Using Unconventional Methods to Control the Chaotic Behavior of Switched Time Systems: Application to a Stepper Motor

Abstract

In this paper we suggest a method to control the chaotic behavior of the stepper motor into a periodic one. In fact, using the supply frequency as a bifurcation parameter, we show that as the frequency is increased beyond a critical value the motor steps become irregular and even chaotic hence it becomes unpractical to be controlled in open loop mode. To circumvent the problem we propose a slight perturbation to the frequency in order to regularize the steps for high frequencies. The approach consists in using several heuristic methods such as Practical Swarm Optimization (PSO), Genetic Algorithms (GA) and Ant Colony Optimization (ACO) to obtain the optimal switching instances which define the change in the supply state (polarization). The numerical simulations performed on a stepper model show that regularization of the motor steps can be achieved for a large range of power supply frequencies ranging from quasiperiodic behavior to chaotic behavior.

Keywords

• Practical Swarm Optimization
• Ant Colony Optimization
• Genetic Algorithms
• Switched time systems
• Chaos control.