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EN
In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.
EN
The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.
EN
In the paper a construction of a control system for 2nd order, uncertain-parameter plant is discussed. The considered model of the plant is described by state space equation or by equivalent transfer function and it describes a huge class of real control plants, for example – electric drives or oriented PV systems. As a controller the digital proportional (P) controller was employed. The control system is going to be implemented at the microcontroller platform. Results are by the example depicted.
4
Content available The agent, state-space model of the mobile robot
EN
The paper is devoted to present a new agent model of wheeled mobile robot. The proposed model based on nonlinear state space, discrete model of kinematics and employes Braitenberg algorithm to control the robot during move to target with passing obstacles. As a real robot the Khepera robot with IR proximity sensors was considered. The proposed agent model can be generalized onto another similar classes of devices. Results of experiments show that the proposed model correctly describes the behaviour of real device during realization of different jobs, for example obstacle passing.
PL
W artykule zaprezentowano nowy model agentowy kołowego robota mobilnego. Proponowany model bazuje na nieliniowym równaniu stanu opisującym kinematykę robota i wykorzystuje algorytm Braitenberga z zadanym punktem końcowym w celu omijania przeszkód. Jako przykład rzeczywistego robota rozważono robot Khepera III z czujnikami IR do wykrywania i omijania przeszkód. Zaproponowany model agentowy może być uogólniony na inne klasy podobnych urządzeń. Wyniki symulacji pokazują, że zaproponowany model dobrze opisuje zachowanie się rzeczywistego urządzenia podczas realizacji różnych zadań, np. przy omijaniu przeszkód.
EN
A new, state space, discrete-time, and memory-efficient model of a one-dimensional heat transfer process is proposed. The model is derived directly from a time-continuous, state-space semigroup one. Its discrete version is obtained via a continuous fraction expansion method applied to the solution of the state equation. Fundamental properties of the proposed model, such as decomposition, stability, accuracy and convergence, are also discussed. Results of experiments show that the model yields good accuracy in the sense of the mean square error, and its size is significantly smaller than that of the model employing the well-known power series expansion approximation.
EN
In the paper two non-integer order, state space models of heat transfer process are compared. The first uses a known Caputo operator and the second – a new operator proposed by Caputo and Fabrizio in 2015. Both discussed models are modifications of a known, integer order, state space, semigroup model of heat transfer process. Parameters of both models were identified by means of optimization of MSE cost function with the use of simplex method, available in MATLAB. Both proposed models have been compared in the aspect of accuracy and convergence. Analytical and numerical results show that the Caputo-Fabrizio model is faster convergent and easier to implement than the Caputo model. However, its accuracy in the sense of MSE cost function is worse.
EN
The paper is intended to show a new state space, non integer order model of an one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space semigroup model. The fractional order derivative with respect to time is by a new operator proposed by Caputo and Fabrizio, the non integer order spatial derivative is expressed by Riesz operator. The Caputo-Fabrizio operator can be directly implementated using MATLAB, because it does not require us to apply any approximation. Analytical formulae of step response are given, the system decomposition was discussed also. Main results from the paper show that the use of Caputo Fabrizio operator allows us to obtain the simple in implementation and analysis model of the considered heat transfer process. The accuracy of the proposed model in the sense of a MSE cost function is satisfying.
EN
In the paper the practical stability problem for the discrete, non-integer order model of one dimmensional heat transfer process is discussed. The conditions associating the practical stability to sample time and maximal size of finite-dimensional approximation of heat transfer model are proposed. These conditions are formulated with the use of spectrum decoposition property and practical stability conditions for scalar, positive, fractional order systems. Results are illustrated by a numerical example.
PL
W pracy zaproponowano nowe modele transmitancyjne niecałkowitego rzedu w postaci transmitancji hybrydowych, zawierających zarówno część całkowitego, jak i niecałkowitego rzędu. Rozważono modele z opóźnieniem i bez opóźnienia. Jako przykłady rozważono doświadczalny obiekt cieplny oraz silnik indukcyjny prądu przemiennego, sterowany częstotliwościowo. Wyniki eksperymentów potwierdziły przydatność proponowanych modeli do opisu rozwązanych systemów dynamicznych.
