abstract: Toward the ambitious long-term goal of a fleet of cooperating Flexible Autonomous Machines operating in an uncertain Environment (FAME), this thesis addresses various control objectives for ground vehicles. There are two main objectives within this thesis, first is the use of visual information to control a Differential-Drive Thunder Tumbler (DDTT) mobile robot and second is the solution to a minimum time optimal control problem for the robot around a racetrack. One method to do the first objective is by using the Position Based Visual Servoing (PBVS) approach in which a camera looks at a target and the position of the target with respect to the camera is estimated; once this is done the robot can drive towards a desired position (x_ref, z_ref). Another method is called Image Based Visual Servoing (IBVS), in which the pixel coordinates (u,v) of markers/dots placed on an object are driven towards the desired pixel coordinates (u_ref, v_ref) of the corresponding markers. By doing this, the mobile robot gets closer to a desired pose (x_ref, z_ref, theta_ref). For the second objective, a camera-based and noncamera-based (v,theta) cruise-control systems are used for the solution of the minimum time problem. To set up the minimum time problem, optimal control theory is used. Then a direct method is implemented by discretizing states and controls of the system. Finally, the solution is obtained by modeling the problem in AMPL and submitting to the nonlinear optimization solver KNITRO. Simulation and experimental results are presented. The DDTT-vehicle used within this thesis has different components as summarized below: (1) magnetic wheel-encoders/IMU for inner-loop speed-control and outer-loop directional control, (2) Arduino Uno microcontroller-board for encoder-based inner-loop speed-control and encoder-IMU-based outer-loop cruise-directional-control, (3) Arduino motor-shield for inner-loop speed-control, (4) Raspberry Pi II computer-board for outer-loop vision-based cruise-position-directional-control, (5) Raspberry Pi 5MP camera for outer-loop cruise-position-directional control. Hardware demonstrations shown in this thesis are summarized: (1) PBVS without pan camera, (2) PBVS with pan camera, (3) IBVS with 1 marker/dot, (4) IBVS with 2 markers, (5) IBVS with 3 markers, (6) camera and (7) noncamera-based (v,theta) cruise control system for the minimum time problem. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2016

Robotics has been the subject of academic study from as early as 1948. For much of this time, study has focused on very specific applications in very well controlled environments. For example, the first commercial robots (1961) were introduced in order to improve the efficiency of production lines. The tasks undertaken by these robots were simple, and all that was required of a control algorithm was speed, repetitiveness and reliability in these environments. Now however, robots are being used to move around autonomously in increasingly unpredictable environments, and the need for robotic control algorithms that can successfully react to such conditions is ever increasing. In addition to this there is an ever-increasing array of robots available, the control algorithms for which are often incompatible. This can result in extensive redesign and large sections of code being re-written for use on different architectures. The thesis presented here is that a new generic approach can be created that provides robust high quality smooth paths and time-optimal path tracking to substantially increase applicability and efficiency of autonomous motion plans. The control system developed to support this thesis is capable of producing high quality smooth paths, and following these paths to a high level of accuracy in a robust and near time-optimal manner. The system can control a variety of robots in environments that contain 2D obstacles of various shapes and sizes. The system is also resilient to sensor error, spatial drift, and wheel-slip. In achieving the above, this system provides previously unavailable functionality by generically creating and tracking high quality paths so that only minor and clear adjustments are required between different robots and also be being capable of operating in environments that contain high levels of perturbation. The system is comprised of five separate novel component algorithms in order to cater for five different motion challenges facing modern robots. Each algorithm provides guaranteed functionality that has previously been unavailable in respect to its challenges. The challenges are: high quality smooth movement to reach n-dimensional goals in regions without obstacles, the navigation of 2D obstacles with guaranteed completeness, high quality smooth movement for ground robots carrying out 2D obstacle navigation, near time-optimal path tracking, and finally, effective wheel-slip detection and compensation. In meeting these challenges the algorithms have tackled adherence to non-holonomic constraints, applicability to a wide range of