H∞ Suboptimal Tracking Control for Bilinear Power Converter Systems with Dynamic Feedback - Theory and Experiment

In this thesis, bilinear power converters are considered that arise for state-averaged models in continuous conduction mode. Since such power converters are often not feedback linearizable with respect to the output to be controlled,they are an interesting and demanding class of control systems. One control objective for the considered system class is to include trajectory tracking in the system equations. With a state and input transformation into the so called error system representation, where the error between real variables and reference variables is considered, the error system equations show to be time-varying. Another objective is to cope with disturbances, noise, parameter uncertainties, etc. Therefore, integral feedback is included in the feedback strategy, which leads to input-affine systems with a special structure due to the originally bilinear system equations. A slightly different strategy is a disturbance feedback approach. It addresses the same control objectives, is structurally similar to integral feedback and allows for more freedom in choice of feedback design parameters. However, it is less general and requires online-replanning of the reference trajectory. For state feedback design, we choose H∞ control with a quadratic performance functional since we want to have low control effort and want to keep the error of the output to be controlled small in case of appearing disturbances. Finally, so as to address stability properties in the closed-loop, integral Input-to-State Stability (iISS) theory is a good choice to cope with nonzero disturbances. In order to guarantee stability for the closed-loop system in the presence of disturbances, we link the solution of the nonlinear H control problem with iISS. It is possible to derive conditions, when the suboptimal state feedback H∞ control problem for the bilinear power converter systems with integral feedback / disturbance feedback and trajectory tracking can be solved. At the same time, it can be shown that the closed-loop systems is iISS. To underline the generality of the approach, the obtained theory for bilinear power converter systems is extended to general bilinear systems and it is even possible to discuss the more demanding multiple-input case. Equipped with the required theory to solve the posed control problem, we address the experimental setup of a boost converter / DC motor system. Here, the control task is to track the angular velocity of the motor shaft and attenuate appearing load disturbances. Therefore, we implement disturbance feedback and proof boundedness of trajectories for the online-replanning of the approximate trajectory generation method. Various experiments are presented in order to investigate the applicability of the approach.In der vorliegenden Dissertation werden bilineare Leistungskonvertersysteme untersucht, wie sie für Modellgleichungen mit gemittelten Zuständen im kontinuierlichen Betrieb (engl. "continuous conduction mode")auftreten. Da eine große Zahl dieser Leistungskonverter nicht eingangs-zustandslinearisierbar hinsichtlich des Regelausgangs und dann oft sogar nicht-minimalphasig sind, zählen sie zur Klasse der schwierig zu regelnden Systeme. Ein Regelungsziel für die betrachtete Systemklasse ist die Berücksichtigung von Referenztrajektorien für einen Wunschausgang des Systemmodells. Dazu wird ein sogenanntes Fehlersystem eingeführt, das die Differenz zwischen tatsächlichen Größen und Referenzgrößen widerspiegelt. Aufgrund der Bilinearität der ursprünglichen Modellgleichung ist dieses Fehlersystem dann zeitvariant. Ein weiteres Ziel ist das Ausregeln von auftretenden Störungen, Messrauschen, Modellunsicherheiten, usw., was üblicherweise anhand eines Integratoranteils (kurz: I-Anteils) im Regelgesetz berücksichtigt wird. Ein I-Anteil ist eine dynamische Erweiterung der Zustandsgleichungen und führt zu einem zusätzlichen Zustand. Damit die zusätzliche Differentialgleichung nicht entkoppelt vorliegt, muss mit einer geeigneten Eingangstransformation dafür gesorgt werden, dass der Integriererzustand im Regelgesetz vorkommt. Dadurch wird jedoch die ursprüngliche Bilinearität der Gleichungen zerstört, so dass am Ende ein eingangsaffines System vorliegt, das aber natürlich aufgrund der Bilinearität der ursprünglichen Systemgleichungen eine spezifische Struktur aufweist. Eine ähnliche Herangehensweise wie beim I-Anteil ermöglicht die Schätzung und Rückführung der Störung, womit dieselben Regelungsziele verfolgt werden wie bei der Variante mit dem I-Anteil. Hier führt die dynamische Erweiterung mit dem Schätzer im Gegensatz zum I-Anteil allerdings wieder auf eine bilineare Systemgleichung. Allerdings ist dieser Ansatz weniger allgemein und erfordert eine Neuplanung der Referenztrajektorien in Echtzeit, birgt aber mehr Freiheiten in der Wahl der Reglerparameter für den geschlossenen Regelkreis. Als Rückführstrategie wird eine H∞-Zustandsregelung gewählt, um auftretenden Störungen mit möglichst minimalem Stellaufwand auszuregeln. Außerdem soll gleichzeitig der Fehler des Regelausgangs klein gehalten werden. Um schließlich die Stabilität des geschlossenen Regelkreises für nichtverschwindende Störungen untersuchen zu können, wird die sogenannten integral Input-to-State Stability (iISS) verwendet. Als Ergebnis der Arbeit können Bedingungen formuliert werden, wann eine suboptimale H∞-Zustandsregelung gefunden werden kann. Unter Annahme dieser Bedingungen folgt dann sofort die iISS-Eigenschaft des geschlossenen Regelkreises. Die Allgemeinheit des Verfahrens zeigt sich dadurch, dass es sogar möglich ist, den vorgestellten Ansatz auf allgemeine bilineare Systeme mit mehreren Eingängen zu erweitern. Das experimentelle Beispiel eines Hochsetzstellers in Kombination mit einem Gleichstrommotor wird dann zum Testen des Regelentwurfsverfahrens herangezogen. Dabei ist die Regelungsaufgabe, die Winkelgeschwindigkeit der Motorwelle einer vorgegeben Referenztrajektorie nachfahren zu lassen und auftretende Laststörungenauszuregeln. Dazu wurde die Variante der dynamischen Erweiterung anhand der Rückführung der Störung mit Trajektorienneuplanung verwendet. Mit einer suboptimalen H∞-Zustandsregelung wird der Regelkreis geschlossen, so dass iISS gewährleistet werden kann. Für die Echtzeitgenerierung der durch ein Approximationsverfahren ermöglichten Trajektorienneuplanung wird außerdem Beschränktheit gezeigt. Eine Vielzahl von Experimenten dient der genaueren Untersuchung des Verfahrens

