On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Development of a vehicle dynamics controller for obstacle avoidance

As roads become busier and automotive technology improves, there is considerable potential for driver assistance systems to improve the safety of road users. Longitudinal collision warning and collision avoidance systems are starting to appear on production cars to assist drivers when required to stop in an emergency. Many luxury cars are also equipped with stability augmentation systems that prevent the car from spinning out of control during aggressive lateral manoeuvres. Combining these concepts, there is a natural progression to systems that could assist in aiding or performing lateral collision avoidance manoeuvres. A successful automatic lateral collision avoidance system would require convergent development of many fields of technology, from sensors and instrumentation to aid environmental awareness through to improvements in driver vehicle interfaces so that a degree of control can be smoothly and safely transferred between the driver and vehicle computer. A fundamental requirement of any collision avoidance system is determination of a feasible path that avoids obstacles and a means of causing the vehicle to follow that trajectory. This research focuses on feasible trajectory generation and development of an automatic obstacle avoidance controller that integrates steering and braking action. A controller is developed to cause a specially modified car (a Mercedes `S' class with steer-by-wire and brake-by-wire capability) to perform an ISO 3888-2 emergency obstacle avoidance manoeuvre. A nonlinear two-track vehicle model is developed and used to derive optimal controller parameters using a series of simulations. Feedforward and feedback control is used to track a feasible reference trajectory. The feedforward control loops use inverse models of the vehicle dynamics. The feedback control loops are implemented as linear proportional controllers with a force allocation matrix used to apportion braking effort between redundant actuators. Two trajectory generation routines are developed: a geometric method, for steering a vehicle at its physical limits; and an optimal method, which integrates steering and braking action to make full use of available traction. The optimal trajectory is obtained using a multi-stage convex optimisation procedure. The overall controller performance is validated by simulation using a complex proprietary model of the vehicle that is reported to have been validated and calibrated against experimental data over several years of use in an industrial environment

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system

Design, testing and validation of model predictive control for an unmanned ground vehicle

The rapid increase in designing, manufacturing, and using autonomous robots has attracted numerous researchers and industries in recent decades. The logical motivation behind this interest is the wide range of applications. For instance, perimeter surveillance, search and rescue missions, agriculture, and construction. In this thesis, motion planning and control based on model predictive control (MPC) for unmanned ground vehicles (UGVs) is tackled. In addition, different variants of MPC are designed, analysed, and implemented for such non-holonomic systems. It is imperative to focus on the ability of MPC to handle constraints as one of the motivations. Furthermore, the proliferation of computer processing enables these systems to work in a real-time scenario. The controller's responsibility is to guarantee an accurate trajectory tracking process to deal with other specifications usually not considered or solved by the planner. However, the separation between planner and controller is not necessarily defined uniquely, even though it can be a hybrid process, as seen in part of this thesis. Firstly, a robust MPC is designed and implemented for a small-scale autonomous bulldozer in the presence of uncertainties, which uses an optimal control action and a feed-forward controller to suppress these uncertainties. More precisely, a linearised variant of MPC is deployed to solve the trajectory tracking problem of the vehicle. Afterwards, a nonlinear MPC is designed and implemented to solve the path-following problem of the UGV for masonry in a construction context, where longitudinal velocity and yaw rate are employed as control inputs to the platform. For both the control techniques, several experiments are performed to validate the robustness and accuracy of the proposed scheme. Those experiments are performed under realistic localisation accuracy, provided by a typical localiser. Most conspicuously, a novel proximal planning and control strategy is implemented in the presence of skid-slip and dynamic and static collision avoidance for the posture control and tracking control problems. The ability to operate in moving objects is critical for UGVs to function well. The approach offers specific planning capabilities, able to deal at high frequency with context characteristics, which the higher-level planner may not well solve. Those context characteristics are related to dynamic objects and other terrain details detected by the platform's onboard perception capabilities. In the control context, proximal and interior-point optimisation methods are used for MPC. Relevant attention is given to the processing time required by the MPC process to obtain the control actions at each actual control time. This concern is due to the need to optimise each control action, which must be calculated and applied in real-time. Because the length of a prediction horizon is critical in practical applications, it is worth looking into in further detail. In another study, the accuracies of robust and nonlinear model predictive controllers are compared. Finally, a hybrid controller is proposed and implemented. This approach exploits the availability of a simplified cost-to-go function (which is provided by a higher-level planner); thus, the hybrid approach fuses, in real-time, the nominal CTG function (nominal terrain map) with the rest of the critical constraints, which the planner usually ignores. The conducted research fills necessary gaps in the application areas of MPC and UGVs. Both theoretical and practical contributions have been made in this thesis. Moreover, extensive simulations and experiments are performed to test and verify the working of MPC with a reasonable processing capability of the onboard process

