Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Legal and political regulation of higher education in Portugal: an evolutionary perspective on the current policy issues and the problem of order

The higher education system in Europe is currently under stress and the debates over its reform and future are gaining momentum. Now that, for most countries, we are in a time for change, in the overall society and the whole education system, the legal and political dimensions have gained prominence, which has not been followed by a more integrative approach of the problem of order, its reform and the issue of regulation, beyond the typical static and classical cost-benefit analyses. The two classical approaches for studying (and for designing the policy measures of) the problem of the reform of the higher education system - the cost-benefit analysis and the legal scholarship description - have to be integrated. This is the argument of our paper that the very integration of economic and legal approaches, what Warren Samuels called the legal-economic nexus, is meaningful and necessary, especially if we want to address the problem of order (as formulated by Joseph Spengler) and the overall regulation of the system. On the one hand, and without neglecting the interest and insights gained from the cost-benefit analysis, or other approaches of value for money assessment, we will focus our study on the legal, social and political aspects of the regulation of the higher education system and its reform in Portugal. On the other hand, the economic and financial problems have to be taken into account, but in a more inclusive way with regard to the indirect and other socio-economic costs not contemplated in traditional or standard assessments of policies for the tertiary education sector. In the first section of the paper, we will discuss the theoretical and conceptual underpinning of our analysis, focusing on the evolutionary approach, the role of critical institutions, the legal-economic nexus and the problem of order. All these elements are related to the institutional tradition, from Veblen and Commons to Spengler and Samuels. The second section states the problem of regulation in the higher education system and the issue of policy formulation for tackling the problem. The current situation is clearly one of crisis with the expansion of the cohorts of young students coming to an end and the recurrent scandals in private institutions. In the last decade, after a protracted period of extension or expansion of the system, i. e., the continuous growth of students, universities and other institutions are competing harder to gain students and have seen their financial situation at risk. It seems that we are entering a period of radical uncertainty, higher competition and a new configuration that is slowly building up is the growth in intensity, which means upgrading the quality of the higher learning and getting more involvement in vocational training and life-long learning. With this change, and along with other deep ones in the Portuguese society and economy, the current regulation has shown signs of maladjustment. The third section consists of our conclusions on the current issue of regulation and policy challenge. First, we underline the importance of an evolutionary approach to a process of change that is essentially dynamic. A special attention will be given to the issues related to an evolutionary construe of policy analysis and formulation. Second, the integration of law and economics, through the notion of legal economic nexus, allows us to better define the issues of regulation and the concrete problems that the universities are facing. One aspect is the instability of the political measures regarding the public administration and on which the higher education system depends financially, legally and institutionally, to say the least. A corollary is the lack of clear strategy in the policy reforms. Third, our research criticizes several studies, such as the one made by the OECD in late 2006 for the Ministry of Science, Technology and Higher Education, for being too static and neglecting fundamental aspects of regulation such as the logic of actors, groups and organizations who are major players in the system. Finally, simply changing the legal rules will not necessary per se change the behaviors that the authorities want to change. By this, we mean that it is not only remiss of the policy maker to ignore some of the critical issues of regulation, namely the continuous non-respect by academic management and administrative bodies of universities of the legal rules that were once promulgated. Changing the rules does not change the problem, especially without the necessary debates form the different relevant quarters that make up the higher education system. The issues of social interaction remain as intact. Our treatment of the matter will be organized in the following way. In the first section, the theoretical principles are developed in order to be able to study more adequately the higher education transformation with a modest evolutionary theory and a legal and economic nexus of the interactions of the system and the policy challenges. After describing, in the second section, the recent evolution and current working of the higher education in Portugal, we will analyze the legal framework and the current regulatory practices and problems in light of the theoretical framework adopted. We will end with some conclusions on the current problems of regulation and the policy measures that are discusses in recent years.

Fuzzy, integer and fractional-order control: Application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Fractional order control on a wind turbine benchmark

This paper is about a hierarchical structure with an event-based supervisor in a higher level and a fractional-order proportional integral (FOPI) in a lower level applied to a wind turbine. The event-based supervisor analyzes the operation conditions to determine the state of the wind turbine. This controller operate in the full load region and the main objective is to capture maximum power generation while ensuring the performance and reliability required for a wind turbine to be integrated into an electric grid. The main contribution focus on the use of fractional-order proportional integral controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. Comparisons between fractional-order pitch control and a default proportional integral pitch controller applied to a wind turbine benchmark are given and simulation results by Matlab/Simulink are shown in order to prove the effectiveness of the proposed approach.

Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.

Optimal controllers with complex order derivatives

This paper studies the optimization of complex-order algorithms for the discrete-time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complexorder control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex-order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

Fractional order modelling of fractional-order holds

Discrete time control systems require sample- and-hold circuits to perform the conversion from digital to analog. Fractional-Order Holds (FROHs) are an interpolation between the classical zero and first order holds and can be tuned to produce better system performance. However, the model of the FROH is somewhat hermetic and the design of the system becomes unnecessarily complicated. This paper addresses the modelling of the FROHs using the concepts of Fractional Calculus (FC). For this purpose, two simple fractional-order approximations are proposed whose parameters are estimated by a genetic algorithm. The results are simple to interpret, demonstrating that FC is a useful tool for the analysis of these devices.

The effect of fractional order in variable structure control

This paper studies fractional variable structure controllers. Two cases are considered namely, the sliding reference model and the control action, that are generalized from integer into fractional orders. The test bed consists in a mechanical manipulator and the effect of the fractional approach upon the system performance is evaluated. The results show that fractional dynamics, both in the switching surface and the control law are important design algorithms in variable structure controllers.

Introducing the fractional-order Darwinian PSO

One of the most well-known bio-inspired algorithms used in optimization problems is the particle swarm optimization (PSO), which basically consists on a machinelearning technique loosely inspired by birds flocking in search of food. More specifically, it consists of a number of particles that collectively move on the search space in search of the global optimum. The Darwinian particle swarm optimization (DPSO) is an evolutionary algorithm that extends the PSO using natural selection, or survival of the fittest, to enhance the ability to escape from local optima. This paper firstly presents a survey on PSO algorithms mainly focusing on the DPSO. Afterward, a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts is proposed. The fractional-order optimization algorithm, denoted as FO-DPSO, is tested using several well-known functions, and the relationship between the fractional-order velocity and the convergence of the algorithm is observed. Moreover, experimental results show that the FO-DPSO significantly outperforms the previously presented FO-PSO.

Bilirubin directly disrupts membrane lipid polarity and fluidity, protein order, and redox status in rat mitochondria

Background/Aims: Unconjugated bilirubin (UCB) impairs crucial aspects of cell function and induces apoptosis in primary cultured neurones. While mechanisms of cytotoxicity begin to unfold, mitochondria appear as potential primary targets. Methods: We used electron paramagnetic resonance spectroscopy analysis of isolated rat mitochondria to test the hypothesis that UCB physically interacts with mitochondria to induce structural membrane perturbation, leading to increased permeability, and subsequent release of apoptotic factors. Results: Our data demonstrate profound changes on mitochondrial membrane properties during incubation with UCB, including modified membrane lipid polarity and fluidity (P , 0:01), as well as disrupted protein mobility(P , 0:001). Consistent with increased permeability, cytochrome c was released from the intermembrane space(P , 0:01), perhaps uncoupling the respiratory chain and further increasing oxidative stress (P , 0:01). Both ursodeoxycholate, a mitochondrial-membrane stabilising agent, and cyclosporine A, an inhibitor of the permeability transition, almost completely abrogated UCB-induced perturbation. Conclusions: UCB directly interacts with mitochondria influencing membrane lipid and protein properties, redox status, and cytochrome c content. Thus, apoptosis induced by UCB may be mediated, at least in part, by physical perturbation of the mitochondrial membrane. These novel findings should ultimately prove useful to our evolving understanding of UCB cytotoxicity.

Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Fractional order models of leaves

Leaves are mainly responsible for food production in vascular plants. Studying individual leaves can reveal important characteristics of the whole plant, namely its health condition, nutrient status, the presence of viruses and rooting ability. One technique that has been used for this purpose is Electrical Impedance Spectroscopy, which consists of determining the electrical impedance spectrum of the leaf. In this paper we use EIS and apply the tools of Fractional Calculus to model and characterize six species. Two modeling approaches are proposed: firstly, Resistance, Inductance, Capacitance electrical networks are used to approximate the leaves’ impedance spectra; afterwards, fractional-order transfer functions are considered. In both cases the model parameters can be correlated with physical characteristics of the leaves.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.