Tesi sul tema "Actuators Saturation"

La thèse est consacrée au développement d'une méthodologie de stabilité et de stabilisation pour les systèmes linéaires paramètres-dépendants et à retard soumis à la saturation de la commande. Dans le processus industriel, l'amplitude du signal de commande est généralement limitée par les contraintes de sécurité, les limites du cycle physique, etc. Pour cette raison, un outil de synthèse et d'analyse approprié est nécessaire pour décrire avec précision les caractéristiques des systèmes saturés à paramètres linéaires variables. Dans la première partie, une forme dépendante des paramètres de la condition de secteur généralisée (GSC) est considérée pour résoudre le problème de stabilisation saturée. Plusieurs stratégies de contrôle de rétroaction sont étudiées pour stabiliser les systèmes LPV/qLPV saturés. Conditions de stabilisation nécessaires et suffisantes via la formulation d'inégalité matricielle linéaire paramétrée proposée pour les contrôleurs de retour d'état conformes aux exigences de conception (c'est-à-dire l'ensemble admissible des conditions initiales, la région estimée du domaine de convergence asymptotique, la stabilité et les performances robustes sous l'influence des perturbations, etc.). La relaxation des PLMI conçus est illustrée par les résultats de comparaison à l'aide d'une fonction de Lyapunov dépendante des paramètres. Dans la deuxième partie, les développements de stabilité dépendant du délai basés sur la fonctionnelle de Lyapunov-Krasovskii (LKF) sont présentés. Les techniques modernes de limitation avancées sont utilisées avec un équilibre entre conservatisme et complexité de calcul. Ensuite, des analyses de stabilisation de saturation pour les contrôleurs d'ordonnancement de gain. Inspirée des méthodes de système à retard incertain, une nouvelle condition de stabilisation est dérivée de l'analyse de stabilisation dépendante du retard pour le système à retard LPV soumis à des contraintes de saturation. Dans cet aspect, les contrôleurs de rétroaction à programmation de gain stabilisants améliorent les performances et la stabilité du système saturé et fournissent un grand domaine d'attraction. On peut souligner que la formulation dérivée est générale et peut être utilisée pour le contrôle de la conception de nombreux systèmes dynamiques. Enfin, pour maximiser la région d'attraction tout en garantissant la stabilité asymptotique du système en boucle fermée, un problème d'optimisation est inclus dans la stratégie de conception de commande proposée
The dissertation is devoted to developing a methodology of stability and stabilization for the linear parameter-dependent (PD) and time-delay systems (TDSs) subject to control saturation. In the industrial process, control signal magnitude is usually bounded by the safety constraints, the physical cycle limits, and so on. For this reason, a suitable synthesis and analysis tool is needed to accurately describe the characteristics of the saturated linear parameter-varying (LPV) systems. In the part one, a parameter-dependent form of the generalized sector condition (GSC) is considered to solve the saturated stabilization problem. Several feedback control strategies are investigated to stabilize the saturated LPV/qLPV systems. Necessary and sufficient stabilization conditions via the parameterized linear matrix inequality (PLMI) formulation proposed for the feedback controllers conforming to the design requirements (i.e., the admissible set of the initial conditions, the estimated region of the asymptotic convergence domain, the robust stability and performance with the influence of perturbations, Etc.). The relaxation of the designed PLMIs is shown through the comparison results using a parameter-dependent Lyapunov function (PDLF). In the second part, the delay-dependent stability developments based on Lyapunov-Krasovskii functional (LKF) are presented. The modern advanced bounding techniques are utilized with a balance between conservatism and computational complexity. Then, saturation stabilization analyzes for the gain-scheduling controllers. Inspired by uncertain delay system methods, a novel stabilization condition is derived from the delay-dependent stabilizing analysis for the LPV time-delay system subject to saturation constraints. In this aspect, the stabilizing gain-scheduling feedback controllers improve the performance and stability of the saturated system and provide a large attraction domain. It can be emphasized that the derived formulation is general and can be used for the design control of many dynamic systems. Finally, to maximize the attraction region while guaranteeing the asymptotic stability of the closed-loop system, an optimization problem is included to the proposed control design strategy

Event-triggered control is a recent approach in control theory which aims at reducing the communication load in networked control systems by adapting the communication among the components to the current needs. In more detail, the information exchange over the feedback link only takes place if certain event conditions, that guarantee a desired control performance, are satisfied. This thesis analyzes the consequences of actuator saturation on the stability of the event-triggered control loop. Based on linear matrix inequalities, stability criteria have been derived which can be used to determine regions in the state space that guarantee a stable behavior. Furthermore, the existence of a lower bound on the minimum inter-event time is shown. Due to integrator windup, actuator saturation may severely degrade the performance of the event-triggered closed-loop system. In order to overcome this problem, the stability criteria have been extended by incorporating a static anti-windup structure. Finally, the effects of transmission delays in the feedback link are analyzed and a procedure to deal with their consequences is proposed. The results are illustrated by simulations and by experiments with a wirelessly controlled first-order tank system.

