Chaos suppression of Fractional order Willamowski–Rössler Chemical system and its synchronization using Sliding Mode Control

Abstract

Most of the Real systems shows chaotic behavior when they approach complex states. Especially in physical and chemical systems these behaviors define the character of the system. The control of these chaotic behaviors is of very high practical importance and hence mathematical models of these chaotic systems proves vital in deciding the control structures. One such model of chemical reactors is the Willamowski–Rössler system (WR). In this paper we derive a fractional order sliding mode control scheme where the states of the WR system are driven back to the defined equilibrium points. We have also synchronized master and slave fractional order WR system using sliding mode control. As the entire control law is defined in fractional order, we derived a new methodology to prove the stability of the controller. The numerical simulation and analysis are achieved with LabVIEW.

Keywords

• willamowski–rössler system
• fractional order
• chaos control
• lyapunov stability
• sliding mode
• 34h10
• 26a33
• 34a08