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1

Synteza nieprzełączającego dyskretnego ślizgowego regulatora prądu falownika sieciowego

Sawiński Albert, Chudzik Piotr, Tatar Karol

Przegląd Elektrotechniczny

|

2026

|

R. 102, nr 4

204--212

PL

Praca zawiera propozycję rozwiązania problemu obecności zaburzeń napięciowych w systemie mikrosieci przy wykorzystaniu odpowiedniego algorytmu sterowania w postaci nieprzełączającego dyskretnego ślizgowego regulatora prądu sieciowego. Zaprojektowany został model matematyczny filtra LCL, który stanowi element pośredni pomiędzy siecią energetyczną a falownikiem sieciowym. Na podstawie tego modelu opracowany został algorytm sterowania, którego działanie przetestowane zostało za pomocą zaawansowanego modelu symulacyjnego. W eksperymencie symulacyjnym uwzględniono postać zaburzenia napięciowego pomierzonego w warunkach rzeczywistych, w zakładzie przemysłowym. Zakończenie artykułu stanowi prezentacja uzyskanych wyników przeprowadzonych testów.

EN

The paper presents a proposed solution to the problem of voltage disturbances occurring in microgrid systems by employing an appropriate control algorithm in the form of a non-switching discrete sliding-mode grid-current regulator. A mathematical model of an LCL filter, serving as an intermediary element between the power grid and the grid-synchronized inverter, has been developed. Based on this model, a control algorithm was designed and its performance evaluated using an advanced simulation model. The simulation study incorporates a voltage disturbance waveform measured under real-world conditions in an industrial facility. The paper concludes with a presentation and discussion of the obtained test results.

2

On the gain synthesis of dynamic and integral sliding mode controllers for quad rotorcraft trajectory tracking

Benítez Daniel, Ortega Jovani, Ordaz Patricio, Espinoza Eduardo S.

International Journal of Applied Mathematics and Computer Science

|

2026

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Vol. 36, no. 1

23--35

EN

This study explores the development of two control strategies based on the sliding mode approach for quad rotorcraft trajectory tracking. A dynamic and an integral-type controller are designed to ensure that the sliding surface reaches zero within a finite time, resulting in a PD-like structure. Since this structure aids in determining the gains of robust PD controllers, it is utilized for comparative analysis. To account for uncertain dynamics and external disturbances, this work proposes an offline linear matrix inequality (LMI) algorithm that guarantees ultimate uniform stability for both sliding mode controllers. The primary advantage of the proposed LMI-based strategy is its ability to simplify the implementation of a sliding mode controller in complex systems, overcoming challenges associated with their intricate tuning process. Since the proposed algorithm applies to all three controllers, it facilitates the identification of the most effective one based on the system’s dynamic response. A comparative analysis based on error criteria is performed through numerical simulations to validate the effectiveness of the proposed strategies. In addition, a second comparative analysis is conducted between two widely used robust control strategies from the literature and the proposed ISMC. Finally, the effectiveness of the designed algorithm is evaluated using a complex reference trajectory featuring high maneuverability and high-speed flight.

3

On robustness to a topological perturbation in fluid mechanics

Abdelbari Merwan, Nachi Khadra, Sokołowski Jan, Novotny Antonio Andre

International Journal of Applied Mathematics and Computer Science

|

2025

|

Vol. 35, no. 1

69--81

EN

The robustness to topological perturbations in geometrical domains filled by a fluid flowing in Stokes-Darcy regime is considered. The cost functional is given by the energy dissipation in the fluid. The topological perturbation is carried out by the nucleation of an infinitesimal circular obstacle, which can be considered as a small measurement device. Our approach is based on the topological derivative method, which has been previously employed in the shape and topology optimization problems. The topological derivative (TD) measures the sensitivity of a given shape functional with respect to topological domain perturbations. The TD is used to determine the location of the small device placement, through a distributed control problem. By taking into account the effect of the disturbance term or uncertain input data in the TD expression, the problem of robustness to topological perturbation for the energy functional can be formulated as a minimax optimization problem with a pointwise observation. Numerical examples illustrate the efficiency of the proposed topological derivative method.