This thesis extends the use of neural-network-based model reference adaptive control to systems that occur as cascades. In general, these systems are not feedback linearizable. The approach taken is that of approximate feedback linearization of upper subsystems whilst treating the lower-subsystem states as virtual actuators. Similarly, lower-subsystems are also feedback linearized. Typically, approximate inverses are used for linearization purposes. Model error arising from the use of an approximate inverse is minimized using a neural-network as an adaptive element. Incorrect adaptation due to (virtual) actuator saturation and dynamics is avoided using the Pseudocontrol Hedging method. Using linear approximate inverses and linear reference models generally result in large desired pseudocontrol for large external commands. Even if the provided external command is feasible (null-controllable), there is no guarantee that the reference model trajectory is feasible. In order to mitigate this, nonlinear reference models based on nested-saturation methods are used to constrain the evolution of the reference model and thus the plant states. The method presented in this thesis lends itself to the inner-outer loop control of air vehicles, where the inner-loop controls attitude dynamics and the outer-loop controls the translational dynamics of the vehicle. The outer-loop treats the closed loop attitude dynamics as an actuator. Adaptation to uncertainty in the attitude, as well as the translational dynamics, is introduced, thus minimizing the effects of model error in all six degrees of freedom and leading to more accurate position tracking. A pole-placement approach is used to choose compensator gains for the tracking error dynamics. This alleviates timescale separation requirements, allowing the outer loop bandwidth to be closer to that of the inner loop, thus increasing position tracking performance. A poor model of the attitude dynamics and a basic kinematics model is shown to be sufficient for accurate position tracking. In particular, the inner-outer loop method was used to control an unmanned helicopter and has subsequently been applied to a ducted-fan, a fixed-wing aircraft that transitions in and out of hover, and a full-scale rotorcraft. Experimental flight test results are also provided for a subset of these vehicles.

Thesis (MScEng)--University of Stellenbosch, 2000.
ENGLISH ABSTRACT: A unified method is proposed to treat saturation in both Multi-Input-Multi-Output MIMO and Single-Input-Single-Output controllers. This method offers superior performance over existing MIM 0 anti-saturation schemes. The anti-saturation problem is posed as a linear programming problem. A practical and efficient implementation of the algorithm is developed by transforming the problem into its dual linear programming form. The problem, in dual form, is then solved using the dual simplex method rather than the primal simplex method. The nature of the problem when expressed in dual form and the properties of the dual simplex method are harmonised to guarantee an initial basic feasible solution and an optimal bounded final solution in a finite, predictable and minimal number of iterations. The resultant controller never saturates, hence cannot windup. Furthermore the resultant controller always applies the optimal control effort to the plant to minimise the error signal input as follows: • The controller is governed such that while the future free response combined with the present forced response of the controller results in no saturation limits being exceeded, now or at some time in the future, the normal linear response of the controller prevails. • When the future free response combined with the present forced response of the controller will result in a saturation limit being reached, now or at some time in the future, the present time input signal into the controller is optimally governed to prevent the saturation limit from being exceeded at any future time.
AFRIKAANSE OPSOMMING: 'n Metode word voorgestel waarmee versadiging in enkel-inset enkel-uitset en meer-inset meeruitset (MIMU) stelsels beheer kan word. Die metode presteer beter as ander huidige teenversadiging- maatreels vir (MIMU) beheerders. Die teen-versadigings-probleem word as 'n lineere programmeringsprobleem herformuleer. 'n Praktiese en effektiewe implementering van die algoritme word verkry deur die probleem na die duale vorm te transformeer. Die probleem, in duale vorm, word opgelos met die duale simplex metode, in plaas van die direkte metode. Die eienskappe van hierdie formulering is 'n gewaarborgde, aanvanklike, bereikbare oplossing en 'n optimale, begrensde, finale oplossing in 'n eindige, voorspelbare en minimum aantal stappe. Die uiteindelike beheerder versadig nooit nie, en wen gevolglik nie op nie. Die beheerder wend altyd die optimale aanleg-inset aan om die foutsein te minimeer soos volg: • Wanneer die nul-inset gedrag saam met die huidige inset-gedrag geen beperkings nou of in die toekoms saloorskry nie, word geen beperkende aksie geneem nie, en tree die beheerder dus lineer op. • Sodra die toekomstige nul-inset gedrag saam met die huidige inset-gedrag, nou of later versadiging sou veroorsaak, word die huidige inset tot die beheerder optimaal begrens om latere versadiging te voorkom.

