Dynamiken för en starkt accelerande robot har modellerats. Modellen linjäriseras så att roboten beskrivs som ett linjärt tidsvariabelt system. Denna representation beskriver roboten väl då robotens anblåsningsvinkel, vilket är vinkeln mellan robotkroppen och robotens hastighet, är liten. Eftersom det ej är möjligt att mäta alla robotens tillstånd har en observatör tagits fram i form av ett Kalmanfilter. Problematik vid framtagandet av observatören diskuteras i rapporten. Den linjära tidsvariabla modellen har använts till att ta fram två regulatorer. En LQ-regulator och en H∞-regulator. Hur dessa tas fram och vilka problem som finns diskuteras i rapporten. För att kunna se fördelar och nackdelar beträffande prestanda och robusthet har en mängd tester gjort. Testerna visar på olika fördelar hos de olika reglersystemen. Till exempel är det lättare att få bra prestanda med LQ-regulatorn än H∞-regulatorn om systemet som styrs stämmer bra överens med systemet som använts vid reglerdesignen. H∞-regulatorn har bättre förmåga att anpassa sig till modellförändringar givet att observatören gör bra skattningar. Det är dock svårt att utnämna en generell vinnare.

The objective of adaptive control is to design a controller that can adjust its behaviour to tolerate uncertain or time-varying parameters. An adaptive controller typically consists of a linear time-invariant (LTI) compensator together with a tuning mechanism which adjusts the compensator parameters and yields a nonlinear controller. Because of the nonlinearity, the transient closed-loop behaviour is often poor and the control signal may become unduly large. Although the initial objective of adaptive control was to deal with time-varying plant parameters, most classical adaptive controllers cannot handle rapidly changing parameters. Recently, the use of a linear periodic (LP) controller has been proposed as a new approach in the field of model reference adaptive control [1]. In this new approach, instead of estimating plant parameters, the “ideal control signal” (what the control signal would be if the plant parameters and states were measurable) is estimated. The resulting controller has a number of desirable features: (1) it handles rapid changes in the plant parameters, (2) it provides nice transient behaviour of the closed-loop system, (3) it guarantees that the effect of the initial conditions declines to zero exponentially, and (4) it generates control signals which are modest in size. Although the linear periodic controller (LPC) has the above advantages, it has some imperfections. In order to achieve the desirable features, a rapidly varying control signal and a small sampling period are used. The rapidly time-varying control signal requires fast actuators which may not be practical. The second weakness of the LPC [1] is poor noise rejection behaviour. The small sampling period results in large controller gains and correspondingly poor noise sensitivity, since there is a clear trade-off between tracking and noise tolerance. As the last drawback, this controller requires knowledge of the exact plant relative degree. Here we extend this work in several directions: (i) In [1], the infinity-norm is used to measure the signal size. Here we redesign the controller to yield a new version which provides comparable results when the more common 2-norm is used to measure signal size, (ii) A key drawback of the controller of [1] is that the control signal moves rapidly. Here we redesign the control law to significantly alleviate this problem, (iii) The redesigned controller can handle large parameter variation and in the case that the sign of high frequency gain is known, the closed-loop system is remarkably noise-tolerant, (iv) We prove that in an important special case, we can replace the requirement of knowledge of the exact relative degree with that of an upper bound on the relative degree, at least from the point of view of providing stability, and (v) A number of approaches to improve the noise behaviour of the controller are presented. Reference: [1] D. E. Miller, “A New Approach to Model Reference Adaptive Control”, IEEE Transaction on Automatic Control, Vol. 48, No. 5, pages 743-756, May 2003.

