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This work addresses issues in energy harvesting that have plagued the potential use of harvesting through the piezoelectric effect at the MEMS scale. Effective energy harvesting devices typically consist of a cantilever beam substrate coated with a thin layer of piezoceramic material and fixed with a tip mass tuned to resonant at the dominant frequency of the ambient vibration. The fundamental natural frequency of a beam increases as its length decreases, so that at the MEMS scale the resonance condition occurs orders of magnitude higher than ambient vibration frequencies rendering the harvester ineffective. Here we study two new geometries for MEMS scale cantilever harvesters. The zigzag and spiral geometries have low fundamental frequencies which can be tuned to the ambient vibrations. The second issue in energy harvesting is the frequency sensitivity of the linear vibration harvesters. A nonlinear hybrid energy harvester is presented that has a wide frequency bandwidth and large power output. Finally, linear and nonlinear energy harvesting devices are designed for powering the cardiovascular pacemakers using the vibrations in the chest area induced by the heartbeats. The mechanical and electromechanical vibrations of the zigzag structure are analytically modeled, verified with Rayleigh's method, and validated with experiments. An analytical model of coupled bending torsional vibrations of spiral structure is presented. A novel approximation method is developed for analyzing the electromechanical vibrations of energy harvesting devices. The unified approximation method is effective for linear, nonlinear mono-stable, and nonlinear bi-stable energy harvesting. It can also be utilized for piezoelectric, electromagnetic or hybrid energy harvesters. The approximation method accurately approximates the effect of energy harvesting on vibrations of energy harvester with changes in damping ratio and excitation frequency. Experimental investigations are performed to verify the analytical model of the nonlinear hybrid energy harvester. A detailed experimental parametric study of the nonlinear hybrid design is also performed. Linear and nonlinear energy harvesting devices have been designed that can generate sufficient amounts of power from the heartbeat induced vibrations. The nonlinear devices are effective over a wide range of heart rate. / Ph. D.

This dissertation addresses fundamental theoretical problems relevant to flight control for aerial vehicles and weapons in highly uncertain dynamical environment. The approach taken in this dissertation is the L1 adaptive control, which is elaborated from its design perspective for output feedback solution and is extended to time-varying reference systems to support augmentation of gain-scheduled baseline controllers. Compared to conventional adaptive controllers, L1 control has the following advantages: i) it has guaranteed uniformly bounded transient response for system's both signals, input and output; ii) it enables fast adaptation while maintains a bounded away from zero time-delay margin. The proposed adaptive control approach can recover the nominal performance of the flight control systems in the presence of rapid variation of uncertainties. Furthermore, the benefit of L1 adaptive control is its promise for development of theoretically justified tools for Verification and Validation (V&V) of adaptive systems. Adaptive control for uncertain systems usually needs to handle two types of uncertainties: matched and unmatched uncertainties. Both of these two uncertainties will appear in practical flight control problems. In this dissertation, adaptive approaches which can compensate for these two types of uncertainties will be discussed respectively. Two architectures of L1 adaptive control, namely L1 state feedback adaptive control and L1 output feedback adaptive control, are studied. The state feedback adaptive control is applied for compensation of matched uncertainties. Although the state feedback scheme is capable of handling certain type of unmatched uncertainties, such approach is not explored in this dissertation. On the other hand, the output feedback approach is mainly aimed to solve problems in the presence of unmatched uncertainties. The dissertation first discusses the state feedback L1 adaptive control for time-invariant reference systems. The adaptive controller is designed to augment an existing baseline controller. The closed loop system of the plant and the baseline controller is time-invariant. This closed loop system, which is a Linear Time Invariant (LTI) system, determines the dynamics of the reference system. The adaptive feedback can compensate for nonlinear state- and time-dependent uncertainty with uniformly bounded transient response. In this dissertation we discuss the Multi-Input Multi-Output (MIMO) extension of the method. Two flight control examples,Unmanned Combat Aerial Vehicle (UCAV) and Aerial Refueling Autopilot, are considered in the presence of nonlinear uncertainties and control surface failures. The L1 adaptive controller without any redesign leads to scaled response for system's both signals, input and output, dependent upon changes in the initial conditions, system parameters and uncertainties. The time-delay margin analysis for these two examples verifies the theoretical claims. Next, the output feedback approach is studied. The adaptive output feedback controller can be applied to reference systems that do not verify the Strict Positive Real (SPR) condition for their input-output transfer function. In this dissertation, specific design guidelines are presented that render the approach suitable for practical applications. A missile autopilot design example is given to demonstrate the benefits of the design approach. Finally, the L1 state feedback adaptive controller is extended to time-varying reference systems. The adaptive controller intends to augment a gain-scheduled baseline controller. The reference system, which is determined by the closed loop system of the plant and the baseline gain-scheduled controller, is time-varying. The adaptive controller with time-varying reference system is proved to have guaranteed performance bounds similar to those obtained for the case of linear time-invariant reference systems. With this result, the aerial refueling application can be extended to a complete scenario, which includes a racetrack maneuver for an aircraft. The concluding chapter discusses the challenging issues for future research. / Ph. D.

