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This thesis is concerned with developing a control and condition monitoring system for a class of fault tolerant actuators with high levels of redundancy. The High Redundancy Actuator (HRA) is a concept inspired by biomimetics that aims to provide fault tolerance using relatively large numbers of actuation elements which are assembled in parallel and series configurations to form a single actuator. Each actuation element provides a small contribution to the overall force and displacement of the system. Since the capability of each actuation element is small, the effect of faults within the individual element of the overall system is also small. Hence, the HRA will gracefully degrade instead of going from fully functional to total failure in the presence of faults. Previous research on HRA using electromechanical technology has focused on a relatively low number of actuation elements (i.e. 4 elements), which were controlled with multiple loop control methods. The objective of this thesis is to expand upon this, by considering an HRA with a larger number of actuation elements (i.e. 12 elements). First, a mathematical model of a general n-by-m HRA is derived from first principles. This method can be used to represent any size of electromechanical HRA with actuation elements arranged in a matrix form. Then, a mathematical model of a 4-by-3 HRA is obtained from the general n-by-m model and verified experimentally using the HRA test rig. This actuator model is then used as a foundation for the controller design and condition monitoring development. For control design, two classical and control method-based controllers are compared with an H_infinity approach. The objective for the control design is to make the HRA track a position demand signal in both health and faulty conditions. For the classical PI controller design, the first approach uses twelve local controllers (1 per actuator) and the second uses only a single global controller. For the H_infinity control design, a mixed sensitivity functions is used to obtain good tracking performance and robustness to modelling uncertainties. Both of these methods demonstrate good tracking performance, with a slower response in the presence of faults. As expected, the H_infinity control method's robustness to modelling uncertainties, results in a smaller performance degradation in the presence of faults, compared with the classical designs. Unlike previous work, the thesis also makes a novel contribution to the condition monitoring of HRA. The proposed algorithm does not require the use of multiple sensors. The condition monitoring scheme is based on least-squares parameter estimation and fuzzy logic inference. The least-squares parameter estimation estimates the physical parameters of the electromechanical actuator based on input-output data collected from real-time experiments, while the fuzzy logic inference determines the health condition of the actuator based on the estimated physical parameters. Hence, overall, a new approach to both control and monitoring of an HRA is proposed and demonstrated on a twelve elements HRA test rig.

Nos últimos anos, tem havido grande interesse em estudar manipuladores paralelos, aplicados principalmente em simuladores de voo, com seis graus de liberdade. O interesse em estruturas cinemáticas paralelas é motivado por sua alta rigidez e excelente capacidade de posicionamento em relação às estruturas cinemáticas seriais. Além disso, como os atuadores são posicionados em uma base, eles podem ser aplicados em cargas pesadas e ainda apresentam baixo consumo de energia, tendo em vista que vários atuadores atuam simultaneamente no mesmo corpo. A presente tese apresenta o projeto de três controladores, sendo eles, o controlador H infinito com realimentação de saída, o controlador PID e o controlador Fuzzy, com isto, esta metodologia poderá ser empregada na construção de um futuro simulador de voo. O modelo dos atuadores foi obtido através de uma entrada degrau de tensão nos motores, medindo os seus deslocamentos através dos encoders acoplados, individualmente, a cada um dos respectivos eixos dos motores. Sabendo-se a relação de transmissão do mecanismo de movimento entre o motor e cada haste dos atuadores obtém-se o deslocamento de cada haste a partir da rotação de cada motor medida pelo correspondente encoder e com isso obtém-se o modelo matemático de cada atuador em conjunto com seu sistema de transmissão. Entretanto, na prática, cada atuador é ligeiramente diferente dos outros, o que leva a comportamento e desempenho diferentes entre si. Isso afeta o comportamento da plataforma fazendo com que a trajetória final desejada não possa ser seguida adequadamente, algo que é extremamente necessário em simuladores de voo. Assim, uma das contribuições importantes deste trabalho é, em primeiro lugar, apresentar uma metodologia de padronização das respostas dos atuadores de modo a que todos eles tenham no final, um comportamento igual o mais próximo possível, particularmente em termos de velocidade e de posicionamento. Com os dados da cinemática e da dinâmica da plataforma compondo o modelo completo do sistema foram realizadas várias simulações que aplicadas na plataforma de Stewart real validaram o modelo e mostraram a eficiência das técnicas de controle aplicadas no controle de posição e orientação da plataforma. Para validar o projeto da