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Phase Plane Analysis for Linear and Nonlinear Systems

Module by: Jeannie Falcon

Summary: This module includes three interactive examples for studying system stability using phase plane analysis in LabVIEW. The equations used in the examples are from the textbook "Applied Nonlinear Control" by Jean-Jacques E. Slotine and Weiping Li.

The attached zip file includes three examples for phase plane analysis developed in LabVIEW. The systems used in the examples were described as examples in the book Applied Nonlinear Control by Jean-Jacues E. Slotine and Weiping Li.

Phase planes for first and second order systems can be generated by plotting the system states against each other. A second order system can be represented by (Slotine & Li):

Figure 1
Figure 1 (Graphic1.png)

where x1 and x2 are the states of the system and f1 and f2 are functions of the states.

Multiple system trajectories can be generated for various initial conditions and shown on the same phase plane plot. This technique can be used to study stability in both linear and nonlinear systems.

Download the zip file with LabVIEW VIs here. Requires LabVIEW 8.20 and LabVIEW Simulation Module 8.20

Figure 2
Figure 2 (Graphic2.jpg)

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