robots and tasks, fast real-time creation of paths and controls, sensor error compensation, and compensation for perturbation. This thesis presents each of the above algorithms individually. It is shown that existing methods are unable to produce the results provided by this thesis, before detailing the operation of each algorithm. The methodology employed is varied in accordance with each of the five core challenges. However, a common element of methodology throughout the thesis is that of gradient descent within a new type of potential field, which is dynamic and capable of the simultaneous creation of high-quality paths and the controls required to execute them. By relating global to local considerations through subgoals, this methodology (combined with other elements) is shown to be fully capable of achieving the aims of the thesis. It is concluded that the produced system represents a novel and significant contribution as there is no other system (to the author’s knowledge) that provides all of the functionality given. For each component algorithm there are many control systems that provide one or more of its features, but none that are capable of all of the features. Applications for this work are wide ranging as it is comprised of five component algorithms each applicable in their own right. For example, high quality smooth paths may be created and followed in any dimensionality of space if time optimality and obstacle avoidance are not required. Broadly speaking, and in summary, applications are to ground-based robotics in the areas of smooth path planning, time optimal travel, and compensation for unpredictable perturbation.

This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The control problem is solved both on an open track and while safely driving no closer than a fixed distance behind another locomotive. In contrast to other research in the field, this thesis achieves a real-time capable and embeddable closed-loop optimization with advanced modeling and numerical solving techniques with a non-linear optimal control problem. This controller is first formulated as a non-convex control problem and then converted to an advanced convex second-order cone problem with the intent of using a simple numerical solver, ensuring global optimality, and improving control robustness. Convex and non-convex numerical methods of solving the control problem are investigated and closed-loop performance results with a simulated vehicle are presented under realistic modeling conditions on advanced tracks both on desktop and embedded computer architectures. It is observed that the controller is capable of robust vehicle driving in cases both with and without modeling uncertainty. The benefits of pairing the optimal controller with a parameter estimator are demonstrated for cases where very large mismatches exists between the controller model and the simulated vehicle. Stopping performance is consistently within 25cm of target stations, and the worst case closed-loop optimization time was within 100ms for the computation of a 1000 point control horizon on an i7-6700 machine. / Thesis / Master of Applied Science (MASc) / This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. It is deployed on a commuter vehicle and directly manages the motoring and braking systems. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The final control implementation is capable of safe, high accuracy and optimal driving all while computing fast enough to reliably deploy on a rail vehicle.

Thermodynamic processes in finite time are in general irreversible. But there are chances to avoid irreversibility. For instance, there are canonical ensembles of special quantum systems with a given probability distribution describing the likelihood to find the system at time t=0 in a particular state with energy E_i(0), which can be controlled in a specific way, such that the initial probability distribution is recovered at the end of the process (t=T), but the state energies did change, hence E_i(0) is not equal to E_i(T). This allows to change thermodynamic quantities (expectation values) adiabatically, reversibly and in finite time. Such special processes are called Shortcuts to Adiabaticity. The presented thesis analyzes the origin of these shortcuts utilizing special Hamiltonian systems with dynamical algebra. Their main feature is to provide canonical invariance, which means a canonical ensemble stays canonical under Hamiltonian dynamics. This invariance carried by the dynamical algebra will be discussed using Lie group theory. In addition, the persistence of the dynamical algebra with respect to calculating expectation values will be deduced. This allows to benefit from all intrinsic symmetries within the discussion of ensemble trajectories. In consequence, these trajectories will evolve under Hamiltonian dynamics on a specific manifold given by the so-called Casimir companion. In addition, the deformation of this manifold due to non-Hamiltonian (dissipative) dynamics will be discussed, which allows to present