A survey of differential flatness-based control applied to renewable energy sources

Conference ProceedingsThis paper presents an overview of various methods used to minimize the fluctuating impacts of power generated from renewable energy sources. Several sources are considered in the study (biomass, wind, solar, hydro and geothermal). Different control methods applied to their control are cited, alongside some previous applications. Hence, it further elaborates on the adoptive control principles, of which includes; Load ballast control, dummy load control, proportional integral and derivative (PID) control, proportional integral (PI) control, pulse-width modulation (PWM) control, buck converter control, boost converter control, pitch angle control, valve control, the rate of river flow at turbine, bidirectional diffuser-augmented control and differential flatnessbased controller. These control operations in renewable energy power generation are mainly based on a steady-state linear control approach. However, the flatness based control principle has the ability to resolve the complex control problem of renewable energy systems while exploiting their linear properties. Using their flatness properties, feedback control is easily achieved which allows for optimal/steady output of the system components. This review paper highlights the benefits that range from better control techniques for renewable energy systems to established robust grid (or standalone generations) connections that can bring immense benefits to their operation and maintenance costs

A non-linear model based feed forward flatness control approach to speed governor systems of hydropower plants

Ovo istraživanje je dio projekta sanacije kojim se hidro-mehanički regulator brzine hidroelektrane (HEPP) zamjenjuje s novim, digitalnim. Na temelju ranijeg istraživanja procjene HEPP modela, simulacijska istraživanja u Matlab/Simulink okruženju provedena su u svrhu razvijanja najbolje filozofije za proizvodnju digitalnog regulatora brzine. Kako bi se moglo ponuditi odgovarajuće rješenje za reguliranje učestalosti punjenja energetskog sustava, regulator brzine bi u okviru dopuštenih granica trebao što brže reagirati na zadane promjene. U svrhu kompenzacije pokazatelja nezadovoljavajuće performanse uobičajenog proporcionalno-integralnog (PI) regulatora, konstruiran je novi regulator zasnovan na teoriji diferencijalne ravnomjernosti. Novi je regulator konstruiran dodavanjem postojećem PI regulatoru povratne sprege na ravnomjernosti zasnovan dio unaprijedne sprege. Rezultat je bolji rad nego s konvencionalnim PI regulatorom.This study is a part of a refurbishment project, which renews the hydro-mechanical speed governor of a hydroelectric power plant (HEPP) with a new digital one. Based on the previous study of the project, which covers the validation of the HEPP model, the simulation studies implemented in Matlab/Simulink environment are conducted to design the best controller philosophy for the digital speed governor controller. In order to be able to give satisfactory response to the load frequency control of the power system, the speed governor should respond to the set point changes as quickly as possible within the safe margins. In order to compensate unsatisfactory performance indices of conventional proportional-integral (PI) controller, a new controller based on the differential flatness theory is designed. The new controller is constructed by adding on a flatness-based feed forward part to the existing PI feedback controller, which results in improved performance compared to the conventional PI controller

FLATNESS BASED CONTROL OF MICRO-HYDROKINETIC RIVER ELECTRIFICATION SYSTEM

Published ThesisIn areas where adequate water resource is available, hydrokinetic energy conversion systems are currently gaining recognition, as opposed to other renewable energy sources such as solar or wind energy. The operational principle of hydrokinetic energy is not similar to traditional hydropower generation that explores use of the potential energy of falling water, which has drawbacks such as the expensive construction of dams and the disturbance of aquatic ecosystems. Hence, hydrokinetic energy generates electricity by making use of underwater turbines to extract the kinetic energy of flowing water, with no construction of dams or diversions. A hydrokinetic turbine uses flowing water, which varies with climatic conditions throughout the year, to power the shaft of a generator, hence, generating an unstable energy output. The aim of this dissertation is to develop a controller that will be used to stabilize the output voltage and frequency generated in a hydrokinetic energy system. An overview of various methods used to minimize the fluctuating impacts of power generated from renewable energy sources is included in the current conducted research. Several renewable energy sources such as biomass, wind, solar, hydro and geothermal have been discussed in the literature review. Different control methods and topologies have been cited. Hence, the study elaborates on the adoptive control principles, which include the load ballast control, dummy load control, proportional integral and derivative (PID) controller system, proportional integral (PI) controller system, pulse-width modulation (PWM) control, pitch angle control, valve control, the rate of river flow at the turbine, bidirectional diffuser-augmented control and differential flatness based controller. These control operations in renewable energy power generation are mainly based on a linear control approach. In the case whereby a PI power controller system has been developed for a variable speed hydrokinetic turbine system, a DC-DC boost converter is used to keep constant DC link voltage. The input DC current is regulated to follow the optimized current reference for maximum power point operation of the turbine system. The DC link voltage is controlled to feed the current in the grid through the line side PWM inverter. The active power is regulated by q-axis current while the reactive power is regulated by d-axis current. The phase angle of utility voltage is detected using PLL (phased locked loop) in a d-q synchronous reference frame. The proposed scheme is modelled and simulated using MATLAB/ Simulink, and the results give a high quality power conversion solution for a variable speed hydrokinetic system. In the second case, whereby the differential flatness concept is applied to a controller, the idea of this concept is to generate an imaginary trajectory that will take the system from an initial condition to a desired output generating power. This control concept has the ability to resolve complex control problems such as output voltage and frequency fluctuations of renewable energy systems, while exploiting their linear properties. The results show that the generated outputs are dynamically adjusted during the voltage regulation process. The advantage of the proposed differential flatness based controller over the traditional PI control resides in the fact that decoupling is not necessary and the system is much more robust as demonstrated by the modelling and simulation studies under different operating conditions, such as changes in water flow rate

