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1

Bezpośrednie polowo-zorientowane sterowanie silnikiem indukcyjnym tolerujące uszkodzenia czujników prądu z wykorzystaniem podwójnego zmodyfikowanego obserwatora Luenbergera

Adamczyk Michał, Orłowska-Kowalska Teresa

Przegląd Elektrotechniczny

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2023

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R. 99, nr 4

43--50

PL

W artykule przedstawiono analizę bezpośredniego polowo-zorientowanego sterowania silnikiem indukcyjnym tolerującego uszkodzenia wszystkich czujników prądów stojana. Do detekcji i kompensacji uszkodzeń czujników prądu zaproponowano podwójny zmodyfikowany obserwator Luenbergera. Dodatkowo, w porównaniu do aktualnie stosowanych rozwiązań, zastosowanie opisanej modyfikacji wektora błędu obserwatora umożliwiło zwiększenie jego odporności na zmiany parametrów silnika oraz dokładności estymacji prądu stojana. Badania eksperymentalne potwierdziły wysoką skuteczność proponowanego rozwiązania.

EN

The article presents an analysis of direct field-oriented control of an induction motor that tolerates failure of all stator current sensors. A dual modified Luenberger observer has been proposed for the detection and compensation of faults in current sensors. Additionally, compared to recent solutions, the use of the described modification of the observer's error vector allowed to increase its robustness to changes in motor parameters and the accuracy of stator current estimation. Experimental studies confirmed the high effectiveness of the proposed solution.

2

Analiza wpływu czasu martwego falownika napięcia oraz jego kompensacji na jakość estymacji prądu stojana w układzie napędowym z silnikiem indukcyjnym

Adamczyk Michał, Orłowska-Kowalska Teresa

Przegląd Elektrotechniczny

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2023

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R. 99, nr 4

1--5

PL

W artykule przedstawiono szczegółową analizę wpływu czasu martwego falownika napięcia (FN) oraz jego kompensacji na jakość estymacji prądu stojana stosowanej w układach napędowych z silnikami indukcyjnymi (SI), tolerujących uszkodzenia czujników prądu (CS-FTC). Badania zostały zrealizowane w zakresie niskich prędkości kątowych, wynoszących od 1% do 20% wartości znamionowej, zarówno dla pracy silnikowej jak i prądnicowej, dla różnych wartości czasu martwego. Wyniki pokazują istotną poprawę jakości estymacji prądu stojana, co jest szczególnie ważne w przypadku kompensacji uszkodzeń czujników prądu w napędach z SI.

EN

This article presents a detailed analysis of the impact of voltage source inverter (VSI) dead time and its compensation on the quality of stator current estimation used in the current sensor fault-tolerant control (CS-FTC) of induction motor (IM) drives. The tests were carried out in the low angular velocity range, from 1% to 20% of the rated value, both for motoring and regenerating modes, for different values of dead time. The results show a significant improvement in the quality of stator current estimation, which is particularly important in the case of fault compensation in IM drive systems that tolerate faults of current sensors.

3

Reliability-aware zonotopic tube-based model predictive control of a drinking water network

Khoury Boutrous, Nejjari Fatiha, Puig Vicenç

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

197--211

EN

A robust economic model predictive control approach that takes into account the reliability of actuators in a network is presented for the control of a drinking water network in the presence of uncertainties in the forecasted demands required for the predictive control design. The uncertain forecasted demand on the nominal MPC may make the optimization process intractable or, to a lesser extent, degrade the controller performance. Thus, the uncertainty on demand is taken into account and considered unknown but bounded in a zonotopic set. Based on this uncertainty description, a robust MPC is formulated to ensure robust constraint satisfaction, performance, stability as well as recursive feasibility through the formulation of an online tube-based MPC and an accompanying appropriate terminal set. Reliability is then modelled based on Bayesian networks, such that the resulting nonlinear function accommodated in the optimization setup is presented in a pseudo-linear form by means of a linear parameter varying representation, mitigating any additional computational expense thanks to the formulation as a quadratic optimization problem. With the inclusion of a reliability index to the economic dominant cost of the MPC, the network users’ requirements are met whilst ensuring improved reliability, therefore decreasing short and long term operational costs for water utility operators. Capabilities of the designed controller are demonstrated with simulated scenarios on the Barcelona drinking water network.

