Dinâmica e controle de caos de um sistema pendular com memória de forma

Abstract

This work deals with the dynamics and control of a pendulum system coupled with shape memory alloys (SMAs) springs. To construct the system’s dynamics a polynomial temperature dependent constitutive model for the SMA is employed. The system’s dynamics is characterized displaying a variety of responses like chaotic motion, transient chaos, coexisting periodic orbits and a variety of n-periodic orbits. All the behaviours are identified by their Lyapunov exponents. The extended time delay feedback technique is applied to control the system with two distinct types of controllers: a mechanical and a thermal. The stability of the orbits is identified using Floquet multipliers. Discussions about sub-harmonic orbits stability and the relation between energy consumption and the controller’s parameters are made. The thermal controller uses the thermomechanical behaviour of the SMA for actuation. The results display the usage possibility of SMA actuator on chaos control and shad light into the relation between the Floquet multipliers of an orbit and the ETDF control.