Actuator saturation is a well studied subject regarding control theory. However, little research exist regarding aircraft behavior during actuator saturation. This paper aims to identify flight mechanical parameters that can be useful when analyzing actuator saturation. The studied aircraft is an unstable delta-canard aircraft. By varying the aircraft’s center-of-gravity and applying a square wave input in pitch, saturated actuators have been found and investigated closer using moment coeÿcients as well as other flight mechanical parameters. The studied flight mechanical parameters has proven to be highly relevant when analyzing actuator saturation, and a simple connection between saturated actuators and moment coeÿcients has been found. One can for example look for sudden changes in the moment coeÿcients during saturated actuators in order to find potentially dangerous flight cases. In addition, the studied parameters can be used for robustness analysis, but needs to be further investigated. Lastly, the studied pitch square wave input shows no risk of aircraft departure with saturated elevons during flight, provided non-saturated canards, and that the free-stream velocity is high enough to be flyable.
Styrdonsmättning är ett välstuderat ämne inom kontrollteorin. Däremot existerar det lite forskning gällande flygplansbeteende vid styrdonsmättning. Syftet med den här rap-porten är att identifiera flygmekaniska parametrar som kan vara användbara vid analys av styrdonsmättning av ett instabilt delta-canard flygplan. Genom att variera flygplan-ets tyngdpunkt och applicera en pulsinmatning i tippled har styrdonsmättning hittats och undersökts närmare med momentkoeÿcienter, men även med andra flygmekaniska parametrar. De studerade parametrarna har visat sig vara mycket relevanta vid analys av styrdonsmättning och ett enkelt samband mellan mättade styrdon och momentcoeÿcienter har hittats. Det går till exempel att leta efter plötsliga ändringar i momentkoeÿcienterna under mättning av styrdon för att hitta potentiellt farliga flygsituationer. De studerade parametrarna kan användas i en robusthetsanalys, men vidare forskning krävs. Den studerade pulsinmatningen i tippled visar även att så länge canarderna inte ligger i mät-tning, trots att elevonerna ligger i mättning, så är det ingen fara att flyga, förutsatt att flyghastigheten är tillräckligt hög.

Orientador: Marcelo Carvalho Minhoto Teixeira
Resumo: Este trabalho dedica-se ao estudo do problema de controle robusto envolvendo custo H∞ para sistemas lineares chaveados no tempo contínuo, sujeitos à saturação no atuador e com incertezas politópicas, considerando leis de chaveamento e controladores chaveados dependentes da saída da planta. Os métodos propostos oferecem novas condições baseadas em Desigualdades Matriciais Lineares (LMIs - do inglês, Linear Matrix Inequalities) para o projeto de controladores chaveados utilizando funções de Lyapunov dependentes de parâmetros. O método é baseado em um resultado recentemente introduzido na literatura para o projeto de controle H∞ de saída o qual evita igualdades matriciais lineares (LMEs - do inglês, Linear Matrix Equalities) e a necessidade de impor restrições nas matrizes de saída do sistema, isto é, as matrizes de saída do sistema podem ser de posto linha incompleto. Com o objetivo de estender estes resultados, a restrição de saturação no atuador é estudada. Análises teóricas e resultados de simulações mostram que os novos procedimentos são menos conservativos quando comparados a métodos publicados recentemente na literatura. No método proposto, as condições são uma classe particular de desigualdades matriciais bilineares (BMIs - do inglês, Bilinear Matrix Inequalities), as quais contêm alguns termos bilineares devido à multiplicação de matrizes por escalares. Estes termos estão relacionados à combinação convexa das matrizes de chaveamento bem como a outros parâmetros escalare... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: This thesis is devoted to the study of the robust H∞ control problem of continuous-time switched linear systems subject to actuator saturation with polytopic uncertainties, considering an output-dependent switching law and a switched static output feedback controller. The proposed method offers new sufficient conditions based on linear matrix inequalities (LMIs) for designing the switched controllers using parameter-dependent Lyapunov functions. The method is based on a static output feedback H∞ control design recently presented in the literature that avoids linear matrices equalities (LMEs) and the need to impose any constraints on output system matrices, that is, the output matrices of the system are allowed to be of non-full row rank. In order to extend those results, the actuator saturation constraint is also studied. Theoretical analyses and simulation results show that these new procedures are less conservative than recent methods available in the literature. The conditions of the proposed methods are a particular class of Bilinear Matrix Inequalities (BMIs), which contain some bilinear terms as the product of a matrix and a scalar, related to a suitable convex combination and scalars parameters to provide extra free dimensions in the solution space. The hybrid algorithm Differential Evolution-Linear Matrix Inequality (DE-LMI), is proposed for obtaining feasible solutions of this particular NP-hard problem. Examples show that the proposed methodologies reduce the design ... (Complete abstract click electronic access below)
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Includes abstract.
Includes bibliographical references (leaves 101-106).
This thesis aims at studying some of the techniques used to deal with constraints with special application to the Proton beam steering control at iThemba LABS. The steering of charged particles occurring in research plants is one of the interests of control systems. In this work an investigation of the algorithm for the control of the proton beam steering system in the radiotherapy treatment facility at iThemba LABS is conducted. This algorithm is intended to autonomously maintain the beam centered with reference to the axis of the beamline, and keep the beam front parallel to the central axis of the beamline as stated by van Tubbergh and De Kock, 2006. Furthermore, the algorithm is responsible for monitoring the distribution of the proton beam, in a plane normal to the beam travel direction.