a framework for modeling irreversible processes based on Hamiltonian systems with dynamical algebra. An application of this framework based on the parametric harmonic oscillator will be presented by determining time-optimal controls for transitions between two equilibrium as well as between non-equilibrium and equilibrium states. The latter one will lead to time-optimal equilibration strategies for a statistical ensemble of parametric harmonic oscillators. / Thermodynamische Prozesse in endlicher Zeit sind im Allgemeinen irreversibel. Es gibt jedoch Möglichkeiten, diese Irreversibilität zu umgehen. Ein kanonisches Ensemble eines speziellen quantenmechanischen Systems kann zum Beispiel auf eine ganz spezielle Art und Weise gesteuert werden, sodass nach endlicher Zeit T wieder eine kanonische Besetzungverteilung hergestellt ist, sich aber dennoch die Energie des Systems geändert hat (E(0) ungleich E(T)). Solche Prozesse erlauben das Ändern thermodynamischer Größen (Ensemblemittelwerte) der erwähnten speziellen Systeme in endlicher Zeit und auf eine adiabatische und reversible Art. Man nennt diese Art von speziellen Prozessen Shortcuts to Adiabaticity und die speziellen Systeme hamiltonsche Systeme mit dynamischer Algebra. Die vorliegende Dissertation hat zum Ziel den Ursprung dieser Shortcuts to Adiabaticity zu analysieren und eine Methodik zu entwickeln, die es erlaubt irreversible thermodynamische Prozesse adequat mittels dieser speziellen Systeme zu modellieren. Dazu wird deren besondere Eigenschaft ausgenutzt, die kanonische Invarianz, d.h. ein kanonisches Ensemble bleibt kanonisch bezüglich hamiltonscher Dynamik. Der Ursprung dieser Invarianz liegt in der dynamischen Algebra, die mit Hilfe der Theorie der Lie-Gruppen näher betrachtet wird. Dies erlaubt, eine weitere besondere Eigenschaft abzuleiten: Die Ensemblemittelwerte unterliegen ebenfalls den Symmetrien, die die dynamische Algebra widerspiegelt. Bei näherer Betrachtung befinden sich alle Trajektorien der Ensemblemittelwerte auf einer Mannigfaltigkeit, die durch den sogenannten Casimir Companion beschrieben wird. Darüber hinaus wird nicht-hamiltonsche/dissipative Dynamik betrachtet, welche zu einer Deformation der Mannigfaltigkeit führt. Abschließend wird eine Zusammenfassung der grundlegenden Methodik zur Modellierung irreversibler Prozesse mittels hamiltonscher Systeme mit dynamischer Algebra gegeben. Zum besseren Verständnis wird ein ausführliches Anwendungsbeispiel dieser Methodik präsentiert, in dem die zeitoptimale Steuerung eines Ensembles des harmonischen Oszillators zwischen zwei Gleichgewichtszuständen sowie zwischen Gleichgewichts- und Nichtgleichgewichtszuständen abgeleitet wird.

Carefree handling refers to the ability of a pilot to operate an aircraft without the need to continuously monitor aircraft operating limits. At the heart of all carefree handling or maneuvering systems, also referred to as envelope protection systems, are algorithms and methods for predicting future limit violations. Recently, envelope protection methods that have gained more acceptance, translate limit proximity information to its equivalent in the control channel. Envelope protection algorithms either use very small prediction horizon or are static methods with no capability to adapt to changes in system configurations. Adaptive approaches maximizing prediction horizon such as dynamic trim, are only applicable to steady-state-response critical limit parameters. In this thesis, a new adaptive envelope protection method is developed that is applicable to steady-state and transient response critical limit parameters. The approach is based upon devising the most aggressive optimal control profile to the limit boundary and using it to compute control limits. Pilot-in-the-loop evaluations of the proposed approach are conducted at the Georgia Tech Carefree Maneuver lab for transient longitudinal hub moment limit protection. Carefree maneuvering is the dual of carefree handling in the realm of autonomous Uninhabited Aerial Vehicles (UAVs). Designing a flight control system to fully and effectively utilize the operational flight envelope is very difficult. With the increasing role and demands for extreme maneuverability there is a need for developing envelope protection methods for autonomous UAVs. In this thesis, a full-authority automatic envelope protection method is proposed for limit protection in UAVs. The approach uses adaptive estimate of limit parameter dynamics and finite-time horizon predictions to detect impending limit boundary violations. Limit violations are prevented by treating the limit boundary as an obstacle and by correcting nominal control/command inputs to track a limit parameter safe-response profile near the limit boundary. The method is evaluated using software-in-the-loop and flight evaluations on the Georgia Tech unmanned rotorcraft platform- GTMax. The thesis also develops and evaluates an extension for calculating control margins based on restricting limit parameter response aggressiveness near the limit boundary.