Nanotribological surface characterization by frequency modulated torsional resonance mode AFM

The aim of this work is to develop an experimental method to measure in-plane surface properties on the nanometer scale by torsional resonance mode atomic force microscopy and to understand the underlying system dynamics. The invention of the atomic force microscope (AFM) and the advances in development of new AFM based techniques have significantly enhanced the capability to probe surface properties with nanometer resolution. However, most of these techniques are based on a flexural oscillation of the force sensing cantilever which are sensitive to forces perpendicular to the surface. Therefore, there is a need for highly sensitive measurement methods for the characterization of in-plane properties. To this end, scanning shear force measurements with an AFM provide access to surface properties such as friction, shear stiffness, and other tribological surface properties with nanometer resolution. Dynamic atomic force microscopy utilizes the frequency response of the cantilever-probe assembly to reveal nanomechanical properties of the surface. The frequency response function of a cantilever in torsional motion was investigated by using a numerical model based on the finite element method (FEM). We demonstrated that the vibration of the cantilever in a torsional oscillation mode is highly sensitive to lateral elastic (conservative) and visco-elastic (non-conservative) in-plane material properties, thus, mapping of these properties is possible in the so-called torsional resonance mode AFM (TR-mode). The theoretical results were then validated by implementing a frequency modulation (FM) detection technique to torsion mode AFM. This method allows for measuring both conservative and non-conservative interactions. By monitoring changes of the resonant frequency and the oscillation amplitude, we were able to map elastic properties and dissipation caused by the tip-sample interaction. During approach and retract cycles, we observed a slight negative detuning of the torsional resonance frequency, depending on the tilt angle between the oscillation plane and the surface before contact to the HOPG surface. This angle leads to a mixing of in-plane (horizontal) and out-of-plane (vertical) sample properties. These findings have a significant implication for the imaging process and the adjustment of the microscope and may not be ignored when interpreting frequency shift or energy dissipation measurements. To elucidate the sensitivity of the frequency modulated torsional resonance mode AFM (FM-TR-AFM) for the energy dissipation measurement, different types of samples such as a compliant material (block copolymer), a mineral (chlorite) and a macromolecule (DNA) were investigated. The measurement of energy dissipation on these specimens indicated that the TR-AFM images reveal a clear difference for the domains which have different mechanical properties. Simultaneously a topographic and a chemical contrast are obtained by recording the detuning and the dissipation signal caused by the tip-surface interaction. Using FM-TR-AFM spectroscopically, we investigated frequency shift versus distance curves on the homopolymer polystyrene (PS). Depending on the molecular weight, the frequency detuning curve displayed two distinct regions. Firstly, a rather compliant surface layer was probed; secondly, the less mobile bulk of the polymer was sensed by the oscillatory motion of the tip. The high sensitivity of this technique to mechanical in-plane properties suggests that it can be used to discriminate different chemical properties (e.g. wetting) of the material by simultaneously measuring energy dissipation and surface topography

