Abstract Summary
With the increasing demand for energy consumption in recent years, several areas of science have been looking to produce clean and renewable energy. In this context, several devices are used, such as converting mechanical movement of sea waves, portal frame systems, and so on Nowadays, with the energy demand consumption, the development and analysis of mathematical models to predict and obtain energy harvesting is increasing every day. By the other hand, devices that have been gaining prominence are those that have the Shape Memory Alloy Effect (SMA) because the SMA materials have a memory feature and can return to their original shape without heating. Therefore, in this paper, we explore the dynamic behavior using bifurcation diagrams, Lyapunov exponents, basis and attraction and entropy of a magnetic structure acting on a mass coupled to spring with the SMA behavior driven by a DC motor with limited power supply. The changes observed in the scan of the analyzed parameters of the adopted mathematical model, showed an influence on the average output power because of its coupling to the magnetic mass displacement. This dynamic analysis supported control designs that suppress chaotic behavior, and thus determine a constant energy production process. Determining the non-linear dynamic behavior of the system for energy collection makes it possible to establish parameters that allow the maximum collection of average power and to establish analyzes such as control design for suppression of chaos. Therefore, the aim of this work was also applied two control techniques: the Optimal Linear Feedback (OLFC) control due to its high computational efficiency and SDRE (State Dependent Riccati Equation) both to suppress the chaotic behavior and thus maintain the energy production in a periodic orbit. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.
