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1

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

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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.

2

Odporny regulator stanu dla napędu z połączeniem sprężystym

Wróbel Karol, Śleszycki Kacper

Przegląd Elektrotechniczny

|

2023

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R. 99, nr 7

9--12

PL

W pracy przedstawiono regulator stanu pracujący w strukturze regulacji prędkości układu napędowego z połączeniem sprężystym odporny na zmiany momentu bezwładności maszyny roboczej. Współczynniki regulatora dobrano z wykorzystaniem metody optymalizacji numerycznej, w sposób zapewniający odporność na zmianę parametrów. Sygnały sprzężeń zwrotnych pochodzą z czujników pomiarowych oraz z symulatora momentu skrętnego. Przedstawiono wyniki badań symulacyjnych i eksperymentalnych opracowanej struktury sterowania.

EN

The paper presents a robust state controller operating in the speed control system of the drive system with an elastic connection. The controller was tuned using the numerical optimization method so that it was robust to changes in the mechanical time constant of the load machine. The feedback signals are provided by the speed sensors and simulator of the shaft torque. The results of simulation and experimental tests of the developed control structure are presented.

3

Extended state observer based robust feedback linearization control applied to an industrial CSTR

Medjebouri Ali

Journal of Automation Mobile Robotics and Intelligent Systems

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2023

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Vol. 17, No. 4

68--78

EN

In the chemical and petrochemical industry, the Continuous Stirred Tank Reactors (CSTR) are, without doubt, one of the most popular processes. From a control point of view, the mathematical model describing the temporal evolution of the CSTR has a strongly nonlinear cross-coupled character. Moreover, modeling errors such as external disturbances, neglected dynamics, and parameter variations or uncertainties make its control task a very difficult challenge. Even though this problem has been the subject of a wide number of control strategies, this article attempts to propose a viable, robust, nonlinear decoupling control scheme. The idea behind the proposed approach lies in the design of two nested control loops. The inner loop is responsible for the compensation of the nominal model nonlinear cross-coupled terms via static nonlinear feedback; whereas the outer loop, designed around an Extended State Observer (ESO) of which the additional state gathers the global effect of modeling errors, is charged to instantaneously estimate, and then to compensate the ESO extended state. This way, the CSTR complex dynamics are reduced to a series of decoupled linear subsystems easily controllable using a simple Proportional-Integral (PI) linear control to ensure the robust pursuit of reference signals respecting the desired performance. The presented control validation was performed numerically by an objective comparison to a classical PID controller. The obtained results clearly show the viability and the effectiveness of the proposed control strategy for dealing with such nonlinear, strongly cross-coupled plants subject to a wide range of disturbances despite the precision of their described mathematical model.

4

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.

5

Robust predictive attitude control with stochastic dynamics

Violino Elia, Bousson Kouamana

Journal of Applied Mathematics and Computational Mechanics

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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.

6

Design a robust quantitative feedback theory controller for cyber-physical systems: ship course control problem

Abadi Ali Soltani Sharif, Hosseinabadi Pooyan Alinaghi, Ordys Andrew, Grimble Michael

Archives of Control Sciences

|

2022

|

Vol. 32, No. 3

589--605

EN

One of the most critical problems in all practical systems is the presence of uncertainties, internal and external disturbances, as well as disturbing noise, which makes the control of the system a challenging task. Another challenge with the physical systems is the possibility of cyber-attacks that the system’s cyber security against them is a critical issue. The systems related to oil and gas industries may also be subjected to cyber-attacks. The subsets of these industries can be mentioned to the oil and gas transmission industry, where ships have a critical role. This paper uses the Quantitative Feedback Theory (QFT) method to design a robust controller for the ship course system, aiming towards desired trajectory tracking. The proposed controller is robust against all uncertainties, internal and external disturbances, noise, and various possible Deception, Stealth, and Denial-of-Service (DOS) attacks. The robust controller for the ship system is designed using the QFT method and the QFTCT toolbox in MATLAB software. Numerical simulations are performed in MATLAB/Simulink for two case studies with disturbances and attacks involving intermittent sinusoidal and random behavior to demonstrate the proposed controller.

