A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Sensor fault diagnosis of singular delayed LPV systems with inexact parameters: an uncertain system approach

In this paper, sensor fault diagnosis of a singular delayed linear parameter varying (LPV) system is considered. In the considered system, the model matrices are dependent on some parameters which are real-time measurable. The case of inexact parameter measurements is considered which is close to real situations. Fault diagnosis in this system is achieved via fault estimation. For this purpose, an augmented system is created by including sensor faults as additional system states. Then, an unknown input observer (UIO) is designed which estimates both the system states and the faults in the presence of measurement noise, disturbances and uncertainty induced by inexact measured parameters. Error dynamics and the original system constitute an uncertain system due to inconsistencies between real and measured values of the parameters. Then, the robust estimation of the system states and the faults are achieved with H8 performance and formulated with a set of linear matrix inequalities (LMIs). The designed UIO is also applicable for fault diagnosis of singular delayed LPV systems with unmeasurable scheduling variables. The efficiency of the proposed approach is illustrated with an example.Peer ReviewedPostprint (author's final draft

Unknown input observer approaches to robust fault diagnosis

This thesis focuses on the development of the model-based fault detection and isolation /fault detection and diagnosis (FDI/FDD) techniques using the unknown input observer (UIO) methodology. Using the UI de-coupling philosophy to tackle the robustness issue, a set of novel fault estimation (FE)-oriented UIO approaches are developed based on the classical residual generation-oriented UIO approach considering the time derivative characteristics of various faults. The main developments proposed are:- Implement the residual-based UIO design on a high fidelity commercial aircraft benchmark model to detect and isolate the elevator sensor runaway fault. The FDI design performance is validated using a functional engineering simulation (FES) system environment provided through the activity of an EU FP7 project Advanced Fault Diagnosis for Safer Flight Guidance and Control (ADDSAFE).- Propose a linear time-invariant (LTI) model-based robust fast adaptive fault estimator (RFAFE) with UI de-coupling to estimate the aircraft elevator oscillatory faults considered as actuator faults.- Propose a UI-proportional integral observer (UI-PIO) to estimate actuator multiplicative faults based on an LTI model with UI de-coupling and with added H∞ optimisation to reduce the effects of the sensor noise. This is applied to an example on a hydraulic leakage fault (multiplicative fault) in a wind turbine pitch actuator system, assuming that thefirst derivative of the fault is zero. - Develop an UI–proportional multiple integral observer (UI-PMIO) to estimate the system states and faults simultaneously with the UI acting on the system states. The UI-PMIO leads to a relaxed condition of requiring that the first time derivative of the fault is zero instead of requiring that the finite time fault derivative is zero or bounded. - Propose a novel actuator fault and state estimation methodology, the UI–proportional multiple integral and derivative observer (UI-PMIDO), inspired by both of the RFAFE and UI-PMIO designs. This leads to an observer with the comprehensive feature of estimating faults with bounded finite time derivatives and ensuring fast FE tracking response.- Extend the UI-PMIDO theory based on LTI modelling to a linear parameter varying (LPV) model approach for FE design. A nonlinear two-link manipulator example is used to illustrate the power of this method

Actuator multiplicative fault estimation in discrete-time LPV systems using switched observers

This paper proposes an observer for the joint state and fault estimation devoted to discrete-time linear parameter varying (LPV) systems subject to actuator faults. The major contribution of this work is that the observer is able to estimate multiplicative faults, contrarily to the existing approaches, that consider additive faults. The main characteristic of this observer is that it is scheduled not only by means of the endogenous varying parameters of the faulty model, but also by the input vector. Another contribution of this paper consists in adding a switching component in order to guarantee the feasibility of the conditions for designing the observer gains. It is proved that, as long as the input sequence satisfies some characteristics, the convergence of the observer error dynamics to zero is assured. A numerical example is used to demonstrate the effectiveness of the proposed strategy.This work has been funded by the Spanish Government (MINECO) through the projects CICYT ECOCIS (ref. DPI2013-48243-C2-1-R), by MINECO and FEDER through the project CICYT HARCRICS (ref. DPI2014-58104-R), by AGAUR through the contracts FI-DGR 2014 (ref. 2014FI_B1 00172) and FI-DGR 2015 (ref. 2015FI_B2 00171), by the DGR of Generalitat de Catalunya (SAC group Ref. 2014/SGR/374), and by the National Council of Science and Technology (CONACyT) of Mexico.Peer Reviewe