Οι ηλεκτροµηχανικές συσκευές αποθήκευσης δεδοµένων πολύ µικρής κλίµακας που βασίζονται στη χρήση ανιχνευτών (probes) αποτελούν ανερχόµενες εναλλακτικές επιλογές για τη βελτίωση της πυκνότητας αποθήκευσης, του χρόνου πρόσβασης των δεδοµένων και της απαιτούµενης ισχύος σε σχέση µε τις συµβατικές αποθηκευτικές συσκευές. Μία υλοποίηση µιας τέτοιας συσκευής χρησιµοποιεί θερµοµηχανικές µεθόδους για την αποθήκευση πληροφορίας σε λεπτές µεµβράνες πολυµερών υλικών. Σε αυτή την περίπτωση, η ψηφιακή πληροφορία αποθηκεύεται µε τη µορφή κοιλωµάτων πάνω στο πολυµερές υλικό, οι οποίες δηµιουργούνται από τις άκρες των ανιχνευτών διαµέτρου µερικών nm. Με στόχο την αύξηση του ρυθµού εγγραφής και ανάγνωσης χρησιµοποιούνται διατάξεις από ανιχνευτές που λειτουργούν παράλληλα, µε κάθε ανιχνευτή να εκτελεί λειτουργίες εγγραφής/ανάγνωσης/διαγραφής σε ξεχωριστό αποθηκευτικό πεδίο. Βασικές απαιτήσεις κατά τη λειτουργία τέτοιων συσκευών αποτελούν η εξαιρετικά µεγάλη ακρίβεια και η µικρή καθυστέρηση κατά τη µετακίνηση των ανιχνευτών πάνω από το πολυµερές υλικό. Η παρούσα διατριβή έχει ως αντικείµενο τη µελέτη των διατάξεων κίνησης και τη σχεδίαση πρωτότυπων αρχιτεκτονικών ελέγχου, που οδηγούν στη βελτίωση της απόδοσης των απαιτούµενων, σε συσκευές τέτοιου τύπου, λειτουργιών ελέγχου. Η µετατόπιση του αποθηκευτικού µέσου σε σχέση µε τη διάταξη των ανιχνευτών επιτυγχάνεται µε τη χρησιµοποίηση µικρής κλίµακας scanners, που έχουν δυνατότητες κίνησης σε δύο κατευθύνσεις (x/y). Πληροφορία για τη θέση του microscanner στις δύο κατευθύνσεις παρέχεται από θερµικούς αισθητήρες ανίχνευσης θέσης που κατασκευάζονται µαζί µε τη διάταξη µε τους ανιχνευτές και τοποθετούνται πάνω από το κινητό πλαίσιο. Η πλήρης κατανόηση της συµπεριφοράς των διατάξεων αυτών αποτελεί απαραίτητο στοιχείο για τον αποτελεσµατικό σχεδιασµό και την ανάλυση των συστηµάτων ελέγχου. Στα πλαίσια της διατριβής δηµιουργήθηκε ένα πλήρες µοντέλο της διάταξης του microscanner και των θερµικών αισθητήρων ανίχνευσης θέσης. Σύγκριση της απόκρισης του µοντέλου µε τις πειραµατικές µετρήσεις καταδεικνύει ότι το µοντέλο προσεγγίζει µε εξαιρετική ακρίβεια την απόκριση του συστήµατος. Το σύστηµα ελέγχου περιλαµβάνει, στην αρχή, τη λειτουργία αναζήτησης/ αποκατάστασης, κατά την οποία το σύστηµα εντοπίζει τη θέση όπου απαιτείται να πραγµατοποιηθεί εγγραφή ή ανάγνωση πληροφορίας µε εκκίνηση µία αυθαίρετη θέση του κινητού πλαισίου. Απαίτηση του συστήµατος κατά τη λειτουργία αυτή είναι η ελαχιστοποίηση του χρόνου πρόσβασης των δεδοµένων. Η γρήγορη πρόσβαση στα δεδοµένα αποτελεί µια σηµαντική πρόκληση στις συµβατικές αποθηκευτικές συσκευές. Με το πλεονέκτηµα των ελαφρύτερων µηχανικών µερών, οι υπό µελέτη συσκευές αποθήκευσης βασισµένες στην τεχνολογία MEMS θεωρούνται βασικές υποψήφιες για τη βελτίωση του χρόνου πρόσβασης των δεδοµένων. Οι σχετικές προοπτικές των συσκευών αυτών διερευνώνται αναλυτικά στα πλαίσια της διατριβής. Συγκεκριµένα, αρχικά µελετάται η απόδοση διαφόρων συστηµάτων µε βάση τη θεωρία ελέγχου βέλτιστου χρόνου. Τα αποτελέσµατα της µελέτης δίνουν το θεωρητικά βέλτιστο χρόνο πρόσβασης και την εξάρτησή του από τις παραµέτρους του κάθε