Plataforma de Stewart como uma possível base de movimento de um simulador de voo, foi implementada a dinâmica longitudinal e lateral de um Boeing 747-100, e com o auxilio de um sensor inercial Xsens® MTi-G, foram realizadas as medições dos ângulos de Euler da Plataforma. Os resultados obtidos pelos três controladores foram satisfatórios e ilustram o desempenho e a robustez da metodologia proposta. / In recent years there has been great interest in studying parallel manipulators, mainly applied in flight simulators, with six degrees of freedom. The interest in parallel kinematic structures is motivated by its high stiffness and excellent positioning capability in relation to serial kinematic structures. Furthermore, since the actuators are positioned on a base, they can handle heavy loads and also have low power consumption, considering that several actuators act on the same platform. This thesis presents the design of three controllers, which are, H-infinity controller with output feedback, PID controller and Fuzzy controller, so that this methodology can be employed in building a future flight simulator. The actuators models were obtained by a step voltage input to the engines and measuring their displacements by the encoders that are coupled to each of the respective axes of the motors. Knowing the relation from the motion transmission mechanism between the motor and the spindle of each actuator, the displacement of each spindle is obtained from the rotation of each motor measured by the corresponding encoder and thus we obtain the mathematical model of each actuator together with its transmission system. However, in practice, each actuator is slightly different from others, which leads to different behavior and performance of each. This affects the behavior of the platform making the final desired trajectory cannot be properly followed something that is extremely necessary in flight simulators. Thus, one of the important contributions of this work is first to present a methodology to standardize the actuators responses so that they all have in the end a behavior equal a close as possible, particularly in terms of velocity and positioning. With the kinematics data and platform dynamics composing the complete system model, several simulations applied to the real Stewart Platform validate the model and show the effectiveness of control techniques applied to control the position and orientation of the platform. In order to validate the Stewart Platform design as a possible base for a motion flight simulator, the longitudinal and lateral dynamics of a Boeing 747-100 model were implemented, and with the aid of an inertial sensor Xsens® MTi-G, measurements of the Euler angles of the platform were performed. The results obtained by the three controllers were satisfactory and illustrate the performance and robustness of the proposed methodology.

One of the main tasks for an industrial robot is to move the end-effector in a predefined path with a specified velocity and acceleration. Different applications have different requirements of the performance. For some applications it is essential that the tracking error is extremely small, whereas other applications require a time optimal tracking. Independent of the application, the controller is a crucial part of the robot system. The most common controller configuration uses only measurements of the motor angular positions and velocities, instead of the position and velocity of the end-effector. The development of new cost optimised robots has introduced unwanted flexibilities in the joints and the links. The consequence is that it is no longer possible to get the desired performance and robustness by only measuring the motor angular positions.  This thesis investigates if it is possible to estimate the end-effector position using Bayesian estimation methods for state estimation, here represented by the extended Kalman filter and the particle filter. The arm-side information is provided by an accelerometer mounted at the end-effector. The measurements consist of the motor angular positions and the acceleration of the end-effector. In a simulation study on a realistic flexible industrial robot, the angular position performance is shown to be close to the fundamental Cramér-Rao lower bound. The methods are also verified in experiments on an ABB IRB4600 robot, where the dynamic performance of the position for the end-effector is significantly improved. There is no significant difference in performance between the different methods. Instead, execution time, model complexities and implementation issues have to be considered when choosing the method. The estimation performance depends strongly on the tuning of the filters and the accuracy of the models that are used. Therefore, a method for estimating the process noise covariance matrix is proposed. Moreover, sampling methods are analysed and a low-complexity analytical solution for the continuous-time update in the Kalman filter, that does not involve oversampling, is proposed.  