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.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.

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.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Encapsulamento de monómeros da lenhina pela β-ciclodextrina: estudos químico e de biodegradação

Mestrado em Engenharia Química.Ramo Tecnologias de Protecção Ambiental

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.

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.

Remediação Ambiental

A agricultura é uma das atividades mais antigas realizadas pelo Homem, sendo de grande importância para a obtenção tanto de bens alimentares como de bens para outros fins. No entanto desde o início constatou-se que as culturas eram afetadas por pragas e doenças que levavam à perda das colheitas. Este motivo deu origem à necessidade de nesses termos surgiu a aplicação de substâncias com o objetivo de proteger as colheitas. Os pesticidas são substâncias naturais ou sintéticas, aplicadas com o objetivo de proteger as plantas eliminando pragas e doenças. Para além da potencial toxicidade destas substâncias, em alguns casos a sua degradação no meio ambiente por microrganismos, hidrólise, radiação solar, etc. dá origem a produtos de degradação tanto ou mais tóxicos que os próprios pesticidas. A utilização deste tipo de substâncias acarreta problemas, visto a sua aplicação ser feita de forma a compensar perdas que ocorrem por meio de degradação, lixiviação, entre outros processos. Este tipo de aplicação leva a que haja contaminação do meio ambiente por parte dos pesticidas, pondo em risco tanto a saúde humana como os restantes seres vivos. A utilização de ciclodextrinas no encapsulamento destes compostos tem como objetivo aumentar a estabilidade do composto e promover a sua libertação de forma controlada. No presente trabalho pretende-se efetuar um estudo comparativo sobre a fotodegradação do herbicida terbutilazina e do fungicida pirimetanil livres e quando encapsulados com 2- hidroxipropil-β- ciclodextrina. De forma a quantificar os pesticidas ao longo do estudo foi utilizado o método analítico de HPLC de fase reversa. Os resultados permitiram constatar que a terbutilazina é fotoquimicamente estável, nas condições aplicadas, visto que ao fim de 75 dias de as soluções de pesticida livre em água desionizada e em água do rio apresentarem ainda 98% do pesticida inicial e as soluções de pesticida encapsulado em água desionizada e em água do rio apresentarem ainda 98% do pesticida inicial. Neste caso particular não foi possível, no intervalo de tempo considerado, avaliar a influência do encapsulamento no processo de fotodegradação da terbutilazina. Dada a baixa fotodegradação observada optou-se pela adição de peróxido de hidrogénio às soluções de controlo e 35 mM de HP-β-CD e acetona às soluções de 0 mM e 17,5 mM de HP-β-CD, para tentar promover a degradação do pesticida. Através dos resultados obtidos constatou-se que particularmente para as soluções onde foi adicionada acetona houve um aumento da velocidade de degradação no entanto esta ainda ocorria de forma lenta e muito semelhante quer para o pesticida livre quer para o encapsulado. Relativamente ao estudo da fotodegradação do pirimetanil verificou-se que ao fim de 4 dias de irradiação as soluções de pesticida livre apresentavam já alguma degradação do pesticida e tendo o período de irradiação uma duração de 53 dias foi possível para este pesticida determinar os parâmetros cinéticos em algumas das soluções. Quanto as soluções de água desionizada e água do rio com pirimetanil livre ambas apresentaram degradação do pesticida verificando-se uma cinética de reação de 1ª ordem com constantes de 0,0018 dias-1 e de 0,0060 dias-1 respetivamente. Para a solução de água desionizada com pirimetanil encapsulado não foi detetada degradação do pesticida, já para a solução com pirimetanil encapsulado em água do rio verificou-se a existência de degradação que correspondeu a uma cinética de degradação de 1ª ordem com uma constante de 0,0013 dias-1. Através dos resultados obtidos pode-se concluir que o encapsulamento do pirimetanil com 2-hidroxipropil-β-ciclodextrina é vantajoso visto diminuir a quantidade de pesticida utilizado e aumentar a eficácia do controlo das pragas.

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.

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.

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.

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.

Organization knowledge management change from a complex adaptive systems perpective with ability for ambidexeterity

We are working on the confluence of knowledge management, organizational memory and emergent knowledge with the lens of complex adaptive systems. In order to be fundamentally sustainable organizations search for an adaptive need for managing ambidexterity of day-to-day work and innovation. An organization is an entity of a systemic nature, composed of groups of people who interact to achieve common objectives, making it necessary to capture, store and share interactions knowledge with the organization, this knowledge can be generated in intra-organizational or inter-organizational level. The organizations have organizational memory of knowledge of supported on the Information technology and systems. Each organization, especially in times of uncertainty and radical changes, to meet the demands of the environment, needs timely and sized knowledge on the basis of tacit and explicit. This sizing is a learning process resulting from the interaction that emerges from the relationship between the tacit and explicit knowledge and which we are framing within an approach of Complex Adaptive Systems. The use of complex adaptive systems for building the emerging interdependent relationship, will produce emergent knowledge that will improve the organization unique developing.

Fuzzy Monte Carlo mathematical model for load curtailment minimization in transmission power systems

This paper presents a methodology which is based on statistical failure and repair data of the transmission power system components and uses fuzzyprobabilistic modeling for system component outage parameters. Using statistical records allows developing the fuzzy membership functions of system component outage parameters. The proposed hybrid method of fuzzy set and Monte Carlo simulation based on the fuzzy-probabilistic models allows catching both randomness and fuzziness of component outage parameters. A network contingency analysis to identify any overloading or voltage violation in the network is performed once obtained the system states by Monte Carlo simulation. This is followed by a remedial action algorithm, based on optimal power flow, to reschedule generations and alleviate constraint violations and, at the same time, to avoid any load curtailment, if possible, or, otherwise, to minimize the total load curtailment, for the states identified by the contingency analysis. In order to illustrate the application of the proposed methodology to a practical case, the paper will include a case study for the Reliability Test System (RTS) 1996 IEEE 24 BUS.