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PL
Artykuł opiera się na kilku znaczących pozycjach w literaturze przedmiotu związanych z liniowymi nierównościami macierzowymi i ich zastosowaniem do syntezy okrętowych układów sterowania. Pierwsza część artykułu nawiązuje do liniowych nierówności macierzowych. Druga część poświęcona jest opisowi dwóch publikacji, zawierających zastosowanie liniowych nierówności macierzowych wdrożonych do zastosowań morskich na rzeczywistych obiektach. W podsumowaniu przedstawiono zalety i wady proponowanej metody numerycznej.
EN
The paper is a short review of publications about the use of linear matrix inequalities for synthesis of marine controlled object models. The first part is a short description of linear matrix inequalities. The second part presents two publications where linear matrix inequalities were implemented in marine industry. The summary describes advantages and disadvantages of the proposed numerical method.
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EN
This paper explains the basics of the Linear Matrix Inequalities (LMI), with examples of simulations and calculations created in Matlab/Simulink programming environment where the controlled plant is the “Blue Lady” ship model. First chapter of this paper gives a short overview of publications describing the use of Linear Matrix Inequalities method. Second chapter contains basic definitions and equations for the LMI method. Chapter three presents the use of LMI method for ship control by describing controller synthesis for the “Blue Lady”. Chapter four compares the operation of two controllers, the first one consisting of three independent proper adjusted PID controllers and the second one being a multivariable LMI controller. Finally conclusions from the above comparison are drawn.
EN
This paper explains the basics of the Linear Matrix Inequalities (LMI), with examples of simulations and calculations created in Matlab/Simulink programming environment where the controlled plant is the “Blue Lady” ship model. First chapter of this paper gives a short overview of publications describing the use of Linear Matrix Inequalities method. Second chapter contains basic definitions and equations for the LMI method. Chapter three presents the use of LMI method for ship control by describing controller synthesis for the “Blue Lady”. Chapter four compares the operation of two controllers, the first one consisting of three independent proper adjusted PID controllers and the second one being a multivariable LMI controller. Finally conclusions from the above comparison are drawn
PL
Artykuł zawiera opis stanowiska badawczego, znajdującego się w laboratorium Akademii Morskiej w Gdyni, które wykorzystuje platformę czasu rzeczywistego xPC Target ze środowiska Matlab wersja 2011b. We wstępie scharakteryzowano model obiektu zastosowanego w stanowisku badawczym, jakim jest model statku „Blue Lady”. W drugim rozdziale przedstawiono krótki opis pakietu xPC Target. Kolejne kroki, związane z konfiguracją sprzętu i oprogramowania stanowiska badawczego, opisano w rozdziale 3. Natomiast ostatni rozdział przedstawia syntezę regulatora LMI (Linear Matrix Inequalities) oraz wyniki symulacji przeprowadzonych na komputerze w narzędziu symulacyjnym pakietu Matlab, tj. w Simulinku, porównane z wynikami przeprowadzonymi na stanowisku badawczym w czasie rzeczywistym.
EN
This article is a description of a lab station in Maritime Academy in Gdynia which uses a real time platform, the xPC Target from Matlab 2011b software in 64-bit version. Preface describes, in general, the lab station where the controlled system is a “Blue Lady” ship model. First chapter contains a short description of the xPC Target software. Second chapter shows steps required to configure hardware and software of the lab station. Third and final chapter is the LMI (Linear Matrix Inequalities) controller synthesis and simulation results, where results obtained from a computer simulation using Matlab’s simulation tool Simulink are compared with results obtained from the real time lab station.
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PL
W pierwszej części artykułu przedstawiono krótki opis sieci Ethernet, następnie sieci Ethernet Industrial. W części drugiej zaprezentowano konfigurację dwóch sterowników PLC pracujących w sieci Ethernet Industrial. Wymieniona konfiguracja została wykonana w Laboratorium Sterowników Programowalnych na Wydziale Elektrycznym Akademii Morskiej w Gdyni.
