Observability and observer design for switched linear systems

Hybrid vehicles, HVAC systems in new/old buildings, power networks, and the like require safe, robust control that includes switching the mode of operation to meet environmental and performance objectives. Such switched systems consist of a set of continuous-time dynamical behaviors whose sequence of operational modes is driven by an underlying decision process. This thesis investigates feasibility conditions and a methodology for state and mode reconstruction given input-output measurements (not including mode sequence). An application herein considers insulation failures in permanent magnet synchronous machines (PMSMs) used in heavy hybrid vehicles. Leveraging the feasibility literature for switched linear time-invariant systems, this thesis introduces two additional feasibility results: 1) detecting switches from safe modes into failure modes and 2) state and mode estimation for switched linear time-varying systems. This thesis also addresses the robust observability problem of computing the smallest structured perturbations to system matrices that causes observer infeasibility (with respect to the Frobenius norm). This robustness framework is sufficiently general to solve related robustness problems including controllability, stabilizability, and detectability. Having established feasibility, real-time observer reconstruction of the state and mode sequence becomes possible. We propose the embedded moving horizon observer (EMHO), which re-poses the reconstruction as an optimization using an embedded state model which relaxes the range of the mode sequence estimates into a continuous space. Optimal state and mode estimates minimize an L2-norm between the measured output and estimated output of the associated embedded state model. Necessary conditions for observer convergence are developed. The EMHO is adapted to solve the surface PMSM fault detection problem

Identification of unknown structural loads from dynamic measurements using robust observers

The global trends in the construction of complex structures e.g. high buildings, wind turbines or airplanes\u27 tend to make the structures more intelligent by integrating sensing units together with evaluation algorithms which allow the check of structure integrity permanently. This process of structural integrity characterization strategy referred to as Structural Health Monitoring (SHM). Special SHM parameters like material properties and load characteristics are essential when assessment of fatigue life of a structure and its components is done. Therefore, the time history of an external load is an important quantity in the forecast of the remaining lifetime. Furthermore, the load localization problem becomes an important issue, especially in the case of impacts, since the aircraft industry started to use new composite materials more extensively where the impacts cause delaminations which are not detectable by visual inspections. In many practical applications, however, the measurement of external loads is limited or not possible due to sensor limitations or the unknown nature of the external forces. Therefore, indirect load history estimation is a subject of extensive studies in the last two decades. The estimation procedure leads to a so called inverse problem which is \u27ill-posed\u27 in the mathematical sense so that the existence, uniqueness or stability of solution is violated. First of all, this work provides a closer investigation to a variety of existing algorithms of force history reconstruction and location estimation which have been established by mechanical engineers. Secondly, research is carried out for possible candidate methods among the other engineering disciplines. The main focus of the thesis is concentrated on comprehensive design analysis and further development of the qualified algorithms. In particular, model based robust observers are considered as candidates for the online loads and states reconstruction. The aspects of proper model building that allow releasing the sensor placement procedure (from collocated to non-collocated), while simultaneously reducing the model complexity are introduced for the observer design. An innovative model free passive technique for automatic impact location detection is elaborated and extended by incorporation of a fast robust load estimation method. In addition, a novel approach of rank deficiency compensation is proposed for the direct time deconvolution procedure in the non-collocated case. Selected algorithms are grouped according to their ability to fulfill the load reconstruction requirements and tested either in simulation environment or on laboratory structures. The results are systemized in a form of strong and weak sides for every particular algorithm which might serve for the on-field application and future research in this area

Adaptive model-based battery management - Predicting energy and power capability

The battery is the limiting system for automotive electrication due to cost, size, and uncertain degradation. To be competitive the battery must therefore be used optimally. This thesis address the on-line battery management problem, with primary objectives to:(i) enable optimal usage of the battery by providing accurate estimates of its power and energy capability, while (ii) ensuring durability by keeping the battery inside predefined operating limits at all times. This means translating measurable information of current, voltage, and temperature into cell related quantities such as state-of-charge (SOC) and state-of health (SOH), and vehicle related quantities such as power capability and available energy.The main difficulty of battery management is that battery cells have complex, non-linear dynamics that changes with both operating conditions, usage history, and age. This thesis and he appended papers proposes a system of adaptive algorithms for on-line battery estimation. Several aspects are considered, from modelling and parameter estimation to estimation of SOC, energy, and power. Recursive algorithms are proposed for estimation of parameters and SOC, while power and energy are estimated using algebraic expressions derived from equivalent circuit battery models. The algorithms are evaluated on lithium-ion battery cell data collected laboratory tests. For the cell chemistries considered, the evaluation indicates that accuracy within 2% can be achieved for both SOC and power, also in cases with limited prior information about the cell

REACHING A TARGET WITHIN A GPS-DENIED OR COSTLY AREA: A TWO-STAGE OPTIMAL CONTROL APPROACH

In this thesis, a new class of problem is studied where a mobile agent is controlled to reach a target. Especially, the target is enclosed within a special area. The presence of this area requires a controller to have two stages: the outer stage steers the mobile agent to enter such area while the inner stage steers the mobile agent towards the target. We consider two types of the special area: a time-costly area and a GPS-denied area. For the time-costly area, we formulate a two-stage optimal control problem where time is explicitly specified in the cost function. We solve the problem by solving its subproblems. The key subproblem is a nonconvex quadratic programming with two quadratic constraints (QC2QP). We study the QC2QP independently and prove the necessary and sufficient conditions for strong duality in a general QC2QP. Such conditions enable efficient solution methods for a QC2QP utilizing its dual and semidefinite relaxation. For the GPS-denied area, we formulate another two-stage optimal control problem where perturbation is considered. To deal with the perturbation, we propose a robust controller using the variable horizon model predictive control. The performance of the two-stage controller for each type of the special area is demonstrated in simulations. We construct and implement a two-stage controller that can steer a quadrotor to reach a target enclosed within a denied area. Such controller utilizes the formulation and solution methods in the theoretical study. We show experimental results where the controller can run in real-time using off-the-shelf fast optimization solvers. We also conduct a bat experiment to learn bat's strategy for target reaching inside a denied area

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

A fast optmization algorithm for Moving Horizon Estimation.

The Moving Horizon Estimation (MHE) is a technique that allows to estimate the states of a system considering constraints, either when they are effected by noise or are not measured. This method can be associated with control techniques such as Model Predictive Control. The core of the mathematics formulation of MHE consists of an optimization problem that can easily become huge as the horizon and the number of states of the system increase. This leads inevitably to a large computational time that makes dicult the implementation of the algorithm for on-line purpose. In this work we show through several simulations on linear random systems that if we assume box constraints on the states and output noises, we can eciently apply the Nesterov's Fast Gradient method for solving the optimization problem faster than using the standard optimization algorithms such as Interior Point Method or Active Set Method