<p>This thesis is divided in to two different parts. The first part includes examination of the measurementsystem of an industrial robot using a resolver sensor. The main focus is on methods for suppressing noise in the angularvelocity signal without increasing timedelay. Five different methods are investigated. Three of these are based on oversampling: burstsamplingmethod, meanvaluemethod and correlationmethod. The meanvaluemethod and the correlationmethod have given good results. The two other methods are: extended kalmanfiltering and computation of the angular velocity without using numeric method to compute the angle. Extended kalmanfilter gives the overall best result. </p><p>In part two the control structure design of an industrial robot has been studied and how different sampling times and motorinertias affect the disturbance rejection and stability of the control loop. Different control structure designs have also been studied with the aim to suppress disturbances. Mainly H-infinity and GIMC designs have been compared with an ordinary PID controller. Here it can be shown that both the H-infinity and the GIMC controller yields good disturbance rejection. But both the methods lack in the robustness of model uncertainty.</p>

This paper presents the development of building up a controlled MEMS acceleration sensor. The first samples have archived a resolution of better than 500 ug and a bandwidth of more than 200 Hz. A theoretical model is built from the physical principles of the complete sensor system, consisting of the MEMS sensor, the charge amplifier and the PWM driver for the sensor element. A reduced order model of the system is used to design a robust control with the Mixed-Sensitivity H-infinity Approach. Limitations for the control design are given since the system contains time delays and an unstable pole imposed by the electrostatic spring softening effect. The theoretical model might be inaccurate or lacks of completeness, because the parameters for the theoretical model building vary from sample to sample or might be not known. A new two-stage identification scheme is deployed to obtain directly the system parameters from the samples. The focus of this paper is the complete system development and identification process including practical tests in a DSP TI-TMS320C3000 environment with 12/14-bit A/D-D/A converters. / Der Artikel beschreibt die Entwicklungsschritte eines geregelten MEMS-Beschleunigungssensors. Die ersten Prototypen erreichten dabei eine Auflösung von weniger als 500 ug und eine Bandbreite von mehr als 200 Hz. Ein theoretisches Modell für den Reglerentwurf wird aus den physikalischen Zusammenhängen des Gesamtsystems, bestehend aus dem mechanischen Sensorelement, dem Ladungsverstärker und der PWM-Treiberstufe, gebildet. Für den Reglerentwurf wird der H-Infinity Mixed-Sensitivity Approach verwendet. Wegen Systemtotzeiten und dem Effekt der elektrostatischen Federerweichung sind Grenzen für die Wahl der Bandbreite zu beachten. Da Parameter für das theoretische Modell stark variieren oder schwer zu bestimmen sind, wird eine 2-Stufen-Identifikationsmethode vorgeschlagen, um ein Modell für den Reglerentwurf zu erhalten. Praktische Tests wurden mit einem DSP TI-TMS320C3000 mit 12/14-Bit A/D-D/A Wandlerstufen durchgeführt.

Extremely large telescopes (ELTs) are the next generation of ground-based reflecting telescopes of optical wavelengths. ELTs possess an aperture of more than 20 meters and share a number of common features, particularly the use of a segmented primary mirror and the use of adaptive optics systems. In 2005, the European Southern Observatory introduced a new giant telescope concept, named the European Extremely Large Telescope (E-ELT), which is scheduled for operation in 2018. The E-ELT will address key scientific challenges and will aim for a number of notable firsts, including discovering Earth-like planets around other stars in the ``habitable zones'' where life could exist, attempting to uncover the relationship between black holes and galaxies, measuring the properties of the first stars and galaxies, and probing the nature of dark matter and dark energy. In 2009, a feasibility study, conducted by National Instruments, proved the feasibility of the real-time (RT) control system architecture for the E-ELT's nearly 1,000 mirror segments with 3,000 actuators and 6,000 sensors. The goal of the RT control system was to maintain a perfectly aligned field of mirrors at all times with a loop-time of 1 ms. The study assumed a prescribed controller algorithm. This research report prescribes the optimal controller algorithms for large segmented telescopes. In this respect, optimal controller designs for the primary mirror of the E-ELT, where optimality is formulated in the [H-2] and [H-infinity] frameworks are derived. Moreover, the designed controllers are simulated to show that the desired performance metrics are met. / text