Increasing the sensitivity to low mass dark matter in CRESST-III with a new DAQ and signal processing

Das vorherrschende LambdaCDM-Modell der Kosmologie sagt einen großen Beitrag nicht leuchtender, vornehmlich über Schwerkraft wechselwirkender Materie zum Gesamtenergiegehalt des Universums voraus. Diese so genannte dunkle Materie stellt Experimentalphysiker durch ihre schwer fassbare Natur seit fast einem Jahrhundert vor große Herausforderungen. Zum Zeitpukt der Veröffentlichung dieser Arbeit liegt nach wie vor kein unstrittiger experimenteller Nachweis von dunkle-Materie-Teilchen vor. Das favorisierte Paradigma geht davon aus, dass dunkle-Materie-Teilchen ein thermisches Relikt aus einer früheren Epoche des Universums sind. Diese Teilchen, sogenannte WIMPs, sind schwach wechselwirkend, massiv und stabil. Diese WIMPs befinden sich in der dichten und heissen Anfangsphase des Universums im thermischen Gleichgewicht mit allen anderen Teilchen. Durch die Expansion des Universums reduzierten sich Energie-und WIMP-Dichte soweit, dass Produktion und Vernichtung zum Erliegen kamen und die zu diesem Zeitpunkt vorherrschende WIMP-Dichte eingefroren wurde. Im weiteren Verlauf sind WIMPs vor allem als die dominierende gravitative Komponente für die Entwicklung des Universums relevant. Unter der Annahme einer nur aus WIMP bestehenden Zusammensetzung der dunklen Materie werden Teilchenmassen wenigstens von ~GeV/c2 erwartet. Leichtere WIMPs würden in zu großer Menge entstehen. Das Fehlen positiver Signale aus den verschiedenen Versuchen, dunkle-Materie-Teilchen zu detektieren, lenkte die Aufmerksamtkeit auf einer Reihe von nicht-Standard Szenarien, die nicht an den genannten Massenbereich gebunden sind. Das CRESST-Experiment ist eine der erfolgreichsten experimentellen Bemühungen, die versuchen, dieses Mysterium der Natur zu lösen. Ziel ist es, in der Milchstraße vorhandene dunkle Materie mit einem empfindlichen Teilchenetektor direkt nachzuweisen. Eine exzellente Energieauflösung und die Möglichkeit, zwischen verschiedenen Teilchenarten zu unterscheiden, sind zwei entscheidende Punkte, die CRESST zu einem wettbewerbsfähigen Experiment im Bereich der Suche nach dunkler Materie machen. Die zweite Stufe des Experiments erreichte eine weltweit führende Empfindlichkeit für dunkle-Materieteilchen mit einer Masse unter 1,7 GeV/c2. Der Energieschwelle, die eng mit der Energieauflösung verbunden ist, kommt hierbei eine Schlüsselrolle zu. Die neue Stufe des Experiments, CRESST-III, wurde speziell optimiert, um diesen Parameter weiter zu verbessern und eine bisher unerreichte Empfindlichkeit gegenüber Wechselwirkungen mit Energien <100eV zu erreichen. Das erste Kapitel dieser Doktorarbeit widmet sich der Darstellung des kosmologischen Standardszenarios und der wichtigsten Beweise für das Vorhandensein dunkler Materie. Das zweite Kapitel konzentriert sich auf die wichtigsten experimentellen Techniken, die zur Identifizierung der dunklen-Materie-Teilchen eingesetzt werden. Die gesuchte Signatur bei der direkten Suche wird mit Fokus auf das CRESST Experiment diskutiert. Das dritte Kapitel konzentriert sich auf kryogene Detektoren, den CRESST-Aufbau im Laboratori Nazionali del Gran Sasso und die neu eingesetzten CRESST-III-Detektormodule. Das vierte Kapitel ist ganz der Optimierung des entscheidenden Parameters gewidmet: der Energieschwelle. Eine neue Datenerfassung und eine neuartige auf der Optimum Filter-Technik basierende Analyse werden beschrieben und mit der herkömmlichen Erfassung und Datenverarbeitung verglichen. Die Verbesserung der Empfindlichkeit und die Erweiterung der Nachweisgrenze zu geringeren Massen werden quantifiziert. Das fünfte und letzte Kapitel führt eine neue Betriebskonfiguration für die von CRESST hergestellten Temperatursensoren ein. Ein erster Proof Of Principle durch einen erfolgreich betriebenen Detektor wird präsentiert. Die notwendigen weiteren Verbesserungen für eine dauerhafte Verwendung der neuen Konfiguration werden diskutiert

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics