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1

Zeroing the transfer matrix of the Roesser model of 2-D linear systems

Kaczorek Tadeusz

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 4

513--519

EN

Controllability, observability and the transfer matrix of the discrete 2-D Roesser model are analyzed. It is shown that the controllability of the Roesser model is invariant under state feedbacks and the observability under output feedbacks. Sufficient conditions are established for the zeroing of the transfer matrix of the Roesser model.

2

Sterowanie układem lewitacji magnetycznej w warunkach zakłóceń stochastycznych

Mrotek Mikołaj, Szymankiewicz Adrian, Michalski Jacek, Kozierski Piotr

Pomiary Automatyka Robotyka

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2022

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R. 26, nr 3

5--16

PL

W niniejszej pracy przedstawiono możliwość zredukowania wpływu zakłóceń stochastycznych na jakość regulacji dzięki estymacji stanu z wykorzystaniem algorytmu rozszerzonego filtru Kalmana. Przeprowadzono eksperymenty na laboratoryjnym układzie lewitacji magnetycznej firmy Inteco, którego model matematyczny jest nieliniowy. Przyjęto metodę sterowania z użyciem wektora stanu i algorytmem lokowania biegunów dla modelu zlinearyzowanego w wybranym punkcie pracy. Dla różnych poziomów zaszumienia sygnału pomiarowego zbadano działanie układu ze sprzężeniem zwrotnym od stanu mierzonego oraz estymowanego. W celu oceny regulacji, dla obu realizacji sprzężenia dokonano weryfikacji jakości działania algorytmu. Porównano otrzymane przebiegi czasowe każdej zmiennej stanu oraz obliczone, całkowe wskaźniki jakości bazujące na uchybie regulacji. Jakość estymacji oceniono na podstawie wskaźnika błędu średniokwadratowego oraz bazującego na błędach estymat i pomiarów. Syntezy regulatora dokonano na podstawie modelu ciągłego, a następnie wyznaczono jego postać dyskretną w celu numerycznej implementacji algorytmu rozszerzonego filtru Kalmana. Dokonano synchronizacji bloków wykonawczych z wybranym okresem próbkowania. Wyniki przeprowadzonych badań pozwalają wnioskować o przewadze regulacji w układzie, w którym brana jest informacja o wektorze stanu z estymacji, w porównaniu z bezpośrednim sprzężeniem zwrotnym bez filtracji Kalmana.

EN

This paper presents the possibility of reducing impact of stochastic disturbances on the quality of control by implementation of state estimation using the extended Kalman filter algorithm. Experiments were carried out on the Inteco magnetic levitation laboratory system, which mathematical model is nonlinear. A control method with the use of a state vector and a pole placement algorithm was adopted for the model which was linearized at the selected working point. For different levels of noise in the measurement signal, the operation of the system with a feedback from the measured and estimated state was tested. In order to assess the regulation, the quality of the algorithm was verified for both implementations of the feedback. The obtained time plots of each state variable were compared and the calculated integral quality indices, based on the control error, were compared. The quality of the estimation was assessed on the basis of the following mean square error and based on the errors between estimation and measurements indices. The controller was synthesized on thebasis of the continuous model, and then its discrete form was numerically implement as the extender Kalman filter algorithm. The executive blocks were synchronized with the selected sampling period. The results of the performed research allow to conclude about the advantage of control in the system in which the information about the state vector from the estimation is taken, in comparison with the direct feedback without Kalman filtering.

3

Algorytm regulacji odpornej ADRC - dobór nastaw i sposób dyskretnej implementacji