Στην παρούσα διδακτορική διατριβή αναλύθηκαν και μελετήθηκαν διάφορα συστήματα (ΗμΕ) προκειμένου να παρουσιαστεί η μοντελοποίηση τους. Κατά τη μοντελοποίηση αυτή, μελετήθη-καν τα χαρακτηριστικά τους και αναλύθηκε η συμπεριφορά τους. Στη συνέχεια, αναπτύχθηκαν νόμοι ελέγχου, οι οποίοι εφαρμόστηκαν στα συστήματα των ΗμΕ προκειμένου να επιτευχθεί ο έλεγχος της συμπεριφοράς τους. Αναλυτικότερα τα ζητήματα με τα οποία ασχολήθηκε η διατριβή αυτή παρουσιάζονται παρακάτω. Αρχικά πραγματοποιήθηκε η μοντελοποίηση των κάτωθι συστημάτων ΗμΕ: α) ένα σύστημα ΗμΕ του κυρίαρχου βαθμού ελευθερίας, β) ένα σύστημα ΗμΕ δύο βαθμών ελευθερίας και γ) ένα σύστημα ΗμΕ του κυρίαρ-χου βαθμού ελευθερίας στη μοντελοποίηση του οποίου λαμβάνεται υπόψιν η παρουσία του αέρα. Στη συνέχεια της διδακτορικής αυτής παρουσιάζονται και αναλύονται οι ελεγκτές οι οποίοι αναπτύχθηκαν και χρησιμοποιήθηκαν για τη μελέτη των συστημάτων αυτών και οι οποίοι είναι οι εξής: α) ένας Σθεναρός PID ελεγκτής, β) ένας Σθεναρός Η-infinity ελεγκτής, γ) ένας Σθεναρός Διακοπτικός PID ελεγκτής και δ) ένας H-infinity ελεγκτής προκαθορισμένων κερδών. Από την εφαρμογή των προτεινόμενων νόμων ελέγχου στα συστήματα ΗμΕ προκύπτουν τα αποτελέσματα της διδακτορικής αυτής διατριβής. Τα αποτελέσματα αυτά χωρίζονται σε δύο κατηγορίες. Αρχικά σε αυτά που αφορούν τη συμπεριφορά και τα χαρακτηριστικά των συστημάτων των ΗμΕ και στη συνέχεια σε αυτά τα οποία σχετίζονται με την εφαρμογή των νόμων ελέγχου στα συστήματα των ΗμΕ. Η κύρια συνεισφορά της διδακτορικής διατριβής αναφέρεται τόσο στην πρόταση νέων τεχνικών ελέγχου για τα συστήματα των ΗμΕ καθώς και η εφαρμογή με επιτυχία των τεχνικών αυτών στα συστήματα τα οποία μελετήθηκαν κατά τη διεκπόνηση της διατριβής. / In the present Phd thesis different systems of Electrostatic micro Actuators (EmA) have been presented and analyzed. During the modeling process the systems have been observed in order to provide the special characteristics and the special behavior of each model. In addition special control laws have been presented in order to control the movement of the movable parts of the EmAs. In general the main issues of this PhD thesis are presented in the sequel. Firstly the modeling of the following EmAs is presented: a) an EmA whose one plate is moving parallel to the x-axis b) an EmA whose plate is moving parallel to the x-axis and is also making an angular rotation c) an EmA system with squeezed film damping effects (presence of air between the moving surfaces). In the sequel the control laws that have been designed for the aforementioned systems are presented. The designed controllers are: a) a Robust PID controller b) a Robust Switching PID controller c) a robust Η-infinity controller and d) a robust Gain Scheduled H-infinity controller. In the last part of this thesis, the simulation results are presented concering both the behavior of the systems as well as the results provided by the application of the control laws.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