4

Robust dual-hormone controller for full closed-loop glucose regulation in people with type 1 diabetes: An in silico study

Fushimi Emilia, Bianchi Fernando Daniel, De Battista Hernán, Garelli Fabricio

Biocybernetics and Biomedical Engineering

|

2025

|

Vol. 45, iss. 3

329--339

EN

Current advanced methods for glucose control in people with type 1 diabetes (T1D), often referred to as artificial pancreas (AP) or automated insulin delivery (AID) systems, rely on the administration of a single hormone (insulin) to regulate blood glucose (BG). In general, these systems depend on patient-specific information usually obtained from the conventional insulin therapy to account for inter-patient variability. On the other hand, dual-hormone (DH) systems that use insulin and its counterregulatory hormone, glucagon, have the potential of further improving BG control. However, DH systems are still under development or in earlier testing stages. Since glucagon is not used in the traditional therapy for T1D, the sensitivity of each individual to this hormone is typically unknown. Here, a DH controller based on robust control is proposed. The controller in charge of glucagon dosing, based on H∞ optimal control, does not require any individualization, thus overcoming one of the challenges faced by DH approaches. The strategy is evaluated in silico and compared to previous works involving a personalized glucagon controller and its single-hormone counterpart. Results suggest that the robust control strategy allows satisfactory glucose outcomes without the need for individualization.

5

Robust control of motion in presence of uncertain parameters and control constraints

Jastrzębski Marcin, Kabziński Jacek, Mosiołek Przemysław

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2024

|

Vol. 72, nr 5

art. no. e150335

EN

The paper describes a novel, simple servo drive position controller, using solely the knowledge about the structure of the nonlinear model and the constraints met by individual components of the model. The desired behavior of the position and velocity signals is obtained by imposing a time-varying constraint on the signal aggregating information about the position and velocity tracking errors. The method allows you to determine the maximum control (servo drive current) necessary to achieve the control goal under the existing initial conditions and the selected reference trajectory. The control is constrained and consists in appropriate reaction when the trajectory approaches the barrier, the shape of which is responsible for the imposed properties of the transient and quasi-steady state tracking error. In addition to the derivation of the control, a discussion of its possible variants and basic properties is presented. Control with time-varying constraints has been introduced, which allows the control objectives to be met with limited conservatism of the imposed constraints. The influence of technical factors related to actual speed and position measurements was discussed and the operation of the real drive on a laboratory stand was presented.

6

A high-accuracy Stewart–lift platform based on a programmable logic controller – comparative case studies

Pawuś Dawid, Witek Michał, Klar Łukasz, Bochenek Krzysztof

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2024

|

Vol. 72, nr 5

art. no. 1511046

EN

The study reports the results of a comparative analysis of advanced high-accuracy Stewart-lift platform along with a comparative study of dynamic control. A control system powered by a programmable logic controller (PLC) was used. The properties of the system were described using a dynamic model using the Lagrange method. The real object was verified by performing several tests and comparing them using quality indicators. The results of verification tests conclusively demonstrate the system suitability for applications within industrial automation and robotics systems.

7

Robust estimation based nonlinear higher order sliding mode control strategies for PMSG-WECS

Nazir Awais, Khan Safdar Abbas, Khan Malak Adnan, Alam Zaheer, Khan Imran, Irfan Muhammad, Rehman Saifur, Nowakowski Grzegorz

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2023

|

Vol. 71, nr 5

art. no. e147063

EN

The wind energy conversion systems (WECS) suffer from an intermittent nature of source (wind) and the resulting disparity between power generation and electricity demand. Thus, WECS are required to be operated at maximum power point (MPP). This research paper addresses a sophisticated MPP tracking (MPPT) strategy to ensure optimum (maximum) power out of the WECS despite environmental (wind) variations. This study considers a WECS (fixed pitch, 3KW, variable speed) coupled with a permanent magnet synchronous generator (PMSG) and proposes three sliding mode control (SMC) based MPPT schemes, a conventional first order SMC (FOSMC), an integral back-stepping-based SMC (IBSMC) and a super-twisting reachability-based SMC, for maximizing the power output. However, the efficacy of MPPT/control schemes rely on availability of system parameters especially, uncertain/nonlinear dynamics and aerodynamic terms, which are not commonly accessible in practice. As a remedy, an off-line artificial function-fitting neural network (ANN) based on Levenberg-Marquardt algorithm is employed to enhance the performance and robustness of MPPT/control scheme by effectively imitating the uncertain/nonlinear drift terms in the control input pathways. Furthermore, the speed and missing derivative of a generator shaft are determined using a high-gain observer (HGO). Finally, a comparison is made among the stated strategies subjected to stochastic and deterministic wind speed profiles. Extensive MATLAB/Simulink simulations assess the effectiveness of the suggested approaches.