Theoretical and experimental explorations in atomic force microscopy

Nanotechnology is the capability to build by controlling the arrangement of individual atoms and molecules. Such a technology would be founded on the ability to control, manipulate and investigate matter at the atomic scale. The invention of atomic force microscope (AFM) and the advances in micro-cantilever based scanning probe technology have significantly enhanced the experimental capability to probe and modify matter at the nanoscale. However, it is still severely limited in achieving the necessary bandwidth, sensitivity and resolution. To further the advances in this field an in-depth understanding of the nature and effects of the tip-sample interactions is imperative. A complementary approach involving theoretical investigations and experimental advances is best suited to overcome the current limitations of this technology.;This thesis investigates the atomistic phenomena associated with material modification at the tip-sample contact theoretically because such information is inaccessible to experimental observation. Molecular dynamics studies of nanoindentation of crystalline silicon and gold, representative of semiconductor and metallic substrates, shed light on the mechanics of plastic deformation and defect formation. Silicon undergoes a densification transformation to amorphous phase in the deformed region via the formation of interstitials. In gold a pyramidal defect structure is formed via a three step mechanism consisting of nucleation, glide and reaction of dislocations. This mechanism dictates the dependence of defect structure on the crystallography of the indented surface as observed in experimental studies performed by other researchers.;The experimental studies develop a new small amplitude non-contact AFM technique. In this frequency modulation method, changes in the cantilever\u27s resonance induced by the tip-sample interactions are detected from its thermal noise response. By eliminating the need for positive feedback it enables maintaining an extremely small tip-sample separation for extended periods of time at room temperatures. Consequently, this technique is particularly suited for studying highly localized slowly evolving atomic or molecular scale phenomena at ambient temperatures. The experiments performed in ambient room conditions have achieved tip-sample separations less than 2 nm for time periods in excess of 30 min. At such small separations a narrowband signal at 250 Hz is imaged with a force sensitivity of 14 fN in a bandwidth of 0.4 Hz

Control of nonlinear flexible space structures

With the advances made in computer technology and efficiency of numerical algorithms over last decade, the MPC strategies have become quite popular among control community. However, application of MPC or GPC to flexible space structure control has not been explored adequately in the literature. The work presented in this thesis primarily focuses on application of GPC to control of nonlinear flexible space structures;This thesis is particularly devoted to the development of various approximate dynamic models, design and assessment of candidate controllers, and extensive numerical simulations for a realistic multibody flexible spacecraft, namely, Jupiter Icy Moons Orbiter (JIMO)---a Prometheus class of spacecraft proposed by NASA for deep space exploratory missions;A stable GPC algorithm is developed for Multi-Input-Multi-Output (MIMO) systems. An end-point weighting (penalty) is used in the GPC cost function to guarantee the nominal stability of the closed-loop system. A method is given to compute the desired end-point state from the desired output trajectory. The methodologies based on Fake Algebraic Riccati Equation (FARE) and constrained nonlinear optimization, are developed for synthesis of state weighting matrix. This makes this formulation more practical. A stable reconfigurable GPC architecture is presented and its effectiveness is demonstrated on both aircraft as well as spacecraft model;A representative in-orbit maneuver is used for assessing the performance of various control strategies using various design models. Different approximate dynamic models used for analysis include linear single body flexible structure, nonlinear single body flexible structure, and nonlinear multibody flexible structure. The control laws evaluated include traditional GPC, feedback linearization-based GPC (FLGPC), reconfigurable GPC, and nonlinear dissipative control. These various control schemes are evaluated for robust stability and robust performance in the presence of parametric uncertainties and input disturbances. Finally, the conclusions are made with regard to the efficacy of these controllers and potential directions for future research

Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings.Comment: Revtex, 35 pages, 13 Postscript figures included, in press with New Journal of Physics, Special Issue on The Physics of the Cytoskeleto

Fabrication and characterization of self-sensing and self-actuating piezoresistive microscale silicon cantilevers for an integrated scanning probe microscopy and scanning electron microscopy system

Zum ersten Mal ist eine Kombination aus SPM und REM in einem System mit einem selbstaktuierenden und selbstdektierenden piezoresistiven mikrometerkleinen Siliziumcantilever erfolgreich demonstriert worden. Es ermöglicht hochauflösende AFM- und REM-Aufnahmen. Der Vorteil besteht darin, dass AFM die Topographie der Probenoberfläche liefert, während REM-Aufnahmen nur zweidimensional sind und nicht zwingend deutlich ist, wo sich Berg oder Tal befinden. Die Integration von Aktuation und Detektion in den Cantilever reduziert nicht nur die Größe des AFMs und macht das Lasersystem für die Erfassung der Cantileververbiegung überflüsissig, sondern bietet ein einfach zu bedienendes System, weil der Laserstrahl nicht mehr justiert werden muss. Die Doktorarbeit präsentiert die erste umfassende Charakerisierung der Verhaltens eines selbstaktuierenden und selbstdektierenden piezoresistiven mikrometerkleinen Siliziumcantilevers. Der Verhalten ist von parasitärer Wärme beeinflusst, die von der thermischen Anregung und der Verbiegungserfassung herrührt, von der Luftdämpfung, dem Rauschen und dem Übersprechen. Die lineare Abhängigkeit von der Temperatur und der Anregungsleistung zeigen die Resonanzfrequenz, die Güte, die statische Verbiegung und die Schwingungsampltitude in den Messungen. Auch die Wheatstone-Brücke bringt Temperaturänderung in den Cantilever, die die Resonanzfrequenz stärker beeinflusst als die Anregungsleistung, denn die Brücke ist an einer kritischen Stelle plaziert, wo die mechanische Spannung am größten ist. Die Änderung der Güte und der Schwingungsamplitude mit dem Luftdruck lässt sich in den intrischen, den molekularen und den viskosen Bereich einteilen, während die Resonanzfrequenz linear mit dem Luftdruck abfällt. Ein komplett neues SPM-REM-System mit einem selbstaktuierenden und selbstdektierenden piezoresistiven mikrometerkleinen Siliziumcantilever, das hochauflösende Bilder, Charakterisierung und Manipulation der Probenoberfläche in verschiedenen SPM-Moden ermöglicht, ist präsentiert worden.For the first time, the combination of SPM and SEM within one system using a self-actuating and self-sensing piezoresistive microscale silicon cantilever has been successfully demonstrated. It is capable of high resolution AFM and SEM images. The advantage is that AFM gives the topography of the specimen surface, wheeas the SEM image is only two-dimensional and it is not necessarily clear where there is a hill or a valley. The integration of the actuation and sensing into the cantilever does not only reduce the size of the AFM and make a laser system for beam deflection detection redundant, it also offers an easy-to-use system by obviating the need for laser beam alignment. The PhD thesis presents the first extensive characterization of the performance of the self-sensing and self-actuating piezoresistive microscale silicon cantilever. The performance is influenced by parasitic heating resulting from the thermal beam actuation and deflection detection, by air damping, noise, and cross-talk. The linear temperature and drive power dependency of fundamental frequency, quality factor, deflection at pure beam bending, and maximum amplitude of beam oscillation is demonstrated by measurements. The Wheatstone bridge also introduces a temperature change to the beam, which affects the fundamental frequency more than the drive power does, because the bridge is placed at a crucial position where there is maximum stress. The variation of quality factor and maximum amplitude of beam oscillation in relation to air pressure clearly falls into three regions, intrinsic, molecular and viscous, whereas the fundamental frequency decays linearly with air pressure. A completely new SPM-SEM system with a self-actuating and self-sensing piezoresistive microscale silicon cantilever is presented that is capable of high resolution imaging, characterization, and manipulation in different SPM modes

