Chaotic systems are found in mathematic systems of hydraulics,planetary motion, weather, and convection. Chaotic behavior results in atotally unpredictable system with a bounded response. Mathematical toolsand graphical techniques are developed in this paper to assist in theanalysis of chaotic systems. As exemplified by the Lorenz equations forthree variables. Graphical techniques are used to locate the attractorsand phase plane plots provide a roadmap which illustrates the boundednature and non-repeating oscillatory motion for the chaotic systemshown. In order to eliminate the effect of chaotic behavior in theLorenz equations, the linearization techniques of Taylor series andinput state are implemented for the design of a PID and state variablefeedback controller. The resulting stable time and frequency responsesare presented
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