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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
41

Active Vibration Control of Multibody Systems : Application to Automotive Design

Olsson, Claes January 2005 (has links)
Active vibration control to reduce vibrations and structure borne noise is considered using a powerful multi-disciplinary virtual design environment which enables control system design to be considered as an integral part of the overall vehicle design. The main application studied is active automotive engine vibration isolation where, first, the potential of large frequency band multi-input multi-output H2 feedback control is considered. Facilitated by the virtual environment, it is found necessary to take non-linear characteristics into account to achieve closed-loop stability. A physical explanation to why receiver structure flexibility insignificantly affect the open and closed-loop characteristics in case of total force feedback in contrast to acceleration feedback is then given. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed. Next, applying state-of-the-art algorithms for recursive parameter estimation, time-domain adaptive filtering is shown to lack sufficient tracking performance to deal with multiple spectral components of transient engine excitations corresponding to rapid car accelerations. Finally, plant non-linearity as well as transient excitation are successfully handled using narrow band control based on feedback of disturbance states estimates. To deal with the non-linear characteristics, an approach to generate linear parameter varying descriptions of non-linear systems is proposed. Parameter dependent quadratic stability is assessed using a derived affine closed-loop system representation. This thesis also considers actuator saturation induced limit cycles for observer-based state feedback control systems encountered when dealing with the active isolation application. It is stressed that the fundamental observer-based anti-windup technique could imply severely deteriorated closed-loop characteristics and even sustained oscillations. That is in the case when the observer is fed by the saturated control signal in contrast to the computed one. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed-loop stability are provided for the two observer implementations.
42

Ammonium Feedback Control in Wastewater Treatment Plants

Åmand, Linda January 2014 (has links)
The aeration process is often the single largest consumer of electricity in a wastewater treatment plant. Aeration in biological reactors provides microorganisms with oxygen which is required to convert ammonium to nitrate. Ammonium is toxic for aqueous ecosystems and contributes to eutrophication. The importance of aeration for the treatment results in combination with the high costs motivates automatic control of the aeration process. This thesis is devoted to ammonium feedback control in municipal wastewater treatment plants. With ammonium feedback control, the aeration intensity is changed based on a measurement of the outlet ammonium concentration. The main focus of the thesis is design, implementation, evaluation and improvement of ammonium PI (proportional-integral) controllers. The benefits of ammonium feedback control are established through long-term experiments at three large wastewater treatment plants in Stockholm, Sweden. With ammonium feedback control, energy savings up to around 10 % were achieved compared to keeping the dissolved oxygen concentration constant. The experiments generated several lessons learned with regard to implementation and evaluation of controllers in full-scale operation. The thesis has established guidelines on how to design ammonium feedback controllers for situations when cost-effective operation is the overall aim. Simulations have demonstrated the importance to limit the dissolved oxygen concentration in the process and under what conditions the energy saving with ammonium feedback control is large. The final part of the thesis treats improvements of ammonium PI control through minor modifications to the control structure or controller. Three strategies were studied: gain scheduling control, repetitive control, and a strategy reacting to oxygen peaks in the last aerobic zone. The strategies all had their benefits but the ammonium feedback controller was the key factor to improved aeration control.
43