συστήµατος. Στη συνέχεια, περιγράφεται η αρχιτεκτονική ελέγχου για τη λειτουργία αναζήτησης και παρουσιάζονται τα αποτελέσµατα που αντλήθηκαν από το περιβάλλον προσοµοίωσης και από την πειραµατική διάταξη. Τα αποτελέσµατα καταδεικνύουν ότι οι χρόνοι πρόσβασης των δεδοµένων που είναι δυνατό να επιτευχθούν µε τις συσκευές αυτές, είναι σηµαντικά µικρότεροι σε σχέση µε τις συµβατικές. Στη συνέχεια, ακολουθεί η λειτουργία παρακολούθησης, όπου η θέση των ανιχνευτών πρέπει να παραµένει στο κέντρο του επιθυµητού καναλιού, κατά τη διάρκεια εγγραφής/ανάγνωσης των δεδοµένων. Η απαίτηση για µεγάλη ακρίβεια στη µετακίνηση πάνω από τη νοητή γραµµή του κέντρου του καναλιού, της µίας ή περισσότερων κεφαλών που χρησιµοποιούνται κατά την εγγραφή/ανάγνωση, είναι σηµαντική για όλους τους τύπους αποθηκευτικών συσκευών. Οι απαιτήσεις για ακρίβεια γίνονται ακόµα πιο µεγάλες και κρίσιµες, στην περίπτωση των υπό µελέτη αποθηκευτικών συσκευών, όπου η ψηφιακή πληροφορία αποθηκεύεται σε µία περιοχή µε µέγεθος µερικών nm. Το σύστηµα ελέγχου, κατά τη λειτουργία αυτή, οφείλει να παρακολουθεί το επιθυµητό σήµα αναφοράς, και ταυτόχρονα να έχει ικανοποιητική απόρριψη των διαταραχών και να επιτυγχάνει την απαιτούµενη ακρίβεια ως προς τον προσδιορισµό της θέσης. Παράλληλα, σηµαντικό παράγοντα βελτιστοποίησης αυτής της λειτουργίας, αποτελεί ο ρυθµός εγγραφής/ανάγνωσης των δεδοµένων. Η πρώτη προσέγγιση για την αρχιτεκτονική ελέγχου, κατά τη λειτουργία αυτή, βασίζεται στην παρεχόµενη από τους θερµικούς αισθητήρες ανίχνευσης, πληροφορία της θέσης του microscanner. Η αρχιτεκτονική βασίζεται στον αλγόριθµο του γραµµικού τετραγωνικού ρυθµιστή (LQG) και η αξιολόγησή της γίνεται µε κριτήρια την ικανότητα παρακολούθησης της εισόδου, την απόρριψη των διαταραχών και την ακρίβεια ως προς τον προσδιορισµό της θέσης. Τα αποτελέσµατα που εξήχθησαν, κατά την υλοποίηση της αρχιτεκτονικής ελέγχου στην πειραµατική διάταξη, αναδεικνύουν ότι η αρχιτεκτονική πληρεί τις απαιτήσεις και η ακρίβεια µερικών nm που επιτυγχάνεται στον προσδιορισµό της θέσης επιτρέπει την αξιόπιστη εγγραφή και κατόπιν ανάγνωση δεδοµένων από την αποθηκευτική συσκευή. Μειονέκτηµα της παραπάνω προσέγγισης αποτελεί ο χαµηλής συχνότητας θόρυβος των θερµικών αισθητήρων, που επηρεάζει τη σωστή λειτουργία του κλειστού συστήµατος σε µεγάλες περιόδους λειτουργίας της συσκευής. Το πρόβληµα αυτό επιλύεται µε µία πρωτότυπη προσέγγιση που αναπτύχθηκε στα πλαίσια της διατριβής και βασίζεται στην πληροφορία, την προερχόµενη από τους θερµικούς αισθητήρες ανίχνευσης θέσης, σε συνδυασµό µε το προερχόµενο από το αποθηκευτικό µέσο σήµα σφάλµατος θέσης. Ο σχεδιασµός του συστήµατος ελέγχου, στην περίπτωση αυτή, εκµεταλλεύεται την εκ των προτέρων γνώση των χαρακτηριστικών θορύβου ως προς τη συχνότητα των δύο αισθητήρων ανίχνευσης θέσης, έτσι ώστε το σύστηµα ελέγχου που προκύπτει να χρησιµοποιεί την πιο αξιόπιστη µέτρηση σε κάθε περιοχή συχνοτήτων. Το πλαίσιο του σθεναρού ελέγχου, H∞, χρησιµοποιείται κατά το σχεδιασµό αυτής της αρχιτεκτονικής ελέγχου, µε διαχωρισµό ως προς τη συχνότητα. Με χρήση αυτής της µεθόδου, το σύστηµα ελέγχου δεν επηρεάζεται από τον χαµηλής συχνότητας