This thesis deals with complete design and manufacturing of autonomous two wheeled self-balancing robot. The goal of this thesis is to maintain the robot in up-right position and to follow black line using camera. The robot is controlled using Raspberry Pi and driven by DC motors. This thesis includes the design and implementation of hardware and software parts. Subsequently there was created the dynamic model in Matlab/Simulink. Based on this model, the LQR and PID controller was designed.

The thesis introduces an overview of techniques for filtering of unobserved variables using a state-space representation of a model and state inequality constraints. It is mainly aimed at a derivation of the linear Kalman filter, its extension into a form of a non-linear filter and imposing state constraints. The state uniform model with noise bounds and the sequential importance sampling, as a method of particle filters using Monte Carlo simulations, are described as alternative methods. These three methods are applied on a simple semi-structural model for a monetary policy analysis. The filtration is based on Czech macroeconomic data and reflects an imposed non-negative state constraint on the interest rate. Results of the algorithms are compared and discussed.

The dissertation consists of three papers which apply Bayesian econometric techniques to monitoring macroeconomic and macro-financial developments in the economy. Its aim is to illustrate how Bayesian methods can be employed in standard areas of economic research (estimating systemic risk in the banking sectors, nowcasting GDP growth) and also in a more original area (monitoring developments in sovereign bond markets). In the first essay, we address a task which analytical departments in central banks or commercial banks face very often - nowcasting foreign demand of a small open economy. On the example of the Czech economy, we propose an approach to nowcast foreign GDP growth rates for the Czech economy. For presentation purposes, we focus on three major trading partners: Germany, Slovakia and France. We opt for a simple method which is very general and which has proved successful in the literature: the method based on bridge equation models. A battery of models is evaluated based on a pseudo-real- time forecasting exercise. The results for Germany and France suggest that the models are more successful at backcasting, nowcasting and forecasting than the naive random walk benchmark model. At the same time, the various models considered are more or less successful depending on the forecast horizon....

This thesis aims to investigate the possibility of using a mathematical model to detect several common faults in a hydraulic rock drill. To this end, a parameterized state space model of the hydraulic drill, which simulate its behavior, is created. The model parameters are divided into two categories where different estimation methods are used to determine their values. The first category consists mainly of the parameters that are assumed to be invariant and independent of the various operating conditions. Experimental data are used to estimate these parameters. The other category is the variables that change depending on the machine’s current condition and operating settings. These include the response from the rock and internal leakages in the hydraulic drill. These parameters are estimated by integrating the impact piston position measurements in the simulation algorithm. The model is simulated for different fault modes, and the resulting estimated parameters are studied. It is shown that the resulting distributions for some of the estimated parameters differ between the fault modes, which makes fault detection possible. Furthermore, a condition monitoring system based on the estimated parameters provided by the model is designed and evaluated. It is shown that the performance and the robustness of the monitoring system depend on the machine’s operating settings and condition, where the system performs best for an operating pressure of 220 bar and the internal cylinder leakages.

Controlling a high-dimensional dynamical system with continuous state and action spaces in a partially unknown environment like a gas turbine is a challenging problem. So far often hard coded rules based on experts´ knowledge and experience are used. Machine learning techniques, which comprise the field of reinforcement learning, are generally only applied to sub-problems. A reason for this is that most standard RL approaches still fail to produce satisfactory results in those complex environments. Besides, they are rarely data-efficient, a fact which is crucial for most real-world applications, where the available amount of data is limited. In this thesis recurrent neural reinforcement learning approaches to identify and control dynamical systems in discrete time are presented. They form a novel connection between recurrent neural networks (RNN) and reinforcement learning (RL) techniques. RNN are used as they allow for the identification of dynamical systems in form of high-dimensional, non-linear state space models. Also, they have shown to be very data-efficient. In addition, a proof is given for their universal approximation capability of open dynamical systems. Moreover, it is pointed out that they are, in contrast to an often cited statement, well able to capture long-term dependencies. As a first step towards reinforcement learning, it is shown that RNN can well map and reconstruct (partially observable) MDP. In the so-called hybrid RNN approach, the resulting inner state of the network is then used as a basis for standard RL algorithms. The further developed recurrent control neural network combines system identification and determination of an optimal policy in one network. In contrast to most RL methods, it determines the optimal policy directly without making use of a value function. The methods are tested on several standard benchmark problems. In addition, they are applied to different kinds of gas turbine simulations of industrial scale.

