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Wyniki wyszukiwania dla: FRACTIONAL PID CONTROLLER
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Design of weighted PID controllers for control of the Stewart-Gough platform
PublikacjaStewart-Gough platform (SGP) is a popular parallel type manipulator that involves a 6 degrees of freedom (DOF) motion. In this paper, the process of mathematical modelling of SGP is presented. Two selected control algorithms that use PID controllers and weighted PID controllers are designed. Both control systems using these algorithms are implemented in MATLAB environment as well as on the actual SGP. Parameters of the controllers...
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Boundary problems for fractional differential equations
PublikacjaIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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Optymalizacja nastaw regulatorów PID do sterowania suwnicą 3D
PublikacjaSuwnica stanowi ciekawy, a zarazem skomplikowany obiekt sterowania, który znajduje zastosowanie w różnych gałęziach przemysłu. W artykule przedstawiono obiekt sterowania wraz jego układami sterowania wykorzystującymi regulatory PID. Następnie dobrano parametry regulatorów wybranymi metodami inżynierskimi i optymalizacyjnymi. Przeprowadzono szczegółową analizę porównawczą zaproponowanych rozwiązań.
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Model reference method and continuous-time system identification in tuning the PID controllers.
PublikacjaW pracy opisano zagadnienie doboru nastaw sterowników PID w układach regulacji automatycznej. W rozważaniach wzięto pod uwagę zarówno klasyczną strukturę jednopętlowego układu sterowania z regulatorem PID umieszczonym w torze głównym, jak też odmienną realizację I-PD z członem całkującym występującym w torze głównym i sterownikiem proporcjonalno-różniczkującym ulokowanym w dodatkowej pętli sprzężenia zwrotnego. Ponieważ powszechnie...
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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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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 differential equations with causal operators
PublikacjaWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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Implementacja automatycznych metod strojenia nastaw regulatora PID w sterowniku programowalnym
PublikacjaZainteresowanie środowiska przemysłowego klasycznymi algorytmami regulacji, dającymi akceptowalne wyniki pracy i stabilność w odniesieniu do zmiennych warunków otoczenia, wciąż jest bardzo duże. W artykule opisano wybrane inżynierskie metody doboru nastaw regulatora PID. Przedstawiono implementację sprzętową jednej z nich (metoda Åströma-Hägglunda) w sterowniku programowalnym PLC, umożliwiającą automatyczny dobór nastaw regulatora....
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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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On Sample Rate Conversion Based on Variable Fractional Delay Filters
PublikacjaThe sample rate conversion algorithm based on variable fractional delay filters is often used if the resampling ratio cannot be expressed as the ratio of small integer numbers or if it is not constant. The main advantage of such solution is that it allows for arbitrary resampling ratios which can even be changed during the resampling process. In this paper a discussion on influence of different approaches to fractional filter...
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Measurement system based on USB Z-Wave controller
PublikacjaA wireless measurement system based on the Z-Wave standard is presented in this paper. The system is composed of a U SB Z-Stick Gen5 controller connected to a Personal Computer and a Fibaro controller FGRGBWM-441. Operation of the system is controlled by software written in C++ using OpenZWave library. Some metrological aspects of the system are evaluated: accuracy, linearity, resolution and frequency of voltage measurements.
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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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Dataset of phase portraits of the fractional prey-predator model with Holling type-II interaction (without predator harvesting)
Dane BadawczeThe need for a fractional generalization of a given classical model is often due to new behaviors which cannot be taken into account by the model. In this situation, it can be useful to look for a fractional deformation of the initial system, trying to fit the fractional exponent of differentiation in order to catch properly the data.
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Square root RC Nyquist filter of fractional delay
PublikacjaIn this paper we propose a discrete-time FIR (finite impulse response) filter which couples the role of square root Nyquist filter with fractional delay filter. This filter enables to substitute for a cascade of square root RC (SRRC) Nyquist filter and fractional delay filter in one device/algorithm. The aim is to compensate for transmission delay in communication system. Statistically defined performances, e.g. BER (bit error...
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Self-Optimizing Adaptive Vibration Controller
PublikacjaThis paper presents a new approach to rejection of sinusoidal disturbances acting at the output of a discrete-time linear stable plant with unknown dynamics. It is assumed that the frequency of the sinusoidal disturbance is known, and that the output signal is contaminated with wideband measurement noise. The proposed controller, called SONIC (self-optimizing narrowband interference canceller), combines the coefficient fixing technique,...
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Intelligent turbogenerator controller based on artifical neural network
PublikacjaThe paper presents a desing of an intelligent controller based on neural network (ICNN). The ICNN ensures at the same time two fundamental functions : the maintaining of generator voltage at the desired value and the damping of the electromechanical oscillations. Its performance is evaluted on a single machine infinite bus power system through computer simulations. The dynamic and transient operation of the proposed controller...
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On Applications of Fractional Derivatives in Circuit Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited...
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublikacjaThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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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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Robust design in delta domain for SISO plants: PI and PID controllers
PublikacjaW pracy przedstawiono zunifikowaną metodę numerycznie odpornej syntezy sterowników (regulatorów) działających w dyskretnym czasie w układach sterowania skalarnymi obiektami czasu ciągłego. Wykorzystano dyskretnoczasowe modele takich obiektów, oparte na tak zwanym operatorze delta, charakteryzującym się korzystnymi odpornościowymi cechami w przypadku stosowania dostatecznie małych wartości okresu próbkowania przetwarzanych sygnałów....