Orientador: Aparecido Augusto de Carvalho
Abstract: Electrical stimulation is a promising technique for motor rehabilitation in cases of spinal cord injury. Stimulator saturation is important in the control system designs applied to electrical stimulation. The negligence of the actuator saturation in the electrical stimulation can lead to unwanted control results, which evidences the muscular fatigue effects. For the first time a switched controller subject to actuator saturation for electrically stimulated lower limb is proposed. The dynamic limb extension model is nonlinear and uncertain. The uncertain nonlinear system described by Takagi-Sugeno fuzzy models operating within an operating region in the state space is considered in this study. In addition, fault in the actuator, muscle activation uncertainty, and muscular non-idealities, such as fatigue, spasms, and tremor were considered at three three severity levels. The switched controller is compared to parallel distributed compensation technique. Simulations denote better results of the switched controller by dealing with parametric uncertainties. On the other hand, a challenge for FES control systems is to monitor torque in muscle contractions. In isotonic contraction applications, measuring torque is difficult. The novelty in this study is the proposal of a new nonlinear model, whose state variables are angular position, angular velocity and angular acceleration. In this new model the torque variable is replaced by the angular acceleration. Experimental tests list the ... (Complete abstract click electronic access below)
Resumo: A estimulação elétrica é uma técnica promissora para reabilitação motora em casos de lesão medular. A saturação do estimulador também é um requisito importante no projeto de sistemas de controle aplicados à estimulação elétrica. A negligência da saturação do atuador pode conduzir a resultados de controle indesejados, que evidencia os efeitos de fadiga muscular. Pela primeira vez é proposto um controlador chaveado sujeito à saturação para membro inferior estimulado eletricamente. O modelo dinâmico de extensão do membro inferior é não linear e incerto. O sistema descrito por modelos fuzzy Takagi-Sugeno e operando dentro de uma região de operação no espaço de estados é considerado neste trabalho. Além disto, falha do atuador, incerteza de ativação muscular, e não idealidades musculares, tais como fadiga, espasmos e tremor foram considerados em três níveis de severidade. O controle chaveado é comparado com a compensação distribuída paralela. Simulações denotam melhores resultados do controlador chaveado lidando com incertezas paramétricas da planta. Por outro lado, um desafio dos sistemas de controle para estimulação elétrica funcional é monitorar a dinâmica do torque em contrações musculares. Em aplicações de contração isotônica, medir o torque é algo difícil. A novidade neste estudo é a proposta de um novo modelo não linear, cujas variáveis de estado são posição angular, velocidade angular e aceleração angular. Neste novo modelo a variável torque é substituída adequadamente pel... (Resumo completo, clicar acesso eletrônico abaixo)
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Orientador: Marcelo Carvalho Minhoto Teixeira
Resumo: Esta tese propõe projetos de controle H_infinito e controle H_infinito chaveado para uma classe de sistemas lineares com incertezas invariantes no tempo, nos quais apenas a derivada do vetor de estado é considerada para realimentação. Neste cenário, as estratégias propostas utilizam dinâmicas auxiliares, cujas variáveis de estado estão disponíveis para realimentação, para controlar a planta original. São propostas estruturas e procedimentos de projeto por meio de desigualdades matriciais lineares. A primeira estrutura de controle apresentada, considera a saturação do atuador e um integrador para definir a estratégia de controle, e se as condições propostas são factíveis, assegura que o ponto de equilíbrio do sistema de malha fechada seja localmente assintoticamente estável, para todas as condições iniciais em uma região elipsoidal, contida em uma determinada região definida para a nova dinâmica. Na segunda estrutura, é proposta uma técnica sem o uso de integradores para definir as estratégias para o controle chaveado e controle H_infinito chaveado, para plantas com e sem saturação da entrada de controle. Na terceira estrutura, considera-se um caso mais geral porém com o uso de integradores para definir as estratégias para o controle chaveado e controle H_infinito chaveado, para plantas sem saturação da entrada de controle. Embora todos os projetos propostos considerem a dinâmica auxiliar, são asseguradas as propriedades de estabilidade, taxa de decaimento e custo garantido pa... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: This thesis proposes H_infinite switched control designs for a class of linear systems with time invariant uncertainties, where only the derivative of the state vector is considered for feedback. In this scenario, the proposed strategies use auxiliary dynamics, whose state variables is accessible for feedback, to control the original plant. The proposed structures and design procedures are based on LinearMatrix Inequalities (LMIs). The first structure considers the actuator saturation and an integrator to define the control strategy, and if the proposed conditions are feasible, it assures that the equilibrium point of the closed-loop system is locally asymptotically stable, for all initial conditions in an ellipsoidal region, which is within a given region defined for this new dynamic. In the second structure, we adopted a technique without the use of integrators to define the strategies for the switched control and H_infinite switched control, for plants with and without control input saturation. In the third structure, we study a more general case, however, with the use of integrators to define the strategies for the switched control and H_infinite switched control, for plants without control input saturation. Although all proposed designs consider the auxiliary dynamics, it is assured the stability, decay rate proprieties, and H_infinite guaranteed cost for the original plant. Simulation examples and practical implementation illustrate the effectiveness of the proposed app... (Complete abstract click electronic access below)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O controle chaveado pode ser eficientemente utilizado no controle de sistemas fuzzy TakagiSugeno (T-S) incertos, que possuam funções de pertinência incertas e modelos locais conhecidos. Como estes sistemas fuzzy podem representar exatamente uma classe de sistemas não lineares incertos em uma região do espaço de estados, é interessante utilizá-los para descrever sistemas não lineares, usando no projeto do controlador o modelo fuzzy que descreve exatamente o sistema não linear. Porém, como a representação através de combinação convexa obtida é válida apenas em uma região do espaço de estados, garantias de que o estado do sistema permaneça nessa região devem ser obtidas. Neste trabalho são propostas condições que garantem a estabilização local, com a especificação da taxa decaimento, de uma classe de sistemas não lineares contínuos no tempo, incertos e com saturação no atuador, utilizando o controle chaveado. Os projetos dos controladores são realizados com base no modelo fuzzy T-S que representa exatamente o sistema não linear e os procedimentos de projeto fornecem uma região na qual as condições iniciais devam estar, tal que, o sistema não linear seja exatamente descrito pelo modelo fuzzy T-S incerto durante toda a trajetória de estado do sistema e ainda que esta trajetória permaneça dentro de uma região de operação previamente especificada. Em geral, o controle chaveado não possui restrição na frequência de chaveamento dos ganhos, o que pode levar ao chattering, que se manifesta pelo chaveamento em frequência infinitamente rápida dos ganhos de realimentação. Visando a eliminação do chattering no controle chaveado, propõe-se uma nova técnica de suavização do controle chaveado, o controle chaveado suave. Esta nova lei de controle pode ser utilizada nas mesmas condições do controle chaveado e é baseada no conceito do mínimo suave, definido neste trabalho. Além disso, são propostos procedimentos de projeto que consideram distúrbios para ambas as leis de controle chaveada e chaveada suave. Ademais, neste trabalho também se apresenta uma implementação da lei de controle chaveada em um sistema Ball Balancer fabricado pela Quanser.
The switched control can be efficiently used for controlling uncertain Takagi-Sugeno (T-S) fuzzy systems, which have uncertain membership functions and known local models. Because these fuzzy systems can exactly represent a class of uncertain nonlinear systems in a given operation region in the state space, it is interesting to use them to describe nonlinear systems, performing the controller design based on a T-S fuzzy model that exactly describes the nonlinear system. However, the perfect representation of the uncertain nonlinear system by the T-S fuzzy model as a convex combination is only valid in the operation region. Therefore, it is necessary to assure conditions such that the state of the system remains in that region. This work proposes conditions to ensure the local stabilization, with decay rate, of a class of uncertain continuoustime nonlinear systems with saturation on the actuator, using a switched control. The designs of the controllers are performed based on the T-S fuzzy model which exactly describes the nonlinear system and the design procedures provide a region in which the initial conditions must be such that the nonlinear system is exactly described by the uncertain T-S fuzzy model along the whole state trajectory of the system and this trajectory remains in a specified operation region. Usually, the switched control has no bound on the frequency of the feedback gains switching, and this can lead to chattering, which is manifested by infinitely fast frequency of the feedback gains switching. In order to avoid the chattering in the switched control, this work proposes a new technique to smooth the switched control, the smooth switched control. This new control law can be used under the same conditions as the switched control and it is based on the concept of smooth minimum, which is defined in this work. In addition, design procedures considering disturbances for both switched and smooth switched control laws are proposed. Furthermore, in this work it is also presented an implementation of the proposed switched control law in a Ball Balancer system manufactured by Quanser.

