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Tytuł:
Influence of time delay on fractional-order PI-controlled system for a second-order oscillatory plant model with time delay
Autorzy:
Sadalla, T.
Horla, D.
Giernacki, W.
Kozierski, P.
Powiązania:
https://bibliotekanauki.pl/articles/140432.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional-order control
FOPI controller
stability analysis
time delay
tracking
Opis:
The paper aims at presenting the influence of an open-loop time delay on the stability and tracking performance of a second-order open-loop system and continuoustime fractional-order PI controller. The tuning method of this controller is based on Hermite- Biehler and Pontryagin theorems, and the tracking performance is evaluated on the basis of two integral performance indices, namely IAE and ISE. The paper extends the results and methodology presented in previous work of the authors to analysis of the influence of time delay on the closed-loop system taking its destabilizing properties into account, as well as concerning possible application of the presented results and used models.
Źródło:
Archives of Electrical Engineering; 2017, 66, 4; 693-704
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order PIλDµA controller design based on Bode’s ideal function
Autorzy:
Bettou, Khalfa
Charef, Abdelfatah
Powiązania:
https://bibliotekanauki.pl/articles/27312016.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
Bode’s ideal transfer function
fractional order control
classical PIDA controller
fractional order PIDA controller
robustness
Opis:
The fractional order proportional, integral, derivative and acceleration (PIλDµA) controller is an extension of the classical PIDA controller with real rather than integer integration action order λ and differentiation action order µ. Because the orders λ and µ are real numbers, they will provide more flexibility in the feedback control design for a large range of control systems. The Bode’s ideal transfer function is largely adopted function in fractional control systems because of its iso-damping property which is an essential robustness factor. In this paper an analytical design technique of a fractional order PIλDµA controller is presented to achieve a desired closed loop system whose transfer function is the Bode’s ideal function. In this design method, the values of the six parameters of the fractional order PIλDµA controllers are calculated using only the measured step response of the process to be controlled. Some simulation examples for different third order motor models are presented to illustrate the benefits, the effectiveness and the usefulness of the proposed fractional order PIλDµA controller tuning technique. The simulation results of the closed loop system obtained by the fractional order PIλDµA controller are compared to those obtained by the classical PIDA controller with different design methods found in the literature. The simulation results also show a significant improvement in the closed loop system performances and robustness using the proposed fractional order PIλDµA controller design.
Źródło:
Archives of Control Sciences; 2023, 33, 2; 425--458
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Note on describing function analysis of fractional order nonlinear control systems
Autorzy:
Yeroglu, C.
Tan, N.
Powiązania:
https://bibliotekanauki.pl/articles/206045.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
describing function
fractional order control
limit cycle
nonlinear systems
relay auto-tuning
stability margin
Opis:
This paper presents extensions of some results, obtained for the analysis of classical nonlinear control systems, to the nonlinear fractional order systems. It is shown that the results related to limit cycle prediction using describing function method can be applied to the fractional order plants. The frequency and the amplitude of the limit cycle are used for auto-tuning of the PID controller for nonlinear control systems with fractional order transfer functions. Fractional order control system with parametric uncertainty is also considered for the nonlinear case. On the other hand, a New method is provided for stability margin computation for fractional order nonlinear control system with parametric uncertainty structure using the Nyquist envelopes of the fractional order uncertain plant and the describing function that represents the nonlinearity of the system. Maximum perturbation bounds of the parameters of the fractional order plant are computed. Numerical examples are included to illustrate the methods presented.
Źródło:
Control and Cybernetics; 2015, 44, 2; 233-255
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Review, design, stabilization and synchronization of fractional-order energy resources demand-supply hyperchaotic systems using fractional-order PD-based feedback control scheme
Autorzy:
Soukkou, Ammar
Soukkou, Yassine
Haddad, Sofiane
Benghanem, Mohamed
Rabhi, Abdelhamid
Powiązania:
https://bibliotekanauki.pl/articles/27322620.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
fractional-order systems
fractional-order control
Lyapunov stability theory
multiobjective optimization
artificial hummingbird algorithm
stabilization
synchronization
energy resources demand-dupply systems
Opis:
This paper introduces a fractional-order PD approach (F-oPD) designed to control a large class of dynamical systems known as fractional-order chaotic systems (F-oCSs). The design process involves formulating an optimization problem to determine the parameters of the developed controller while satisfying the desired performance criteria. The stability of the control loop is initially assessed using the Lyapunov’s direct method and the latest stability assumptions for fractional-order systems. Additionally, an optimization algorithm inspired by the flight skills and foraging behavior of hummingbirds, known as the Artificial Hummingbird Algorithm (AHA), is employed as a tool for optimization. To evaluate the effectiveness of the proposed design approach, the fractional-order energy resources demand-supply (Fo-ERDS) hyperchaotic system is utilized as an illustrative example.
