Fractional control of dynamic systems

The concepts involved with fractional calculus (FC) theory are applied in almost all areas of science and engineering. Its ability to yield superior modeling and control in many dynamical systems is well recognized. In this article, we will introduce the fundamental aspects associated with the application of FC to the control of dynamic systems.

Control and dynamics of fractional order systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fixed point transformations in the adaptive control of fractional-order MIMO systems

Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, in connection with visco-elastic phenomena [5, 6]. The topic later obtained quite general attention [7, 8, 9], and also found new applications in material science [10], analysis of earth-quake signals [11], control of robots [12], and in the description of diffusion [13], etc.

Implementation contexts of a Tuberculosis Control Program in Brazilian prisons

OBJECTIVE To analyze the influence from context characteristics in the control of tuberculosis in prisons, and the influence from the program implementation degrees in observed effects.METHODS A multiple case study, with a qualitative approach, conducted in the prison systems of two Brazilian states in 2011 and 2012. Two prisons were analyzed in each state, and a prison hospital was analyzed in one of them. The data were submitted to a content analysis, which was based on external, political-organizational, implementation, and effect dimensions. Contextual factors and the ones in the program organization were correlated. The independent variable was the program implementation degree and the dependent one, the effects from the Tuberculosis Control Program in prisons.RESULTS The context with the highest sociodemographic vulnerability, the highest incidence rate of tuberculosis, and the smallest amount of available resources were associated with the low implementation degree of the program. The results from tuberculosis treatment in the prison system were better where the program had already been partially implemented than in the case with low implementation degree in both cases.CONCLUSIONS The implementation degree and its contexts – external and political-organizational dimensions – simultaneously contribute to the effects that are observed in the control of tuberculosis in analyzed prisons.

Application of fractional algorithms in the control of a robotic bird

In this paper, it is studied the dynamics of the robotic bird in terms of time response and robustness. It is analyzed the wing angle of attack and the velocity of the bird, the tail influence, the gliding flight and the flapping flight. The results are positive for the construction of flying robots. The development of computational simulation based on the dynamic of the robotic bird should allow testing strategies and different algorithms of control such as integer and fractional controllers.

A type system for access control in an object-oriented language

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

Risk factors for recurrent wheezing in infants: a case-control study

ABSTRACT OBJECTIVE To evaluate the association between recurrent wheezing and atopy, the Asthma Predictive Index, exposure to risk factors, and total serum IgE levels as potential factors to predict recurrent wheezing. METHODS A case-control study with infants aged 6-24 months treated at a specialized outpatient clinic from November 2011 to March 2013. Evaluations included sensitivity to inhalant and food antigens, positive Asthma Predictive Index, and other risk factors for recurrent wheezing (smoking during pregnancy, presence of indoor smoke, viral infections, and total serum IgE levels). RESULTS We evaluated 113 children: 65 infants with recurrent wheezing (63.0% male) with a mean age of 14.8 (SD = 5.2) months and 48 healthy infants (44.0% male) with a mean age of 15.2 (SD = 5.1) months. In the multiple analysis model, antigen sensitivity (OR = 12.45; 95%CI 1.28–19.11), positive Asthma Predictive Index (OR = 5.57; 95%CI 2.23–7.96), and exposure to environmental smoke (OR = 2.63; 95%CI 1.09–6.30) remained as risk factors for wheezing. Eosinophilia ≥ 4.0% e total IgE ≥ 100 UI/mL were more prevalent in the wheezing group, but failed to remain in the model. Smoking during pregnancy was identified in a small number of mothers, and secondhand smoke at home was higher in the control group. CONCLUSIONS Presence of atopy, positive Asthma Predictive Index and exposure to environmental smoke are associated to recurrent wheezing. Identifying these factors enables the adoption of preventive measures, especially for children susceptible to persistent wheezing and future asthma onset.

Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.

On the fractional order control of heat systems

The differentiation of non-integer order has its origin in the seventeenth century, but only in the last two decades appeared the first applications in the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated namely the fractional PID and the Smith predictor. Extensive simulations are presented assessing the performance of the proposed fractional-order algorithms.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Complex dynamics in the trajectory control of redundant manipulators

Redundant manipulators allow the trajectory optimization, the obstacle avoidance, and the resolution of singularities. For this type of manipulators, the kinematic control algorithms adopt generalized inverse matrices that may lead to unpredictable responses. Motivated by these problems this paper studies the complexity revealed by the trajectory planning scheme when controlling redundant manipulators. The results reveal fundamental properties of the chaotic phenomena and give a deeper insight towards the development of superior trajectory control algorithms.

Integer vs. fractional order control of a hexapod robot

This paper studies the performance of integer and fractional order controllers in a hexapod robot with joints at the legs having viscous friction and flexibility. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. The controller performance is analised through the Nyquist stability criterion. A set of model-based experiments reveals the influence of the different controller implementations upon the proposed metrics.

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Describing function of two masses with backlash

This paper analyzes the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional dynamics is compared with that of standard models.

Fractional control of heat diffusion systems

The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.