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efficient fractional delay hilbert transform filter in the farrow structure
PublikacjaIn this paper the design and application of a Fractional Delay Hilbert Transform Filter (FDHTF) into an adaptive sub-sample delay estimation between two separated sinusoidal signals is considered. The FDHTF incorporates the functions of Hilbertian and variable fractional delay filtering of the incoming signal simultaneously, in one stage. In traditional approach each of these operations was performed separately. Obtained value...
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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The QDMC Model Predictive Controller for the Nuclear Power Plant Steam Turbine Control
PublikacjaThere are typically two main control loops with PI con trollers operating at each turbo-generator set. In this paper a model predictive controller QDMC for the steam turbine is proposed - instead of a typical PI controller. The QDMC controller utilize a step-response model for the controlled system. This model parameters are determined, based on the simplified and linear model of turbo-generator set, which parameters are identified...
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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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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublikacjaAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublikacjaIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Numerical Method for Stability Testing of Fractional Exponential Delay Systems
PublikacjaA numerical method for stability testing of fractional exponential systems including delays is presented in this contribution. We propose the numerical test of stability for a very general class of systems with a transfer function, which includes polynomials and exponentials of fractional powers of the Laplace variable s combined with delay terms. Such a system is unstable if any root of its characteristic equation, which usually...
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublikacjaIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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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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Designing a ship course controller by applying the adaptivebackstepping method
PublikacjaThe article discusses the problem of designing a proper and efficient adaptive course-keeping control system for a seagoingship based on the adaptive backstepping method. The proposed controller in the design stage takes into account thedynamic properties of the steering gear and the full nonlinear static maneuvering characteristic. The adjustable parametersof the achieved nonlinear control structure were tuned up by using 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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Zastosowanie detektora fotojonizacyjnego (PID) w analizie środowiskowej. Application of photoionization detector in environmental analysis
PublikacjaNa podstawie studium literaturowego przedstawiono zastosowania detektora fotojonizacyjnego (photoionization detector - PID) w analizie środowiskowej. Omówiono zarówno kierunki wykorzystania w bezpośrednich metodach analitycznych jako czujnika, jak i w oznaczeniach chromatograficznych. Przedstawiono budowę i zasadę działania detektora oraz różne warianty instalowania detektora w układzie chromatograficznym, a także sposoby łączenia...
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Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control
PublikacjaIn this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzymodel is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and theparameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation(RLSE) algorithm. The rules of the fuzzy model can be added, replaced or...
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Variable Ratio Sample Rate Conversion Based on Fractional Delay Filter
PublikacjaIn this paper a sample rate conversion algorithm which allows for continuously changing resampling ratio has been presented. The proposed implementation is based on a variable fractional delay filter which is implemented by means of a Farrow structure. Coefficients of this structure are computed on the basis of fractional delay filters which are designed using the offset window method. The proposed approach allows us to freely...
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Variable Fractional Delay Filter Design Using a Symmetric Window
PublikacjaIn this paper a numerically efficient method for designing a nearly optimal variable fractional delay (VFD) filter based on a simple and well-known window method is presented. In the proposed method a single window extracted from the optimal filter with fixed fractional delay (FD) is divided into even and odd part. Subsequently, the odd part is discarded and symmetric even part of the extracted window is used to design a family...
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublikacjaIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublikacjaThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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PLC-based Implementation of Stochastic Optimization Method in the Form of Evolutionary Strategies for PID, LQR, and MPC Control
PublikacjaProgrammable logic controllers (PLCs) are usually equipped with only basic direct control algorithms like proportional-integral-derivative (PID). Modules included in engineering software running on a personal computer (PC) are usually used to tune controllers. In this article, an alternative approach is considered, i.e. the development of a stochastic optimizer based on the (μ,λ) evolution strategy (ES) in a PLC. For this purpose,...
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Fractional Differential Calculus
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Integrated controller for ultra high frequency technique laboratory
PublikacjaDepartment of Microwave and Antenna Engineering decided to modernize the laboratory of Ultra High Frequency Techniques. The main change was to replace measurement of the field distribution inside rectangular waveguides by analysing the fields around striplines. This involved the need to overcome several technical and conceptual problems. Precise positioning of the probe and reading the field distribution near the stripline is important...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublikacjaIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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PRZEMYSŁOWE UKŁADY STEROWANIA PID [2020/21]
Kursy Online -
PRZEMYSŁOWE UKŁADY STEROWANIA PID [2023/24]
Kursy Online -
Intelligent PI controller and its application to dissolved oxygen tracking problem
PublikacjaThe paper addresses design, calibration, implementation and simulation of the intelligent PI controller used for dissolved oxygen (DO) tracking in wastewater treatment plant (WWTP). The calibration process presented in this paper utilizes both engineering and scientific methods. Verification of the control system design method was obtained via simulation experiments.
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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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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublikacjaWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublikacjaStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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A complex variable fractional-delay FIR filter structure
PublikacjaW artykule wprowadzamy strukturę zespolonego filtru o skończonej odpowiedzi impulsowej (ang. finite impulse response - FIR) ze zmiennym opóźnieniem ułamkowym (ang. fractional delay - FD). Strukturę tę otrzymujemy na podstawie przestrajanego filtru FD FIR o współczynnikach rzeczywistych. Stanowi ona połączenie zbioru liniowo-fazowych filtrów FIR o współczynnikach stałych rzeczywistych i dwóch łańcuchów mnożąco-akumulujących, zawierających...
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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublikacjaIn this letter drawbacks of the aforementioned paper are pointed out. The proposed approach is improved with minor modifications of the discrete frequency response. This allows for design of fractional delay filters which are close to optimal and can be efficiently implemented in the frequency domain using the sliding DFT based structure. Alternatively, the derived equivalent closed form formulae for offset windows can be used...
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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...