Visual servo control for a human-following robot

Burke, Michael Glen 03 1900 (has links)
Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: This thesis presents work completed on the design of control and vision components for use in a monocular vision-based human-following robot. The use of vision in a controller feedback loop is referred to as vision-based or visual servo control. Typically, visual servo techniques can be categorised into imagebased visual servoing and position-based visual servoing. This thesis discusses each of these approaches, and argues that a position-based visual servo control approach is more suited to human following. A position-based visual servo strategy consists of three distinct phases: target recognition, target pose estimation and controller calculations. The thesis discusses approaches to each of these phases in detail, and presents a complete, functioning system combining these approaches for the purposes of human following. Traditional approaches to human following typically involve a controller that causes platforms to navigate directly towards targets, but this work argues that better following performance can be obtained through the use of a controller that incorporates target orientation information. Although a purely direction-based controller, aiming to minimise both orientation and translation errors, suffers from various limitations, this thesis shows that a hybrid, gain-scheduling combination of two traditional controllers offers better targetfollowing performance than its components. In the case of human following the inclusion of target orientation information requires that a definition and means of estimating a human’s orientation be available. This work presents a human orientation measure and experimental results to show that it is suitable for the purposes of wheeled platform control. Results of human following using the proposed hybrid, gain-scheduling controller incorporating this measure are presented to confirm this. / AFRIKAANSE OPSOMMING: Die ontwerp van ’n visiestelsel en beheer-komponente van ’n enkel-kamera robot vir die volging van mense word hier aangebied. Die gebruik van visuele terugvoer in die beheerlus word visie-gebaseerde of visuele servobeheer genoem. Visuele servobeheer tegnieke kan tipies onderskei word tussen beeld-gebaseerde servobeheer en posisie-gebaseerde visuele servobeheer. Altwee benaderings word hier bespreek. Die posisie-gebaseerde benadering word aanbeveel vir die volging van mense. Die posisie-gebaseerde servobeheertegniek bestaan uit drie duidelike fases: teiken herkenning, teiken oriëntasie bepaling en die beheerder berekeninge. Benaderings tot elk van hierdie fases word hier in detail bespreek. Dan word ’n volledige funksionele stelsel aangebied wat hierdie fases saamvoeg sodat mense gevolg kan word. Meer tradisionele benaderings tot die volging van mense gebruik tipies ’n beheerder wat die platvorm direk laat navigeer na die teikens, maar hier word geargumenteer dat beter werkverrigting verkry kan word deur ’n beheerder wat die teiken oriëntasie inligting ook gebruik. ’n Suiwer rigting-gebaseerde beheerder, wat beide oriëntasie en translasie foute minimeer, is onderhewig aan verskeie beperkings. Hier word egter aangetoon dat ’n hibriede, aanwinsskedulerende kombinasie van die twee tradisionele beheerders beter teikenvolging werkverrigting bied as die onderliggende twee tegnieke. In die geval van die volging van mense vereis die insluiting van teiken oriëntasie inligting dat ’n definisie van die persoon se oriëntasie beskikbaar is en dat dit geskat kan word. ’n Oriëntasie maatstaf vir mense word hier aangebied en dit word eksperimenteel getoon dat dit geskik is om ’n platvorm met wiele te beheer. Die resultate van die volging van mense wat die voorgestelde hibriede, aanwins-skedulerende beheerder gebruik, met hierdie maatstaf, word ter ondersteuning aangebied.
44

Kill Zone Analysis for a Bank-to-Turn Missile-Target Engagement

January 2016 (has links)
abstract: With recent advances in missile and hypersonic vehicle technologies, the need for being able to accurately simulate missile-target engagements has never been greater. Within this research, we examine a fully integrated missile-target engagement environment. A MATLAB based application is developed with 3D animation capabilities to study missile-target engagement and visualize them. The high fidelity environment is used to validate miss distance analysis with the results presented in relevant GNC textbooks and to examine how the kill zone varies with critical engagement parameters; e.g. initial engagement altitude, missile Mach, and missile maximum acceleration. A ray-based binary search algorithm is used to estimate the kill zone region; i.e. the set of initial target starting conditions such that it will be "killed". The results show what is expected. The kill zone increases with larger initial missile Mach and maximum acceleration & decreases with higher engagement altitude and higher target Mach. The environment is based on (1) a 6DOF bank-to-turn (BTT) missile, (2) a full aerodynamic-stability derivative look up tables ranging over Mach number, angle of attack and sideslip angle (3) a standard atmosphere model, (4) actuator dynamics for each of the four cruciform fins, (5) seeker dynamics, (6) a nonlinear autopilot, (7) a guidance system with three guidance algorithms (i.e. PNG, optimal, differential game theory), (8) a 3DOF target model with three maneuverability models (i.e. constant speed, Shelton Turn & Climb, Riggs-Vergaz Turn & Dive). Each of the subsystems are described within the research. The environment contains linearization, model analysis and control design features. A gain scheduled nonlinear BTT missile autopilot is presented here. Autopilot got sluggish as missile altitude increased and got aggressive as missile mach increased. In short, the environment is shown to be a very powerful tool for conducting missile-target engagement research - a research that could address multiple missiles and advanced targets. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2016
45