4

Integrated fault-tolerant control of a quadcopter UAV with incipient actuator faults

Kantue Paulin, Pedro Jimoh O.

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 4

601--617

EN

An integrated approach to the fault-tolerant control (FTC) of a quadcopter unmanned aerial vehicle (UAV) with incipient actuator faults is presented. The framework is comprised of a radial basis function neural network (RBFNN) fault detection and diagnosis (FDD) module and a reconfigurable flight controller (RFC) based on the extremum seeking control approach. The dynamics of a quadcopter subject to incipient actuator faults are estimated using a nonlinear identification method comprising a continuous forward algorithm (CFA) and a modified golden section search (GSS) one. A time-difference-of-arrival (TDOA) method and the post-fault system estimates are used within the FDD module to compute the fault location and fault magnitude. The impact of bi-directional uncertainty and FDD detection time on the overall FTC performance and system recovery is assessed by simulating a quadcopter UAV during a trajectory tracking mission and is found to be robust against incipient actuator faults during straight and level flight and tight turns.

5

Fault-tolerant tracking control for a non-linear twin-rotor system under ellipsoidal bounding

Kukurowski Norbert, Mrugalski Marcin, Pazera Marcin, Witczak Marcin

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

171--183

EN

A novel fault-tolerant tracking control scheme based on an adaptive robust observer for non-linear systems is proposed. Additionally, it is presumed that the non-linear system may be faulty, i.e., affected by actuator and sensor faults along with the disturbances, simultaneously. Accordingly, the stability of the robust observer as well as the fault-tolerant tracking controller is achieved by using the ℋ∞ approach. Furthermore, unknown actuator and sensor faults and states are bounded by the uncertainty intervals for estimation quality assessment as well as reliable fault diagnosis. This means that narrow intervals accompany better estimation quality. Thus, to cope with the above difficulty, it is assumed that the disturbances are over-bounded by an ellipsoid. Consequently, the performance and correctness of the proposed fault-tolerant tracking control scheme are verified by using a non-linear twin-rotor aerodynamical laboratory system.

6

A multi-model based adaptive reconfiguration control scheme for an electro-hydraulic position servo system

Zhang Zhao, Yang Zhong, Liu Shuchang, Chen Shuang, Zhang Xiaokai

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

185--196

EN

Reliability and safety of an electro-hydraulic position servo system (EHPSS) can be greatly reduced for potential sensor and actuator faults. This paper proposes a novel reconfiguration control (RC) scheme that combines multi-model and adaptive control to compensate for the adverse effects. Such a design includes several fixed models, one adaptive model, and one reinitialized adaptive model. Each of the models has its own independent controller that is based on a complete parametrization of the corresponding fault. A proper switching mechanism is set up to select the most appropriate controller to control the current plant. The system output can track the reference model asymptotically using the proposed method. Simulation results validate robustness and effectiveness of the proposed scheme. The main contribution is a reconfiguration control method that can handle component faults and maintain the acceptable performance of the EHPSS.

7

Health management using fault detection and fault tolerant control of multicellular converter applied in more electric aircraft system

Mahboub Mohamed Abdelbasset, Rouabah Boubakeur, Kafi Mohamed Redouane, Toubakh Houari

Diagnostyka

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2022

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Vol. 23, No. 2

art. no. 2022212

EN

The increased cost of fuel and maintenance in aircraft system lead to the concept of more electric aircraft, moreover this concept increase the use of power electronic converters in aircraft power system. Since in this application, the reliability is a crucial feature. Therefore, the use of more efficient, reliable and robust power converter with health management capability will be a big challenge. Multicellular topology of power converters has the required performance in terms of efficiency and robustness. However, the increased complexity of control and more power components (power switches and capacitors) goes along with an increase in possibility of failure in multicellular topology. Therefore, the main contribution of this paper is the use of multicellular topology advantageous with fault diagnosis and fault tolerant control in order to increase the robustness reliability. The health management using a fault detection with Fuzzy Pattern Matching (FPM) algorithm when a failure in power switches or flying capacitors of multicellular converter and a Fault Tolerant Control (FTC) with sliding mode of second parallel three cells multicellular converters. Simulation results with Matlab show the increased efficiency and the continuity of work during failure mode in aircraft power system.