Advances in gain-scheduling and fault tolerant control techniques

This thesis presents some contributions to the state-of-the-art of the fields of gain-scheduling and fault tolerant control (FTC). In the area of gain-scheduling, the connections between the linear parameter varying (LPV) and Takagi-Sugeno (TS) paradigms are analyzed, showing that the methods for the automated generation of models by nonlinear embedding and by sector nonlinearity, developed for one class of systems, can be easily extended to deal with the other class. Then, two measures, based on the notions of overboundedness and region of attraction estimates, are proposed in order to compare different models and choose which one can be considered the best one. Later, the problem of designing state-feedback controllers for LPV systems has been considered, providing two main contributions. First, robust LPV controllers that can guarantee some desired performances when applied to uncertain LPV systems are designed, by using a double-layer polytopic description that takes into account both the variability due to the varying parameter vector and the uncertainty. Then, the idea of designing the controller in such a way that the required performances are scheduled by the varying parameters is explored, which provides an elegant way to vary online the behavior of the closed-loop system. In both cases, the problem reduces to finding a solution to a finite number of linear matrix inequalities (LMIs), which can be done efficiently using the available solvers. In the area of fault tolerant control, the thesis first shows that the aforementioned double-layer polytopic framework can be used for FTC, in such a way that different strategies (passive, active and hybrid) are obtained depending on the amount of available information. Later, an FTC strategy for LPV systems that involves a reconfigured reference model and virtual actuators is developed. It is shown that by including the saturations in the reference model equations, it is possible to design a model reference FTC system that automatically retunes the reference states whenever the system is affected by saturation nonlinearities. In this way, a graceful performance degradation in presence of actuator saturations is incorporated in an elegant way. Finally, the problem of FTC of unstable LPV systems subject to actuator saturations is considered. In this case, the design of the virtual actuator is performed in such a way that the convergence of the state trajectory to zero is assured despite the saturations and the appearance of faults. Also, it is shown that it is possible to obtain some guarantees about the tolerated delay between the fault occurrence and its isolation, and that the nominal controller can be designed so as to maximize the tolerated delay.Aquesta tesi presenta diverses contribucions a l'estat de l'art del control per planificació del guany i del control tolerant a fallades (FTC). Pel que fa al control per planificació del guany, s'analitzen les connexions entre els paradigmes dels sistemes lineals a paràmetres variants en el temps (LPV) i de Takagi-Sugeno (TS). Es demostra que els mètodes per a la generació automàtica de models mitjançant encastament no lineal i mitjançant no linealitat sectorial, desenvolupats per una classe de sistemes, es poden estendre fàcilment per fer-los servir amb l'altra classe. Es proposen dues mesures basades en les nocions de sobrefitació i d'estimació de la regió d'atracció, per tal de comparar diferents models i triar quin d'ells pot ser considerat el millor. Després, es considera el problema de dissenyar controladors per realimentació d'estat per a sistemes LPV, proporcionant dues contribucions principals. En primer lloc, fent servir una descripció amb doble capa politòpica que té en compte tant la variabilitat deguda al vector de paràmetres variants i la deguda a la incertesa, es dissenyen controladors LPV robustos que puguin garantir unes especificacions desitjades quan s'apliquen a sistemes LPV incerts. En segon lloc, s'explora la idea de dissenyar el controlador de tal manera que les especificacions requerides siguin programades pels paràmetres variants. Això proporciona una manera elegant de variar en línia el comportament del sistema en llaç tancat. En tots dos casos, el problema es redueix a trobar una solució d'un nombre finit de desigualtats matricials lineals (LMIs), que es poden resoldre fent servir algorismes numèrics disponibles i molt eficients. En l'àrea del control tolerant a fallades, primerament la tesi mostra que la descripció amb doble capa politòpica abans esmentada es pot utilitzar per fer FTC, de tal manera que, en funció de la quantitat d'informació disponible, s'obtenen diferents estratègies (passiva, activa i híbrida). Després, es desenvolupa una estratègia de FTC per a sistemes LPV que fa servir un model de referència reconfigurat combinat amb la tècnica d'actuadors virtuals. Es mostra que mitjançant la inclusió de les saturacions en les equacions del model de referència, és possible dissenyar un sistema de control tolerant a fallades que resintonitza automàticament els estats de referència cada vegada que el sistema es veu afectat per les no linealitats de la saturació en els actuadors. D'aquesta manera s'incorpora una degradació elegant de les especificacions en presència de saturacions d'actuadors. Finalment, es considera el problema de FTC per sistemes LPV inestables afectats per saturacions d'actuadors. En aquest cas, es porta a terme el disseny de l'actuador virtual de tal manera que la convergència a zero de la trajectòria d'estat està assegurada tot i les saturacions i l'aparició de fallades. A més, es mostra que és possible obtenir garanties sobre el retard tolerat entre l'aparició d'una fallada i el seu aïllament, i que el controlador nominal es pot dissenyar maximitzant el retard tolerat