Avec l'évolution des technologies, la complexité des systèmes informatiques ne cesse de s'accroître. Parmi ces systèmes, on retrouve les logiciels critiques qui doivent offrir une garantie de sûreté de fonctionnement qui s'avère crucial et pour lesquels un dysfonctionnement peut avoir des conséquences graves. Les méthodes formelles fournissent des outils permettant de garantir mathématiquement l'absence de certaines erreurs. Ces méthodes sont indispensables pour assurer les plus hauts niveaux de sûreté. Mais l'application de ces méthodes sur un code système bas niveau se heurte à des difficultés d'ordre pratique et théorique. Les principales difficultés concernent la prise en compte des aspects bas niveau, comme les pointeurs et les interactions avec le matériel spécifique. De plus, le fait que ces systèmes soient concurrents conduit à une augmentation exponentielle du nombre de comportements possibles, ce qui rend plus difficile leur vérification. Dans cette thèse, nous proposons une méthodologie pour la spécification et la vérification par model-checking de ce type de systèmes, en particulier, ceux implémentés en C. Cette méthodologie est basée sur la traduction de la sémantique de C en TLA+, un langage de spécification formel adapté à la modélisation de systèmes concurrents. Nous avons proposé un modèle de mémoire et d'exécution d'un programme C séquentiel en TLA+. En se basant sur ce modèle, nous avons proposé un ensemble de règles de traduction d'un code C en TLA+ que nous avons implémenté dans un outil, appelé C2TLA+. Nous avons montré comment ce modèle peut s'étendre pour modéliser les programmes C concurrents et gérer la synchronisation entre plusieurs processus ainsi que leur ordonnancement. Pour réduire la complexité du model-checking, nous avons proposé une technique permettant de réduire significativement la complexité de la vérification. Cette réduction consiste pour un code C à agglomérer une suite d'instructions lors de la génération du code TLA+, sous réserve d'un ensemble de conditions.Nous avons appliqué la méthodologie proposée dans cette thèse sur un cas d'étude réel issu de l'implémentation d'un micronoyau industriel,sur lequel nous avons vérifié un ensemble de propriétés fonctionnelles. L'application de la réduction a permis de réduire considérablement le temps de la vérification, ce qui la rend utilisable en pratique.Les résultats ont permis d'étudier le comportement du système, de vérifier certaines propriétés et de trouver des bugs indétectables par des simples tests. / Software systems are critical and complex. In order to guarantee their correctness, the use of formal methodsis important. These methods can be defined as mathematically based techniques, languages and tools for specifying and reasoning about systems. But, the application of formal methods to software systems, implemented in C, is challenging due to the presence of pointers, pointer arithmetic andinteraction with hardware. Moreover, software systems are often concurrent, making the verification process infeasible. This work provides a methodology to specify and verify C software systems usingmodel-checking technique. The proposed methodology is based on translating the semantics of Cinto TLA+, a formal specification language for reasoning about concurrent and reactive systems. We define a memory and execution model for a sequential program and a set of translation rules from C to TLA+ that we developed in a tool called C2TLA+. Based on this model, we show that it can be extended to support concurrency, synchronization primitives and process scheduling. Although model-checking is an efficient and automatic technique, it faces the state explosion problem when the system becomes large. To overcome this problem, we propose a state-space reduction technique. The latter is based on agglomerating a set of C instructions during the generation phase of the TLA+ specification. This methodology has been applied to a concrete case study, a microkernel of an industrial real-time operating system, on which a set of functional properties has been verified. The application of the agglomeration technique to the case study shows the usefulness of the proposed technique in reducing the complexity of verification. The obtained results allow us to study the behavior of the system and to find errors undetectable using traditional testing techniques.