8

Sterowanie tolerujące uszkodzenia przekształtnika dla napędu z silnikiem synchronicznym o magnesach trwałych

Łuczak Dominik, Siembab Krzysztof, Brock Stefan

Poznan University of Technology Academic Journals. Electrical Engineering

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2020

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No. 102

7--15

PL

Artykuł przedstawia algorytm sterowania tolerującego uszkodzenia dla trójfazowego przekształtnika energoelektronicznego zasilającego silnik synchroniczny o magnesach trwałych. Zaprezentowano rekonfigurację topologii przekształtnika po wykryciu uszkodzenia w jednej z gałęzi oraz zaproponowany został zmodyfikowany algorytm modulacji wektora przestrzennego. Wyniki badań symulacyjnych i eksperymentalnych potwierdzają, że zaproponowany napęd zasilany przez przekształtnik z 4 nieuszkodzonymi kluczami pracuje stabilnie z dobrymi właściwościami dynamicznymi i statycznymi.

EN

The article presents a fault-tolerant control algorithm for a three-phase power electronics converter feeding a permanent magnet synchronous motor. It shows reconfiguration of converter topology after detecting a fault in one of the branches and proposes modified algorithm of space vector modulation. Results of simulation and experimental studies confirm that the proposed drive powered by the converter with 4 healthy switches will work stable with good dynamic and static properties.

9

Health-aware and fault-tolerant control of an octorotor UAV system based on actuator reliability

Salazar Jean Carlo, Sanjuan Adrián, Nejjari Fatiha, Sarrate Ramon

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 1

47--59

EN

A major goal in modern flight control systems is the need for improving reliability. This work presents a health-aware and fault-tolerant control approach for an octorotor UAV that allows distributing the control effort among the available actuators based on their health information. However, it is worth mentioning that, in the case of actuator fault occurrence, a reliability improvement can come into conflict with UAV controllability. Therefore, system reliability sensitivity is redefined and modified to prevent uncontrollable situations during the UAV’s mission. The priority given to each actuator is related to its importance in system reliability. Moreover, the proposed approach can reconfigure the controller to compensate actuator faults and improve the overall system reliability or delay maintenance tasks.

10

Fault tolerant multicontrollers for nonlinear systems: A real validation on a chemical process

Mejdi Sondess, Messaoud Anis, Ben Abdennour Ridha

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 1

61--74

EN

An active sensor fault tolerant controller for nonlinear systems represented by a decoupled multimodel is proposed. Active fault tolerant control requires accurate fault estimation. Thus, to estimate both state variables and sensor faults, a discrete unknown input multiobserver, based on an augmented state multimodel, is designed. The multiobserver gains are computed by solving linear matrix inequalities with equality constraints. A multicontrol strategy is proposed for the compensation of the sensor fault and recovering the desired performances. This strategy integrates a bank of controllers, corresponding to a set of partial models, to generate a set of control laws compensating the fault effect. Then, a switching strategy between the generated local control laws is established in order to apply the most suitable control law that tolerates the fault and maintains good closed loop performances. The effectiveness of the proposed strategy is proven through a numerical example and also through a real time application on a chemical reactor. The obtained results confirm satisfactory closed loop performance in terms of trajectory tracking and fault tolerance.

11

Robust multiple sensor fault-tolerant control for dynamic non-linear systems: Application to the aerodynamical twin-rotor system

Pazera M., Buciakowski M., Witczak M.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 2

297--308

EN

The paper deals with the problem of designing sensor-fault tolerant control for a class of non-linear systems. The scheme is composed of a robust state and fault estimator as well as a controller. The estimator aims at recovering the real system state irrespective of sensor faults. Subsequently, the fault-free state is used for control purposes. Also, the robust sensor fault estimator is developed in a such a way that a level of disturbances attenuation can be reached pertaining to the fault estimation error. Fault-tolerant control is designed using similar criteria. Moreover, a separation principle is proposed, which makes it possible to design the fault estimator and control separately. The final part of the paper is devoted to the comprehensive experimental study related to the application of the proposed approach to a non-linear twin-rotor system, which clearly exhibits the performance of the new strategy.