Centralized Control of Power System Stabilizers

Sanchez Ayala, Gerardo 09 October 2014 (has links)
This study takes advantage of wide area measurements to propose a centralized nonlinear controller that acts on power system stabilizers, to cooperatively increase the damping of problematic small signal oscillations all over the system. The structure based on decision trees results in a simple, efficient, and dependable methodology that imposes much less computational burden than other nonlinear design approaches, making it a promising candidate for actual implementation by utilities and system operators. Details are given to utilize existing stabilizers while causing minimum changes to the equipment, and warranting improvement or at least no detriment of current system behavior. This enables power system stabilizers to overcome their inherent limitation to act only on the basis of local measurements to damp a single target frequency. This study demonstrates the implications of this new input on mathematical models, and the control functionality that is made available by its incorporation to conventional stabilizers. In preparation of the case of study, a heuristic dynamic reduction methodology is introduced that preserves a physical equivalent model, and that can be interpreted by any commercial software package. The steps of this method are general, versatile, and of easy adaptation to any particular power system model, with the aggregated value of producing a physical model as final result, that makes the approach appealing for industry. The accuracy of the resulting reduced network has been demonstrated with the model of the Central American System. / Ph. D.
46

Enhancing Comfort and Robustness in Hydronic Radiator Systems through Integration of Body Heat Predictions : A Study on a Novel LPV Controller / Förbättring av Komfort och Robusthet i Vattenburna Elementsystem genom Integration av Kroppsvärme beräkningar

Pirmohamed, Fahim January 2023 (has links)
The quest to balance occupant comfort with energy efficiency is a key challenge in the field of heating systems, particularly for hydronic radiators. This study addresses this issue by investigating the integration of body heat predictions into a gain-scheduling controller for a hydronic radiator system. Although the benefits of gain-scheduling control strategies are acknowledged in HVAC systems, this exploration into the integration of body heat predictions in hydronic radiator systems presents a novel approach. A Linear Parameter-Varying (LPV) controller was employed and its impact on comfort, energy consumption, and robustness in the face of varying parameters such as the number of occupants, inaccuracies in body heat prediction, and set-point temperature changes was examined. This proposed controller was tested in a simulated house heating system made in Simulink. Findings indicated a substantial enhancement in comfort, especially under low-load scenarios. The controller demonstrated notable robustness against disturbances, highlighting the system’s reliability. Although energy consumption did not show significant reduction, the ability to maintain comfort levels without increasing energy use is a valuable contribution to sustainable heating practices. The results of this study extend our understanding of control strategies in hydronic radiator systems, providing a promising approach towards more comfortable, robust, and energy-efficient solutions. Further research should focus on improving the accuracy of body heat prediction algorithms and incorporating renewable energy sources for increased energy efficiency. In sum, this work represents a significant step towards a more balanced and sustainable future in the operation of hydronic radiator systems. / Denna studie utforskar möjligheten att balansera komfort och energieffektivitet i vattenburna elementsystem genom att integrera kroppsvärmeberäkningar i en gain-scheduling regleralgoritm. Vi presenterar en nyanserad metod som använder en Linjär Parameterberoende (LPV) reglerare. Denna reglerare anpassar sig till varierande parametrar som antal personer i rummet, osäkerheter i kroppsvärmeberäkningar och förändringar i inställd temperatur. Den föreslagna regleraren testades i ett simulerat husvärmesystem skapat i Simulink. Resultaten indikerade en betydande förbättring i komfort, särskilt under låglastscenarier. Regleraren uppvisade också anmärkningsvärd robusthet mot störningar, vilket understrykersystemets tillförlitlighet. Även om ingen signifikant minskning i energiförbrukning observerades, är förmågan att bibehålla komfortnivåer utan att öka energianvändningen ett värdefullt bidrag till hållbara uppvärmningsmetoder. Denna studie utökar vår förståelse för reglerstrategier i vattenburna elementsystem och erbjuder en lovande väg framåt mot mer komfortabla, robusta och energieffektiva lösningar. För framtida forskning bör fokus ligga på att förbättra noggrannheten i kroppsvärmeberäkningsalgoritmer och att integrera förnybara energikällor för ökad energieffektivitet. Sammantaget representerar detta arbete ett betydande steg mot en mer balanserad och hållbar framtid i drift av vattenburna elementsystem.
47

Characterizing and controlling program behavior using execution-time variance

Kumar, Tushar 27 May 2016 (has links)
Immersive applications, such as computer gaming, computer vision and video codecs, are an important emerging class of applications with QoS requirements that are difficult to characterize and control using traditional methods. This thesis proposes new techniques reliant on execution-time variance to both characterize and control program behavior. The proposed techniques are intended to be broadly applicable to a wide variety of immersive applications and are intended to be easy for programmers to apply without needing to gain specialized expertise. First, we create new QoS controllers that programmers can easily apply to their applications to achieve desired application-specific QoS objectives on any platform or application data-set, provided the programmers verify that their applications satisfy some simple domain requirements specific to immersive applications. The controllers adjust programmer-identified knobs every application frame to effect desired values for programmer-identified QoS metrics. The control techniques are novel in that they do not require the user to provide any kind of application behavior models, and are effective for immersive applications that defy the traditional requirements for feedback controller construction. Second, we create new profiling techniques that provide visibility into the behavior of a large complex application, inferring behavior relationships across application components based on the execution-time variance observed at all levels of granularity of the application functionality. Additionally for immersive applications, some of the most important QoS requirements relate to managing the execution-time variance of key application components, for example, the frame-rate. The profiling techniques not only identify and summarize behavior directly relevant to the QoS aspects related to timing, but also indirectly reveal non-timing related properties of behavior, such as the identification of components that are sensitive to data, or those whose behavior changes based on the call-context.
48

Commande robuste pour une classe de systèmes non linéaires à paramètres variants : application aux projectiles guidés / Robust Control for a Class of Nonlinear Parameter-Varying Systems : Application to Guided Projectiles

Sève, Florian 05 December 2016 (has links)
Ce mémoire de thèse traite du développement des dynamiques et des lois de commande de vol d’un projectile d’artillerie gyrostabilisé guidé par une tête découplée. Un modèle non linéaire du projectile est proposé, et sert à calculer un modèle linéarisé de la dynamique de roulis du nez et un modèle q-LPV des chaînes de tangage et de lacet à paramètres fortement variants. Les incertitudes de modélisation sont prises en compte pour concevoir l’autopilote. Des propriétés importantes des projectiles gyrostabilisés, qui sont liées au couplage dynamique tangage/lacet, aux modes internes et à la stabilité, sont mises en valeur grâce au modèle q-LPV. En vue de l’utiliser pour calculer une loi de commande, la dimension de son vecteur des paramètres est réduite et la position des capteurs intégrés dans le nez est considérée. Un seul correcteur linéaire est suffisant pour la dynamique de l’angle de roulis du nez alors qu’une stratégie systématique de commande par séquencement de gains basée sur une linéarisation est élaborée séparément pour générer un correcteur séquencé des facteurs de charge de tangage et de lacet. Des structures de commande fixées d’ordre réduit sont conçues en appliquant la même approche de synthèse linéaire H∞ par façonnage de gain de boucle pour les axes de roulis et de tangage/lacet. De très bonnes propriétés de performance et de robustesse en boucle fermée, comparables à celles fournies par des correcteurs d’ordre plein, sont obtenues. Finalement, l’efficacité de l’autopilote augmenté d’une loi de guidage par navigation proportionnelle pure est vérifiée via de nombreuses simulations non linéaires de trajectoires. Ces dernières correspondent à des scénarios de vol nominaux d’interception de cibles balistiques, non balistiques immobiles, ou manœuvrantes, ainsi qu’à des scénarios considérant des perturbations sur les conditions de tir ou sur les dynamiques du projectile guidé / This thesis addresses the development of the flight dynamics and control laws for an artillery spin-stabilized projectile equipped with a decoupled guidance nose. A projectile nonlinear model is discussed, and it is used for computing a linearized model of the nose roll dynamics along with a q-LPV model of the highly parameter-varying pitch/yaw-dynamics. Modeling uncertainty is taken into account for autopilot design. Important properties specific to spin-stabilized projectiles, which are relevant to pitch/yaw-channel cross-coupling, internal modes and stability, are highlighted using the q-LPV model. In order to use the latter for calculating a control law, the dimension of its parameter vector is reduced and the position of the nose-embedded sensors is considered. A single linear controller is sufficient for the nose roll angle dynamics whereas a systematic linearization-based gain-scheduled control strategy is separately devised to provide a pitch/yaw-axis load factor gain-scheduled controller. Controllers of reduced-order fixed structures are computed by applying the same H∞ linear design loop-shaping approach for the roll and pitch/yaw-axes. Very good closed-loop performance and robustness properties, which are similar to those provided by full order controllers, are obtained. Finally, the effectiveness of the autopilot augmented by a pure proportional navigation guidance law is verified through a variety of nonlinear trajectory simulations. The latter correspond to nominal flight scenarios with ballistic, non-ballistic stationary, and maneuvering interception points, and to scenarios with perturbed launch conditions or guided projectile dynamics
49