No description available.

abstract: Behavior-driven obesity has become one of the most challenging global epidemics since the 1990s, and is presently associated with the leading causes of death in the U.S. and worldwide, including diabetes, cardiovascular disease, strokes, and some forms of cancer. The use of system identification and control engineering principles in the design of novel and perpetually adaptive behavioral health interventions for promoting physical activity and healthy eating has been the central theme in many recent contributions. However, the absence of experimental studies specifically designed with the purpose of developing control-oriented behavioral models has restricted prior efforts in this domain to the use of hypothetical simulations to demonstrate the potential viability of these interventions. In this dissertation, the use of first-of-a-kind, real-life experimental results to develop dynamic, participant-validated behavioral models essential for the design and evaluation of optimized and adaptive behavioral interventions is examined. Following an intergenerational approach, the first part of this work aims to develop a dynamical systems model of intrauterine fetal growth with the prime goal of predicting infant birth weight, which has been associated with subsequent childhood and adult-onset obesity. The use of longitudinal input-output data from the “Healthy Mom Zone” intervention study has enabled the estimation and validation of this fetoplacental model. The second part establishes a set of data-driven behavioral models founded on Social Cognitive Theory (SCT). The “Just Walk” intervention experiment, developed at Arizona State University using system identification principles, has lent a unique opportunity to estimate and validate both black-box and semiphysical SCT models for predicting physical activity behavior. Further, this dissertation addresses some of the model estimation challenges arising from the limitations of “Just Walk”, including the need for developing nontraditional modeling approaches for short datasets, as well as delivers a new theoretical and algorithmic framework for structured state-space model estimation that can be used in a broader set of application domains. Finally, adaptive closed-loop intervention simulations of participant-validated SCT models from “Just Walk” are presented using a Hybrid Model Predictive Control (HMPC) control law. A simple HMPC controller reconfiguration strategy for designing both single- and multi-phase intervention designs is proposed. / Dissertation/Thesis / Doctoral Dissertation Chemical Engineering 2021

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2022 / Using the ARFIMA (autoregressive and fractionally integrated moving aver age) model extended with sGARCH (standard generalised autoregressive con ditional heteroscedasticity) and ’gjrGARCH (Glosten-Jagannathan-Runkle gen eralised autoregressive conditional heteroscedascity) innovations, fractional in tegration approach and state space model, this study has empirically examined persistency of inflation dynamics of Ghana and South Africa, the only two coun tries in Sub-Saharan Africa with Inflation Targeting (IT) monetary policy. The first part of the analysis employed monthly CPI (Consumer Price Index) in flation series for the period January 1971 to October 2014 obtained from the Bank of Ghana (BoG), and for the period January 1995 to December 2014 ob tained from Statistics South Africa. The second part involves the estimation of threshold effect of inflation on economic growth using annual data obtained from the IMF (International Monetary Fund) database for the period 1981 to 2014, for both countries. Results from the study showed that structural breaks, long memory and non linearities (or