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1
Content available Wykorzystanie rachunku niecałkowitego rzędu w sterowaniu suwnicą 3D
Kędziora Michał, Leszczyński Krzysztof, Piotrowski Robert
Pomiary Automatyka Robotyka
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2024
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R. 28, nr 1
63--69
PL
Suwnica 3D jest obiektem stosowanym w różnych gałęziach przemysłu. Z punktu widzenia sterowania, jest to system dynamiczny, nieliniowy i wielowymiarowy. W artykule zaprojektowano dwa układy regulacji: z klasycznym regulatorem PID oraz z regulatorem PID ułamkowego rzędu. Przedstawiono analizę porównawczą zaprojektowanych układów regulacji.
EN
The 3D crane is an object used in various industries. From a control point of view, it is a dynamic, non-linear and multidimensional system. In this paper, two control systems are designed: with a classical PID controller and with a fractional-order PID controller. A comparative analysis of the designed control systems is presented.
2
Content available Fractional discrete model of an electrical drive with brushless micro-motor
Matusiak M., Bąkała M., Wojciechowski R., Ostalczyk P.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2020
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Vol. 68, nr 3
421--427
EN
The use of fractional-order calculus for system modeling is a good alternative to well-known classic integer-order methods, primarily due to the precision with which the modeled object may be mapped. In this study, we created integer and fractional discrete models of a real object – a highspeed brushless micro-motor. The accuracy of the models was verified and compared.
3
Content available A new algorithm for a CFE-approximated solution of a discrete-time noninteger-order state equation
Oprzędkiewicz K., Stanisławski R., Gawin E., Mitkowski W.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2017
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Vol. 65, nr 4
429--437
EN
In the paper, a new method for solution of linear discrete-time fractional-order state equation is presented. The proposed method is simpler than other methods using directly discrete-time version of the Grünwald-Letnikov operator. The method is dedicated to use with any approximator to the operator expressed by a discrete transfer function, e.g. CFE-based Al-Alaoui approximation. A simulation example confirms the usefulness of the method.
4
Content available PLC implementation of fractional PI controller in positioning of electrohydraulic servodrive
Rybarczyk D.
Control and Cybernetics
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2016
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Vol. 45, no. 3
301--316
EN
The article describes the implementation of fractional order PI controller with the Programmable Logic Controller (PLC). The control system proposed is used for positioning of an electrohydraulic drive with Bosch Rexroth servo valve. The controller is based on PLC, working under real time operating system Automation Runtime. User interface is equipped with the touch panel of Power Panel 500 type. In the first part of the paper the fractional order calculus theory is introduced. In addition, some examples of fractional controller implementations in different kinds of objects are presented. The subsequent section focuses on author’s own research. The Oustaloup’s method description is recalled along with its computer implementation. Further, the impact of finite order of the approximation function is verified. The article includes the description of test stand structure, code generation and implementation of PI controller on the dedicated PLC.
5
Content available remote Fractional-order digital filter approximation method for embedded control applications
Tepljakov A., Petlenkov E., Belikov J.
International Journal of Microelectronics and Computer Science
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2014
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Vol. 5, nr 2
54--60
EN
Fractional-order calculus presents a novel modeling approach for systems with extraordinary dynamical properties by introducing the notions of derivatives and integrals of noninteger order. In system theory this gives rise to extensions to linear, time invariant systems to enhance the description of complex phenomena involving memory or hereditary properties of systems. Standard industrial controllers, such as the PID controller and lead-lag compensator, have also been updated to benefit from the effects of noninteger integration and differentiation, and have advantages over classical controllers in case of both conventional and fractional-order process control. However, given the definitions of fractional operators, accurate digital implementation of fractional-order systems and controllers is difficult because it requires infinite memory. In this work we study the specific implementation of a fractional-order PID controller and fractional-order lead-lag compensator based on an infinite impulse response (IIR) filter structure obtained by applying the Oustaloup recursive filter synthesis technique. Software for generating digital fractional-order is developed and tested on an Atmel AVR microcontroller. The results are verified using a MATLAB/Simulink based real-time prototyping platform.
6
Content available Fractional Kalman Filter algorithms for correlated system and measurement noises
Sierociuk D.
Control and Cybernetics
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2013
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Vol. 42, no. 2
471--490
EN
The paper presents a generalization of the Fractional Kalman Filter to a case when correlated system and measurement noises appear. The algorithm proposed is derived in detail for a linear generalized discrete fractional order state-space system for both constant and variable order cases. In order to present the efficiency of the proposed algorithm, results of numerical simulations are presented. Results of numerical experiments are compared with the effect of estimation obtained when using the traditional Fractional Kalman Filter algorithm.
7
Content available Fractional order PID controller in velocity control loop of CNC machine feed-drive module with permanent magnet synchronous motor
Kobyłkiewicz A., Pajdzik R., Waszczuk P.
Pomiary Automatyka Robotyka
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2012
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R. 16, nr 12
144-150
EN
A significant number of publications shows that fractional order controllers can improve performance compared with traditional control algorithms. In this paper, fractional order PID velocity controller of the PMSM motor is presented. In the first step, we compared, by means of simulation research work, the fractional order PID with conventional integer order PID, and we prove the correctness of the applied method. In the second part, we have tested the proposed solution in the real-time control system with the PMSM actuator. The open architecture control system based on the industrial computer (for cyclic real-time communication with power electronics, including current controller and commutation functionality, with the use of Ethernet Powerlink communication protocol) and rapid prototyping platform were used for the evaluation of the developed here velocity control algorithms. Presented in the paper experimental results testify to the usefulness of the proposed solution.
PL
W licznych publikacjach wykazano, że regulatory ułamkowego rzędu mogą zwiększyć skuteczność regulacji w porównaniu z tradycyjnymi algorytmami sterowania. W artykule przedstawiono regulator PID ułamkowego rzędu do sterowania prędkością silnika PMSM. W pierwszej części zaprezentowano wyniki symulacji, porównano regulator PID ułamkowego rzędu z konwencjonalnym regulatorem PID całkowitego rzędu i dowiedziono prawidłowość zastosowanej metody. W drugiej części artykułu przedstawiono wyniki testów zaproponowanego rozwiązania, przeprowadzonych w docelowym systemie sterowania silnikiem PMSM. Otwarta architektura systemu sterowania bazująca na komputerze przemysłowym (do cyklicznego komunikowania się z energoelektroniką w czasie rzeczywistym, realizujący regulację prądu i funkcjonalność komunikacyjną z użyciem protokołu komunikacyjnego Ethernet Powerlink) oraz na systemie do szybkiego prototypowania zostały użyte do oceny zaprojektowanego algorytmu regulacji prędkości. Wyniki przedstawione w artykule potwierdzają przydatność zaproponowanego rozwiązania.
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