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Wyniki wyszukiwania dla: FRACTIONAL ORDER PID,
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Fractional-Order PID Controller (FOPID)-Based Iterative Learning Control for a Nonlinear Boiler System
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Recurrent Neural Network Based Adaptive Variable-Order Fractional PID Controller for Small Modular Reactor Thermal Power Control
PublikacjaThis paper presents the synthesis of an adaptive PID type controller in which the variable-order fractional operators are used. Due to the implementation difficulties of fractional order operators, both with a fixed and variable order, on digital control platforms caused by the requirement of infinite memory resources, the fractional operators that are part of the discussed controller were approximated by recurrent neural networks...
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Fractional Order Dynamic Positioning Controller
PublikacjaImproving the performance of Dynamic Positioning System in such applications as station keeping, position mooring and slow speed references tracking requires improving the position and heading control precision. These goals can be achieved through the improvement of the ship control system. Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control...
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Some applications of fractional order calculus
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Fractional Order Models of Dynamic Systems
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Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublikacjaThe paper presents the methodology for the synthesis of a Fuzzy Multi-Regional Fractional Order PID controller (FMR-FOPID) used to control the average thermal power of a PWR nuclear reactor in the load following mode. The controller utilizes a set of FOPID controllers and the fuzzy logic Takagi-Sugeno reasoning system. The proposed methodology is based on two optimization parts. The first part is devoted to finding the optimal...
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Electromagnetic-based derivation of fractional-order circuit theory
PublikacjaIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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Fractional-order Systems and Synchronous Generator Voltage Regulator
PublikacjaModern regulators of synchronous generators, including voltage regulators, are digital systems, in their vast majority with standard structures contained in the IEEE standard. These are systems described with stationary differential equations of integral order. Differential equations of fractional order are not employed in regulators for synchronous generator control. This paper presents an analysis of the possibilities of using...
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublikacjaIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublikacjaIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...
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Stability of Discrete Fractional Order State-space Systems
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Comparison and validation of integer and fractional order ultracapacitor models
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Time domain validation of ultracapacitor fractional order model
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Diffusion process modeling by using fractional-order models
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Simulation of Signal Propagation Along Fractional-Order Transmission Lines
PublikacjaIn this paper, the simulation method of signal propagation along fractional-order (FO) transmission lines is presented. Initially, fractional calculus and the model of FO transmission line are introduced. Then, the algorithm allowing for simulation of the nonmonochromatic wave propagation along FO transmission lines is presented. It employs computations in the frequency domain, i.e., an analytical excitation is transformed to the...
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Simulation of Wave Propagation in Media Described by Fractional-Order Models
PublikacjaIn this paper, algorithms for simulation of the wave propagation in electromagnetic media described by fractional-order (FO) models (FOMs) are presented. Initially, fractional calculus and FO Maxwell's equations are introduced. The problem of the wave propagation is formulated for media described by FOMs. Then, algorithms for simulation of the non-monochromatic wave propagation are presented which employ computations in the time...
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Signal propagation in electromagnetic media described by fractional-order models
PublikacjaIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Frequency response based identification of fractional order dynamical systems
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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublikacjaThe paper presents research on the approximation of variable-order fractional operators by recurrent neural networks. The research focuses on two basic variable-order fractional operators, i.e., integrator and differentiator. The study includes variations of the order of each fractional operator. The recurrent neural network architecture based on GRU (Gated Recurrent Unit) cells functioned as a neural approximation for selected...
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublikacjaThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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Ultracapacitor modeling and control with discrete fractional order artificial neural network
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Adaptive Feedback Control of Fractional Order Discrete State-Space Systems
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Comparable analysis of PID controller settings in order to ensure reliable operation of active foil bearings
PublikacjaIn comparison to the traditional solutions, active bearings offer great operating flexibility, ensure better operating conditions over a wider range of rotational speeds and are safe to use. In order to ensure optimum bearing performance a bearing control system is used that adapts different geometries during device operation. The selection of optimal controller parameters requires the use of modern optimization methods that make...
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New method of fractional order integrator analog modeling for orders 0.5 and 0.25
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<title>Estimation and control of discrete fractional order states-space systems</title>
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Fractional Variable-Order Derivative and Difference Operators and Their Applications to Dynamical Systems Modelling
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Approximation of Fractional Order Dynamic Systems Using Elman, GRU and LSTM Neural Networks
PublikacjaIn the paper, authors explore the possibility of using the recurrent neural networks (RNN) - Elman, GRU and LSTM - for an approximation of the solution of the fractional-orders differential equations. The RNN network parameters are estimated via optimisation with the second order L-BFGS algorithm. It is done based on data from four systems: simple first and second fractional order LTI systems, a system of fractional-order point...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublikacjaIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Hybrid super‐twisting fractional‐order terminal sliding mode control for rolling spherical robot
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublikacjaIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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An optimal nonlinear fractional order controller for passive/active base isolation building equipped with friction-tuned mass dampers
PublikacjaThis paper presents an optimal nonlinear fractional-order controller (ONFOC) designed to reduce the seismic responses of tall buildings equipped with a base-isolation (BI) system and friction-tuned mass dampers (FTMDs). The parameters for the BI and FTMD systems, as well as their combinations (BI-FTMD and active BI-FTMD or ABI-FTMD), were optimized separately using a multi-objective quantum-inspired seagull optimization algorithm...