12

Adaptive fault-tolerant position control of a hexacopter subject to an unknown motor failure

Falconí G. P., Angelov J., Holzapfel F.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 2

309--321

EN

This paper presents a fault tolerant position tracking controller for a hexarotor system. The proposed controller has a cascaded structure composed of a position and an attitude control loop. The nominal controller is augmented by an adaptive control allocation which compensates for faults and failures within the propulsion system without reconfiguration of the controller. Simultaneously, it is able to implement a degraded control strategy which prioritizes specific control directions in the case of extreme degradation. The main contribution is a controller that is a step closer to application scenarios by including outdoor GPS-based flight tests, onboard computation and the handling of unknown degradation and failure of any rotor.

13

Active fault tolerance control of a wind turbine system using an unknown input observer with an actuator fault

Li S., Wang H., Aitouche A., Tian Y., Christov N.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 1

69--81

EN

This paper proposes a fault tolerant control scheme based on an unknown input observer for a wind turbine system subject to an actuator fault and disturbance. Firstly, an unknown input observer for state estimation and fault detection using a linear parameter varying model is developed. By solving linear matrix inequalities (LMIs) and linear matrix equalities (LMEs), the gains of the unknown input observer are obtained. The convergence of the unknown input observer is also analysed with Lyapunov theory. Secondly, using fault estimation, an active fault tolerant controller is applied to a wind turbine system. Finally, a simulation of a wind turbine benchmark with an actuator fault is tested for the proposed method. The simulation results indicate that the proposed FTC scheme is efficient.

14

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

Xu F., Puig V., Ocampo-Martinez C., Olaru S., Niculescu S. I.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 1

43--61

EN

In this paper, a fault-tolerant control (FTC) scheme is proposed for actuator faults, which is built upon tube-based model predictive control (MPC) as well as set-based fault detection and isolation (FDI). In the class of MPC techniques, tube-based MPC can effectively deal with system constraints and uncertainties with relatively low computational complexity compared with other robust MPC techniques such as min-max MPC. Set-based FDI, generally considering the worst case of uncertainties, can robustly detect and isolate actuator faults. In the proposed FTC scheme, fault detection (FD) is passive by using invariant sets, while fault isolation (FI) is active by means of MPC and tubes. The active FI method proposed in this paper is implemented by making use of the constraint-handling ability of MPC to manipulate the bounds of inputs. After the system has been detected to become faulty, the input-constraint set of the MPC controller is adjusted to actively excite the system for achieving FI guarantees on-line, where an active FI-oriented input set is designed off-line. In this way, the system can be excited in order to obtain more extra system-operating information for FI than passive FI approaches. Overall, the objective of this paper is to propose an actuator MPC scheme with as little as possible of FI conservatism and computational complexity by combining tube-based MPC and set theory within the framework of MPC, respectively. Finally, a case study is used to show the effectiveness of the proposed FTC scheme.

15

An active fault-tolerant control framework against actuator stuck failures under input saturations

Qi X., Theilliol D., He Y., Han J.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 4

749--761

EN

In this paper, a control framework including active fault-tolerant control (FTC) and reference redesign is developed subject to actuator stuck failures under input saturations. FTC synthesis and reference redesign approaches are proposed to guarantee post-fault system safety and reference reachability. Then, these features are analyzed under both actuator stuck failures and constraints before fault-tolerant controller switches. As the main contribution, actuator stuck failures and constraints are unified so that they can be easily considered simultaneously. By means of transforming stuck failures into actuator constraints, the post-fault system can be regarded as an equivalent system with only asymmetrical actuator constraints. Thus, methods against actuator saturations can be used to guarantee regional stability and produce the stability region. Based on this region, stuck compensation is analyzed. Specifically, an unstable open-loop system is considered, which is more challenging. Furthermore, the method is extended to a set-point tracking problem where the reachability of the original reference can be evaluated. Then, a new optimal reference will be computed for the post-fault system if the original one is unreachable. Finally, simulation examples are shown to illustrate the theoretical results.

