Bifurcation and Lyapunov´s exponents characteristics of electrical scalar drive systems

In this study, bifurcation and chaos phenomena in scalar drives of induction machines are investigated. Modified Poincare´s map, Lyapunov exponents and bifurcation diagram are utilised for this purpose. The boundary related to bifurcated response and conditions of chaotic response is also acquired for this purpose using Poincare´s map. In addition, root´locus curve of the system for stability and chaos analysis is derived by changing the controller parameters in constant speed control. In order to prove the chaotic response of the system, the largest Lyapunov´s exponent is determined numerically. In addition, an experimental prototype is prepared to show these phenomena. It is shown that chaotic response of the system can be controlled by adjusting the critical values of the speed controller´s gain value.