Dynamical behaviour and Control of a Magnetic structure, composed by a Shape Memory spring driven by a DC motor with limited power supply to harvesting energy

Abstract

In this work, we explore a non-linear dynamic mathematical model containing Shape Memory Alloy (SMA) and a non-ideal engine for energy production. However, numerical analyzes of the device showed chaotic behavior for a given set of parameters. Thus, we used the classical tools of non-linear dynamics (Lyapunov Maximum Exponent, bifurcation diagrams, phase maps, and Poincaré maps) that corroborated to determine the regions of chaos. However, to produce energy, the chaotic behavior makes the production of unpredictable electric current that compromises the operation of the device. Therefore, we apply two control techniques to suppress the chaotic behavior for a desired periodic orbit. The first is the State-Dependent Riccati Equation (SDRE) which considers the non-linearities of the system and Optimal Linear Feedback Control (OLFC) which employs a linear methodology to control the device. The results were promising due to the trajectory errors between the controllers that show that chaos was suppressed, and the current produced by the system became periodic.