7

Output tracking control of an aircraft subject to additive state dependent disturbance: an optimal control approach

Tanyer Ilker, Tatlicioglu Enver, Zergeroglu Erkan

Archives of Control Sciences

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2021

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Vol. 31, No. 2

267--286

EN

In this paper, model reference output feedback tracking control of an aircraft subject to additive, uncertain, nonlinear disturbances is considered. In order to present the design steps in a clear fashion: first, the aircraft dynamics is temporarily assumed as known with all the states of the system available. Then a feedback linearizing controller minimizing a performance index while only requiring the output measurements of the system is proposed. As the aircraft dynamics is uncertain and only the output is available, the proposed controller makes use of a novel uncertainty estimator. The stability of the closed loop system and global asymptotic tracking of the proposed method are ensured via Lyapunov based arguments, asymptotic convergence of the controller to an optimal controller is also established. Numerical simulations are presented in order to demonstrate the feasibility and performance of the proposed control strategy.

8

Robust LFT-LPV H∞ control of an underactuated inverted pendulum on a cart with optimal weighting functions selection by ga and es

Hasseni Seif-El-Islam, Abdoul Latifa

Acta Mechanica et Automatica

|

2020

|

Vol. 14, no. 4

186--197

EN

This article investigates the robust stabilization and control of the inverted pendulum on a cart against disturbances, measure-ment noises, and parametric uncertainties by the LFT-based LPV technique (Linear-Fractional-Transformation based Linear-Parameter-Varying). To make the applying of the LPV technique possible, the LPV representation of the inverted pendulum on a cart model is devel-oped. Besides, the underactuated constraint of this vehicle is overcome by considering both degrees of freedom (the rotational one and the translational one) in the structure. Moreover, the selection of the weighting functions that represent the desired performance is solved by two approaches of evolutionary algorithms; Genetic Algorithms (GA) and Evolutionary Strategies (ES) to find the weighting functions’ optimal parameters. To validate the proposed approach, simulations are performed and they show the effectiveness of the proposed approach to obtain robust controllers against external signals, as well as the parametric uncertainties.

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

Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions

Koksal Mehmet Emir

Archives of Control Sciences

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2019

|

Vol. 29, No. 3

529--548

EN

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.

11

Usage of a zero-sum differential game in the optimal control of an object described by a nonlinear model

Mikulski L., Kropiowska D.

Technical Transactions

|

2018

|

Vol. 115, iss. 9

109--121

EN

This article presents the usage of a zero-sum differential game to control a nonlinear object, which, in the analysed problem, was a mathematical pendulum. The obtained control was optimal with regard to adopted quality indicator for the worst interference. The two-point boundary value problem was solved numerically by means of the Dircol software application. Numerical solutions, meeting all the necessary optimality conditions, were obtained for different values of the rough parameter and for different values of damping.

PL

W artykule wykorzystano grę różniczkową o sumie zerowej do sterowania obiektem nieliniowym, jakim w analizowanym problemie jest wahadło matematyczne. Uzyskano sterowanie optymalne ze względu na przyjęty wskaźnik jakości, przy najgorszym zakłóceniu. Dwupunktowy problem brzegowy został rozwiązany numerycznie przy wykorzystaniu programu Dircol. Rozwiązania numeryczne spełniające wszystkie warunki konieczne optymalności zostały otrzymane dla różnych wartości parametru szorstkości oraz przy różnych wartościach tłumienia.

12

A novel predictive fuzzy adaptive controller for a two-mass drive system

Serkies P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

|

Vol. 66, nr 1

37--47

EN

In the paper, a novel control structure based on the fuzzy logic and model predictive control methodologies for an elastic two-mass drive system is proposed. In order to reduce the computational requirements of the classical MPC methodology, the multi parametric programming (MPT) approach is used. The robustness of the system is ensured by implementation of three MPT controllers generated for different operation points and a supervisory fuzzy system. The main goal of the fuzzy system is suitable shaping of the control signal. The effectiveness of the proposed approach is checked in simulation and experimental tests. In order to show the properties of the proposed control structure, a critical comparison with an adaptive classical MPC controller is carried out. Both control structures are tested taking into account the performance and possibility of real-time implementation.

13

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.

14

Robust H∞ output feedback control of bidirectional inductive power transfer systems

Swain A., Almakhles D., Neath M. J., Nasiri A.

Archives of Control Sciences

|

2017

|

Vol. 27, no. 1

41--62

EN

Bidirectional Inductive power transfer (IPT) systems behave as high order resonant networks and hence are highly sensitive to changes in system parameters. Traditional PID controllers often fail to maintain satisfactory power regulation in the presence of parametric uncertainties. To overcome these problems, this paper proposes a robust controller which is designed using linear matrix inequality (LMI) techniques. The output sensitivity to parametric uncertainty is explored and a linear fractional transformation of the nominal model and its uncertainty is discussed to generate a standard configuration for μ-synthesis and LMI analysis. An H∞ controller is designed based on the structured singular value and LMI feasibility analysis with regard to uncertainties in the primary tuning capacitance, the primary and pickup inductors and the mutual inductance. Robust stability and robust performance of the system is studied through μ-synthesis and LMI feasibility analysis. Simulations and experiments are conducted to verify the power regulation performance of the proposed controller.