The thesis also investigates two types of control problems. First, the norm-optimal iterative learning control (ILC) algorithm for linear systems is extended to an estimation-based norm-optimal ILC algorithm where the controlled variables are not directly available as measurements. The algorithm can also be applied to non-linear systems. The objective function in the optimisation problem is modified to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. Second, H∞ controllers are designed and analysed on a linear four-mass flexible joint model. It is shown that the control performance can be increased, without adding new measurements, compared to previous controllers. Measuring the end-effector acceleration increases the control performance even more. A non-linear model has to be used to describe the behaviour of a real flexible joint. An H∞-synthesis method for control of a flexible joint, with non-linear spring characteristic, is therefore proposed. / En av de viktigaste uppgifterna för en industrirobot är att förflytta verktyget i en fördefinierad bana med en specificerad hastighet och acceleration. Exempel på användningsområden för en industrirobot är bland annat bågsvetsning eller limning. För dessa typer av applikationer är det viktigt att banföljningsfelet är extremt litet, men även hastighetsprofilen måste följas så att det till exempel inte appliceras för mycket eller för lite lim. Andra användningsområden kan vara punktsvetsning av bilkarosser och paketering av olika varor. För dess applikationer är banföljningen inte det viktiga, istället kan till exempel en tidsoptimal banföljning krävas eller att svängningarna vid en inbromsning minimeras. Oberoende av applikationen är regulatorn en avgörande del av robotsystemet. Den vanligaste regulatorkonfigurationen använder bara mätningar av motorernas vinkelpositioner och -hastigheter, istället för positionen och hastigheten för verktyget, som är det man egentligen vill styra.  En del av utvecklingsarbetet för nya generationers robotar är att reducera kostnaden men samtidigt förbättra prestandan. Ett sätt att minska kostnaden kan till exempel vara att minska dimensionerna på länkarna eller köpa in billigare växellådor. Den här utvecklingen av kostnadsoptimerade robotar har infört oönskade flexibiliteter i leder och länkar. Det är därför inte längre möjligt att få den önskade prestandan och robustheten genom att bara mäta motorernas vinkelpositioner och -hastigheter. Istället krävs det omfattande matematiska modeller som beskriver dessa oönskade flexibiliteter. Dessa modeller kräver mycket arbete att dels ta fram men även för att identifiera parametrarna. Det finns automatiska metoder för att beräkna modellparametrarna men oftast krävs det en manuell justering för att få bra prestanda.  Den här avhandlingen undersöker möjligheterna att beräkna verktygspositionen med hjälp av bayesianska metoder för tillståndsskattning. De bayesianska skattningsmetoderna beräknar tillstånden för ett system iterativt. Med hjälp av en matematisk modell över systemet predikteras vad tillståndet ska vara vid nästa tidpunkt. Efter att mätningar av systemet vid den nya tidpunkten har genomförts justeras skattningen med hjälp av dessa mätningar. De metoder som har använts i avhandlingen är det så kallade extended Kalman filtret samt partikelfiltret.  Informationen på armsidan av växellådan ges av en accelerometer som är monterad på verktyget. Med hjälp av accelerationen för verktyget och motorernas vinkelpositioner kan en skattning av verktygspositionen beräknas. I en simuleringsstudie för en realistisk vek robot har det visats att skattningsprestandan ligger nära den teoretiska undre gränsen, känd som Raooch mätstörningar som påverkar roboten. För att underlätta trimningen så har en metod för att skatta processbrusets kovariansmatris föreslagits. En annan viktig del som påverkar prestandan är modellerna som används i filtren. Modellerna för en industrirobot är vanligtvis framtagna i kontinuerlig tid medan filtren använder modeller i diskret tid. För att minska felen som uppkommer då de tidskontinuerliga modellerna överförs till diskret tid har olika samplingsmetoder studerats. Vanligtvis används enkla metoder för att diskretisera vilket innebär problem med prestanda och stabilitet. För att hantera dessa problem införs översampling vilket innebär att tidsuppdateringen sker med en mycket kortare sampeltid än vad mätuppdateringen gör. För att undvika översampling kan det motsvarande tidskontinuerliga filtret användas för att prediktera tillstånden vid nästa diskreta tidpunkt. En analytisk lösning med låg beräkningskomplexitet till detta problem har föreslagits.  Vidare innehåller avhandlingen två typer av reglerproblem relaterade till industrirobotar. För det första har den så kallade norm-optimala iterative learning control styrlagen utökats till att hantera fallet då en skattning av den önskade reglerstorheten används istället för en mätning. Med hjälp av skattningen av systemets tillståndsvektor kan metoden nu även användas till olinjära system vilket inte är fallet med standardformuleringen. Den föreslagna metoden utökar målfunktionen i optimeringsproblemet till att innehålla inte bara väntevärdet av den skattade reglerstorheten utan även skattningsfelets kovariansmatris. Det innebär att om skattningsfelet är stort vid en viss tidpunkt ska den skattade reglerstorheten vid den tidpunkten inte påverka resultatet mycket eftersom det finns en stor osäkerhet i var den sanna reglerstorheten befinner sig.  För det andra har design och analys av H∞-regulatorer för en linjär modell av en vek robotled, som beskrivs med fyra massor, genomförts. Det visar sig att reglerprestandan kan förbättras, utan att lägga till fler mätningar än motorns vinkelposition, jämfört med tidigare utvärderade regulatorer. Genom att mäta verktygets acceleration kan prestandan förbättras ännu mer. Modellen över leden är i själva verket olinjär. För att hantera detta har en H∞-syntesmetod föreslagits som kan hantera olinjäriteten i modellen. / Vinnova Excellence Center LINK-SIC