regime shifts) are largely responsible for inflation persistence, hence the ever-changing nature of inflation rates of Ghana and South Africa. ARFIMA(3,0.35,1)-‘gjrGARCH(1,1) under Generalised Error Distribution (GED) and ARFIMA(3,0.50,1)-‘gjrGARCH(1,1) under Student-t Distribution (STD) mod els provided the best fit for persistence in the conditional mean (or level) of CPI for Ghana and South Africa, respectively. The results from these models pro vided evidence of time-varying conditional mean and volatility in CPI inflation rates of both countries. The two models also revealed an asymmetric effect of inflationary shocks, where negative shocks appear to have greater impact than positive shocks, in terms of persistence on the conditional mean with time varying volatility. This thesis proposes a model that combines fractional integration with non linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa. We tested for non-linear deterministic terms in the context of fractional integration and esti mated the fractional differencing parameters, d to be 1.11 and 1.32 respectively, for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. New ev idence from this thesis depicts that inflation rate of Ghana is highly persistent and non-mean reverting, with an estimated fractional differencing parameter, d > 1.0, and will therefore require some policy action to steer inflation back to stability. However, the South African inflation series was found to be a cyclical process with an order of integration estimated to be d = 0.7, depicting mean reversion, with the length of the cycles approximated to last for 80 months. Finally, the thesis incorporated structural breaks, long memory, non-linearity, and some explanatory variables into a state space model and estimated the threshold effect of inflation on economic growth. The empirical results suggest that inflation below the estimated levels of 9% and 6% for Ghana and South Africa respectively, will be conducive for economic growth. The policy implications of these results for both countries are as follows. First, both series had similar properties responsible for inducing inflation persistence such as structural breaks, non-linearities, long memory and asymmetric re sponse to negatives shocks - but with varied degrees of magnitude. For both countries, the conditional mean and unobserved components such as volatility for both countries were found to be time-varying. This thesis, therefore, recom mends to the BoG and the South African Reserve Bank (SARB) - responsible for monetary policies, and the Finance Ministers of both governments - respon sible for fiscal policies, to take the above-mentioned properties into account in the formulation of their monetary policies. Second, the thesis recommends that the BoG and the SARB consolidate the IT policy, since keeping inflation below the targets set of 9% and 6%, respectively for Ghana and South Africa, will boost economic growth. Third, policymakers could also design measures (monetary and fiscal policies) such as increase in interest rates, credit control, and reduction of unnecessary expenditure, among others, to control inflation due to its adverse effects on market volatility. Even though an increase in interest rates could assist in curtailing the recent and anticipated increase in inflation rates in both countries, where targets have been missed by Ghana and South Africa, it will also be prudent to legislate monetary policies around demand-supply side since the problem of both coun tries appears to be more of a structuralist than a monetarist. It is, therefore, recommended that both countries tighten the IT monetary policy in order to re duce inflation persistence. This will eventually impact on poverty and income distribution with ramifications for