Źródło:
Archives of Control Sciences; 2023, 33, 3; 539--563
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of optimal control for multi-order fractional optimal control problems
Autorzy:
Kamocki, Rafał
Powiązania:
https://bibliotekanauki.pl/articles/2134888.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
existence of optimal control
multi-order fractional control system
lower closure theorem
Opis:
In this article we focus on optimal control problems involving a nonlinear fractional control system of different orders with Caputo derivatives, associated to a Lagrange cost functional. Based on a lower closure theorem for orientor fields combined with Filippov’s approach, we derive an existence result for at least one optimal solution for such a problem.
Źródło:
Archives of Control Sciences; 2022, 32, 2; 279--303
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analiza sterowania ułamkowego PIλDμ mocą reaktora jądrowego
Analysis of fractional order PIλDμ power control of a nuclear reactor
Autorzy:
Puchalski, B.
Duzinkiewicz, K.
Rutkowski, T.
Powiązania:
https://bibliotekanauki.pl/articles/408118.pdf
Data publikacji:
2013
Wydawca:
Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
Tematy:
regulator ułamkowy
regulator PID
reaktor PWR
zaawansowane systemy sterowania
model punktowy kinetyki neutronów
fractional order control
PID controller
PWR reactor
advanced control systems
point kinetics model
Opis:
W 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 optymalny, minimalizując klasyczne całkowe wskaźniki jakości określane na bazie odpowiedzi skokowej. Na przykładzie najpierw układu oscylacyjnego drugiego rzędu, a potem na przykładzie liniowego modelu reaktora PWR otrzymanego z linearyzacji modelu nieliniowego w określonym punkcie pracy wykazano, że proponowany ułamkowy regulator PIλDμ może stać się alternatywą dla powszechnie stosowanego klasycznego regulatora PID.
In this paper, the synthesis of fractional–order PIλDμ power controller for the PWR (Pressurized Water Reactor) nuclear reactor is presented. For this purpose the point kinetics and heat transfer nonlinear model of the PWR nuclear reactor with thermal feedback mechanisms from lumped fuel and coolant temperature was used. The parameters of the fractional-order PIλDμ controller were tuned due to optimization of the standard integral performance indexes determined on the basis of the step response. Firstly – the typical second order oscillatory dynamic system and secondly – the linear PWR nuclear reactor model derived from nonlinear model was used to show that the fractional order PIλDμ controller may become a alternative to standard PID controller.
Źródło:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2013, 4; 63-68
2083-0157
2391-6761
Pojawia się w:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order tube model reference adaptive control for a class of fractional order linear systems
Autorzy:
Balaska, Hanane
Ladaci, Samir
Djouambi, Abdelbaki
Schulte, Horst
Bourouba, Bachir
Powiązania:
https://bibliotekanauki.pl/articles/330930.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional order system
linear system
model reference adaptive control
fractional adaptive control
performance tube
fractional order TMRAC
system ułamkowego rzędu
system liniowy
sterowanie adaptacyjne
Opis:
We introduce a novel fractional order adaptive control design based on the tube model reference adaptive control (TMRAC) scheme for a class of fractional order linear systems. By considering an adaptive state feedback control configuration, the main idea is to replace the classical reference model with a single predetermined trajectory by a fractional order performance tube guidance model allowing a set of admissible trajectories. Besides, an optimization problem is formulated to compute an on-line correction control signal within specified bounds in order to update the system performance while minimizing a control cost criterion. The asymptotic stability of the closed loop fractional order control system is demonstrated using an extension of the Lyapunov direct method. The dynamical performance of the fractional order tube model reference adaptive control (FOTMRAC) is compared with the standard fractional order model reference adaptive control (FOMRAC) strategy, and the simulation results show the effectiveness of the proposed control method.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 3; 501-515
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order PI controllers for TCP packet flow ensuring given modulus margins
Autorzy:
Krajewski, W.