Model-based Fault Diagnosis and Fault Accommodation for Space Missions : Application to the Rendezvous Phase of the MSR Mission

The work addressed in this thesis draws expertise from actions undertaken between the EuropeanSpace Agency (ESA), the industry Thales Alenia Space (TAS) and the IMS laboratory (laboratoirede l’Intégration du Matériau au Système) which develop new generations of integrated Guidance, Navigationand Control (GNC) units with fault detection and tolerance capabilities. The reference mission isthe ESA’s Mars Sample Return (MSR) mission. The presented work focuses on the terminal rendezvoussequence of the MSR mission which corresponds to the last few hundred meters until the capture. Thechaser vehicle is the MSR Orbiter, while the passive target is a diameter spherical container. The objectiveat control level is a capture achievement with an accuracy better than a few centimeter. The research workaddressed in this thesis is concerned by the development of model-based Fault Detection and Isolation(FDI) and Fault Tolerant Control (FTC) approaches that could significantly increase the operational andfunctional autonomy of the chaser during rendezvous, and more generally, of spacecraft involved in deepspace missions. Since redundancy exist in the sensors and since the reaction wheels are not used duringthe rendezvous phase, the work presented in this thesis focuses only on the thruster-based propulsionsystem. The investigated faults have been defined in accordance with ESA and TAS requirements andfollowing their experiences. The presented FDI/FTC approaches relies on hardware redundancy in sensors,control redirection and control re-allocation methods and a hierarchical FDI including signal-basedapproaches at sensor level, model-based approaches for thruster fault detection/isolation and trajectorysafety monitoring. Carefully selected performance and reliability indices together with Monte Carlo simulationcampaigns, using a high-fidelity industrial simulator, demonstrate the viability of the proposedapproaches.Les travaux de recherche traités dans cette thèse s’appuient sur l’expertise des actionsmenées entre l’Agence spatiale européenne (ESA), l’industrie Thales Alenia Space (TAS) et le laboratoirede l’Intégration du Matériau au Système (IMS) qui développent de nouvelles générations d’unités intégréesde guidage, navigation et pilotage (GNC) avec une fonction de détection des défauts et de tolérance desdéfauts. La mission de référence retenue dans cette thèse est la mission de retour d’échantillons martiens(Mars Sample Return, MSR) de l’ESA. Ce travail se concentre sur la séquence terminale du rendez-vous dela mission MSR qui correspond aux dernières centaines de mètres jusqu’à la capture. Le véhicule chasseurest l’orbiteur MSR (chasseur), alors que la cible passive est un conteneur sphérique. L’objectif au niveaude contrôle est de réaliser la capture avec une précision inférieure à quelques centimètres. Les travaux derecherche traités dans cette thèse s’intéressent au développement des approches sur base de modèle de détectionet d’isolation des défauts (FDI) et de commande tolérante aux défaillances (FTC), qui pourraientaugmenter d’une manière significative l’autonomie opérationnelle et fonctionnelle du chasseur pendant lerendez-vous et, d’une manière plus générale, d’un vaisseau spatial impliqué dans des missions située dansl’espace lointain. Dès lors que la redondance existe dans les capteurs et que les roues de réaction ne sontpas utilisées durant la phase de rendez-vous, le travail présenté dans cette thèse est orienté seulementvers les systèmes de propulsion par tuyères. Les défaillances examinées ont été définies conformément auxexigences de l’ESA et de TAS et suivant leurs expériences. Les approches FDI/FTC présentées s’appuientsur la redondance de capteurs, la redirection de contrôle et sur les méthodes de réallocation de contrôle,ainsi que le FDI hiérarchique, y compris les approches à base de signaux au niveau de capteurs, les approchesà base de modèle de détection/localisation de défauts de propulseur et la surveillance de sécuritéde trajectoire. Utilisant un simulateur industriel de haute-fidélité, les indices de performance et de fiabilitéFDI, qui ont été soigneusement choisis accompagnés des campagnes de simulation de robustesse/sensibilitéMonte Carlo, démontrent la viabilité des approches proposées