economic growth and/or development. The fourth implication of these results is that governments and central banks should be mindful of the actions and decisions they take, in the sense that unguarded decisions and unnecessary alarms could raise uncertainties in the economy, which could, in turn, affect the future trajectory of inflation. Finally, the thesis recommends that governments of both countries strengthen the pri vate sector, which is the engine of growth. For small and open economies such as Ghana and South Africa, this will grow the economy through job creation and restore investor confidence. / National Research Foundation (NRF), Department of Science and Technology (DST), Telkom’s Tertiary Education Support Programme (TESP) and the NRF-DST Centre of Excellence for Mathematical and Statistical Sciences (CoE-MaSS)

Die vorliegende Arbeit ist motiviert durch die breite Anwendung von Schwenkantrieben in vielfältigen konventionellen und neuen Technologiefeldern: In Windenergieanlagen führen Schwenkantriebe die Gondel samt Rotor der momentanen Windrichtung nach. Bei Radioteleskopen erlauben sie die hochpräzise azimutale Ausrichtung der Parabolantenne. Und im Sektor der Baumaschinen kommen sie zum Schwenken der Ausleger von Kranen und fördertechnischen Großgeräten zum Einsatz. Trotz des zunächst einfach erscheinenden Aufbaus der Schwenkantriebssysteme erweisen sich sowohl ihre mechanische Dimensionierung als auch ihre sichere Betriebsführung als herausfordernd. So belegen Messdaten und Betriebserfahrungen die Neigung der Antriebsstränge zu niederfrequenten Drehschwingungen. Außerdem treten große Spitzenlasten während der Schwenkrichtungsumkehr in den Getriebestufen auf. In diesem Forschungsbeitrag werden Methoden vorgestellt, mit denen elektromechanische Schwenkantriebssysteme modelliert, dynamisch analysiert und regelungstechnisch optimiert werden können. Dazu wird der schwingungsfähige mechanische Antriebsstrang eines Beispielschwenkwerks als detailliertes Mehrkörpersystem-Simulationsmodell abgebildet. Um auch Wechselwirkungen mit den elastischen Umgebungsstrukturen, der Antriebsregelung und den Betriebslasten zu erfassen, wird ein domänenübergreifendes Modellierungsvorgehen verfolgt. Es erfolgt eine messtechnische Validierung des mechatronischen Gesamtsystemmodells. Mit dem Vorliegen treffsicherer Systemmodelle eröffnet sich die Möglichkeit, ein modellbasiertes Mehrgrößenregelverfahren (LQG) auszulegen und simulativ zu erproben. Im Vergleich zur bisherigen proportional-integralen (PI) Antriebsregelung verspricht dies die aktive Dämpfung von Triebstrangschwingungen bei gleichzeitiger Erhöhung der Arbeitsgeschwindigkeit. Um für beliebige elastische Antriebssysteme das Optimierungspotenzial abschätzen zu können, erfolgt ein systematischer Vergleich der beiden Regelstrategien. Anschließend wird ein praxisnahes Vorgehen zur Regelungsauslegung vorgestellt. Besonderer Fokus liegt neben der Robustheit auch auf der begrenzten Anzahl verfügbarer Sensoren bei industriellen Antrieben. Zudem wird auch das oftmals beträchtliche Getriebespiel als signifikante Nichtlinearität der Regelstrecke berücksichtigt. Um eine Reduktion der Spitzenlasten während der Drehrichtungsumkehr des Schwenkantriebes zu erreichen, wird abschließend ein Konzept zur zeit- und belastungsoptimierten Durchquerung des Getriebespiels erarbeitet. Da die konventionelle Drehzahlregelung des Schwenkantriebs hierbei nur um ein Zusatzmodul erweitert wird, bietet sich das Vorgehen insbesondere zur Ertüchtigung bestehender Antriebe an.:1 Einleitung 1.1 Motivation 1.2 Konkretisierte Problemstellung 1.3 Aufbau der Arbeit 2 Grundlagen und Forschungsstand 2.1 Modellbildung und Simulation von Antriebssystemen 2.1.1 Mehrkörpersystem-Simulation von Antriebssystemen 2.1.2 Modellbildung von