A non-ideal portal frame energy harvester controlled using a pendulum

A model of energy harvester based on a simple portal frame structure is presented. The system is considered to be non-ideal system (NIS) due to interaction with the energy source, a DC motor with limited power supply and the system structure. The nonlinearities present in the piezoelectric material are considered in the piezoelectric coupling mathematical model. The system is a bi-stable Duffing oscillator presenting a chaotic behavior. Analyzing the average power variation, and bifurcation diagrams, the value of the control variable that optimizes power or average value that stabilizes the chaotic system in the periodic orbit is determined. The control sensitivity is determined to parametric errors in the damping and stiffness parameters of the portal frame. The proposed passive control technique uses a simple pendulum to tuned to the vibration of the structure to improve the energy harvesting. The results show that with the implementation of the control strategy it is possible to eliminate the need for active or semi active control, usually more complex. The control also provides a way to regulate the energy captured to a desired operating frequency.     

Nonlinear control in an electromechanical transducer with chaotic behaviour

The electromechanical transducer considered in this work is composed of a mechanical oscillator linked to an electronic circuit. Simulations results have determined that for some combination of parameters the electromechanical system is subject to chaotic motion with resonant transient behavior, and after the resonant transient the mechanical system (MS) synchronizes with the electrical system (ES). In order to improve the transient response, avoiding both the chaotic and resonant behaviors, a nonlinear control system is designed, a feedback control strategy is used to drive the system into the desired periodic orbit, and a nonlinear feedforward strategy is used to keep the system into the periodic orbit, obtained by the Fourier series. Two control techniques are used and compared, namely: the state dependent Ricatti equation and the optimal linear feedback control. Numerical simulations results are shown in order to compare the results, considering parametric uncertainties. Additionally, the energy transfer “pumping” between the ES and the MS is also analysed.     

On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system

This paper demonstrates that vibration mitigation and energy harvesting can be achieved simultaneously by using of an electricity-generating from autoparametric vibration absorber system (AVAS) and non-ideal system (NIS). The NIS consists of a simple portal frame excited by a small dc motor with eccentric mass, with limited power supply and located on the top. The AVAS consists of a cantilever beam with tip mass parallel coupled to NIS. A piezoelectric material is considered for energy harvesting installed in the base of the AVAS and an electric circuit is connected to the piezoelectric material in order to produce voltage output. Several numerical simulations were carried out focusing on the passage through the resonance of NIS, when the motor rotational frequency is near the portal frame natural frequency and when the non-ideal subsystem frequency is approximately twice the absorber beam frequency (two-to-one internal resonance). The results showed the existence of Sommerfeld effect in NIS and saturation phenomenon in the NIS–AVAS.     

A note on polynomial chaos expansions for designing a linear feedback control for nonlinear systems

This paper presents a polynomial chaos-based framework for designing optimal linear feedback control laws for nonlinear systems with stochastic parametric uncertainty. The spectral decomposition of the original stochastic dynamical model in an orthogonal polynomial basis, prescribed by the Wiener–Askey scheme, provides a deterministic model from which the optimal linear control law is designed. Optimality of the proposed control law is proved by solving the Hamilton–Jacobi–Bellman equation, and asymptotic stability of the controlled nonlinear systems is guaranteed in the Lyapunov sense. We are especially interested in synchronization of chaotic systems. For this reason, the control strategy is applied in the trajectory tracking of periodic orbits for the Duffing oscillator and the Rössler system with uncertain stochastic parameters and initial conditions. The results are verified with Monte Carlo simulations.     

An analytical approximated solution and numerical simulations of a non-ideal system with saturation phenomenon

Nonlinear Dynamics - Nowadays, researches about non-ideal problems have been increased considerably in technical-scientific community. Nonlinear problems have been widely studied due to their...     

Plotting the Words of Econophysics

Text mining is applied to 510 articles on econophysics to reconstruct the lexical evolution of the discipline from 1999 to 2020. The analysis of the relative frequency of the words used in the articles and their “visualization” allow us to draw some conclusions about the evolution of the discipline. The traditional areas of research, financial markets and distribution of wealth, remain central, but they are flanked by other strands of research—production, currencies, networks—which broaden the discipline by pushing towards a dialectical application of traditional concepts and tools drawn from statistical physics.     

An overview on the appearance of the Sommerfeld effect and saturation phenomenon in non-ideal vibrating systems (NIS) in macro and MEMS scales

This paper was written in honor of Prof. Viktor Olimpanovich Kononenko from Ukraine and takes into account reports of recent progress about non-ideal vibrating systems (NIS) published in the period from 2004 to 2017. New and old studies of NIS, with limited power supply (small DC motors or electrodynamical shakers), are usually used in laboratory tests, and therefore, the investigation of mutual interactions of driven and driving sub-system is very important. In this paper, main properties of NIS have been reviewed, such as the Sommerfeld effect, i.e., jump phenomena and the increase in power supply that is required by an excitation source operating near resonance; the possibility of saturation phenomenon occurrence, i.e., the transference of energy from higher frequency and lower amplitude to lower frequency and higher amplitude mode; and the existence of regular (periodic motion) and irregular (chaotic motion) behaviors, depending on the value of control parameters (voltage of a DC motor). This paper is divided into two goals: on the one hand will be treated about NIS and on the other hand will be provided an overview of the main engineering applications, analyzing their physical phenomena involved and the adequate methodologies to deal with them.