Fractional describing function of systems with Coulomb friction

This paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed into two components, namely, the viscous and the Coulomb friction. The system dynamics is analyzed in the DF perspective revealing a fractional-order behavior. The reliability of the DF method is evaluated through the signal harmonic contents.

Executive Function Impairments in Patients with Depression

Depression, the most prevalent psychiatric disorder, has a lifelong risk of 20% and is related to high rates of death among the patients. Thus, this study aims to conduct a systematic review of changes in executive functions of adult patients diagnosed with depression. We found 1381 articles; however, only 28 were selected and recovered. The inclusion criteria was the assessment of executive functions with at least one neuropsychological test, and articles that evaluated primarily adult individuals with depression, without comparison to other psychiatric disorders. Although most of the studies (25 out of 28 analyzed) have shown deficits in some executive subcomponents, these findings are not conclusive because they used different parameters of assessment. Moreover, many variables were not controlled, such as the different subtypes of the disorder, the high level of severity, comorbidity and the use of drugs. Most studies showed different deficits in executive functions in depressed patients, but further longitudinal studies are needed in order to confirm these findings.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Modified Discrete PSO to Increase the Delivered Energy Probability in Distribution energy Systems

This paper proposes a PSO based approach to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The statistical failure and repair data of distribution components is the main basis of the proposed methodology that uses a fuzzyprobabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A Modified Discrete PSO optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Integer/fractional decomposition of the impulse response of fractional linear systems

The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.

Limit Cycle Prediction of Systems with Fractional Controllers and Backlash

This article investigates the limit cycle (LC) prediction of systems with backlash by means of the describing function (DF) when using discrete fractional-order (FO) algorithms. The DF is an approximate method that gives good estimates of LCs. The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.

Analysis of Systems with Backlash and Impacts through the Describing Function

This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. The dynamics is illustrated using the Nyquist and Bode plots and the results are compared with those of standard models.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.