Schwenkwerken 2.2 Anwendungsbereiche von Schwenkantrieben 2.2.1 Turmdrehkrane 2.2.2 Windenergieanlagen 2.2.3 Radioteleskope 2.2.4 Baumaschinen 2.3 Untersuchtes Beispielschwenkwerk 2.3.1 Antriebstechnik 2.3.2 Bisherige Untersuchungen an Schaufelradbaggern 3 Modellbildung und Simulation von Schwenkwerken 3.1 Mechanische Komponenten 3.1.1 Schwenkantriebe 3.1.2 Elastische Tragstrukturen am Getriebeausgang 3.1.3 Weitere Antriebsstränge des Gesamtsystems 3.2 Elektrische und informationsverarbeitende Domäne 3.2.1 Aktorik – Elektrische Antriebsmaschine 3.2.2 Informationsverarbeitung – Antriebsregelung 3.2.3 Informationserfassung – Winkelmesssysteme 3.3 Betriebslasten 3.3.1 Quasistatische Lasten 3.3.2 Simulation der bodenmechanischen Interaktion bei Schaufelradbaggern 3.4 Messdatengestützte Validierung der Systemmodelle 3.4.1 Beschreibung des Messaufbaus 3.4.2 Betriebsschwingungsanalyse 3.4.3 Validierung Schwenkwerk – Reversiervorgang 3.4.4 Validierung Gesamtsystem – Grab-Schwenk-Prozess 3.5 Ableitung eines mechanischen Minimalmodells 3.6 Zwischenfazit 4 Drehzahlregelung elastischer Antriebssysteme 4.1 Allgemeine Grundlagen 4.1.1 Führungs- und Störungsverhalten 4.1.2 Stabilität und Performanz 4.1.3 Singulärwertzerlegung von Frequenzgangmatrizen 4.2 Motor mit elastisch gekoppeltem Abtrieb 4.2.1 Proportional-Integrale Eingrößenregelung 4.2.2 Zustandsregelung 4.2.3 Generalisierter Vergleich der Regelungskonzepte 4.3 Erweiterung auf Mehrmotorenantriebe 4.4 Konzeption und Umsetzung einer Zustandsregelung 4.4.1 Auslegung eines optimalen Zustandsreglers 4.4.2 Rekonstruktion des Zustandsvektors bei Antrieben mit Verzahnungsspiel 4.4.3 Analyse des Gesamtkonzeptes 4.5 Zwischenfazit 5 Verzahnungsspiel in elastischen Antriebssträngen 5.1 Ursachen 5.2 Modellbildung 5.2.1 Klassische Modellierung als Totzone 5.2.2 Erweitertes Spielmodell nach Nordin 5.2.3 Hysterese 5.3 Auswirkungen 5.3.1 Antriebsstrangbelastung 5.3.2 Folgen auf Gesamtsystemebene 5.3.3 Zwischenfazit 5.4 Regelstrategien für spielbehaftete Antriebe 5.4.1 Lineare Eingrößenregelung 5.4.2 Mehrgrößenregelung – Zustandsraummethoden 5.4.3 Umschaltende lineare Regler 5.4.4 Modellprädiktive Regelung 5.4.5 Invertierung der Nichtlinearität 5.4.6 Zwischenfazit 5.5 Konzeption und Umsetzung einer Strategie zum lastminimierten Spieldurchlauf 5.5.1 Optimaltrajektorie zur Spieldurchquerung 5.5.2 Realisierung der Spieldurchquerung 5.5.3 Simulative Verifizierung 6 Zusammenfassung und Ausblick / The present work is motivated by the wide application of slewing drives and yaw drives in a variety of conventional and emerging fields of technology: In wind turbines, yaw drives track the nacelle and rotor according to the current wind direction. In radio telescopes, they enable high-precision azimuthal alignment of the parabolic antenna. And in the construction machinery sector, they are used to rotate the booms of cranes and bucket wheel excavators. At first glance the design of slewing drive systems seems to be simple, but their mechanical dimensioning as well as their reliable operation turn out to be challenging. Measurement data and operating experience show that the drive trains are prone to low-frequency torsional vibrations. In addition, large peak loads occur during reversals of the slewing direction. In this thesis, methods are presented for the modeling, dynamical analysis and control optimization of electromechanical slewing drive systems. Therefore, the mechanical drive train of an exemplary slewing gearbox unit is represented as a detailed multibody system simulation model. A cross-domain modeling approach is pursued in order to capture interactions with the surrounding flexible structures, the drive control and the operating loads as well. The resulting overall mechatronic system model is validated by measurement. The