EN
IN the paper new, transfer function, non integer order models are proposed. The considered models have a form of hybrid transfer functions containing both integer order and non integer order parts. Models with and without delay were discussed. As examples an experimental heat plant and AC motor were tested. Results of experiments show that the proposed hybrid models are useful tool to modeling of dynamic systems.
EN
In the paper new, interval models of IR proximity sensors are presented. The dependence between distance and signal from sensor is described with the use of exponential function and two parameter Mittag-Leffler function with interval parameters. Identification method for was also proposed. Results of experiments show, that two parameter Mittag-Leffler function most accurate describes a behaviour of proximity IR sensor, than exponential function.
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.
EN
A new, state space, non-integer order model for the heat transfer process is presented. The proposed model is based on a Feller semigroup one, the derivative with respect to time is expressed by the non-integer order Caputo operator, and the derivative with respect to length is described by the non-integer order Riesz operator. Elementary properties of the state operator are proven and a formula for the step response of the system is also given. The proposed model is applied to the modeling of temperature distribution in a one dimensional plant. Results of experiments show that the proposed model is more accurate than the analogical integer order model in the sense of the MSE cost function.
PL
W pracy omówiono problem sterowalności względem wyjścia dla systemu liniowego, stacjonarnego, opisanego transmitancją operatorową z niepewnością parametryczną współczynników licznika i mianownika tej transmitancji. Sformułowano proste warunki sterowalności względem wyjścia dla rozważanej klasy systemów dynamicznych, bazujące na geometrycznej interpretacji zer i biegunów transmitancji. Wyniki zilustrowano przykładami obliczeniowymi.
EN
In the paper a controllability problem for a linear, time-invariant dynamic system with parametric uncertainty of transfer function elements is considered. Simple controllability conditions, based onto geometrical interpretation of roots and zeros of transfer function were formulated. Results were by a numerical examples depicted.
14
PL
W pracy omówiono opis dynamiki kąta elewacji orientowanego ogniwa słonecznego z wykorzystaniem przedziałowego równania stanu. Omówiono również metodę identyfikacji przedziałowych parametrów modelu na podstawie przebiegu czasowego odpowiedzi skokowej rzeczywistego obiektu. Zastosowanie proponowanej metody identyfikacji pokazano na przykładzie rzeczywistego laboratoryjnego ogniwa słonecznego.
EN
In the paper a description of dynamics an elevation angle for oriented PV system with the use of an interval state space equation is discussed. A step response based identification method for the considered model was also presented. An example of the identification for experimental PV system was also presented.
15
Content available Systemy SCADA w środowisku Android
PL
W pracy zaprezentowano implementację systemu SCADA na urządzeniu mobilnym, pracującym pod nadzorem systemu operacyjnego Android. Aplikacja została przygotowana w Javie, z wykorzystaniem SDK Androida dla Eclipse, zgodnie z regułami programowania obiektowego. Połączenie z nadzorowanym sterownikiem PLC odbywa się za pomocą protokołu Modbus TCP i bezprzewodowego Ethernetu (Wi-Fi lub komórkowe). Wykonane testy wykazały poprawność działania proponowanego systemu.
EN
In the paper an implementation of SCADA at mobile device, working under Android is presented. The application was prepared with use of Java and SDK Android for Eclipse with respect to Object Oriented Programming rules. The connection to supervised PLC is realized with the use of Modbus TCP and wireless Ethernet. Results of tests show, that the proposed system runs properly.
PL
W pracy przedstawiono propozycję aplikacji SCADA przeznaczonej do monitorowania w czasie rzeczywistym temperatury rdzeni transformatorów zasilających zakład przemysłowy. Omówiono założenia i sposób realizacji projektu z wykorzystaniem typowych, dostępnych na rynku elementów systemów automatyki. Aplikacja umożliwia monitorowanie temperatury transformatorów oraz alarmowanie w przypadku przekroczenia wartości ostrzegawczych i alarmowych przez temperaturę. Prezentowana aplikacja została wdrożona praktycznie w zakładzie przemysłowym.
EN
In the paper a proposition of SCADA application dedicated to real-time temperature monitoring of transformers cores powering a factory is presented. The assumptions and method of project realization with the use of typical components were discussed. The proposed application makes possible temperature monitoring and warning and alarming, when the maximal permissible values of temperature are exceed. The presented SCADA system was practically applied in factory.