碩士
國立成功大學
航空太空工程學系
82
Saturating actuator exists in the real-world control system. When the controller has relatively slow dynamics, such as integrator and long time constant poles, the limitation of the control energy due to a saturating actuator may result in serious performance degradations (e.g. large overshoot & long settlingtime) and even cause system instability.This dissertation deals with a two-step design method for the system with saturating actuators. In the first stage, a linear controller is designedwithout considering saturation effect, where H-inf,LQG/LTR or other design method can be applied. Then, in the second stage, an anti-windup controller has further been introduced to suppress the effect of the saturating actuators. This dissertation has focused on the second stage. In this dissertation, the stability of the saturating system and the anti-reset windup compensated system is discussed. Some anti-reset windup method are reviewed. The Park's anti-reset windup method is extended to discrete-time cases. Based on the anti-reset windup scheme introduced by Astrom, a systematic methodology to design an anti-reset windup compensator, called the filter compensating method, is proposed. This design method can be used to meet the design requirement by adjusting the weighting matrices, which ensures the compensated system to be totally stable and the effect of the saturating actuator can be reduced in a great amount. The effectiveness of the proposed compensation method are shown inthe illustrated example and the experiment.

碩士
建國科技大學
電機工程系暨研究所
97
This paper aims to explore robust stability analysis of time delay system. Robust stability for time delay system has been attracting the attention of many researchers. Time delay is frequently encountered in various control systems, and the existence of the delay is a source of instability. Therefore, the stability problem of time delay systems has been one of the most popular research areas in control systems over the years. Time delay system is often occurring in the transmission of information or material between different parts of a system. Transportation systems, communication systems, chemical processing systems, and power systems are examples of time delay systems. In control system design, the limited power supply is the form of a saturating actuator in a practical system. In this thesis, one delay dependent robust stability criteria based on Lyapunov-Krasovskii functional combining with LMI approach has been developed and derived step by step. The proposed stabilization criteria is relatively simple to be checked by simulations and can be applied to the time delay systems with actuator saturation and perturbation. The given systems have been proven to be asymptotically stable.