Michalski Jacek, Retinger Marek, Kozierski Piotr, Puchalski Radosław

Pomiary Automatyka Robotyka

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2022

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R. 26, nr 2

5--13

PL

W niniejszej pracy został przedstawiony algorytm regulacji odpornej Active Disturbance Rejection Control obiektem aerodynamicznym o dwóch stopniach swobody. Pokazano pełne wyprowadzenia równań algorytmu regulacji oraz wartości nastaw w zależności od pożądanych właściwości układu, na podstawie dynamiki obiektu oscylacyjnego drugiego rzędu. Dokonano dyskretyzacji równań algorytmu regulacji i zaproponowano jego dyskretną implementację. Testy przeprowadzono na laboratoryjnym zestawie aerodynamicznym firmy Inteco, którego model matematyczny jest silnie nieliniowy, ma dwa stopnie swobody i sprzężenia skrośne. Jakość działania oceniona została na podstawie przebiegów czasowych, a także całkowych wskaźników jakości. Przeprowadzone badania pokazują przewagę zastosowanego algorytmu nad regulacja PID dla badanego systemu. Przedstawiony algorytm regulacji cechuje się także większą przenośnością - nastawy dobierane są tylko w oparciu o rząd obiektu i teoretycznie raz dobrane są właściwe, niezależnie od modelu matematycznego. Zaproponowane równania dyskretne mogą zostać zaimplementowane z użyciem dowolnego języka programowania dla teoretycznie dowolnego obiektu, przy uwzględnieniu rzędu jego dynamiki.

EN

This paper presents the robust Active Disturbance Rejection Control method in an aerodynamical object with two degrees of freedom. Full derivation of control algorithm equations and the settings values depending on the desired properties of the system, based on the dynamics of the second order oscillating object, have been shown. The equations of the control algorithm were discretized and its discrete implementation was proposed. The tests were carried out on the Inteco aerodynamical laboratory kit, whose mathematical model is strongly non-linear, has two degrees of freedom and crosscoupling. The quality of operation was assessed on the basis of time graphs as well as integral quality indices. The conducted research shows the advantage of the applied algorithm over PID control for the tested system. The presented control algorithm is also more portable - the settings are selected only on the basis of the object order and once selected are correct regardless of the mathematical model. The proposed discrete equations can be implemented using any programming language theoretically for any object, taking into account the order of its dynamics.

4

Sufficient conditions for uniform global asymptotic stabilization of affine discrete-time systems with periodic coefficients

Czornik Adam, Makarov Evgenii, Niezabitowski Michał, Popova Svetlana, Zaitsev Vasilii

Archives of Control Sciences

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2021

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Vol. 31, No. 1

81--98

EN

Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.

5

Poles and zeros assignment by state feedbacks in positive linear systems

Kaczorek Tadeusz

Archives of Control Sciences

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2021

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Vol. 31, No. 3

593--605

EN

Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n × n system matrix A the sum of n−1 its entries is less than one.

6

Efficiency analysis of parallel computing applied to auto-tuning of state feedback speed controller for PMSM drive

Szczepański Rafał, Tarczewski Tomasz, Grzesiak Lech M.

Poznan University of Technology Academic Journals. Electrical Engineering

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2019

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No. 100

145--156

EN

Nowadays the simulation is inseparable part of researcher's work. Its computation time may significantly exceed the experiment time. On the other hand, multi-core processors are common in personal computers. These processors can be used to reduce computation time by using parallel computing on multiple cores. The most popular software applied to simulate behavior of the plant is MATLAB/Simulink. A single simulation of Simulink model cannot be computed by multiple cores, but there are many engineering problems, that require a multiple simulation of the same model with different parameters. In these problems, the parallel computing can be employed to decrease the overall simulation time. In this paper the parallel computing is used to speed-up the auto-tuning process of state feedback speed controller for PMSM drive. In order to obtain the optimal coefficients of the controller, an Artificial Bee Colony optimization algorithm is employed.

7

Almost periodic synchronization of fuzzy cellular neural networks with time-varying delays via state-feedback and impulsive control

Li Yongkun, Wang Huimei, Meng Xiaofang

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 2

337--349

EN

In this paper, we are concerned with drive-response synchronization for a class of fuzzy cellular neural networks with time varying delays. Based on the exponential dichotomy of linear differential equations, the Banach fixed point theorem and the differential inequality technique, we obtain the existence of almost periodic solutions of this class of networks. Then, we design a state feedback and an impulsive controller, and construct a suitable Lyapunov function to study the problem of global exponential almost periodic synchronization for the drive-response systems considered. At the end of the paper, we provide an example to verify the effectiveness of the theoretical results.

8

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.

9

Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks

Borawski K.

Przegląd Elektrotechniczny

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2017

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R. 93, nr 11

176--180

EN

The modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks is investigated. It is shown that: 1) There is a class of nonpositive and unstable R, L, e circuits that can be stabilized and modified to positive ones by state feedback; 2) There is a class of nonpositive and stable R, L, e circuits that can be modified by state feedback to positive ones without loss of stability. The modification of stability and positivity of linear descriptor electrical circuits is addressed. Considerations are illustrated by examples of linear electrical circuits.