Entwurf eines Beobachterbasierten Robusten Nichtlinearen Reglers

Due to observers ability in the estimation of internal system states, observers play an important role in the field of control and monitoring of dynamical systems. In reality, using sensors to measure the desired system states may be costly and/or affects the reliability of technical systems. Besides, some signals are impractical or inaccessible to be measured and using of sensors leads to significant errors such as stochastic noise. The solution of using observers is well-known since 1964. Besides the estimation of system states, some observers are able to estimate unknown inputs affecting the system dynamics such as disturbance forces or torques. These features are helpful for supervision and fault diagnosis tasks by monitoring the sensors and system components or for advanced control purposes by realizing observer-based control for practical systems. Among the state and disturbance observers, Proportional-Integral-Observer (PIO) is highly appreciated because of its simple structure and design procedure. Furthermore, using sufficiently high gain PIO, a robust estimation of system states and unknown inputs can be achieved. Besides taking the advantages of high gain design, the disadvantages of large overshoot and strong influence from measurement noise (as typical drawbacks of high gain utilization) in the control and estimation performance can not be neglected. Recently, some researches have been done to overcome the disadvantages of high gain observers and to adaptively adjust the gain of observer based on the resulting actual performance. Considering the advantages and disadvantages of high gain PIO besides the recent developments, it is evident that there are still open problems and questions to be solved in the area of optimal design of PIO and robust nonlinear control approaches based on PIO. On the other hand, the PI-Observer can be used in combination with linear/nonlinear control approaches (due to its simple structure and capability to estimate the system states and disturbances) to improve the performance and robustness of the closed-loop control results. Therefore, this thesis focuses on development and improvement of high gain Proportional-Integral-Observer as well as utilization of this observer in combination with well-known robust control approaches for possible general application in nonlinear systems. The Modified Advanced PIO (MAPIO) is introduced in this work as the extended version of Advanced PIO (APIO) to tune the gain of PIO according to the current situation. A cost function is defined so that the estimation performance and the related energy can be evaluated. Comparison between advanced observer design approaches has been done in the task of reconstructing the nonlinear characteristics and estimating the external inputs (contact forces) acting to elastic mechanical structures. Simulation results in open-loop and closed-loop cases verified that the performance of MAPIO in the task of unknown input estimation is more robust to different levels of measurement noise in comparison to previous methods e.g. APIO and standard high/low gain PIO. Furthermore, a new gain design approach of Proportional-Integral-Observer is proposed to overcome the disadvantages of high gain PIO and to realize the estimation of fast dynamical behaviors like unknown impact force. The dynamics of this force input is assumed as unknown. The idea of funnel control is taking into consideration to design the PIO gain. The important advantage of the proposed approach compared to previously published PIO gain design is the self-adjustment of observer gains according to the actual estimation situation inside the predefined funnel area. In this thesis it is shown that the proposed funnel PI-Observer algorithm allows adaptive PIO gain calculation, being able to be situatively adjusted even in the presence of measurement noise. Stability proof of funnel PI-Observer is investigated according to the switching observer condition and Lyapunov theory. The effectiveness of the proposed method is evaluated by simulation and experimental results using an elastic beam test rig. Furthermore, a nonlinear MIMO mechanical system is used to verify the effectiveness of the proposed method in the closed-loop context. Additionally, this thesis provides two new PI-Observer-based robust controllers as PIO-based sliding mode control and PIO-based backstepping control to improve the position tracking performance of a hydraulic differential cylinder system in the presence of uncertainties e.g. modeling errors, disturbances, and measurement noise. To use the linear PIO for estimation of system states and unknown inputs, the input-output feedback linearization approach is used to linearize the