development of accurate system models enables a model-based multivariable control method (LQG) to be designed and tested by simulation. Compared to conventional proportional integral (PI) drive control, this promises active damping of drive train vibrations while simultaneously increasing the operating speed. To estimate the optimization potential for arbitrary elastic drive systems, a systematic comparison of both control strategies is performed. Subsequently, a practical procedure for designing the control system is presented. In addition to robustness, special focus is placed on the limited number of available sensors in industrial drives. Furthermore, the considerable gear backlash is also accounted for as a significant nonlinearity of the controlled system. To reduce peak loads during the reversal of the rotational direction, a novel approach for time- and load-optimized traversing of the gearbox backlash is developed. Since the conventional speed control algorithm is only extended by an additional module, the method is particularly suitable for retrofitting existing drives.:1 Einleitung 1.1 Motivation 1.2 Konkretisierte Problemstellung 1.3 Aufbau der Arbeit 2 Grundlagen und Forschungsstand 2.1 Modellbildung und Simulation von Antriebssystemen 2.1.1 Mehrkörpersystem-Simulation von Antriebssystemen 2.1.2 Modellbildung von Schwenkwerken 2.2 Anwendungsbereiche von Schwenkantrieben 2.2.1 Turmdrehkrane 2.2.2 Windenergieanlagen 2.2.3 Radioteleskope 2.2.4 Baumaschinen 2.3 Untersuchtes Beispielschwenkwerk 2.3.1 Antriebstechnik 2.3.2 Bisherige Untersuchungen an Schaufelradbaggern 3 Modellbildung und Simulation von Schwenkwerken 3.1 Mechanische Komponenten 3.1.1 Schwenkantriebe 3.1.2 Elastische Tragstrukturen am Getriebeausgang 3.1.3 Weitere Antriebsstränge des Gesamtsystems 3.2 Elektrische und informationsverarbeitende Domäne 3.2.1 Aktorik – Elektrische Antriebsmaschine 3.2.2 Informationsverarbeitung – Antriebsregelung 3.2.3 Informationserfassung – Winkelmesssysteme 3.3 Betriebslasten 3.3.1 Quasistatische Lasten 3.3.2 Simulation der bodenmechanischen Interaktion bei Schaufelradbaggern 3.4 Messdatengestützte Validierung der Systemmodelle 3.4.1 Beschreibung des Messaufbaus 3.4.2 Betriebsschwingungsanalyse 3.4.3 Validierung Schwenkwerk – Reversiervorgang 3.4.4 Validierung Gesamtsystem – Grab-Schwenk-Prozess 3.5 Ableitung eines mechanischen Minimalmodells 3.6 Zwischenfazit 4 Drehzahlregelung elastischer Antriebssysteme 4.1 Allgemeine Grundlagen 4.1.1 Führungs- und Störungsverhalten 4.1.2 Stabilität und Performanz 4.1.3 Singulärwertzerlegung von Frequenzgangmatrizen 4.2 Motor mit elastisch gekoppeltem Abtrieb 4.2.1 Proportional-Integrale Eingrößenregelung 4.2.2 Zustandsregelung 4.2.3 Generalisierter Vergleich der Regelungskonzepte 4.3 Erweiterung auf Mehrmotorenantriebe 4.4 Konzeption und Umsetzung einer Zustandsregelung 4.4.1 Auslegung eines optimalen Zustandsreglers 4.4.2 Rekonstruktion des Zustandsvektors bei Antrieben mit Verzahnungsspiel 4.4.3 Analyse des Gesamtkonzeptes 4.5 Zwischenfazit 5 Verzahnungsspiel in elastischen Antriebssträngen 5.1 Ursachen 5.2 Modellbildung 5.2.1 Klassische Modellierung als Totzone 5.2.2 Erweitertes Spielmodell nach Nordin 5.2.3 Hysterese 5.3 Auswirkungen 5.3.1 Antriebsstrangbelastung 5.3.2 Folgen auf Gesamtsystemebene 5.3.3 Zwischenfazit 5.4 Regelstrategien für spielbehaftete Antriebe 5.4.1 Lineare Eingrößenregelung 5.4.2 Mehrgrößenregelung – Zustandsraummethoden 5.4.3 Umschaltende lineare Regler 5.4.4 Modellprädiktive Regelung 5.4.5 Invertierung der Nichtlinearität 5.4.6 Zwischenfazit 5.5 Konzeption und Umsetzung einer Strategie zum lastminimierten Spieldurchlauf 5.5.1 Optimaltrajektorie zur Spieldurchquerung 5.5.2 Realisierung der Spieldurchquerung 5.5.3 Simulative Verifizierung 6 Zusammenfassung und Ausblick