Viaro, U.
Powiązania:
https://bibliotekanauki.pl/articles/205939.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
fractional-order PI controllers
robust control
TCP congestion control
delayed systems
Opis:
An Active Queue Management (AQM) robust control strategy for Traffic Control Protocol (TCP) data transfer is proposed. To this purpose, the TCP behaviour is first approximated by a second–order model with delayed input obtained from the linearization of an efficient and commonly used nonlinear fluid–based model. The adopted feedback control structure uses a fractional– order PI controller. To ensure the desired robustness, the parameter regions where such a controller guarantees a given modulus margin (inverse of the H1 norm of the sensitivity function) are derived. An example commonly used in the literature is worked out to show that the suggested graphically–based design technique is simple to apply while it limits the effects of disturbances and of the unmodelled dynamics.
Źródło:
Control and Cybernetics; 2014, 43, 4; 493-505
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Design of multivariable fractional order PID controller using covariance matrix adaptation evolution strategy
Autorzy:
Sivananaithaperumal, S.
Baskar, S.
Powiązania:
https://bibliotekanauki.pl/articles/229730.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order controller
PID control
CMAES algorithm
distillation column
Opis:
This paper presents an automatic tuning of multivariable Fractional-Order Proportional, Integral and Derivative controller (FO-PID) parameters using Covariance Matrix Adaptation Evolution Strategy (CMAES) algorithm. Decoupled multivariable FO-PI and FO-PID controller structures are considered. Oustaloup integer order approximation is used for the fractional integrals and derivatives. For validation, two Multi-Input Multi- Output (MIMO) distillation columns described byWood and Berry and Ogunnaike and Ray are considered for the design of multivariable FO-PID controller. Optimal FO-PID controller is designed by minimizing Integral Absolute Error (IAE) as objective function. The results of previously reported PI/PID controller are considered for comparison purposes. Simulation results reveal that the performance of FOPI and FO-PID controller is better than integer order PI/PID controller in terms of IAE. Also, CMAES algorithm is suitable for the design of FO-PI / FO-PID controller.
Źródło:
Archives of Control Sciences; 2014, 24, 2; 235-251
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Design of a fuzzy fractional order adaptive impedance controller with integer order approximation for stable robotic contact force tracking in uncertain environment
Autorzy:
Cao, Hongli
Powiązania:
https://bibliotekanauki.pl/articles/2106174.pdf
Data publikacji:
2022
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
adaptive impedance control
contact interactions
fractional order
fuzzy logic
integer order approximation
Opis:
Current research in robot compliance control is unable to take both transient contact force overshoots and steady-state force tracking problems into account. To address this problem, we propose a fuzzy fractional order (FO) adaptive impedance controller to avoid the force overshoots in the contact stage while keeping force error in the dynamic tracking stage, where traditional control algorithms are not competent. A percentage gain is adopted to map FO parameters to integer order (IO) parameters by their natural properties, and a fuzzy logical controller is introduced to improve the system stability. The simulation results indicate that the proposed controller can be made more stable than and superior to the general impedance controller, and the force tracking results also have been compared with the previous control methods.
Źródło:
Acta Mechanica et Automatica; 2022, 16, 1; 16--26
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Obszary stabilności układu regulacji z regulatorem ułamkowym dla niestabilnego obiektu pierwszego rzędu z opóźnieniem
Design of fractional order controller for a first order unstable plant with delay
Autorzy:
Nartowicz, T.
Powiązania:
https://bibliotekanauki.pl/articles/277265.pdf
Data publikacji:
2011
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
układy regulacji
regulatory ułamkowego rzędu
control systems
fractional order controller
Opis:
Rozważono problem doboru wartości regulatora ułamkowego rzędu zapewniającego zadany zapas stabilności układu regulacji z obiektem niestabilnym pierwszego rzędu z opóźnieniem. Transmitancja operatorowa regulatora wynika z zastosowania idealnej transmitancji Bodego jako wzorca dla układu otwartego z regulatorem. Podano komputerową metodę syntezy regulatora ułamkowego rzędu. Ponadto wykorzystując klasyczną metodę podziału D podano prostą analityczną metodę wyznaczania obszarów stabilności w przestrzenie parametrów regulatora, uwzględniając zadane wartości zapasu fazy i modułu. Rozważania zilustrowano przykładem liczbowym i wynikami badań symulacyjnych.