EN
The paper presents an approximation method for elementary fractional order transfer function containing both pole and zero. This class of transfer functions can be applied for example to build model - based special control algorithms. The proposed method bases on Charef approximation. The problem of cancelation pole by zero with useful conditions was considered, the accuracy discussion with the use of interval approach was done also. Results were depicted by examples.
PL
W pracy zaprezentowano system wymiany danych między aplikacją SCADA i mikrokontrolerowym sterownikiem zespołu orientowanych ogniw słonecznych. Aplikacja SCADA została przygotowana w środowisku Wonderware InTouch, sterownik został zbudowany na mikrokontrolerze STM-32L. Opracowany system wymiany danych zawiera dedykowany driver komunikacyjny oraz bazę danych. Wykonane testy wykazały poprawność zaproponowanych rozwiązań. Zaproponowane rozwiązania mogą znaleźć zastosowanie w każdej sytuacji, gdy korzystne jest połączenie aplikacji SCADA z mikrokontrolerem.
EN
In the paper a data exchange system between SCADA application and microcontroller-based controller for oriented PV system is presented. The SCADA application was built with the use of Wonderware InTouch, the controller was constructed with the use of STM-32L microcontroller. The data exchange system contains dedicated communication driver and a database. After tests it turn out, that all proposed solutions were proper and the system runs correctly. The proposed solutions can be applied in each situation, when a microcontroller-based control unit is applied.
PL
W pracy przedstawiono system wspomagania optymalizacji produkcji na wielkoseryjnej linii produkcyjnej, zrealizowany z wykorzystaniem typowego środowiska SCADA WONDERWARE INTOUCH. Przedstawiony system umożliwia zbieranie i obróbkę statystyczną danych opisujących pracę linii i poszczególnych maszyn i może być alternatywą dla środowisk programistycznych dedykowanych specjalnie dla tych celów. System dodatkowo może być w łatwy sposób rozbudowany o funkcje sterowania nadrzędnego, co jest jego zaletą. Dodatkową zaletą przedstawionego rozwiązania Opisany system został wdrożony praktycznie w jednym z zakładów produkcji opakowań blaszanych w Polsce.
EN
In the paper a proposition of large-lot production line optimization support system is presented. The system we deal with was prepared for drink cane production line in factory in Poland. Fundamental assumptions to the presented project were following: firstly, a typical SCADA programming software was expect to apply (to the system realization INTOUCH was used). Next, the system is not expected to neither control nor generate critical alarms for the supervised system. It is required to collect data describing the work of the line only. The first section presents the production line we deal with. The general scheme of line is shown in Figure 1, the cane during consecutive production steps is shown in the Figure 3. The system is controlled with the use of ALLEN BRADLEY PLCs and PACs, the scheme of control system is shown in the Figure 2. Next section describes remarks about the system realization. The architecture of the system is typical, it consists of two parts: scripts and graphical user interface. The data from production system are read via PAC supervising the whole system, next they are prepared to give information about work of the whole line or the selected machine, for example: time since last breakdown (TSLB), current breakdown time (CBT), number of breakdowns, etc. The data preparing is done with the use of scripts. An exemplary algorithm of TSLB assign is shown in Figure 4. The user’s interface offers a broad information about all parameters describing the work of line. The main application window is shown in Figure 5, the exemplary window to monitor the cup press is shown in Figure 6. Main conclusion from the paper is, that the optimization production support system can be built with the use of typical SCADA software. The presented solutions have an additional advantage, that they can be applied in typical SCADA systems, dedicated both to control and supervise production system.
PL
W pracy omówiono metodę pomiaru parametrów opisujących dynamikę i zużycia energii podczas sterowania doświadczalnego, orientowanego ogniwa słonecznego. Omówiono zasady konstrukcji systemu pomiarowego i metodykę badań z użyciem oprogramowania dSPACE i środowiska MATLAB/Simulink oraz sformułowano wnioski dotyczące wykorzystania wyników badań podczas budowy modeli matematycznych rozważanego systemu.
EN
Paper presents an identification dynamics and an energy consumption problem for oriented PV system. The construction of a measuring system and a measure method with the use of dSPACE and MATLAB/Simulink were presented. Conclusions about applications results to build mathematical models of considered system were also formulated.
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