, x₃) master plane. Using this master plane, the required (x₁, x₂ and (x₁, x₃) trajectories can be obtained for any set of initial conditions, by following the procedure illustrated by typical examples.