Non-linear system identification in structural dynamics: advances in characterisation of non-linearities and non-linear modal analysis

Many new methods for theoretical modelling, numerical analysis and experimental testing have been developed in non-linear dynamics in recent years. Although the computational power has greatly improved our ability to predict non-linear behaviour, non-linear system identification, a central topic of this thesis, still plays a key role in obtaining and quantifying structural models from experimental data. The first part of the thesis is motivated by the industrial needs for fast and reliable detection and characterisation of structural non-linearities. For this purpose a method based on the Hilbert transform in the frequency domain is proposed. The method detects and characterises structural non-linearities from a single frequency response function and does not require a priori knowledge of the system. The second part of the thesis is driven by current research trends and advances in non-linear modal analysis and adaptive time series processing using the Hilbert-Huang transform. Firstly, the alternatives of the Hilbert transform, which is commonly used in structural dynamics for the estimation of the instantaneous frequency and amplitude despite suffering from a number of numerical issues, are compared to assess their potential for non-linear system identification. Then, a possible relation between the Hilbert-Huang transform and complex non-linear modes of mechanical systems is investigated. Based on this relation, an approach to experimental non-linear modal analysis is proposed. Since this approach integrates the Hilbert-Huang transform and non-linear modes, it allows not only to detect and characterise structural non-linearities in a non-parametric manner, but also to quantify the parameters of a selected model using extracted non-linear modes. Lastly, a new method for the identification of systems with asymmetric non-linear restoring forces is proposed. The application of all proposed methods is demonstrated on simulated and experimental data.Open Acces

Discriminating between rival biochemical network models: three approaches to optimal experiment design

Background: The success of molecular systems biology hinges on the ability to use computational models to design predictive experiments, and ultimately unravel underlying biological mechanisms. A problem commonly encountered in the computational modelling of biological networks is that alternative, structurally different models of similar complexity fit a set of experimental data equally well. In this case, more than one molecular mechanism can explain available data. In order to rule out the incorrect mechanisms, one needs to invalidate incorrect models. At this point, new experiments maximizing the difference between the measured values of alternative models should be proposed and conducted. Such experiments should be optimally designed to produce data that are most likely to invalidate incorrect model structures. Results: In this paper we develop methodologies for the optimal design of experiments with the aim of discriminating between different mathematical models of the same biological system. The first approach determines the 'best' initial condition that maximizes the L2 (energy) distance between the outputs of the rival models. In the second approach, we maximize the L2-distance of the outputs by designing the optimal external stimulus (input) profile of unit L2-norm. Our third method uses optimized structural changes (corresponding, for example, to parameter value changes reflecting gene knock-outs) to achieve the same goal. The numerical implementation of each method is considered in an example, signal processing in starving Dictyostelium amœbæ. Conclusions: Model-based design of experiments improves both the reliability and the efficiency of biochemical network model discrimination. This opens the way to model invalidation, which can be used to perfect our understanding of biochemical networks. Our general problem formulation together with the three proposed experiment design methods give the practitioner new tools for a systems biology approach to experiment design. </p

Parameter identification for biological models

This thesis concerns the identification of dynamic models in systems biology. and is structured into two parts. Both parts concern building dynamic models from observed data, but are quite different in perspective, rationale and mathematics. The first part considers the development of novel identification techniques that are particularly tailored to (molecular) biology and considers two approaches. The first approach reformulates the parameter estimation problem as a feasibility problem. This reformulation allows the invalidation of models by analysing entire parameter regions. The second approach utilises nonlinear observers and a transformation of the model equations into parameter free coordinates. The parameter free coordinates allow the design of a globally convergent observer, which in turn estimates the parameter values, and further, allows to identify modelling errors or unknown inputs/influences. Both approaches are bottom up approaches that require a mechanistic understanding of the underlying processes (in terms of a biochemical reaction network) leading to complex nonlinear models. The second part is an example of what can be done with classical, well developed tools from systems identification when applied to hitherto unattended problems.In particular, part two of my thesis develops a modelling framework for rat movements in an experimental setup that it widely used to study learning and memory.The approach is a top down approach that is data driven resulting in simple linear models