16

Fault Tolerant-Control: Solutions and Challenges

Witczak M., Pazera M.

Pomiary Automatyka Robotyka

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2016

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R. 20, nr 1

5--16

EN

Fault-Tolerant Control (FTC) systems are intensively investigated both from the theoretical and practical viewpoints. It is reflected in a large number of publications and research teams dealing with this emerging area. FTC is perceived as a technique integrating advanced fault diagnosis techniques and modern control methods that makes it possible a system to continue its mission under a faulty situation. It can be also observed that the fault diagnosis theory is well developed for linear systems. There are also approaches that can be efficiently used to minimize the uncertainty effect of the model of the system being controlled and diagnosed as well as noise and disturbances. This means that the development of analogous strategies for non-linear systems is fully justified. One of the main difficulties in the current development of FTC is the fact that most works presented in the literature treat fault diagnosis and FTC problems separately. Unfortunately, perfect fault diagnosis, and in particular fault identification, is impossible to attain. This justifies the necessity of developing integrated fault diagnosis and FTC, which takes into account such an unappealing phenomenon, both for linear and non-linear systems. As indicates the state-of-the-art regarding FTC, the integration issue is treated cursorily while the lack of suitable solution is replaced with a chain of (possibly conservative) assumptions related to fault diagnosis. Taking into account the above difficulties, the paper focuses on the presentation of modern FTC with analytical and soft computing approaches. An effective FTC methods are discussed along with the integration process of fault diagnosis and FTC.

PL

Systemy sterowania tolerującego uszkodzenia FTC (ang. Fault-Tolerant Control) są obecnie intensywnie badane, zarówno z teoretycznego, jak i praktycznego punktu widzenia. Znajduje to odzwierciedlenie w wielu publikacjach naukowych oraz w liczbie międzynarodowych zespołów zaangażowanych w badania nad tym zagadnieniem. FTC jest postrzegane jako technika integrująca zaawansowane strategie diagnostyki uszkodzeń z nowoczesnymi metodami sterowania, umożliwiająca dalsze funkcjonowanie systemu w warunkach uszkodzeń. Teoria diagnostyki uszkodzeń i sterowania jest dobrze rozwinięta i udokumentowana dla systemów liniowych. Istnieją również rozwiązania zmniejszające zależność między jakością funkcjonowania powyższych metod, a niepewnością modelu opisującego sterowany i diagnozowany, która może być spowodowana takimi czynnikami jak: różnice między kopiami użytych elementów konstrukcyjnych, niestacjonarność systemu, zewnętrzne zakłócenia, szumy pomiarowe, itd. Oznacza to, że opracowywanie analogicznych rozwiązań dla systemów nieliniowych jest w pełni uzasadnione. Jedną z głównych trudności w obecnym rozwoje FTC jest fakt, że większość prac prezentowanych w literaturze traktuje problemy diagnostyki uszkodzeń i FTC niezależnie. Niestety, idealna diagnostyka uszkodzeń, a w szczególności ich identyfikacja (określenie rozmiaru uszkodzeń) jest niemożliwa do uzyskania. Uzasadnia to konieczność projektowania zintegrowanych układów diagnostyki i FTC uwzględniających tą niepożądaną właściwość, zarówno dla układów liniowych, jak i nieliniowych. Jak wskazuje przegląd licznych prac w zakresie FTC oraz monografii związanych z tą tematyką, problem integracji jest traktowany bardzo pobieżnie, a jego rozwiązanie zastępuje się szeregiem (zazwyczaj restrykcyjnych) założeń, jakie musi spełniać układ diagnostyczny stanowiący jeden z elementów FTC. Biorąc pod uwagę powyższe uwarunkowania, referat koncentruje się na prezentacji nowoczesnych rozwiązań w zakresie FTC z zastosowaniem technik analitycznych i metod obliczeń inteligentnych. Omawia się również efektywne metody sterowania tolerującego uszkodzenia wraz z procesem integracji układów sterownia i diagnostyki uszkodzeń.

