Control of chaotic behaviours by using stability boundary locus method

In this thesis, it is aimed to get ride of the system from chaotic behavior by adding PI controller to a system showing chaotic behavior by using the stability boundary locus method. For this purpose, firstly the definition of basic properties and mathematical expressions of PID and PI controllers, and of adjustment methods of PID controller are mentioned. Then, stability analysis of the control systems are mentioned and examples are given on the stability analysis of nonlinear systems by using linerization technique. In addition, Routh-Hurwitz Stability Criteria, Nyquist Stability Criteria, Root Locus Method and Bode Diagram Method are presented. Then, the stability boundary locus method is defined by mathematical expressions and the stability boundary locus is obtained in detail with application examples in the linear control systems with PI controller. Simulation results of application examples are given MATLAB / Simulink environment. Finally, the chaos is explained and a PI controller is designed by using stability boundary locus to remove the system from the chaotic behavior by adding a PI controller to a system showing chaotic behavior. The results are confirmed by simulations in MATLAB / Simulink environment.