EN
The first part of the article is a short description of both Ethernet and Ethernet Industrial networks. The second part is a presentation of a configuration of two Programmable Logic Controllers (PLC) working in Ethernet Industrial network. The configuration was built in Programmable Logic Controllers Laboratory in Gdynia Maritime University.
EN
This paper is devoted to the concept of stability in linear matrix inequalities. Especially to the analysis of a bounded stability region for a multivariable 3DOF system. The study is focused on two different, user defined, bounded LMI regions where poles are calculated with the use on an algorithm and placed in the left half plane of complex variable plane s. It is shown that in the studied case the shape of the region is irrelevant compared to the location of region bounds. And more specifically only the active bounds where the poles are located on it’s limits are significant to controller operation.
EN
There is a need to check the effects of automatic regulation system, before it is used in real conditions when sailing on Silm Lake. Simulink Real-Time platform, which is a component of Matlab software, is designed for simulation of automatic control systems working on the basis of real objects. In the simulations nonlinear mathematical model of real floating training ship is used as a control object. The model contains modeled filters used for longitudinal, transversal and rotational speeds on the basis of position change and transducers for thrusters and steering gear. Above mentioned simulations are conducted in real time, because it allows for taking into account time of the signals propagation and digital signal processing effects. This article presents the real time lab station system configuration. Simulation results for Model Predictve Control system are described and presented.
EN
Controllers based on linear matrix inequalities (LMI) and model predictive control (MPC) both use optimization methods; there are however significant differences between them. In case of LMI controllers, optimization is carried out during controller synthesis, because LMI’s are an optimization tool that requires a linear programming problem being solved. With MPC controllers, however, optimization methods are not used as much in controller synthesis as in controller algorithm operation, to determine optimal control signal values based on the found minimum of the criteria function. A square function is used with boundaries from above and below, which requires a square programming problem, with boundaries for decision variables, being solved. In this paper controller synthesis methods using LMI and MPC are shown, with a focus on the steps that need to be performed, and a comparison of both methods.
EN
Thrust allocation system combines the work of an automatic control system with the ships actuators. On the basis of values of transversal and longitudinal forces and yaw moment determined by the regulator, it specifies commands for the individual thrusters located on board. A modified power distribution system, which takes into account the efficient work of a main engine propeller, is presented. During the research computer simulations were made on the basis of a modified and an unmodified thrust allocation system working with an LMI controller and a mathematical model of a training tanker. “Proposed method” of power distribution results in more efficient work of the controller and guarantees faster determination of the fixed velocity value.
PL
Referat zawiera metodykę doboru parametrów regulatora stanu z wykorzystaniem liniowych nierówności macierzowych (ang. LMI - Linear Matrix Inequalities) metodą lokowania biegunów. W pracy zdefiniowano warunki rozmieszczenia biegunów w lewej półpłaszczyźnie zmiennej zespolonej s i wyznaczono obszary dopuszczalnych położeń biegunów. Na potrzeby rozważanej, liniowej metody projektowania dokonano linearyzacji modelu matematycznego obiektu w wybranym punkcie pracy. Zaprojektowany regulator stanu zastosowany został do sterowania obiektem rzeczywistym, którym był układ kaskadowy dwóch zbiorników. W referacie przedstawione zostały zarówno wyniki badań symulacyjnych jak i badań eksperymentalnych przeprowadzonych na obiekcie rzeczywistym.
EN
The paper describes a state feedback controller design by pole placement method using Linear Matrix Inequalities (LMI) approach. Conditions of pole placement constraints in a left half plane of the complex plane s are defined and allowable region for poles of the closed-loop control system are determined. For the purpose of using the linear design method, the mathematical model of controlled plant was linearized at a selected operating point. The designed state feedback controller was used for controlling the water level in a two-tank cascade system. The paper presents results of both computer simulations and real-time experiments.
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