17

Towards robust predictive fault-tolerant control for a battery assembly system

Seybold L., Witczak M., Majdzik P., Stetter R.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 4

849--862

EN

The paper deals with the modeling and fault-tolerant control of a real battery assembly system which is under implementation at the RAFI GmbH company (one of the leading electronic manufacturing service providers in Germany). To model and control the battery assembly system, a unified max-plus algebra and model predictive control framework is introduced. Subsequently, the control strategy is enhanced with fault-tolerance features that increase the overall performance of the production system being considered. In particular, it enables tolerating (up to some degree) mobile robot, processing and transportation faults. The paper discusses also robustness issues, which are inevitable in real production systems. As a result, a novel robust predictive fault-tolerant strategy is developed that is applied to the battery assembly system. The last part of the paper shows illustrative examples, which clearly exhibit the performance of the proposed approach.

18

Systematic fault tolerant control based on adaptive Thau observer estimation for quadrotor UAVs

Cen Z., Noura H., Younes Y. A.

International Journal of Applied Mathematics and Computer Science

|

2015

|

Vol. 25, no. 1

159--174

EN

A systematic fault tolerant control (FTC) scheme based on fault estimation for a quadrotor actuator, which integrates normal control, active and passive FTC and fault parking is proposed in this paper. Firstly, an adaptive Thau observer (ATO) is presented to estimate the quadrotor rotor fault magnitudes, and then faults with different magnitudes and time-varying natures are rated into corresponding fault severity levels based on the pre-defined fault-tolerant boundaries. Secondly, a systematic FTC strategy which can coordinate various FTC methods is designed to compensate for failures depending on the fault types and severity levels. Unlike former stand-alone passive FTC or active FTC, our proposed FTC scheme can compensate for faults in a way of condition-based maintenance (CBM), and especially consider the fatal failures that traditional FTC techniques cannot accommodate to avoid the crashing of UAVs. Finally, various simulations are carried out to show the performance and effectiveness of the proposed method.

19

Supervisory fault tolerant control of the GTM UAV using LPV methods

Péni T., Vanek B., Szabó Z., Bokor J.

International Journal of Applied Mathematics and Computer Science

|

2015

|

Vol. 25, no. 1

117--131

EN

A multi-level reconfiguration framework is proposed for fault tolerant control of over-actuated aerial vehicles, where the levels indicate how much authority is given to the reconfiguration task. On the lowest, first level the fault is accommodated by modifying only the actuator/sensor configuration, so the fault remains hidden from the baseline controller. A dynamic reallocation scheme is applied on this level. The allocation mechanism exploits the actuator/sensor redundancy available on the aircraft. When the fault cannot be managed at the actuator/sensor level, the reconfiguration process has access to the baseline controller. Based on the LPV control framework, this is done by introducing fault-specific scheduling parameters. The baseline controller is designed to provide an acceptable performance level along all fault scenarios coded in these scheduling variables. The decision on which reconfiguration level has to be initiated in response to a fault is determined by a supervisor unit. The method is demonstrated on a full six-degrees-of-freedom nonlinear simulation model of the GTM UAV.

20

Robust quasi-LPV model reference FTC of a quadrotor UAV subject to actuator faults

Rotondo D., Nejjari F., Puig V.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

7--22

EN

A solution for fault tolerant control (FTC) of a quadrotor unmanned aerial vehicle (UAV) is proposed. It relies on model reference-based control, where a reference model generates the desired trajectory. Depending on the type of reference model used for generating the reference trajectory, and on the assumptions about the availability and uncertainty of fault estimation, different error models are obtained. These error models are suitable for passive FTC, active FTC and hybrid FTC, the latter being able to merge the benefits of active and passive FTC while reducing their respective drawbacks. The controller is generated using results from the robust linear parameter varying (LPV) polytopic framework, where the vector of varying parameters is used to schedule between uncertain linear time invariant (LTI) systems. The design procedure relies on solving a set of linear matrix inequalities (LMIs) in order to achieve regional pole placement and H∞ norm bounding constraints. Simulation results are used to compare the different FTC strategies.