The state-space realization problem is a very basic and fundamental problem of control theory. The topic is also becoming increasingly important as practitioners of both physical and social sciences find it crucial to model very complex systems based on input-output data only. In this thesis, a review of the topic will be given for general nonlinear systems and for the less general linear case as well. The thesis will also present some new theoretical results that contribute to the development of the state-space realization topic. Specifically, an important result will show that if a system can be identified by an input-output equation of a particular form, which is fairly general, then a state-space realization can always be easily derived directly from the input-output map. Finally, the theory will be applied to find a state-space model for a nonlinear hydraulic system based on its input-output data.

Thesis (MEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: The growth in intelligent control has primarily been a reaction to the realisation that nonlinear control theory has been unable to provide practical solutions to present day control challenges. Consequently the chemical industry may be cited for numerous instances of overdesign, which result as an attempt to avoiding operation near or within complex (often more economically viable) operating regimes. Within these complex operating regimes robust control system performance may prove difficult to achieve using conventional (algorithmic) control methodologies. Biological neuronal control mechanisms demonstrate a remarkable ability to make accurate generalisations from sparse environmental information. Neural networks, with their ability to learn and their inherent massive parallel processing ability, introduce numerous opportunities for developing superior control structures for complex nonlinear systems. To facilitate neural network learning, reinforcement learning techniques provide a framework which allows for learning from direct interactions with a dynamic environment. lts promise as a means of automating the knowledge acquisition process is beguiling, as it provides a means of developing control strategies from cause and effect (reward and punishment) interaction information, without needing to specify how the goal is to be achieved. This study aims to establish evolutionary reinforcement learning as a powerful tool for developing robust neurocontrollers for application in highly nonlinear process systems. A novel evolutionary algorithm; Symbiotic, Adaptive Neuro-Evolution (SANE), is utilised to facilitate neurocontroller development. This study also aims to introduce SANE as a means of integrating the process design and process control development functions, to obtain a single comprehensive calculation step for maximum economic benefit. This approach thus provides a tool with which to limit the occurrence of overdesign in the process industry. To investigate the feasibility of evolutionary reinforcement learning in achieving these aims, the SANE algorithm is implemented in an event-driven software environment (developed in Delphi 4.0), which may be applied for both simulation and real world control problems. Four highly nonlinear reactor arrangements are considered in simulation studies. As a real world application, a novel batch distillation pilot plant, a Multi-Effect Batch Distillation (MEBAD) column, was constructed and commissioned. The neurocontrollers developed using SANE in the complex simulation studies, were found to exhibit excellent robustness and generalisation capabilities. In comparison with model predictive control implementations, the neurocontrollers proved far less sensitive to model parameter uncertainties, removing the need for model mismatch compensation to eliminate steady state off-set. The SANE algorithm also proved highly effective in discovering the operating region of greatest economic return, while simultaneously developing a neurocontroller for this optimal operating point. SANE, however, demonstrated limited success in learning an effective control policy for the MEBAD pilot plant (poor generalisation), possibly due to limiting the algorithm's search to a too small region of the state space and the disruptive effects of sensor noise on the evaluation