The paper presents the design problem of fractional order controller satisfying gain and phase margin of the closed-loop system with time-delay first order unstable plant. The transfer function of the controller follows directly from the use of Bode's ideal transfer function as a reference transfer function of the open loop system. Computer method for synthesis of fractional controller is given. Using the classical D-partition method a simple analytical method for determining stability regions respecting phase and gain margins in the controller parameters space is given. The considerations are illustrated by numerical example and results of computer simulation.
Źródło:
Pomiary Automatyka Robotyka; 2011, 15, 2; 595-602
1427-9126
Pojawia się w:
Pomiary Automatyka Robotyka
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed terminal time fractional optimal control problem for discrete time singular system
Autorzy:
Chiranjeevi, Tirumalasetty
Devarapalli, Ramesh
Babu, Naladi Ram
Vakkapatla, Kiran Babu
Rao, R. Gowri Sankara
Garcìa Màrquez, Fausto Pedro
Powiązania:
https://bibliotekanauki.pl/articles/2175112.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order differential equation
discrete time singular system
fractional derivative
linear quadratic optimal control problem
Opis:
This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
Źródło:
Archives of Control Sciences; 2022, 32, 3; 489--506
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Contribution of New Parameter Inverses to Robustification of Fractional-Order Perfect Control for LTI MIMO Discrete-Time State-Space Systems
Autorzy:
Wach, Ł.
Hunek, W. P.
Powiązania:
https://bibliotekanauki.pl/articles/385005.pdf
Data publikacji:
2016
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
LTI MIMO fractional-order systems
perfect control
inverses of nonsquare matrices
stability
Opis:
The paper presents results of application of various right inverses to fractional-order discrete-time perfect control in terms of improving its stability and robustness. For that reason the newly introduced σ-inverse and H-inverse are applied finally to obtain the mentioned above control strategy strictly dedicated to LTI MIMO nonsquare systems described by state-space framework. It is highlighted that parameter σ-inverse and H-inverse with different so called ‘degrees of freedom’ outperform the typical minimum-norm right T-inverse. Moreover, this new approach deals with the same class of problems concerning integer-order systems. The simulation studies performed in Matlab/Simulink environment confirm high potential of proposed here method.
Źródło:
Journal of Automation Mobile Robotics and Intelligent Systems; 2016, 10, 3; 29-33
1897-8649
2080-2145
Pojawia się w:
Journal of Automation Mobile Robotics and Intelligent Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case
Autorzy:
Dzieliński, A.
Czyronis, P. M.
Powiązania:
https://bibliotekanauki.pl/articles/201358.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
discrete-time systems
optimal control
linear quadratic performance index
Opis:
The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 3; 681-690
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems
Autorzy:
Bingi, K.
Ibrahim, R.
Karsiti, M. N.
Hassan, S. M.
Harindran, V. R.
Powiązania:
https://bibliotekanauki.pl/articles/229519.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order controller
set-point weighting
2DOF PID
process control
unstable systems
Opis:
The proportional-integral-derivative (PID) controllers have experienced series of structural modifications and improvements. Example of such modifications are set-point weighting and fractional ordering. While the former is to achieve two-degree-of-freedom (2DOF) ability of set-point tracking and disturbance rejection, the latter is to ensure smooth control action. Therefore, this paper reviews various forms of PID controllers and provides a comparative analysis of 2DOF PID and 2DOF fractional order PID (FOPID) controllers. The paper also discusses the conversion of one PID form to another. For the comparative analysis of the various controllers, a class of unstable systems are considered. Simulation result shows that in most cases the conversion from one form to another does not significantly affect the performance of the system. It is also observed that the 2DOF controllers (2DOF PID and 2DOF FOPID) improved significantly the performance of the ordinary PID controllers.
Źródło:
Archives of Control Sciences; 2018, 28, 4; 635-682
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
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