碩士
國立臺灣師範大學
應用電子科技研究所
98
Three control methods for nonlinear systems are proposed in this study. The first controller design is about a wavelet adaptive backstepping controller for affine nonlinear systems. The controller is comprised of a wavelet identifier and actuator saturation. The second controller design is about a wavelet adaptive backstepping controller for nonaffine nonlinear systems. A wavelet adaptive backstepping controller for a nonaffine system is proposed in this paper. The control scheme combines the backstepping technique and adaptive control with wavelet function. The wavelet function has well performance. It is much proper to online compute the system dynamics by tuning its interior parameters. A mean-value estimation method is also proposed to avoid a higher-order derivative problem generated by Taylor linearization expansion.The third controller design is about a wavelet adaptive backstepping controller for nonaffine nonlinear systems with first order filters. Furthermore, the stability of the system with the mean-value theorem is dissected through Lyapunov functions. In the end, simulation results illustrate the application of the proposed scheme.

Autonomous Underwater Vehicles (AUVs) are robots which autonomously carry out desired underwater operations. With the advancements in efficient sensors, actuators and processors, AUVs can be deployed for various applications such as underwater mineral detection, studying life patterns of aquatic plants and animals so that measures can be taken to protect endangered species, scanning deep sea beds for installing underwater pipelines, overhauling and repair of installed pipelines and defence applications which includes carrying as well as detecting warheads. In order to accomplish the aforementioned applications, various sensors are necessary to be installed with the AUV. Thus, deploying a group of AUVs with a distributed sensor configuration, helps in reducing the payloads on a single AUV. Moreover, when AUVs are deployed in a group, larger areas can be scanned in less time and it also makes the mission redundant in case a single AUV fails. There are various approaches of formation control such as behaviour based, synchronization based, virtual structure based and leader-follower based approach. The leader-follower approach is one of the most widely used formation control approaches owing to its simple structure. In this approach, the leader AUV states are sent to the follower AUVs for maintaining the formation. These states are transferred in underwater via acoustic modem. However, the low data rate of acoustic medium introduces communication delay into the AUV motion control system. This delay varies as the distance between the leader and follower AUVs varies with the ocean currents. In the literature [1, 2], most often, this delay is minimized by either transferring least number of AUV states or accurately estimating these states. However, the communication delay can still increase as well as vary significantly due to change in distance between the AUVs with the ocean current. Hence, in this thesis, a leader-follower approach is considered for studying the effects of this variable communication delay on the performance of follower AUVs. Optimal control facilitates path following by optimizing the error between the desired and actual AUV positions [3, 4]. Moreover, when this control is employed for formation control while considering the communication delay among multiple AUVs, it also provides an optimal control law which can handle the effects of delay along with ensuring smooth path following during formation control. Thus, in the thesis, an optimal kinematic control is developed to deal with the communication delay during formation control. In this approach, a linear augmented system comprising the kinematics of both leader as well as the follower AUVs is constructed. This co-operative AUV system also takes into consideration the leader AUV states received by the follower AUVs. Further, an optimal control law is derived for both the leader and follower AUVs. By using these optimal gains, the leader AUV converge to the desired path and also the follower AUVs maintain the formation under the effects of communication delay without yielding oscillations. The performance of the optimal control scheme is compared with a Linear Quadratic Regulator (LQR) based formation controller. The results clearly show that the follower AUVs in case of proposed controller follows the path without oscillations, whereas, in case of LQR, for a chosen set of Qlqr and Rlqr matrices, the response is oscillatory. The simulation results also show that though the steady state error occurs in case of the proposed controller, it is significantly less than LQR. To minimize the aforesaid steady-state error, a convex optimization based modified constrained adaptive control is then proposed in the thesis considering non-linear kinematics and dynamics of AUV. In this approach, the cost function comprising communication delay information based position and velocity error equations is minimized in every iteration. Thus, the effect of communication delay is considered in every sampling time and adaptive control is developed to deal with these effects. This proposed controller also resolves the issue of actuator saturation. However, the results in this case are compared to a backstepping control based formation controller. The backstepping controller is one of the most widely adopted control paradigms for non-linear systems as it considers all the system non-linearities while calculating the control input. Moreover, as backstepping is a Lyapunov function based approach, it also guarantees asymptotic stability of the system. Nevertheless, from the results, it is clearly evident that, under the effects of communication delay, in case of the constrained adaptive control, the AUVs follow the desired path within an accuracy of 5cm, thereby reducing the steady-state error. But in case of backtepping control, with stamping based technique is used in this approach to determine the communication delay. In this technique, the packet of leader AUV states also contains time information at which it is sent. When this packet is received by the follower AUV, the time at which it is received is also noted. The time-difference between these two time-stamps gives the actual delay which is used for controller design. This technique not only increases the packet-size, which subsequently increases the communication delay, it also necessitates that all the clocks pertaining to every AUV to be synchronized. To address increased communication delay and clock synchronization issues, next, a gradient descent method based delay estimator is designed to handle the effects of the time stamping of every sent packet of the leader AUV states. It also does not necessitate time synchronization of AUV system clocks. This estimator is employed along with the developed constrained adaptive controller to reduce the delay and achieve the desired formation control performance. The results show that the gradient-descent method based estimator accurately estimates the communication delay. Moreover, employing the proposed estimator also helps in significantly reducing the communication delay occurring in each sampling-time. The formation control of AUVs considering small or negligible communication delay has been widely studied in the available literature. However, in this thesis, a leader-follower approach based formation control of AUVs under the effects of significantly large variable communication delay has been investigated. Simulations were conducted by implementing a group of a leader AUV and two follower AUVs using MATLAB/Simulink. In case of all the aforementioned proposed algorithms, it is observed that, the AUVs follow the desired formation with accuracy and without oscillations. To verify the efficiency of all the developed control schemes for formation of AUVs, in real-time, an experimental setup is developed. A torpedo-shaped prototype AUV is designed for implementation of proposed control algorithms. Moreover, the hydrodynamic parameters of the developed prototype AUV are also determined. Since, in the proposed constrained adaptive technique which is employed to handle varying communication delay between the AUVs, the determination of the hydrodynamic parameters a priori helps in minimizing the computational burden. Moreover, the determined parameters can also be used for controller design in the future applications. Furthermore, a virtual AUV is considered as the leader AUV and the prototype AUV with Robot Operating System which supports python based programming is employed as the follower AUV. The experimental results also support the observations from the simulation studies. In case of all the aforesaid proposed algorithms such as optimal and constrained adaptive control, the follower AUV follows the desired orientation, under communication delay without oscillations. Moreover, the designed estimator helps in estimating the communication delay accurately and also helps in reducing the delay which occurs due to time-stamping. Thus, from the results it is evident that for small linearization errors or slowly changing paths (as the linearization errors depend on angular velocity of the desired path), the proposed optimal kinematic control law can be employed to deal with communication delay during formation control. Since, the optimal control gains in this case are calculated off-line, it helps in reducing the computation burden, while achieving smooth formation between the AUVs. As the linearization error increases, the constrained adaptive control can be employed for the aforementioned objective. This control adapts on-line to the variable communication delay occurring during formation control and also helps in avoiding actuator saturation. This proposed control being adaptive in nature, still computes the control law within the considered sampling time, thereby adhering to the limit of computation time. Moreover, this adaptive control law when employed along with the gradient descent method based estimator helps in accurately estimating and reducing the communication delay by avoiding time-stamping. However, based on these aforesaid advantages, it is evident that, with the advancements in the processor speed, the adaptive control algorithm offers better performance and the delay estimator can appropriately replace time-stamping technique.