Nos últimos anos, tem havido grande interesse em estudar manipuladores paralelos, aplicados principalmente em simuladores de voo, com seis graus de liberdade. O interesse em estruturas cinemáticas paralelas é motivado por sua alta rigidez e excelente capacidade de posicionamento em relação às estruturas cinemáticas seriais. Além disso, como os atuadores são posicionados em uma base, eles podem ser aplicados em cargas pesadas e ainda apresentam baixo consumo de energia, tendo em vista que vários atuadores atuam simultaneamente no mesmo corpo. A presente tese apresenta o projeto de três controladores, sendo eles, o controlador H infinito com realimentação de saída, o controlador PID e o controlador Fuzzy, com isto, esta metodologia poderá ser empregada na construção de um futuro simulador de voo. O modelo dos atuadores foi obtido através de uma entrada degrau de tensão nos motores, medindo os seus deslocamentos através dos encoders acoplados, individualmente, a cada um dos respectivos eixos dos motores. Sabendo-se a relação de transmissão do mecanismo de movimento entre o motor e cada haste dos atuadores obtém-se o deslocamento de cada haste a partir da rotação de cada motor medida pelo correspondente encoder e com isso obtém-se o modelo matemático de cada atuador em conjunto com seu sistema de transmissão. Entretanto, na prática, cada atuador é ligeiramente diferente dos outros, o que leva a comportamento e desempenho diferentes entre si. Isso afeta o comportamento da plataforma fazendo com que a trajetória final desejada não possa ser seguida adequadamente, algo que é extremamente necessário em simuladores de voo. Assim, uma das contribuições importantes deste trabalho é, em primeiro lugar, apresentar uma metodologia de padronização das respostas dos atuadores de modo a que todos eles tenham no final, um comportamento igual o mais próximo possível, particularmente em termos de velocidade e de posicionamento. Com os dados da cinemática e da dinâmica da plataforma compondo o modelo completo do sistema foram realizadas várias simulações que aplicadas na plataforma de Stewart real validaram o modelo e mostraram a eficiência das técnicas de controle aplicadas no controle de posição e orientação da plataforma. Para validar o projeto da Plataforma de Stewart como uma possível base de movimento de um simulador de voo, foi implementada a dinâmica longitudinal e lateral de um Boeing 747-100, e com o auxilio de um sensor inercial Xsens® MTi-G, foram realizadas as medições dos ângulos de Euler da Plataforma. Os resultados obtidos pelos três controladores foram satisfatórios e ilustram o desempenho e a robustez da metodologia proposta. / In recent years there has been great interest in studying parallel manipulators, mainly applied in flight simulators, with six degrees of freedom. The interest in parallel kinematic structures is motivated by its high stiffness and excellent positioning capability in relation to serial kinematic structures. Furthermore, since the actuators are positioned on a base, they can handle heavy loads and also have low power consumption, considering that several actuators act on the same platform. This thesis presents the design of three controllers, which are, H-infinity controller with output feedback, PID controller and Fuzzy controller, so that this methodology can be employed in building a future flight simulator. The actuators models were obtained by a step voltage input to the engines and measuring their displacements by the encoders that are coupled to each of the respective axes of the motors. Knowing the relation from the motion transmission mechanism between the motor and the spindle of each actuator, the displacement of each spindle is obtained from the rotation of each motor measured by the corresponding encoder and thus we obtain the mathematical model of each actuator together with its transmission system. However, in practice, each actuator is slightly different from others, which leads to different behavior and performance of each. This affects the behavior of the platform making the final desired trajectory cannot be properly followed something that is extremely necessary in flight simulators. Thus, one of the important contributions of this work is first to present a methodology to standardize the actuators responses so that they all have in the end a behavior equal a close as possible, particularly in terms of velocity and positioning. With the kinematics data and platform dynamics composing the complete system model, several simulations applied to the real Stewart Platform validate the model and show the effectiveness of control techniques applied to control the position and orientation of the platform. In order to validate the Stewart Platform design as a possible base for a motion flight simulator, the longitudinal and lateral dynamics of a Boeing 747-100 model were implemented, and with the aid of an inertial sensor Xsens® MTi-G, measurements of the Euler angles of the platform were performed. The results obtained by the three controllers were satisfactory and illustrate the performance and robustness of the proposed methodology.

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