Modeling, Identification and Control of a Guided Projectile in a Wind Tunnel / Modélisation, identification et commande d'un projectile guidé en soufflerie

Strub, Guillaume 20 July 2016 (has links)
Cette thèse présente une méthodologie de conception et d’évaluation de lois de commande pour projectiles guidés, au moyen d’un prototype placé dans une soufflerie via un support autorisant plusieurs degrés de liberté en rotation. Ce dispositif procure un environnement permettant à la fois de caractériser expérimentalement le comportement de la munition et d’évaluer les performances des lois de commande dans des conditions réalistes, et est mis en œuvre pour l’étude d’autopilotes de tangage et de lacet, à vitesse fixe et à vitesse variable, pour un prototype de projectile empenné piloté par canards. La modélisation d’un tel système aboutit à un modèle non-linéaire dépendant de nombreuses conditions de vol telles que la vitesse et des angles d’incidence. Les méthodes de séquencement de gain basées sur des linéarisations d’un modèle non-linéaire sont couramment employées dans l’industrie pour la commande de ce type de systèmes. A cette fin, le système est représenté au moyen d’une famille de modèles linéaires dont les paramètres sont directement estimés à partir de données recueillies sur le dispositif expérimental. L’observation du comportement à différents points de vol permet de considérer la vitesse de l’air comme unique variable de séquencement. La synthèse des différents contrôleurs est réalisée au moyen d’une méthode H∞ multi-objectifs à ordre et structure fixes, afin de garantir la stabilité et la robustesse du système vis-à-vis d’incertitudes liées à la variation du point de fonctionnement. Ces lois de commande sont alors validées au moyen d’analyses de robustesse, puis par leur implémentation sur le dispositif expérimental. Les résultats obtenus lors d’essais en soufflerie correspondent aux simulations numériques et sont conformes aux spécifications attendues. / This work presents a novel methodology for flight control law design and evaluation, using a functional prototype installed in a wind tunnel by the means of a support structure allowing multiple rotational degrees of freedom. This setup provides an environment allowing experimental characterization of the munition’s behavior, as well as for flight control law evaluation in realistic conditions. The design and validation of pitch and yaw autopilots for a fin-stabilized, canard-guided projectile is investigated, at fixed and variable airspeeds. Modeling such a system leads to a nonlinear model depending on numerous flight conditions such as the airspeed and incidence angles. Linearization-based gain scheduling techniques are widely employed in the industry for controlling this class of systems. To this end, the system is represented with a family of linear models whose parameters are directly estimated from experimentally collected data. Observation of the projectile’s behavior for different operating points indicates the airspeed can be considered as the only scheduling variable. Controller synthesis is performed using a multi-objective, fixed-order, fixed-structure H∞ technique in order to guarantee the stability and robustness of the closed-loop against operating point uncertainty. The obtained control laws are validated with robustness analysis techniques and are then implemented on the experimental setup, where wind-tunnel tests results correlate with numerical simulations and conform to the design specifications.
50

Aportació al control del convertidor CC/CA de tres nivells.