θόρυβο των θερµικών αισθητήρων. Τα αποτελέσµατα που εξήχθησαν κατά την υλοποίηση της αρχιτεκτονικής ελέγχου στην πειραµατική διάταξη επιβεβαιώνουν τα παραπάνω. Η µέθοδος αυτή είναι πιο γενική και µπορεί να εφαρµοστεί σε κάθε πρόβληµα ελέγχου, που έχει δύο ή και περισσότερους αισθητήρες µε διαφορετικά χαρακτηριστικά απόδοσης σε διαφορετικές περιοχές συχνοτήτων. / Micro-electro-mechanical-system (MEMS)-based scanning-probe storage devices are emerging as potential ultra-high-density, low-access-time, and low-power alternatives to conventional data storage. One implementation of probe-based storage uses thermomechanical means to store and retrieve information in thin polymer films. Digital information is stored by making indentations on the thin polymer film with the tips of atomic force microscope (AFM) cantilevers, which are a few nanometers in diameter. To increase the data rate, an array of probes is used, in which each probe performs read/write/erase operations over an individual storage field. One of the primary challenges in building such devices is the extreme accuracy and the short latency required in the navigation of the probes over the polymer medium. This dissertation describes the design of novel control architectures and the characterization of their performance. The associated modelling effort, theoretical analysis, simulation work and experimental results are presented. Displacement of the storage medium relative to the array of cantilevers is achieved by using silicon-based micro-scanners with x/y-displacement capabilities. The x/y positional information can be provided by thermal position sensors that are fabricated on the cantilever-array chip and positioned directly above the scan table. A thorough understanding of the dynamics of these parts of the device is essential for effective design and analysis of the control architectures. In this dissertation a complete model of the micro-scanner and the thermal position sensors was developed. Comparison of the model response with the experimental data have shown that the model approximates the system response with an excellent accuracy. In general, the servo system in such a storage device has two functions. First, it locates the target track to which information is to be written or read back from, starting from an arbitrary initial position of the scan table carrying the storage medium. This is achieved by the so-called seek-and-settle procedure. The data access time depends on the duration of this operation, and therefore the minimization of its duration constitutes an important optimization factor. The speed of data access is a significant bottleneck in today’s computing systems. With the advantage of the lighter moving stage MEMS-based storage devices are widely touted to improve access times. In this dissertation these perspectives are examined in detail. Initially the time-optimal control theory has been studied for different system models and their performance has been examined regarding the optimal access time. The results of this study have provided the theoretically optimal access time for