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1
Content available Synchronization of state-feedback-controlled doubly fed induction generator with the grid
Szypulski M., Iwański G.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2018
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Vol. 66, nr 5
675--685
EN
This paper presents state feedback control with a linear-quadratic regulator of a doubly fed induction generator. Resonant terms are added to the plant model in order to provide disturbance rejection and reference tracking. A new approach to controlling a parameter varying linear model of the induction machine is presented, allowing to apply a linear-quadratic regulator to the doubly fed induction generator. The control scheme described herein is suitable for the doubly fed induction generator operating under unbalanced stator voltage conditions, because the controller with resonant terms is built in the stationary αβ coordinate system. In it, the positive and negative symmetrical sequences have equal frequencies. The paper highlights specific problems associated with state feedback control of the doubly fed induction generator, i.e. the process of generator connection to an unbalanced grid. In contrast with classical voltage-oriented cascade control methods, in state feedback control of a stand-alone doubly fed induction generator there is no separate rotor current controller. This may cause over-current problem during DFIG synchronization with the grid which has been solved in this paper. Voltage synchronization and grid operation of the generator were tested in a laboratory rig with a 7.5 kW wound-rotor induction machine.
2
Content available remote Feedback linearization based nonlinear control of magnetic levitation system
Jaroszyński J., Zietkiewicz J.
Studia z Automatyki i Informatyki
|
2016
|
T. 41
35--46
EN
Control of unstable nonlinear system is challenging - for the method relying on objective function this function may not be convex. Feedback linearization derives exact linear model that imitates the dynamics of nonlinear model. In this paper for feedback linearized system linear quadratic control is applied. The method is simulated on magnetic levitation system. Simulation shows that the control assures good performance.
PL
Sterowanie nieliniowymi, niestabilnymi obiektami jest wymagające - jeśli metoda opiera się na funkcji celu, funkcja ta może być niewypukła. Linearyzacja przez sprzężenie zwrotne zapewnia dokładny liniowy model odwzorowujący dynamikę modelu nieliniowego. W artykule do zlinearyzowanego systemu zastosowane jest sterowanie liniowo - kwadratowe. Metoda jest przetestowana symulacyjnie na układzie magnetycznej lewitacji. Otrzymane symulacje pokazują dobrą jakość takiego rozwiązania.
3
Content available Anti-windup strategy for an LQ current controller with oscillatory terms for three-phase grid-tie VSCs in SMES systems
Gałecki A., Grzesiak L., Ufnalski B., Kaszewski A., Michalczuk M.
Power Electronics and Drives
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2016
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Vol. 1 (36), No. 2
65--81
EN
The paper presents a linear-quadratic current controller with damped oscillatory terms designed for three-phase grid-tie voltage source converters used in SMES systems and operated under distorted grid voltage conditions. Special emphasis is placed on a synthesis of an anti-windup mechanism to prevent wind-up derived from the oscillatory terms by the use of a new active damping loop based on a simple moving average method. As a consequence, the current feedback gain may be increased without unwanted overshoot and overruns, and performance of the system can be improved.
4
Content available remote Linear quadratic control with feedback-linearized models
Ziętkiewicz J.
Studia z Automatyki i Informatyki
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2015
|
T. 40
37--49
EN
The paper considers two questions. Firstly, to adjudicate whether the feedback linearization is actually better for control than the plain Jacobian linearization. This issue is settled by using linear quadratic control strategy for above-mentioned linear models. The second question results from the efforts of joining feedback linearization and linear quadratic control: how should the weights of the cost function be calculated for the model obtained from feedback linearization, when the variables are not direct physical values? This paper shows a method of adjusting those weights, which is based on the weights of the quadratic cost functions for Jacobian-linearized model. The two questions are therefore interrelated because the method of adjusting weights gives us similar control strategies for the two different linear models. This is used for the comparison of the two linearization methods. The obtained results show that combining linear quadratic control with feedback linearization yields the performance index usually better, or at least not worse, than when combining it with Jacobian linearization. The former combination can be used successfully for many nonlinear systems.
PL
W pracy rozważane są dwie kwestie. Pierwsza z nich dotyczy sprawdzenia, czy model otrzymany za pomocą linearyzacji przez sprzężenie zwrotne będzie lepiej sprawdzał się w warunkach regulacji niż model otrzymany za pomocą przybliżonej linearyzacji w punkcie pracy. Druga kwestia wynika z próby połączenia modelu otrzymanego przez linearyzację przez sprzężenie zwrotne ze sterowaniem liniowo kwadratowym: jak powinny być dobierane wagi w funkcji kosztu w tym przypadku, kiedy zmienne w tej funkcji nie są bezpośrednio wielkościami fizycznymi? W artykule pokazano metodę pozwalającą na dobór wspomnianych wag z użyciem funkcji kosztu wybranej dla modelu uzyskanego z linearyzacji w punkcie. Powyższe kwestie wiążą się ze sobą, ponieważ taki dobór wag pozwala uzyskać podobną strategię sterowania przy różnych modelach liniowych, co pozwala porównać wykorzystanie tych dwóch modeli w algorytmie sterowania. Otrzymane wyniki pokazują, że połączenie metody linearyzacji przez sprzężenie zwrotne z regulatorem liniowo kwadratowym pozwala uzyskać w większości przypadków lepszy wskaźnik jakości niż przy wykorzystaniu modelu liniowego otrzymanego na podstawie przybliżonej linearyzacji w punkcie. Pierwsze z podejść może być z powodzeniem stosowane dla wielu nieliniowych obiektów.