PL

W pracy rozpatrzono problem modyfikacji stabilności i dodatniości standardowych i deskryptorowych liniowych obwodów elektrycznych poprzez sprzężenie zwrotne od wektora stanu. Pokazano, że: 1) Istnieje klasa niedodatnich i niestabilnych obwodów typu R, L, e, które mogą zostać ustabilizowane i zmodyfikowane do obwodów dodatnich; 2) Istnieje klasa niedodatnich i stabilnych obwodów typu R, L, e, które mogą zostać zmodyfikowane do obwodów dodatnich bez utraty stabilności. Rozpatrywany problem uogólniono dla klasy układów deskryptorowych. Rozważania zilustrowano przykładami obwodów elektrycznych.

10

Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 4

827--831

EN

The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.

11

A novel control-rod drive mechanism via electromagnetic levitation in MNSR

Divandari M., Hashemi-Tilehnoee M., Khaleghi M., Hosseinkhah M.

Nukleonika

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2014

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Vol. 59, No. 2

73--79

EN

In this paper, an electromagnetic levitation system was used with a synchronous motor to navigate the control rod of a small-type research reactor. The result from this prototype magnetic levitation system was in agreement with simulation results. The control system was programmed in MATLAB through open-loop system, closed-loop with state feedback and closed-loop with state feedback integral tracking. The final control system showed the highest performance with a low positioning error. Our results showed that the developed control system has the potential to be used as a reliable actuator in nuclear reactors to satisfy higher performance and safety.

12

Comparison of state feedback and PID control of pressurizer water level in nuclear power plant

Czapliński M., Sokólski P., Duzinkiewicz K., Piotrowski R., Rutkowski T.

Archives of Control Sciences

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2013

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Vol. 23, no. 4

455--471

EN

The pressurizer water level control system in nuclear power plant with pressurized water reactor (PWR) is responsible for coolant mass balance. The main control goal is to stabilize the water level at a reference value and to suppress the effect of time-varying disturbances (e.g. coolant leakage in primary circuit pipeline system). In the process of PWR power plant operation incorrect water level may disturb pressure control or may cause damage to electric heaters which could threaten plant security and stability. In modern reactors standard PID controllers are used to control water level in a pressurizer. This paper describes the performance of state feedback integral controller (SFIC) with reduced-order Luenberger state observer designed for water level control in a pressurizer and compares it to the standard PID controller. All steps from modeling of a pressurizer through control design to implementation and simulation testing in Matlab/Simulink environment are detailed in the paper.

13

Robust H∞ state feedback control for singular systems: A parameter-dependent approach

Zhou Y., Wang D., Li J.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 10a

213-217

EN

The robust H∞ state feedback control problem for both continuous- and discrete-time singular systems with polytopic-type uncertainties is revisited via a parameter-dependent approach. Attention is focused on the design of a parameter-dependent state feedback controller, such that the closed-loop system is admissible with prescribed H∞ noise attenuation level for all parameter uncertainties. Without using decomposition technique to the singular model, sufficient condition for the existence of an H∞ state feedback controller is expressed in terms of strict linear matrix inequalities (LMIs). In case that the LMI conditions are feasible, a suitable state feedback control law is explicitly given. The proposed approach is expected to be less conservative compared with previous results. Numerical examples are also provided to show the effectiveness of the approach.

PL

Analizowany jest odporny system sterowania ze sprzężeniem zwrotnym H∞ dla przypadku systemu dyskretnego i ciągłego i z niepewnościami typu polytopic. Do analizy wykorzystuje się metod. zależności parametrycznych. Sterownik opisany jest liniową macierzą nierowności LMI. (Odporne sterowanie ze sprzężeniem zwrotnym H∞ - metoda zależności parametrycznych)

14

H-infinity control of discrete-time linear systems constrained in state by equality constraints

Filasová A., Krokavec D.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 3

551-560

EN

In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discrete-time systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outper forms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.

15

Gain-scheduled state-feedback control for active cancellation of multisine disturbances with time-varying frequencies

Heins W., Ballesteros P., Bohn C.

