Sergio Adriani David

Partial chaos suppression in a fractional order macroeconomic model

This work investigates the possibility of suppressing chaos in a fractional-nonlinear macroeconomic dynamic model. The system generalizes a model recently reported in the literature in which chaos is strongly present. This description involves the inclusion of the public sector deficit and its coupling with other variables. The system is simulated for integer and non-integer orders that produce a complex dynamics. The time histories and the phase diagrams are presented. The main contribution of this work refers to the adoption of the largest Lyapunov exponent (LLE) criteria based on Wolfs algorithm. This approach improves the response of the system, suppressing, at least partially, the strong presence of chaos reported in previous studies.

Dynamics of Commodities Prices: Integer and Fractional Models

This paper examines the time series of four important agricultural commodities, namely the soybean, corn, coffee and sugar prices. Time series can exhibit long-range dependence and persistence in their observation. The long memory feature of data is a documented fact and there has been an increasing interest in studying such concepts in the perspective of economics and finance. In this work, we start by analyzing the time series of the four commodities by means of the Fractional Fourier Transform (FrFT) to unveil time-frequency patterns in the data. In a second phase, we apply Auto Regressive Integrated Moving Average (ARIMA) and Auto Regressive Fractionally Integrated Moving Average (ARFIMA) models for obtaining the spot price composition and predict future price. The ARFIMA process is a known class of long memory model, representing a generalization of the ARIMA algorithm. We compare the performances of the ARIMA and the ARFIMA models and we show that the ARFIMA has a superior performance for future price forecasting. ∗Address for correspondence: University of São Paulo, Av. Duque de Caxias Norte 225, 13635-900, Brazil 390 S.A. David et al. / Dynamics of Commodities Prices: Integer and Fractional Models

Fractional PID controller in an active image stabilization system for mitigating vibration effects in agricultural tractors

Abstract Recent demands in sophisticated agricultural machinery require passive or active image sensors to be mounted on vehicle frames. The impact produced by vertical displacements due to tire-soil interaction and mechanical engine vibration causes oscillations that reduce the data quality of any activity performed by equipment such as a camera, spectroradiometer, or scanner laser. This paper presents the modeling and simulation of an active system for stabilization of oscillations using a fractional order PID (Proportional-Integral-Derivative) controller. A method for tuning the fractional order PID is presented for a closed-loop dynamic system. Experiments based on simulations are carried out to compare the performance of the active stabilization system with fractional and integer order PID controllers. Common excitation functions are used to assess the performance of the active stabilization system, along with some common vibration disturbances acquired by a field experiment with a tractor-implement set. The results show that the active stabilization system presents better performance, mitigating vibration displacements and accelerations through a closed-loop system with a fractional PID controller. Additionally, numerical results confirm the superior capacity of the fractional controller based system for attenuating the vibration disturbance compared to the classical PID system for different machinery operational conditions such as forward speed and load.

Fractional dynamic behavior in ethanol prices series

Abstract Commodities have an increasing importance in international financial markets due to the cross effects between their equity patterns and their volatility. Brazil is one of the world’s largest producers of ethanol that represents an important energy commodity. In this paper, several tools for investigating the Brazilian ethanol pricing mechanism are adopted, namely the Auto Regressive Integrated Moving Average, Auto Regressive Fractional Integrated Moving Average, Detrended Fluctuation Analyses, and the Hurst and Lyapunov exponents. The data series cover the period from 2010 up to the end of 2014, for the spot price composition, and 2015 for the future price prediction. The results suggest that the ethanol prices series is anti-persistent which implies that a low price level has a tendency to be followed by a high price level and vice versa. Furthermore, the effect of shocks to the price system dissipates in the long run.

A fractional PID controller of an oscillatory system

An oscillatory mechanical platform with many interests in agriculture was modelled and numerically simulated with both traditional and fractional PID controller. A constrained optimization was used to find the best gains for the controllers and the best fractional orders. The performances between the controllers were compared and the results seem to show that fractional PID controllers may be more efficient depending on the application where they are used.