nonlinear model of hydraulic differential cylinder system. Thereupon the result of state and unknown input estimation is integrated into the structure of robust control design (here SMC and backstepping control) to eliminate the effects of uncertainties and disturbances. The introduced PIO-based robust controllers guarantee the ultimate boundness of the tracking error in the presence of uncertainties. The closed-loop stability is proved using Lyapunov theory in both cases. The proposed methods are experimentally validated and the results are compared with the standard SMC and industrial standard approach P-Controller in the presence of measurement noise, model uncertainties, and external disturbances. A general comparison of SMC and backstepping control approaches is provided in the last part of this work.Die Regelung und Überwachung dynamischer Systeme kann voraussetzen, dass Informationen über interne Systemzustände bekannt sind. Die Verwendung von Sensoren zur Erfassung aller Systemzustände kann erhöhte Kosten zur Folge haben und die Systemzuverlässigkeit negativ beeinflussen. Weitere Probleme ergeben sich dadurch, dass ggf. nicht jeder Systemzustand sensorisch erfasst werden kann. Der Beobachter erlaubt die Rekonstruktion aller Systemzustände auf Grundlage weniger Messungen. Neben Systemzuständen können externe Eingangsgrößen wie Reibmomente und Störungen geschätzt werden. Als Konsequenz ermöglicht der Beobachter eine gegenüber Störungen robuste Regelung und Fehlerdiagnose technischer Systeme. Der Proportional-Integral-Observer (PIO) kann mittels bestehender Entwurfsverfahren einfach implementiert werden. Durch Anpassen der Rückkopplungsmatrix eignet sich der PIO zur kombinierten Schätzung von Zuständen und unbekannten Eingangsgrößen. In diesem Zusammenhang spielt die Wahl einer betragsmäßig großen Rückkopplungsverstärkungsmatrix, als sogenannter High Gain Ansatz, eine entscheidende Rolle. Weiterhin hängt die Performance des PIO von der unbekannten Charakteristik der zu schätzenden Eingangsgröße ab. Diese Arbeit befasst sich mit der Entwicklung optimierter Entwurfsverfahren für den Proportional-Integral-Observer und der Entwicklung und Anwendung beobachterbasierter Konzepte zur robusten Regelung nichtlinearer Systeme. In dieser Arbeit wird der modifizierte Advanced PIO (MAPIO) als erweiterte Version des Advanced PIO (APIO) eingeführt. Der Schätzfehler von MAPIO wird über ein Gütefunktional abgebildet. Das Gütefunktional wird durch Anpassung der Rückkopplungsverstärkungsmatrix an die Charakteristik der unbekannten Eingangsgröße minimiert. Die Performance der modifizierten Beobachterentwurfsansätze wird anhand eines praktischen Beispiels bewertet. Geschätzt wird eine unbekannte Kontaktkraft mit nichtlinearer Charakteristik, die auf ein mechanisches System wirkt. Anhand eines Simulationsbeispiels im offenen und geschlossenen Regelkreis wird die Performance von MAPIO gegenüber vorherigen Verfahren APIO und PIO verifiziert. Basierend auf der Idee des Funnel Reglers wird ein neuartiges Entwurfskonzept für den Proportional-Integral-Observer vorgestellt. Die Nachteile des PIO-Konzeptes mit hohem Verstärkungsfaktor können überwunden werden und Schätzungen schneller dynamischer Verhaltensweisen lassen sich realisieren. Der Vorteil der neuartigen Funnel PIO Methode ist, dass der Schätzfehler in einem definierten Bereich, der sogenannten Funnel-Area, verbleibt. In dieser Arbeit wird gezeigt, dass der vorgeschlagene Funnel PIO Algorithmus eine adaptive PIO Verstärkungsberechnung ermöglicht, die auch in Gegenwart von Messrauschen situativ eingestellt werden kann. Der Stabilitätsnachweis von Funnel PIO wird mittels der Lyapunov Theorie untersucht. Die Wirksamkeit der vorgeschlagenen Methode wird durch Simulation und experimentelle Ergebnisse validiert. Eine auf einen elastischen Balken wirkende äußere Kraft mit nichtlinearer Charakteristik wird geschätzt. Ein nichtlineares MIMO System wird verwendet, um die Wirksamkeit der vorgeschlagenen Methode im geschlossenen Regelkreis zu verifizieren. In dieser Arbeit werden zwei neue PI-Observer basierte robuste Regelungen (PIO-basierte Sliding Mode und PIO-basierte Backstepping Regelung) vorgestellt. Die Positionsregelung eines hydraulischen Differentialzylinders in Gegenwart von Modellunsicherheiten, Störungen und Messrauschen wird untersucht. Zur Anwendung der PIO-basierten Störgrößenschätzung wird eine Ein-/Ausgangs-Linearisierung des nichtlinearen Modells vorgenommen. Die Stabilität des geschlossenen Regelkreises wird in beiden Fällen mit der Lyapunov Theorie bewiesen. Die vorgeschlagenen Methoden werden experimentell validiert und die Ergebnisse werden mit dem Standard Sliding Mode Regler und einem P-Regler in Gegenwart von Messrauschen, Modellunsicherheiten und externen Störungen verglichen