8

Robust predictive attitude control with stochastic dynamics

Violino Elia, Bousson Kouamana

Journal of Applied Mathematics and Computational Mechanics

|

2022

|

Vol. 21, nr 4

86--97

EN

The aim of this work is to design a robust predictive attitude controller when the disturbance is not known and it is modelled based on the stochastic theory and not directly from the environment and its laws. The paper starts with a brief introduction about the interest of attitude control, the state of the art, the limitations and the objectives of the research work. Then it moves on the control model chosen for the work. The main part is related to the modelling of the stochastic disturbance and the actuation of the controller. The results obtained match the initial idea about the capability of the controller to work under an unknown disturbance torque. Indeed, the graphical results show, for all the different conditions considered, that the required attitude is always reached, meaning that the aim of this work was achieved.

9

LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials

Sánchez Marcelino, Bernal Miguel

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 2

275--283

EN

This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.

10

Porównanie wybranych algorytmów sterowania napędem PMSM w sterowaniu nadążnym

Skarbek Ł.

Zeszyty Naukowe Akademii Morskiej w Gdyni

|

2017

|

nr 98

222--231

PL

W niniejszym artykule przedstawiono porównanie czterech regulatorów podczas zadania nadążania za zadaną trajektorią. Obiektem symulacji jest napęd z silnikiem PMSM, na którego wale umieszczono dodatkowo masę bezwładną oraz masę skupioną, poruszającą się promieniście. Regulator w żaden sposób nie jest informowany o położeniu masy skupionej. Dodatkowo na układ oddziałuje tarcie, które również nie zostało zamodelowane. Porównano ze sobą regulator PID, regulator ślizgowy w postaci klasycznej, quasi-ślizgowy oraz supertwisting. Na końcu wyniki przedstawiono w tabeli.

EN

This paper presents comparison of four selected tracking control algorithms. The simulated plant is a PMSM drive with additional well-balanced inertia load and a point mass, which is moving radially. The controller has no information about position of the point mass. Moreover, friction is present in the plant, but it is unmodelled in the controller. PID, classical sliding mode, quasi-sliding mode and super-twisting controllers are compared. The paper ends with the table of advantages and disadvantages of investigated control algorithms.

11

Stability analysis and H∞ control of discrete T–S fuzzy hyperbolic systems

Duan R., Li J., Zhang Y., Yang Y., Chen G.

International Journal of Applied Mathematics and Computer Science

|

2016

|

Vol. 26, no. 1

133--145

EN

This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T–S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T–S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and H∞ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T–S fuzzy hyperbolic model with the discrete T–S fuzzy linear one are also given to illustrate the advantage of our approach.

12

Robust LQR and LQI control with actuator failure of a 2DOF unmanned bicycle robot stabilized by an inertial wheel

Owczarkowski A., Horla D.

International Journal of Applied Mathematics and Computer Science

|

2016

|

Vol. 26, no. 2

325--334

EN

Essential ingredients for robust control are the ability to cope with different types of system behavior following modeling imperfections and the ability to assure a certain performance level. In this paper, we propose to use an actuator fault-tolerant control law to govern, during experiments, the stabilization of a bicycle robot with an inertial wheel in order to take into account unmodeled uncertainty introduced by using a linearized model in an LQR fashion. Our proposal is illustrated by signal plots and the values of performance indices obtained from a set of experiments.

13

Reducing the mast vibration of single-mast stacker cranes by gain-scheduled control

Hajdu S., Gáspár P.

International Journal of Applied Mathematics and Computer Science

|

2016

|

Vol. 26, no. 4

791--802

EN

In the frame structure of stacker cranes harmful mast vibrations may appear due to the inertial forces of acceleration or the braking movement phase. This effect may reduce the stability and positioning accuracy of these machines. Unfortunately, their dynamic properties also vary with the lifted load magnitude and position. The purpose of the paper is to present a controller design method which can handle the effect of a varying lifted load magnitude and position in a dynamic model and at the same time reveals good reference signal tracking and mast vibration reducing properties. A controller design case study is presented step by step from dynamic modeling through to the validation of the resulting controller. In the paper the dynamic modeling possibilities of single-mast stacker cranes are summarized. The handling of varying dynamical behavior is realized via the polytopic LPV modeling approach. Based on this modeling technique, a gain-scheduled controller design method is proposed, which is suitable for achieving the goals set. Finally, controller validation is presented by means of time domain simulations.

14

Wielowarstwowy miękko przełączalny predykcyjny regulator prędkości napędu dwumasowego o zmiennych parametrach

Serkies P.J., Wróbel K.

Przegląd Elektrotechniczny

|

2014

|

R. 90, nr 12

7--10

PL

W artykule przedstawiono nowy odporny na zmianę mechanicznej stałej czasowej maszyny roboczej predykcyjny regulator prędkości z miękko przełączanym sterowaniem. Proponowana struktura sterowania bazuje na predykcyjnym regulatorze obliczanym off-line dla różnych wartości nieznanego parametru, następnie w zależności od estymaty tego parametru następuje miękkie przełączanie pomiędzy poszczególnymi prawami sterowania MPC. We wstępie omówiono problematykę sterowania napędami z połączeniem sprężystym i zmiennym momentem bezwładności. W kolejnych rozdziałach przedstawiono model napędu i proponowaną strukturę sterowania. Rozważania teoretyczne zostały poparte badaniami symulacyjnymi.

EN

The paper presents a new robust predictive speed controller with soft-switched controls. The proposed control structure is based on the predictive controller off-line calculated (based on mpQP) for different values of the unknown parameter. Then, depending on the parameter estimates soft switching approach follows between the MPC control laws. A preliminary point discusses the problems of motion control of the drive with elastic coupling and variable parameters. In the following chapters presents a model of the drive and the proposed control structure. Theoretical considerations are supported by simulation studies.

15

Hybrid P–PI sliding mode position and speed controller for variable inertia drive

Brock S.

Przegląd Elektrotechniczny

|

2014

|

R. 90, nr 5

29--34

EN

Control system for a variable inertia drive based on a hybrid P–PI sliding mode controller and reference trajectory generator is described in this paper. Sliding mode block with boundary layer (active for large error values) and the P–PI block (active for small error values) are combined in one controller. Simulation results show that this control approach can decrease tracking error, enhance system robustness and attenuate high frequency chattering in the control signal. The results of simulation are confirmed by experimental studies.

PL

W artykule przedstawiono układ sterowania dla napędu o zmiennej bezwładności. W układzie tym zaproponowano generator trajektorii wzorcowej oraz hybrydowy regulator położenia i prędkości. W regulatorze połączono blok regulatora ślizgowego z warstwą graniczną (aktywny dla dużych wartości uchybu) z blokiem P–PI (aktywnym dla małych wartości uchybu). Badania symulacyjne wykazały, że takie podejście zmniejsza błędy śledzenia, poprawia odporność i eliminuje szybkie oscylacje sygnału sterującego. Badania eksperymentalne potwierdziły wyniki.

16

Rozmyty regulator prędkości obrotowej odporny na zmiany bezwładności

Jakubowski M., Nowakowski K., Zawirski K.

Poznan University of Technology Academic Journals. Electrical Engineering

|

2014

|

No. 80

19--26

PL

W ramach niniejszej pracy zaprezentowane zostały rozmyte regulatory prędkości obrotowej odporne na zmiany bezwładności. Głównym celem pracy było zaprojektowanie oraz właściwe nastrojenie regulatorów rozmytych typu PD oraz PI. Opracowane regulatory zastosowano w układzie napędowym z silnikiem prądu stałego. Projektowanie przeprowadzono w taki sposób, aby badane układy napędowe wykazywały dobre właściwości regulacyjne w szerokim zakresie zmiany bezwładności obciążenia. Analizie poddano szereg badań symulacyjnych, w ramach których rozpatrywano wybrane wskaźniki jakości dla różnych wartości bezwładności oraz momentu obciążenia. Dokonano także analizy porównawczej badanych regulatorów rozmytych z klasycznym regulatorem PID. Przeprowadzone badania symulacyjne potwierdzono na gruncie praktyki.

EN

This paper presents fuzzy speed controllers robust to inertia changes. The main purpose of this paper was to design and tune fuzzy PD and PI controllers. The fuzzy controller in drive system with DC motor were used. The project was performed so that drive systems were revealed good regulatory properties over a wide range of inertia changes. Analysis of series simulation studies including selected quality indicators for different values of inertia and load torque was considered. Furthermore, comparative analysis of fuzzy controller with classical PID controller was conducted. The simulation researches were confirmed on the basis of practice as well.

17

Further results on robust fuzzy dynamic systems with LMI D-stability constraints

Assawinchaichote W.

International Journal of Applied Mathematics and Computer Science

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2014

|

Vol. 24, no. 4

785--794

EN

This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi–Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

18

Odporne sterowanie rozmyte ruchem mobilnego robota kołowego

Jagiełowicz-Ryznar C.

Przegląd Mechaniczny

|

2013

|

nr 6

41--46

PL

Problemy poruszane w artykule koncentrują się na ważnych, współczesnych kwestiach dotyczących projektowania mechatronicznego odpornego sterowania rozmytego ruchem nadążnym mobilnych robotów kołowych. W artykule została przeprowadzona synteza algorytmów sterowania na podstawie teorii stabilności Lapunova wraz z analizą symulacji trzech algorytmów sterowania rozmytego ruchem nadążnym mobilnego robota kołowego z uwzględnieniem niedokładności parametrycznej: analitycznego sterowania ślizgowego, sterowania ślizgowego z rozmytym sterowaniem równoważnym, rozmytego sterowania ślizgowego.

EN

The problems addressed in the article concern important and up-to-date issue of the mechatronic design of the robust control systems of follow-up motion of the mobile wheeled robots. In the article the synthesis of control algorithms based on stability theory of Lapunov was carried out along with simulation analysis of the three control algorithms of the follow-up motion of the mobile wheeled robot with consideration of the parametric inaccuracy: analytic robust sliding control algorithm, robust sliding control algorithm with fuzzy compensation control, fuzzy algorithm of sliding control.

19

Evolutionary method of robust controller computation

Królikowski T., Nikończuk P.

Pomiary Automatyka Robotyka

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2013

|

R. 17, nr 1

80-82

PL

Matematyczne metody doboru współczynników regulatora odpornego w przestrzeniach H∞ są bardzo skomplikowane. Projektant układu regulacji musi wykazywać się znajomością technik analizy funkcjonalnej. Do rozwiązywania problemów optymalizacji tego rodzaju doskonale nadają się algorytmy ewolucyjne. W artykule przedstawiono metodę oraz wyniki symulacji podczas doboru współczynników równania regulatora odpornego. Do doboru użyte są tylko dwa kryteria: sprawdzenie stabilności i zależność geometryczna - minimalizacja największej odległości między krzywymi Nyquista operacji G(jω) i 1/F(jω), gdzie G(jω) i F(jω) są transmitancjami regulatora oraz obiektu regulacji w układzie sprzężenia zwrotnego.

EN

Mathematical methods of robust controller coefficients selection in H∞ spaces are very complicated. A control system integrator has to know functional analysis methods. To solve this kind of problem, evolutionary algorithms can be used. The paper presents both the method and simulation results of evolutionary algorithms application for a robust controller coefficients selection. To select robust controller, only two requirements are used: stability check and geometric dependency - minimizing the maximum distance between Nyquist diagrams of operations - G(jω) and 1/F(jω). Where G(jω) and F(jω) are controller and plant transfer functions in a feedback control system.

20

The Dynamic Model of Closed-Loop Supply Chain with Product Recovering and its Robust Control

Qiu R., Huang X., Lu Z.

Przegląd Elektrotechniczny

|

2012

|

R. 88, nr 9b

1-4

EN

In recent years, closed-loop supply chain (CLSC) operation has been an important method to recover waste materials and products for resource conservation and environmental protection and paid more attention in industry and academia. We establish a dynamic model for closedloop supply chain with product recovering with the consideration of some uncertainties including remanufacturing rate, disposal rate, operation costs and customers’ demand in this paper. Furthermore, we provide some insights about robust operation of closed-loop supply chain and propose a robust H∞ control strategy based on linear matrix inequality (LMI) arithmetic. Some simulations are executed to validate the effectiveness of our control strategy, and the results show that through state feedback control of supply chain inventories, it can not only make the CLSC achieve the goal of restraining uncertainty disturbances, but also result in an ideal operation cost.

PL

Closed loop supply chain (CLCP – zamknięta pętla łańcucha zasobów) jest dziś ważną metodą odzyskiwania zmarnowanego materiału i produktu w celu ochrony środowiska i konserwacji zasobów. Zaproponowano model dynamiczny uwzględniający niepewności typu tempo produkcji, tempo usuwania, koszty operacyjne i żądania klienta.