15

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

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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.

16

Interrupt Timed Automata with Auxiliary Clocks and Parameters

Bérard B., Jovanović A., Haddad S., Lime D.

Fundamenta Informaticae

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2016

|

Vol. 143, nr 3/4

235--259

EN

Interrupt Timed Automata (ITA) are an expressive timed model, introduced to take into account interruptions according to levels. Due to this feature, this formalism is incomparable with Timed Automata. However several decidability results related to reachability and model checking have been obtained. We add auxiliary clocks to ITA, thereby extending its expressive power while preserving decidability of reachability. Moreover, we define a parametrized version of ITA, with polynomials of parameters appearing in guards and updates. While parametric reasoning is particularly relevant for timed models, it very often leads to undecidability results. We prove that various reachability problems, including robust reachability, are decidable for this model, and we give complexity upper bounds for a fixed or variable number of clocks, levels and parameters.

17

Projektowanie i efektywność stabilizatora systemowego minimalizującego normę H∞

Lubośny Z., Dobrzyński K., Klucznik J.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

|

2015

|

Nr 47

111--114

PL

Artykuł opisuje możliwości syntezy krzepkiego stabilizatora systemowego minimalizującego normę H∞, którego właściwości dynamiczne kształtowane są przez wybór odpowiedniej funkcji wagowej. Rozważana jest efektywność metody w procesie projektowania stabilizatora systemowego.

EN

The paper discusses robust PSS synthesis. The PSS is an H∞ controller, what means that minimises H∞ norm of transfer function between the exogenous signals such as reference inputs and disturbances, and the error signals which are to be minimised to meet the control objective. The dynamic properties of the plant are shaped by choosing appropriate weighting function applied to the plant output and input signals. Question appears: does such type of PSS design lead to effective PSS which can be applied in real power system?

18

A robust predictive actuator fault-tolerant control scheme for Takagi-Sugeno fuzzy systems

Witczak P., Witczak M., Korbicz J., Aubrun Ch.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2015

|

Vol. 63, nr 4

977--987

EN

The paper deals with the problem of robust predictive fault-tolerant control for nonlinear discrete-time systems described by the Takagi-Sugeno models. The proposed approach is based on a triple stage procedure, i.e. it starts from fault estimation while the fault is compensated with a robust controller. The robust controller is designed without taking into account the input constraints related with the actuator saturation that may change due to its faulty behaviour. Thus, to check the compensation feasibility, the robust invariant set is developed, which takes into account the input constraints. If the current state does not belong to the robust invariant set, then suitable predictive control actions are performed in order to enhance the invariant set. This appealing phenomenon makes it possible to enlarge the domain of attraction, which makes the proposed approach an efficient solution for the fault-tolerant control. The final part of the paper shows an illustrative example regarding the application of the proposed approach to the twin-rotor system.

19

Robust output regulation of uncertain chaotic systems with input magnitude and rate constraints

Velosa C. M. N., Bousson K.

Acta Mechanica et Automatica

|

2015

|

Vol. 9, no. 4

252--258

EN

The problem of output regulation deserves a special attention particularly when it comes to the regulation of nonlinear systems. It is well-known that the problem is not always solvable even for linear systems and the fact that some demanding applications require not only magnitude but also rate actuator constraints makes the problem even more challenging. In addition, real physical systems might have parameters whose values can be known only with a specified accuracy and these uncertainties must also be considered to ensure robustness and on the other hand because they can be crucial for the type of behaviour exhibited by the system as it happens with the celebrated chaotic systems. The present paper proposes a robust control method for output regulation of chaotic systems with parameter uncertainties and subjected to magnitude and rate actuator constraints. The method is an extension of a work recently addressed by the same authors and consists in decomposing the nonlinear system into a stabilizable linear part plus a nonlinear part and in finding a control law based on the small-gain principle. Numerical simulations are performed to validate the effectiveness and robustness of the method using an aeronautical application. The output regulation is successfully achieved without exceeding the input constraints and stability is assured when the parameters are within the specified intervals. Furthermore, the proposed method does not require much computational effort because all the control parameters are computed offline.

20

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.