process. For industrial applications, starting the evolutionary process from a random initial genetic algorithm population may prove too costly in terms of time and financial considerations. Pretraining the genetic algorithm population on approximate simulation models of the real process, may result in an acceptable search duration for the optimal control policy. The application of this neurocontrol development approach from a plantwide perspective should also have significant benefits, as individual controller interactions are so doing implicitly eliminated. / AFRIKAANSE OPSOMMING: The huidige groei in intelligente beheerstelsels is primêr 'n reaksie op die besef dat nie-liniêre beheerstelsel teorie nie instaat is daartoe om praktiese oplossings te bied vir huidige beheer kwelkwessies nie. Gevolglik kan talle insidente van oorontwerp in die chemiese nywerhede aangevoer word, wat voortvloei uit 'n poging om bedryf in of naby komplekse bedryfsgebiede (dikwels meer ekonomies vatbaar) te vermy. Die ontwikkeling van robuuste beheerstelsels, met konvensionele (algoritmiese ) beheertegnieke, in die komplekse bedryfsgebiede mag problematies wees. Biologiese neurobeheer megamsmes vertoon 'n merkwaardige vermoë om te veralgemeen vanaf yl omgewingsdata. Neurale netwerke, met hulle vermoë om te leer en hulle inherente paralleie verwerkingsvermoë, bied talle geleenthede vir die ontwikkeling van meer doeltreffende beheerstelsels vir gebruik in komplekse nieliniêre sisteme. Versterkingsleer bied a raamwerk waarbinne 'n neurale netwerk leer deur direkte interaksie met 'n dinamiese omgewing. Versterkingsleer hou belofte in vir die inwin van kennis, deur die ontwikkeling van beheerstrategieë vanaf aksie en reaksie (loon en straf) interaksies - sonder om te spesifiseer hoe die taak voltooi moet word. Hierdie studie beaam om evolutionêre versterkingsleer as 'n kragtige strategie vir die ontwikkeling van robuuste neurobeheerders in nie-liniêre prosesomgewings, te vestig. 'n Nuwe evolutionêre algoritme; Simbiotiese, Aanpasbare, Neuro-Evolusie (SANE), word aangewend vir die onwikkeling van die neurobeheerders. Hierdie studie beoog ook die daarstelling van SANE as 'n weg om prosesontwerp en prosesbeheer ontwikkeling vir maksimale ekonomiese uitkering, te integreer. Hierdie benadering bied dus 'n strategie waardeur die insidente van oorontwerp beperk kan word. Om die haalbaarheid van hierdie doelwitte, deur die gebruik van evolusionêre versterkingsleer te ondersoek, is die SANE algoritme aangewend in 'n Windows omgewing (ontwikkel in Delphi 4.0). Die Delphi programmatuur geniet toepassing in beide die simulasie en werklike beheer probleme. Vier nie-liniêre reaktore ontwerpe is oorweeg in die simulasie studies. As 'n werklike beheer toepassing, is 'n nuwe enkelladingsdistillasie kolom, 'n Multi-Effek Enkelladingskolom (MEBAD) gebou en in bedryf gestel. Die neurobeheerders vir die komplekse simulasie studies, wat deur SANE ontwikkel is, het uitstekende robuustheid en veralgemeningsvermoë ten toon gestel. In vergelyking met model voorspellingsbeheer implementasies, is gevind dat die neurobeheerders heelwat minder sensitief is vir model parameter onsekerheid. Die noodsaak na modelonsekerheid kompensasie om gestadigde toestand afset te elimineer, word gevolglik verwyder. The SANE algoritme is ook hoogs effektief vir die soek na die mees ekonomies bedryfstoestand, terwyl 'n effektiewe neurobeheerder gelyktydig vir hierdie ekonomies optimumgebied ontwikkel word. SANE het egter beperkte sukses in die leer van 'n effektiewe beheerstrategie vanaf die MEBAD toetsaanleg getoon (swak veralgemening). Die swak veralgemening kan toegeskryf word aan 'n te klein bedryfsgebied waarin die algoritme moes soek en die negatiewe effek van sensor geraas op die evaluasie proses. Vir industriële applikasies blyk dit dat die uitvoer van die evolutionêre proses vanaf 'n wisselkeurige begintoestand nie koste effektief is in terme van tyd en finansies nie. Deur die genetiese algoritme populasie vooraf op 'n benaderde modelop te lei, kan die soek tydperk na 'n optimale beheerstrategie aansienlik verkort word. Die aanwending van die neurobeheer ontwikkelingstrategie vanuit 'n aanlegwye oogpunt mag aanleiding gee tot aansienlike voordele, aaangesien individuele beheerder interaksies sodoende implisiet uitgeskakel word.