each model and its dependence on the system parameters. The control architecture for the seek operation has been designed. The simulation and experimental results show that the possible access times that can be achieved are significantly smaller than the conventional storage devices. The second function of the control system is to maintain the position of the read/write probes on the centre of the target track as they are being scanned along the length of this track during the normal read/write operation. This is achieved by the so-called track-follow procedure. Precise positioning and navigation of the read/write head(s) on the track centerlines is of paramount importance in all types of storage devices. The requirements become more crucial in the devices under study, where in order to achieve reliable storage and retrieval of data, accuracy in the order of a few nanometers in the scanner motion is needed. Therefore, the tracking of the reference signal, the disturbance rejection capabilities and the positioning resolution are considered as performance measures for the control system in this operation. Similarly, the read/write data rate constitutes an important optimization factor for this operation. The first approach of the control architecture for the track-follow procedure uses the position information from the thermal sensors. The control of the position in the x/y directions is realized using two independent feedback loops and each controller is based on the linear quadratic Gaussian regulator (LQG). For the evaluation of the proposed control architecture a detailed analysis has been performed in terms of the tracking performance, the disturbance rejection and the positioning resolution. The proposed architecture has been implemented in the experimental set-up and the analytical results are in agreement with those obtained experimentally. The experimental results show that the accuracy in the motion of the micro-scanner obtained with the proposed control architecture allows reliable storage and retrieval of data in the storage device. The disadvantage of the above control scheme originates from the low frequency noise of the thermal sensors that affects the closed loop performance for long term operation of the device. A novel control architecture was developed that addresses this problem by using medium-derived position information along with the thermal positioning sensor. The objective of this method is, using the a priori knowledge of the noise characteristics of the two sensors, to create a control structure that utilizes the best measurement in different frequency regions. The framework of the H∞ robust control was used for the design of this new frequency separated control architecture. Using this method the control system is not affected from the low frequency noise of the thermal sensors. The experimental results validate the performance of the proposed method. The developed methodology is more general and can be applied to any control problem that has two or more sensors with different performance characteristics in different frequency regions.

