Abstract
In this paper the concept of phase plane analysis, which is well developed for second-order systems, is extended to a class of third-order non-linear systems. The method of analysis presented is applicable to the unity feedback closed-loop systems, having a third-order linear memory system and a single-valued zero-memory system in cascade combination in the forward path. The technique involves plotting a (x2, x3) master plane having all possible trajectories for x1 = 0. The variation and the initial condition of variable x1 are incorporated by adding an origin shift scale on to the master plane. Using this master plane, the required (x1, x2) and (x1, x3) trajectories can be obtained for any set of initial conditions, following a simple procedure illustrated by typical examples. This technique is also applicable for the analysis of such systems for step inputs.
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