La présente étude est une analyse et une reconstruction interprétative de la centurie de Calliste Cataphygiotès, intitulée De l'union avec Dieu et de la vie contemplative, chapitres syllogistiques et hauts. Notre approche à ce texte pluridisciplinaire est prioritairement philosophique. Dans le but de mettre en valeur l'intérêt philosophique qu'il représente, nous avons concentré notre analyse sur les problèmes liés au rapport de l'intellect avec l'Un, sur l'étude du concept de l'infini, sur son rôle dans la contemplation et sur la méthode dialectique dont Calliste Cataphygiotès s'en sert. Nous avons reconstruit la doctrine de la contemplation, implicite au texte de Calliste et nous avons tenté une reconstruction globale de la centurie qui permettra au lecteur d'apprécier les qualités spéculatives et l'esprit synthétique de ce mystique byzantin presque inconnu. / The present study is an analysis and an interpretative reconstruction of Callistus Cataphygiotes's syllogistic chapters, entitled The union with God and the contemplative life. Our approach to this multidisciplinary text is primarily philosophical. In order to emphasize the philosophical aspect of the text we focused our analysis on issues related to the concept of infinity, its role in contemplation, the relation of the intellect with the One, as well as the dialectical method used by Callistus Cataphygiotes. We rebuilt the doctrine of contemplation, implied in the text of Callistus and we tried to do a complete reconstruction of the text that will allow the reader to appreciate the speculative and the synthetic spirit of this almost unknown Byzantine mystic.

Composed entirely of runes, the 14th century manuscript Codex Runicus is comprised of 101 sheets and contains historical documents such as "Kings until Erik Menved" and "Boundaries between Denmark and Sweden." The end of the codex contains the oldest surviving Nordic music fragment with lyrical text "Drømde mik en drøm i nat um silki ok ærlik pæl" which translates as [I] dreamt me a dream last night of silk and lovely cloth. This melody, alongside three Norwegian folk slåttar written for fiddle, Fjellbekken (The Mountain Stream), Fjøllrosa (The Mountain Rose), and Syrgjefuen (The Bird of Sorrow), is used to generate the pitch material for this composition for string orchestra, english horn and french horn. The piece is contrapuntal in nature. A large portion of the work is formed from essentially five groups or layers of melody that comfortably co-exist towards, as well as away from, each other, their independent natures being most evident in the first half of the piece. Additionally, there are fluctuations within each group itself, for examples, forms of imitation, slippage, change in register, variation in playing technique, and micro-displays of rhythmic independence set against more heterophonic textures (Considerable use of rhythmic embellishment is derived from the ornamental style found in harding fiddle slåttar). Such micro-fluctuations further distinguish the texture-intentional orchestration of each group. Although the use of layered melody forms the framework for the entire composition, there is continual exploration of its possibilities through various parameters such as density vs. transparency, and continuation vs. fragmentation.

Composed entirely of runes, the 14th century manuscript Codex Runicus is comprised of 101 sheets and contains historical documents such as "Kings until Erik Menved" and "Boundaries between Denmark and Sweden." The end of the codex contains the oldest surviving Nordic music fragment with lyrical text "Drømde mik en drøm i nat um silki ok ærlik pæl" which translates as [I] dreamt me a dream last night of silk and lovely cloth. This melody, alongside three Norwegian folk slåttar written for fiddle, Fjellbekken (The Mountain Stream), Fjøllrosa (The Mountain Rose), and Syrgjefuen (The Bird of Sorrow), is used to generate the pitch material for this composition for string orchestra, english horn and french horn. The piece is contrapuntal in nature. A large portion of the work is formed from essentially five groups or layers of melody that comfortably co-exist towards, as well as away from, each other, their independent natures being most evident in the first half of the piece. Additionally, there are fluctuations within each group itself, for examples, forms of imitation, slippage, change in register, variation in playing technique, and micro-displays of rhythmic independence set against more heterophonic textures (Considerable use of rhythmic embellishment is derived from the ornamental style found in harding fiddle slåttar). Such micro-fluctuations further distinguish the texture-intentional orchestration of each group. Although the use of layered melody forms the framework for the entire composition, there is continual exploration of its possibilities through various parameters such as density vs. transparency, and continuation vs. fragmentation.