Thermodynamic processes in finite time are in general irreversible. But there are chances to avoid irreversibility. For instance, there are canonical ensembles of special quantum systems with a given probability distribution describing the likelihood to find the system at time t=0 in a particular state with energy E_i(0), which can be controlled in a specific way, such that the initial probability distribution is recovered at the end of the process (t=T), but the state energies did change, hence E_i(0) is not equal to E_i(T). This allows to change thermodynamic quantities (expectation values) adiabatically, reversibly and in finite time. Such special processes are called Shortcuts to Adiabaticity. The presented thesis analyzes the origin of these shortcuts utilizing special Hamiltonian systems with dynamical algebra. Their main feature is to provide canonical invariance, which means a canonical ensemble stays canonical under Hamiltonian dynamics. This invariance carried by the dynamical algebra will be discussed using Lie group theory. In addition, the persistence of the dynamical algebra with respect to calculating expectation values will be deduced. This allows to benefit from all intrinsic symmetries within the discussion of ensemble trajectories. In consequence, these trajectories will evolve under Hamiltonian dynamics on a specific manifold given by the so-called Casimir companion. In addition, the deformation of this manifold due to non-Hamiltonian (dissipative) dynamics will be discussed, which allows to present a framework for modeling irreversible processes based on Hamiltonian systems with dynamical algebra. An application of this framework based on the parametric harmonic oscillator will be presented by determining time-optimal controls for transitions between two equilibrium as well as between non-equilibrium and equilibrium states. The latter one will lead to time-optimal equilibration strategies for a statistical ensemble of parametric harmonic oscillators. / Thermodynamische Prozesse in endlicher Zeit sind im Allgemeinen irreversibel. Es gibt jedoch Möglichkeiten, diese Irreversibilität zu umgehen. Ein kanonisches Ensemble eines speziellen quantenmechanischen Systems kann zum Beispiel auf eine ganz spezielle Art und Weise gesteuert werden, sodass nach endlicher Zeit T wieder eine kanonische Besetzungverteilung hergestellt ist, sich aber dennoch die Energie des Systems geändert hat (E(0) ungleich E(T)). Solche Prozesse erlauben das Ändern thermodynamischer Größen (Ensemblemittelwerte) der erwähnten speziellen Systeme in endlicher Zeit und auf eine adiabatische und reversible Art. Man nennt diese Art von speziellen Prozessen Shortcuts to Adiabaticity und die speziellen Systeme hamiltonsche Systeme mit dynamischer Algebra. Die vorliegende Dissertation hat zum Ziel den Ursprung dieser Shortcuts to Adiabaticity zu analysieren und eine Methodik zu entwickeln, die es erlaubt irreversible thermodynamische Prozesse adequat mittels dieser speziellen Systeme zu modellieren. Dazu wird deren besondere Eigenschaft ausgenutzt, die kanonische Invarianz, d.h. ein kanonisches Ensemble bleibt kanonisch bezüglich hamiltonscher Dynamik. Der Ursprung dieser Invarianz liegt in der dynamischen Algebra, die mit Hilfe der Theorie der Lie-Gruppen näher betrachtet wird. Dies erlaubt, eine weitere besondere Eigenschaft abzuleiten: Die Ensemblemittelwerte unterliegen ebenfalls den Symmetrien, die die dynamische Algebra widerspiegelt. Bei näherer Betrachtung befinden sich alle Trajektorien der Ensemblemittelwerte auf einer Mannigfaltigkeit, die durch den sogenannten Casimir Companion beschrieben wird. Darüber hinaus wird nicht-hamiltonsche/dissipative Dynamik betrachtet, welche zu einer Deformation der Mannigfaltigkeit führt. Abschließend wird eine Zusammenfassung der grundlegenden Methodik zur Modellierung irreversibler Prozesse mittels hamiltonscher Systeme mit dynamischer Algebra gegeben. Zum besseren Verständnis wird ein ausführliches Anwendungsbeispiel dieser Methodik präsentiert, in dem die zeitoptimale Steuerung eines Ensembles des harmonischen Oszillators zwischen zwei Gleichgewichtszuständen sowie zwischen Gleichgewichts- und Nichtgleichgewichtszuständen abgeleitet wird.