Chaos Control in a Nonideal Vibrating Systems

Abstract

This paper presents two control techniques for a non-ideal system with chaotic behavior. To place and maintain the system in a periodic orbit, the techniques of Time Delayed Feedback Control and Continuous-Delay Control with Saturation are considered. The non-ideal system presented is composed of a mass-spring-damper system, with cubic stiffness, and an external excitation from a power limited DC electric motor driven by an unbalanced rotating mass that provides the non-ideal excitation. To suppress the chaotic behavior, additional damping is considered for the mechanical system, and the damping force is estimated by the proposed control strategies. Dynamic analysis of the system is performed by various techniques, including bifurcation diagrams, phase portraits, power spectral densities, and 0–1 test. Numerical simulations demonstrate the effectiveness of the control strategies leading the system to a stable periodical orbit.