by Petros Kapasouris, Michael Athans, Gunter Stein.
Caption title.
Bibliography: p. 37-38.
Supported in part by the General Electric Corporate Research and Develoment Center. Supported in part by a grant from the NASA Ames and Langley Research Centers. NASA/NAG 2-297

by Petros Kapasouris, Michael Athans, Gunter Stein.
Cover title.
Includes bibliographical references.
Support provided by the General Electric Corporate Research and Development Center. Support provided by the NASA Ames and Langley Research Centers. NAS/NAG 2-297

Low-frequency Inter-area oscillations (0.2–0.8 Hz) have severe influence on the operation of an interconnected power system due to the involvement of numerous generators. The poorly damped inter-area oscillations are detrimental to the power system stability and meeting the goal of maximum power transfer capacity between the areas. Wide-area measurement system-based Wide-Area Damping controllers (WADC) for controlling devices such as FACTS, HVDC effectively damp out these oscillations. However, due to the usage of the communication network to transfer the wide-area signals and the physical limitations of the controller devices in the feedback loop, new problems are encountered in the design of WADC such as time delays and actuator saturation. These problems would degrade the control performance and even lead to the closed-loop instability, therefore it is necessary to consider time delays and actuator saturation limits in the design of WADC. This thesis presents the design of WADC for Thyristor Controlled Series Capacitor (TCSC) device to improve the inter-area oscillation damping of power system subjected to time delay sand actuator saturation. To compensate the time delays, a WADC with prescribed degree of stability is proposed by using delay-dependent approach. Residue approach and Schur balanced model reduction methods are used to obtain input-output control signals and reduced order power system model to design a WADC. The α-stability region is considered to place all the poles of the closed-loop power system in the left of s = −α in the complex s-plane. The sufficient conditions ascertain the existence of the damping controller that guarantees the asymptotic stability of the closed-loop power system with time-delays are derived in Linear Matrix Inequality(LMI)form using Lyapunov-Krasovskii(L-K) functional with Free Weighting Matrix (FWM) approach. The proposed sufficient conditions are solved by using LMI solvers to obtain the parameters of the WADC and delay margin of the closed-loop power system. Actuator saturation is an inevitable phenomenon in control system which degrades the system performance if it is not considered in the controller design. To reduce the influence of actuator saturation, direct and indirect approaches are used to design a WADC for the power system. A generalized sector condition is used to characterize the actuator saturation nonlinearity in the closed-loop formulation. Actuator saturation limits are symmetric and asymmetric in nature. Asymmetric actuator saturation limits needs to be converted into symmetric saturation limits which can be expressed in Linear Matrix Inequality (LMI) form for analysis. In this thesis, a Minimum Absolute Saturation Bound (MASB) and Normalized Saturation Bound (NSB) techniques are used to convert the asymmetric saturation limits into symmetric limits. Based on L–K functional with FWM approach, a delay-dependent stability and stabilization conditions via LMI formulation are derived to guarantee the asymptotic stability of the closed-loop power system with time delays and actuator saturation. The FWM approach provides less conservativeness results, however, it increases the complexity in the design of WADC. To reduce the complexity and conservativeness of the stability conditions, an appropriate L-K functional with Jensen’s integral inequality is proposed to derive a less conservative stability condition. These conditions are cast into the LMI-based convex optimization problem to calculate the delay margin and to determine the parameters of the WADC. Small-signal analysis and time-domain simulations are carried out first using MATLAB/Simulink on a two-area four-machine power system to evaluate the performance of the proposed WADCs for different operating conditions. Then to validate the obtained simulations results in real-time environment, the proposed WADCs are implemented in real-time using an Opal-RT digital simulator. From the obtained results, it is observed that the proposed WADCs enhance the dynamic performance of the power system and provide sufficient damping to inter-area oscillations by compensating the effect of time delay and actuator saturation. Among the proposed WADCs, the DDAWC designed for HWADC using indirect approach exhibits superior performance compared to the WADCs designed using direct approach.

