Ângelo M. Tusset

By Mauricio A. Ribeiro, Jose M. Balthazar, Ângelo M. Tusset, Átila M. Bueno and Hilson H. Daum

In this chapter, we explore a mathematical modelling that describes the nonlinear dynamic behavior of atomic force microscopy (AFM). We propose two control techniques for suppressing the chaotic motion of the system. The proposed model considers the interatomic interactions between the analyzed sample and the cantilever. These acting forces are van der Waals type, and we add a mathematical term that is a simple approximation to the viscoelasticity that possibly occurs in biological samples. We analyzed the behavior of the initial conditions of the proposed mathematical model, which showed a degree of complexity of the basins of attraction that were detected by entropy and uncertainty parameter, both detect if the basins have a fractal behavior. Numerical results showed that the nonlinear dynamic behavior has chaotic regions with the Lyapunov exponent, bifurcation diagram, and the Poincaré map. And, we propose two control techniques to suppress the chaotic movement of the AFM cantilever. First technique is the optimal linear feedback control (OLFC), which does not consider the nonlinearities of mathematical model. On the other hand, the control state dependent Riccati equation (SDRE) considers the nonlinearities of mathematical model. Both control techniques for a desired periodic orbit proved to be efficient.

Part of the book: Chaos Monitoring in Dynamic Systems

By Marcus Varanis, Jose M. Balthazar, Angelo M. Tusset, Mauricio A. Ribeiro and Clivaldo De Oliveira

Non-stationary and nonlinear signals, which can bring important applications in chaotic dynamics, and are found in several scientific and engineering fields. Several processing techniques have been used to understand and extract information from these signals, and the literature shows that time-frequency analysis techniques are suitable tools for this characterization. They allow to examine the time-varying characteristics of the signals. In this chapter, we will explore time-frequency methods applied especially to nonlinear signals. First, we discuss the diverse range of dynamical systems. Then, we introduce the classical time-frequency methods, including the Short-Time Fourier Transform, the Wavelet Transform, the Hilbert Transform, and the Wigner-Ville distribution. These methods have been widely used in the literature in the study of non-stationary operations. Thus, we present emerging methods of time-frequency analysis, taking advantage of post-processing and synchrosqueezing techniques to improve the accuracy and resolution of the time-frequency representation. We present a comprehensive analysis of these emerging methods, comparing them with classical approaches to show their contributions. Our main goal is to highlight the capabilities of these emerging time-frequency analysis methods in capturing and understanding chaotic patterns in signals.

Part of the book: New Insights on Oscillators and Their Applications to Engineering and Science

By Natasha Martins Rodrigues de Jesus, Thais Santos Castro, Teófilo Miguel de Souza, Raphaela Carvalho Machado, José M. Balthazar, Clivaldo de Oliveira, Jeferson Jose de Lima and Angelo M. Tusset

The current critical global climate situation, which is due to greenhouse gas emissions, has led society to look for ways to preserve the environment. One of these is the use of renewable energies, including wind power. This energy uses the wind to operate. Based on this, this work seeks to design and produce wind blades using polymeric materials in an additive manufacturing process, in this case, with a 3D printer. The materials used were ABS, PETG, PLA and Tritan. The shapes developed were straight, curved and curved tip for the Tritan polymeric material, while for the other materials, the shape designed was straight. Once manufactured, the blades were subjected to performance tests with a wind turbine coupled to an alternator consisting of a tripod turbine. During the experiments, the construction materials, the shapes and the angle of attack as a function of the linear wind speed generated by a wind tunnel were changed so that the analysis was consistent. The results obtained were compared to identify the best combinations of the parameters analyzed. In the end, it was concluded that the blades printed with the Tritan polymeric material could be applied to various wind speed conditions—low, medium and high—as well as having good mechanical properties and the best performance in their manufacturing process, making them the best of those studied.

Part of the book: State-of-the-Art of Mathematical Modeling, Dynamics, and Control of Wind Turbines Engineering