Mechanics and Control

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2011

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Vol. 30, no. 3

127-137

EN

The paper presents a discrete-time LTV controller for the rejection of harmonic disturbances with time-verying based on a state-augmented observer-based state-feedback controller with a time-verying internal model and a scheduled state-feed back gain. The control design method is based on quadratic stability for LPV systems. The design is carried out in discrete time and the controller can easily be implemented on real-time hardware.

PL

W pracy przedstawiono dyskretny regulator LTV do eliminacji składowych harmonicznych zakłóceń. Wprowadzony regulator bazuje na sprzężeniu od zmiennych stanu z zależnym od czasu wewnętrznym modelem. Konstrukcja regulatora wykorzystuje własności stabilności układów LPV. Regulator został opisany równaniami dyskretnymi i może być łatwo zaimplementowany w układach czasu rzeczywistego.

16

Pairwise control principle in large-scale systems

Filasova A., Krokavec D.

Archives of Control Sciences

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2011

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Vol. 21, no. 3

227-242

EN

The purpose of the paper is present an algorithm of partially decentralized control design for one type of large-scale linear dynamical system. The pairwise autonomous principle is preferred where design conditions are derived in the bounded real lemma form, and global system stability is reproven to formulate potential application principle in fault tolerant control. The validity of the proposed method is demonstrated by the numerical example.

17

Voltage/current control mode for combined three-phase inverter

Wang H., Yue X., Pei X., Kang Y.

Przegląd Elektrotechniczny

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2010

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R. 86, nr 11a

358-362

EN

For parallel inverters system, controlling the output voltage in normal operation constantly is named the voltage control mode (VCM), and controlling the output current constantly in abnormal operation conditions (such as short circuit) is named the current control mode (CCM). The combined three-phase inverter topology is presented, the equivalent inverter topology with a LCL filter is obtained and mathematical models are built in VCM and CCM. A hybrid control strategy is proposed. The PID control and the repetitive control are used in VCM to obtain the fast dynamic responses and low harmonic distortions. On the other hand, the state feedback control is used in CCM. Pole assignment has been employed in designing parameter of the PID controller and state feedback, and the repetitive control design process is given. Experimental results validate the proposed control using two 400KVA parallel inverters.

PL

Dla równoległego systemu przekształtników zazwyczaj stosuje się system kontroli napięcia VCM i system kontroli prądu CCM (w warunkach specjalnych - np. zwarcia). Zaprezentowano topologie przekształtnika trójfazowego. Odpowiednia topologia przekształtnika z filtrem LCL została przedstawiona. Zaproponowano hybrydową strategię sterowania. System PID sterowania użyty w VCM zapewnia szybką odpowiedź dynamiczną i małe zniekształcenia. W układzie CCM użyto stałego sprzężenia zwrotnego. Sprawdzono położenie biegunów. Wyniki eksperymentu z dwoma 400kVA równoległymi przekształtnikami potwierdziły założenia.

18

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 3

507-512

EN

The notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsystems such that the dynamics of the second subsystem are independent of those of the first one, (ii) the reduced 2D system is positive if and only if the linear transformation matrix is monomial. Necessary and sufficient conditions are established for the existence of a gain matrix such that the matrices of the closed-loop system can be reduced to the common canonical form.

19

State estimate based control design using the unified algebraic approach

Filasova A., Krokavec D.

Archives of Control Sciences

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2010

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Vol. 20, no. 1

5-18

EN

The LMI based method for the control with the state estimate, subject to the input variable constraints in the state feedback control of the linear MIMO systems, is presented in the paper. For this problem are obtained the state feedback as well as the estimator gain matrices that capture the required stability by solving the linear matrix inequalities formulated in the sense of the unified algebraic approach. The method is particularly effective when the input variable constraints and the system output are of interest.

20

Observer state feedback control of discrete-time systems with state equality constraints

Filasova A., Krokavec D.

Archives of Control Sciences

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2010

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Vol. 20, no. 3

253-266

EN

Design conditions for existence of observer-based memory-less feedback control for stabilization of discrete-time systems with equality constraints given on the state variables are presented in the paper. These conditions are associated with eigenstructure assignment based on the singular value decomposition principle. The validity of the proposed method is demonstrated by a numerical example with the equality constraint tying together all state variables.