5
Content available A predictive model of multi-stage production planning for fixed time orders
Kozłowski E., Terkaj W., Gola A., Hajduk M., Świć A.
Management and Production Engineering Review
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2014
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Vol. 5, No. 3
23--32
EN
The traditional production planning model based upon a deterministic approach is well described in the literature. Due to the uncertain nature of manufacturing processes, such model can however incorrectly represent actual situations on the shop floor. This study develops a mathematical modeling framework for generating production plans in a multistage manufacturing process. The devised model takes into account the stochastic model for predicting the occurrence of faulty products. The aim of the control model is to determine the number of products which should be manufactured in each planning period to minimize both manufacturing costs and potential financial penalties for failing to fulfill the order completely.
6
Content available On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question
Przyłuski K. M.
International Journal of Applied Mathematics and Computer Science
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2014
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Vol. 24, no. 4
723--733
EN
In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.
7
Content available Stabilization of linear systems in random horizon via control
Kozłowski E.
Control and Cybernetics
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2013
|
Vol. 42, no. 2
527--541
EN
The control problem with random horizon at finie number of events is investigated in this paper, where the general aim of control is the stabilization (in mean square sense) of linear system at minimum cost. This problem is reduced to the task of optima control with established finite horizon. Moreover, the differences between stabilization with fixed and random horizons are also given. To illustrate those differences a numerical example is included.
8
The linear quadratic stochastic optimal control problem with random horizon at finite number of events independent of states system
Kozłowski E.
Systems Science
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2010
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Vol. 36, no 3
5-11
EN
The aim of the article is to expand the results of the theory of Linear Quadratic Control (the state of the system is described by the stochastic linear equation and the performance criterion has a quadratic form) in the case of random horizon independent of the states of the system. In the present case, the control horizon is a random variable with a discrete distribution and has a limited number of possible realizations (events). This situation is dependent on an external factor (generally independent of the system) and has a random character.
9
Content available The linear-quadratic stochastic optimal control problem with random horizon at the finite number of infinitesimal events
Kozłowski E.
Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica
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2010
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Vol. 10, no. 1
103--115
EN
The aim of the article is to expand the results of the theory of Linear Quadratic Control (the state of the system is described with the help of stochastic linear equation while the quality coefficient is of a quadratic form) in the case of random horizon independent of the states of the system. As for the question under consideration the control system horizon is an independent variable with a discreet decomposition and has got a limited number of possible accomplishments. The above mentioned situation takes places when the number of controls is brought out by the outside factor (generally independent of the system).
10
Content available remote Remarks about DC motor control
Baranowski J., Długosz M., Mitkowski W.
Archives of Control Sciences
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2008
|
Vol. 18, no. 3
289-322
EN
This paper was motivated by known results in the electric motor control where classical control algorithms were verified in the experimental framework. We want to show, that the control theory offers more sophisticated control methods that await their practical implementation. Presented algorithms for both continuous and discrete control and state estimation give many possibilities of improvement in the field of electric drive control. Our results are illustrated with simulations, but with available technology (such as MATLAB/Simulink/RTWT) can be easily verified in practice.
11
Content available remote Sterowanie liniowo-kwadratowe drganiami w układzie zawieszenia magnetoreologicznego
Sapiński B., Martynowicz P.
Czasopismo Techniczne. Mechanika
|
2004
|
R. 101, z. 5-M
335--343
PL
W artykule rozważano zagadnienie sterowania drganiami w układzie zawieszenia magnetoreologicznego. Przyjęto model zawieszenia o dwóch stopniach swobody w płaszczyźnie przechyłów wzdłużnych. Sformułowano model matematyczny układu i zadanie sterowania. Dokonano syntezy regulatora kaskadowego, wykorzystującego rozwiązanie problemu liniowo-kwadratowego. Przeprowadzono obliczenia numeryczne dla układu otwartego i zamkniętego przy wymuszeniach sinusoidalnych, prostokątnych oraz szarpnięciach impulsowych. Porównano wartości wskaźników jakości dla obu układów.
EN
The paper is concerned with a problem of vibration control in magnetorheological suspension system. A two-degree-of-freedom pitch plane model was assumed. A mathematical model for the system and control task was formulated. A cascade controller synthesis with linear-quadratic problem solution implementation was realized. Numerical calculations for open and feedback systems assuming sine, rounded pulse jerk and square displacement-input excitations were carried out. Quality ratings for both systems were compared.
12
Feedback control for discrete descriptor systems
Kurina G.A.
Systems Science
|
2002
|
Vol. 28, nr 2
29-40
EN
The control in the feedback form and the optimal cost are obtained for four linear-quadratic control problems by discrete descriptor systems in a Hilbert space. Special solutions of the implicit operator Riccati equations used here act in all state space and in general case they are not nonnegative definite, unlike the operators in the subspace and the nonnegative definite solutions. The examples show that the operator Riccati equations considered have no nonnegative definite solutions though the corresponding optimal control problems have the unique solutions.
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