The development of graphical and linearization techniques for the design of controllers for chaotic systems

Chaotic systems are found in mathematic systems of hydraulics, planetary motion, weather, and convection. Chaotic behavior results in a totally unpredictable system with a bounded response. Mathematical tools and graphical techniques are developed in this paper to assist in the analysis of chaotic systems. As exemplified by the Lorenz equations for three variables. Graphical techniques are used to locate the attractors and phase plane plots provide a roadmap which illustrates the bounded nature and non-repeating oscillatory motion for the chaotic system shown. In order to eliminate the effect of chaotic behavior in the Lorenz equations, the linearization techniques of Taylor series and input state are implemented for the design of a PID and state variable feedback controller. The resulting stable time and frequency responses are presented