碩士
國立成功大學
電機工程學系碩博士班
93
For a large-scale system, the decentralized control is an important concept. A cascaded system with actuator and state saturation which is consisting of a weighted switching strategy and an inner-loop compensator is presented in this paper. We apply the LQR design methodology for designing the observer-based tracker to simplify the complexity of the system. The realizable low-gain and high design performance of a sample-data controller is realized through the digital redesign method. For obtaining better performance of the tracker, we use the evolutionary programming to tune the parameters of the tracker. Some examples are presented to demonstrate the effects on the proposed methodology.

碩士
國立臺灣海洋大學
輪機工程系
98
Most physical systems in real world were suffered the external disturbance, then the fuzzy controller design for the nonlinear continuous-time systems with multiplicative noises and the nonlinear discrete-time systems with multiplicative noises. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear systems. The actuator saturation may severely degrade the performance of the closed-loop systems that the sufficient conditions are derived to guarantee the stability. The stability conditions developed in this thesis can be coordinated into the Linear Matrix Inequality (LMI) problems. By solving these LMI stability conditions, a Parallel Distributed Compensation (PDC) based fuzzy controller is obtained to stabilize the T-S fuzzy models with multiplicative noises. In order to illustrate the availability and practicability of proposed fuzzy controller design approach, two numerical simulations are provided to express the controlled responses of that dynamic ship positioning systems with multiplicative noises and truck-trailer systems with multiplicative noises.

碩士
國立成功大學
電機工程學系碩博士班
91
A state-space self-tuning control scheme for adaptive digital control of continuous-time singular nonlinear stochastic systems, which have unknown system parameters, measurement noises, deterministic noises, and inaccessible system states is first proposed in this thesis. The singular nonlinear system is mixed with chaos and singular system in unstable impulsive mode; therefore, it is more challenging for control. First, an adjustable auto-regressive moving average (ARMA)-based noise model with estimated states is constructed for state-space self-tuning control of singular nonlinear stochastic systems, then the optimal tracker is proposed. Under this proposed optimal tracker, the stability can also be shown for the hybrid system with the deterministic noise. Next, the conditioning dual-rate digital redesign scheme is developed, which contains a conditioning fast sampling rate digital controller for reducing the bump-transfer effects and a slow sampling rate digital redesign optimal tracker. Finally, a steady-state observer is based on some reasonable initial values for the system identification. As a result, it can be used to design an optimal tracker with saturation actuators. Illustrative examples are given to demonstrate the effectiveness of design methodologies.

碩士
國立成功大學
電機工程學系碩博士班
90
This thesis addresses some basic ideas for the systems analysis and synthesis with input saturation. By utilizing the digital redesign based genetic algorithm (GA), the control systems can obtain well-performance for various input signals and constraints. The control object is to improve the performance without changing the existing structure. Then, the scheme is experienced that tracking a periodic orbit within a chaotic system. With the rapid advances in computers and microprocessors, the important idea is to replace some existing continuous controllers to associate with the digital implementation of digital signal processing chips.

碩士
國立成功大學
電機工程學系碩博士班
92
A novel evolutionary-programming (EP) algorithm including chaotic variable named chaos-evolutionary-programming algorithm (CEPA) has been proposed in this thesis. Due to the nature of chaotic variable, i.e. pseudo-randomness, ergodicity and irregularity, the evolutional process of CEPA makes the individuals of subgenerations distributed ergodically in the defined space and circumvents the premature of the individuals of subgenerations. Then a dual-rate observer-based tracker for a hybrid interval chaotic system with saturating actuators by using the CEPA is developed. The CEPA can search many local minimum or maximum in parallel and thereby increasing the probability of finding the global one. An illustrative example is presented to demonstrate the effectiveness of the proposed algorithm.

碩士
國立臺灣海洋大學
輪機工程學系
102
In this thesis, a H-Infinity performance constrained fuzzy control approach is investigated for a class of nonlinear stochastic systems subject to actuator saturation. The nonlinear stochastic systems considered in this thesis are represented by Takagi-Sugeno fuzzy models with multiplicative noises. According to H-Infinity performance constraint and actuator saturation, it is shown that the stabilization of multiplicative noised Takagi-Sugeno fuzzy models can be formulated as a convex optimizationproblem subject to linear matrix inequalities. The proposed fuzzy control method is accomplished based on the Lyapunov stability theory Simulation study on a continuous-time nonlinear stochastic ship steering system is given to show the performances of the proposed H-Infinity performance constrained fuzzy control methodology. Keywords: Takagi-Sugeno Fuzzy Models, Multiplicative Noises, Actuator Saturation and Performance Constraint.