Alepuz Menéndez, Salvador Simón 13 December 2004 (has links)
La presente tesis estudia, propone y realiza sus principales aportaciones en el campo del control para el convertidor CC/CA de tres niveles, sobre la topología denominada Neutral-Point-Clamped, aunque se puede extender a otras topologías y/o número de niveles. Se presenta una metodología de modelado que emplea funciones de conmutación de fase, el operador de promediado y la transformación D-Q, tal que los modelos obtenidos en el dominio D-Q contienen una información completa sobre la dinámica del sistema. La estrategia de conmutación se puede entender como una extensión de la estrategia PWM senoidal de dos a tres niveles. Esta estrategia es simple y no realiza el control de ninguna de las variables del sistema. En esta tesis, el controlador se encarga de regular todas las variables del sistema, incluido el equilibrio del bus de continua. Este es un enfoque diferente del convencional, donde el equilibrio del bus de continua se consigue mediante la elección adecuada de los estados redundantes del convertidor en la estrategia de conmutación, mientras que el resto de variables se regulan a través del controlador. Para la realización del controlador, se propone la técnica de control lineal multivariable LQR (Linear Quadratic Regulator), complementada con la técnica de control no lineal adaptativo denominada programación de ganancia (Gain Scheduling). Se presenta, además, una metodología de cálculo del controlador. Este control es versátil, abierto y adaptable. En cualquier caso, el controlador se puede adaptar a las necesidades concretas de cada aplicación. El cálculo del controlador se realiza mediante simulación con MatLab-Simulink. Los modelos matemáticos que emplean las funciones de conmutación del convertidor son aquellos que ofrecen un mejor compromiso entre velocidad de simulación y precisión. Para validar el control propuesto, se ha diseñado y construido un equipo experimental donde el controlador se ha mostrado aplicable, útil y eficaz en la regulación de las distintas cargas y aplicaciones experimentadas, incluso con carga no lineal, bajo diferentes condiciones de trabajo y variables a controlar, tanto en régimen permanente como en procesos transitorios. La rapidez y calidad de la respuesta transitoria es comparable a la de otros sistemas de control publicados. Es especialmente interesante el excelente control conseguido del equilibrio del bus de continua. Además, la robustez del control permite cancelar el error estacionario aunque diferentes parámetros del sistema presenten desviaciones significativas respecto los valores esperados. El uso de la programación de ganancia junto con la técnica LQR se ha mostrado muy efectivo, puesto que permite realizar diferentes tipos de control. Se ha comprobado la congruencia entre simulaciones y resultados experimentales obtenidos, lo que valida los modelos de simulación empleados y el proceso de diseño del controlador mediante simulación. / This dissertation study, propose and carry out the main contributions in the field of three-level inverter control, using the topology Neutral-Point-Clamped, although results can be extended to other topologies and/or number of levels. A procedure for modelling is presented, based on line-switching functions, moving average operator and D-Q transformation. Then, the obtained models in D-Q frame contain complete information about system dynamics. Switching strategy is simple and can be considered as an extension of two-level sinusoidal PWM to three level. The system variables are not controlled by the switching strategy. In this work, all the system variables are controlled by the regulator, including DC-link balance. This control approach is different than the conventional one, where DC-link balance is achieved by means of a proper selection of redundant states in the switching strategy, and the other variables are controlled by the regulator. The regulator is based on the multivariable linear control technique LQR (Linear Quadratic Regulator), in combination with the non-linear adaptive control technique Gain Scheduling. Moreover, a methodology for the calculation of the controller is presented. This controller is versatile, open and adaptable. However, the controller can be built depending on the concrete specifications of each application. The controller is calculated by means of simulation using MatLab-Simulink. The mathematical models based on the switching functions of the converter give the best trade-off between simulation speed and precision. In order to validate the proposed controller, an experimental prototype has been designed and implemented. Experimental results show that the controller is useful and effective for the regulation of different loads and applications, even with non-linear loads, different operation points and variables to control, in steady-state and transitory operation. Dynamic response speed and quality are similar to other control systems in the literature. The DC-link balance control achieved is specially interesting. Furthermore, steady-state error is cancelled due to the robustness of the controller, even though significant deviation of different system parameters are present. The use of Gain-Scheduling in combination with LQR is effective, allowing the calculation of regulators with different control strategies. Good agreement between simulations and experimental results has been found. This result validates simulation models and the design method for the controller, based on simulations.

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