On Slide Mode Control of Chaotic Rikitake Two-Disk Dynamo—Chaotic Simulations of the Reversals of the Earth’s Magnetic Field

• 作者: Ahmad Harb Nabil Ayoub
• 来源期刊: 现代非线性理论与应用(英文)
• 学科: 数学
• 关键词: Chaos THEORY Nonlinear CONTROL Magnetic THEORY Sliding-Mode CONTROL THEORY
• 年，卷（期）: 2014,（3）
• 页码范围: 136-143
• 页数: 8页
• 分类号: O1

摘要

The modern nonlinear theory, bifurcation and chaos theory are used in this paper to analyze the dynamics of the Rikitake two-disk dynamo system. The mathematical model of the Rikitake system consists of three nonlinear differential equations, which found to be the same as the mathematical model of the well-known Lorenz system. The study showed that under certain value of control parameter, the system experiences a chaotic behaviour. The experienced chaotic oscillation may simulate the reversal of the Earth’s magnetic field. The main objective of this paper is to control the chaotic behaviour in Rikitake system. So, a nonlinear controller based on the slide mode control theory is designed. The study showed that the designed controller was so effective in controlling the unstable chaotic oscillations.