Super-Twisting Sliding Mode Control and Synchronization of Moore-Spiegel Thermo-Mechanical Chaotic System

Abstract

Chaos has important applications in physics, chemistry, biology, ecology, secure communications, cryptosystems and many scientific branches. Control and synchronization of chaotic systems are important research problems in chaos theory. Sliding mode control is an important method used to solve various problems in control systems engineering. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as insensitivity to parameter uncertainties and disturbance. In this work, we first discuss the properties of the Moore-Spiegel thermo-mechanical chaotic system (1966). The Moore-Spiegel system is a nonlinear thermo-mechanical chaotic oscillator that describes a fluid element oscillating vertically in a temperature gradient with a linear restoring force. The Moore-Spiegel system is a classical example of a 3-D chaotic system. We show that the Moore-Spiegel system has a unique equilibrium at the origin, which is a saddle point. Next, we apply multivariable super-twisting sliding mode control to globally stabilize all the trajectories of the Moore-Spiegel chaotic system. Furthermore, we use multivariable super-twisting sliding mode control for the global chaos synchronization of the identical Moore-Spiegel chaotic systems. Super-twisting sliding mode control is very useful for the global stabilization and synchronization of the Moore-Spiegel chaotic system as it achieves finite time stability for the system. Numerical simulations using MATLAB are shown to illustrate all the main results derived in this work.