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Variable Order Differential Models of Bone Remodelling * *This work was supported by FCT, through IDMEC, under LAETA, projects UID/EMS/50022/2013, BoneSys, joint Polish-Portuguese project Modelling and controlling cancer evolution using fractional calculus, PERSEIDS (PTDC/EMS-SIS/0642/2014) and IF/00653/2012
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Analiza sterowania ułamkowego PIλDμ mocą reaktora jądrowego
PublikacjaW artykule przedstawiono syntezę regulatora PIλDμ niecałkowitego rzędu dla potrzeb sterowania mocą reaktora jądrowego lekko wodnego określanego, jako typu PWR (Pressurized Water Reactor). W tym celu wykorzystano nieliniowy model matematyczny reaktora PWR o parametrach skupionych obejmujący procesy generacji i wymiany ciepła oraz termicznych efektów reaktywnościowych. Nastawy regulatora PIλDμ niecałkowitego rzędu dobrano w sposób...
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Implementation of the FOPID Algorithm in the PLC Controller - PWR Thermal Power Control Case Study
PublikacjaIn the paper authors describe proposition of design and verification procedures of the discrete Fractional Order PID (FOPID) algorithm for control of the Pressurized Water Reactor (PWR) thermal power near its nominal operating point. The FOPID algorithm synthesis consists of: off-line optimal tunning of its parameters in continuous time-domain with LQ (Linear Quadratic) performance index and simplified models of nuclear reactor...
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Wieloobszarowa rozmyta regulacja PID mocy reaktora jądrowego
PublikacjaW artykule przedstawiono wieloobszarowy regulator rozmyty z lokalnymi regulatorami PID dla sterowania mocą reaktora jądrowego typu PWR. Wykorzystano model matematyczny o parametrach skupionych reaktora PWR obejmujący procesy generacji i wymiany ciepła oraz efektów reaktywnościowych. Nastawy lokalnych regulatorów PID zostały dobrane w sposób optymalny, minimalizując całkowy wskaźnik jakości ISE. Na przykładzie pokazano że zastosowane...
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Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative
PublikacjaIn this paper, wave propagation is considered in a medium described by a fractional-order model, which is formulated with the use of the two-sided fractional derivative of Ortigueira and Machado. Although the relation of the derivative to causality is clearly specified in its definition, there is no obvious relation between causality of the derivative and causality of the transfer function induced by this derivative. Hence, causality...
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Systems of Nonlinear Fractional Differential Equations
PublikacjaUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
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Functional delay fractional equations
PublikacjaIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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A Note on Fractional Curl Operator
PublikacjaIn this letter, we demonstrate that the fractional curl operator, widely used in electromagnetics since 1998, is essentially a rotation operation of components of the complex Riemann–Silberstein vector representing the electromagnetic field. It occurs that after the wave decomposition into circular polarisations, the standard duality rotation with the angle depending on the fractional order is applied to the left-handed basis vector...
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Metody strojenia regulatorów typu PID z wykorzystaniem technologii syntezy regulatorów od stanu
PublikacjaUkłady sterujące typu PID są jednymi z najbardziej popularnych regulatorów wykorzystywanych w układach regulacji. W związku z tym znanych jest szereg metod doboru wartości ich parametrów (nastaw). Obok różnych metod inżynierskich czy analitycznych strojenia tego typu regulatorów, dostępne są również podejścia bazujące na optymalizacji. Wskaźnikiem jakości znajdującym w nich zastosowanie jest np. całka z kwadratu uchybu. W artykule...
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Multifunctional PID Neuro-Controller for Synchronous Generator
PublikacjaThis paper deals with a PID Neuro-Controller (PIDNC) for synchronous generator system. The controller is based on artificial neural network and adaptive control strategy. It ensures two functions: maintaining the generator voltage at its desired value and damping electromechanical oscillations. The performance of the proposed controller is evaluated on the basis of simulation tests. A comparative study of the results obtained with...
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublikacjaIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublikacjaIn this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element method (f-SEM) and fractional Finite element method (f-FEM) are crucial in various branches of science and play a significant role. In this review, we discuss the advantages and adaptability of FEM and SEM, which provide the simulations of fractional...
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Design of modified PID controllers for 3D crane control
PublikacjaFrom the control viewpoint, 3D crane is a dynamic, nonlinear and multidimensional electromechanical system. In this paper, five control systems using a set-point weighted PID controllers (modified controllers) are designed. These structures and properties are presented. Optimization process of controllers settings based on integral performance indices is made. Simulation tests of control systems are presented. Comparison of integral...
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About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
PublikacjaRecently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether's type Theorem, in particular ([9],Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis...
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Fractional problems with advanced arguments
PublikacjaThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator
PublikacjaA new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublikacjaIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Implementacja niekonwencjonalnych regulatorów PID w sterowniku programowalnym
PublikacjaNieustanny rozwój systemów sterowania oraz szeroko pojętej automatyki sprawia, że coraz więcej procesów kontrolowanych jest bez udziału człowieka. Problemem są jednak złożone obiekty o charakterystycznych cechach, które uniemożliwiają zastosowanie klasycznych regulatorów, w szczególności PID. W artykule zaprezentowano wybrane zmodyfikowane algorytmy regulatora PID wraz z ich implementacją w sterowniku programowalnym. W celu weryfikacji...