Until very recently, synthetic chemistry has focussed on the creation of chemical entities with desirable properties through the programmed application of isolated chemical reactions, either individually or in a cascade that afford a target compound selectively. By contrast, biological systems operate using a plethora of complex interconnected signaling and metabolic networks with multiple checkpoint controls and feedback loops allowing biological systems to adapt and respond rapidly to external stimuli. Systems chemistry attempts to capture the complexity and emergent phenomena prevalent in the life sciences within a wholly synthetic chemical framework. In this approach, complex phenomena are expressed by a group of synthetic chemical entities designed to interact and react with many partners within the ensemble in programmed ways. In this manner, it should be possible to create synthetic chemical systems whose properties are not simply the linear sum of the attributes of the individual components. Chapter 1 discusses the role of complex networks in various aspects of chemistry- related research from the origin of life to nanotechnology. Further, it introduces the concept of Systems chemistry, giving various examples of dynamic covalent networks, self-replicating systems and molecular logic gates, showing the applications of complex system research. Chapter 2 discusses the components of replicator design. Further, it introduces a network based on recognition mediated reactions that is implemented by length- segregation of the substrates and displays properties of self-sorting. Chapter 3 presents a fully addressable chemical system based on auto- and cross- catalytic properties of product templates. The system is described by Boolean logic operations with different template inputs giving different template outputs. Chapter 4 introduces a dynamic network which fate is determined by a single recognition event. The replicator is capable of exploiting and dominating the exchanging pool of reagents in order to amplify its own formation at the expense of other species through the non-linear kinetics inherent in minimal replication. Chapter 5 focuses on the development of complex dynamic systems from structurally simple molecules. The new approach allows creating multicomponent networks with many reaction pathways operating simultaneously from readily available substrates.

With an ongoing desire to improve product performance, in combination with the continuously growing complexity of engineering structures, there is a need for well-tested and reliable engineering tools that can aid the decision making and facilitate an efficient and effective product development. The technical assessment of the dynamic characteristics of mechanical systems often relies on linear analysis techniques which are well developed and generally accepted. However, sometimes the errors due to linearization are too large to be acceptable, making it necessary to take nonlinear effects into account. Many existing analysis techniques for nonlinear mechanical systems build on the assumption that the input excitation of the system is periodic and deterministic. This often results in highly inefficient analysis procedures when nonlinear mechanical systems are studied in a non-deterministic environment where the excitation of the system is stochastic. The aim of this thesis is to develop and validate new efficient analysis methods for the theoretical and experimental study of nonlinear mechanical systems under stochastic excitation, with emphasis on two specific problem areas; forced response simulation and system identification from measurement data. A fundamental concept in the presented methodology is to model the nonlinearities as external forces acting on an underlying linear system, and thereby making it possible to use much of the linear theories for simulation and identification. The developed simulation methods utilize a digital filter to achieve a stable and condensed representation of the linear subparts of the system which is then solved recursively at each time step together with the counteracting nonlinear forces. The result is computationally efficient simulation routines, which are particularly suitable for performance predictions when the input excitation consist of long segments of discrete data representing a realization of the stochastic excitation of the system. Similarly, the presented identification methods take advantage of linear Multiple-Input-Multiple-Output theories for random data by using the measured responses to create artificial inputs which can separate the linear system from the nonlinear parameters. The developed methods have been tested with extensive numerical simulations and with experimental test rigs with promising results. Furthermore, an industrial case study of a wave energy converter, with nonlinear characteristics, has been carried out and an analysis procedure capable of evaluating the performance of the system in non-deterministic ocean waves is presented.