10-08-2013, 04:17 PM
Stability Analysis of a Non-Linear System by Phase Plane Technique using Matlab
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Abstract
The purpose of this work is to investigate the stability of a non linear system. There are several methods of analyzing the stability of a non linear system, out of which phase plane technique has been used in this work. For a particular non linear system, different cases of stability has been discussed by determinig eigen values using Matlab.This analysis results in stable or unstable system of the considered non linear system for different cases.
INTRODUCTION
The non linear system does not possess the homogeneity an d superposition properties. The stability of the non linear system depends on the input and initial state of the system. Analysis of the non linear system implies the study of behavior of the system when there is a change in the system variables from operating and equivalent point. All practical system are non linear upto some extent, which makes the analysis of non linear systems imperative for a control engineer. Dynamics system are described by their equation of motion, which is often a set of differential equations. In case of non linear system, the differential equation is non linear , which requires a great deal of mathematical labour in calculating the transient response. To overcome these difficulties, a dedicated graphical method of analysis is required for the non linear system. Phase plane analysis is the method which serves the above state purpose. ’Phase plane method is a time domain technique since time is the independent variable for it. Stability analysis of a non linear system is actually the stability analysis about a singular point.
CONCLUSION
The analysis results has been entered in the table above.Separate tables shows the eigen values for each case. The eigen values thus obtained shows the stability of the system.In CASE1 complex roots with negative real part is obtained and the saddle point is obtained which shows system is stable focus and inherently unstable respectively. In CASE2 complex roots with positive real part and saddle which shows system is unstable focus and inherently unstable respectively. In CASE3 real, distinct and negative values are obtained thus system is stable focus.In CASE4 real,distinct and positive values are obtained thus system is unstable focus.The phase trajectory can be drawn