Entwurf eines erweiterten Blockführungskonzeptes für kombinierte Gas- und Dampfkraftwerke auf Basis einer flachheitsbasierten Steuerung

Die zunehmende Einspeisung von Strom aus erneuerbaren Energien hat weitreichende Konsequenzen für das gesamte elektrische Energieversorgungssystem. Insbesondere müssen konventionelle Kraftwerke aufgrund der zunehmenden Schwankungen der Residuallast deutlich flexibler betrieben werden als bisher. Die Flexibilisierung des Betriebs umfasst vielerlei Aspekte, wobei schnelle und präzise Leistungsänderungen eine der wesentlichen Anforderungen ist. In dieser Arbeit liegt der Fokus auf kombinierten Gas- und Dampfkraftwerken, da diese Kraftwerke aufgrund hoher Wirkungsgrade und geringer spezifischer Emissionen weltweit vielfach eingesetzt werden. Um sowohl Bestands- als auch Neubauanlagen flexibler betreiben zu können, kommt eine Reihe von Maßnahmen in Frage. Leittechnische Maßnahmen, wie das in dieser Arbeit untersuchte erweiterte Blockführungskonzept, haben den Vorteil vergleichsweise geringer Kosten im Vergleich zu baulichen Maßnahmen sowie einer schnellen Umsetzung und sicheren Inbetriebnahme. Das erweiterte Blockführungskonzept verfolgt das Ziel, schnelle und präzise Leistungsänderungen zu ermöglichen. Gleichzeitig soll ein möglichst ruhiger und schonender Betrieb der Gesamtanlage sichergestellt werden, insbesondere sollen möglichst wenig Störungen in unterlagerten Regelkreisen angeregt werden. Da aus regelungstechnischer Perspektive Arbeitspunktänderungen wie Lastwechsel zu den Aufgaben einer Steuerung gehören, wird die bestehende Regelung in dieser Arbeit um einen Steuerzweig ergänzt. Dieser besteht aus zwei wesentlichen Komponenten: Kern des Steuerzweiges ist eine modellbasierte Steuerung nach dem flachheitsbasierten Ansatz. Das über das Steuerungsentwurfsmodell einfließende Prozesswissen wird genutzt, um Stellsignale zu berechnen, die auf die Prozessdynamik abgestimmt sind. Dies führt zu besserem Prozessverhalten, Lastwechsel können gegebenenfalls schneller gefahren werden und die Regelung wird entlastet. Darüber hinaus werden alle Stellgrößen ideal aufeinander abgestimmt. Dadurch wird der Tatsache Rechnung getragen, dass es sich um ein Mehrgrößensystem handelt, bei dem sich diverse Prozessgrößen gegenseitig beeinflussen. Die Folge ist eine ruhigere Fahrweise der Anlage. Die zweite zentrale Komponente, die in engem Zusammenhang mit der Steuerung steht, ist eine neuartige Sollwertführung. Die Sollwertführung hat die Aufgabe, aus Zielwertvorgaben für die Leistung geeignete Sollwertverläufe zu bestimmen. Um auch hierbei die Prozessdynamik berücksichtigen zu können, sind Ansatzfunktionen notwendig, die entsprechende Freiheitsgrade bieten. Gleichzeitig müssen gewisse Randbedingungen durch den Steueralgorithmus eingehalten werden. Beides wird durch den Einsatz von sogenannten Bézierkurven gewährleistet, zudem zeichnen sich diese durch einfache Konstruktions-vorschriften und numerische Stabilität aus. Das erweiterte Blockführungskonzept wird im Rahmen dieser Arbeit detailliert vorgestellt und in Simulationen an einem nichtlinearen Anlagenmodell getestet. In diesem Zusammenhang wird insbesondere der Vergleich zum klassischen Blockführungskonzept nach dem Stand der Technik hervorgehoben. Darüber hinaus wird der Einfluss der Sollwertführung detailliert untersucht. Hierzu gehört sowohl die Berechnung optimaler Sollwertverläufe als auch die Erweiterung um eine prädiktive Online-Sollwertführung zur Bereitstellung von sogenannter Sekundärregelleistung. Die Simulationsergebnisse zeigen die erwarteten deutlichen Verbesserungen des Regelverhaltens der Anlage, gleichzeitig kann durch eine geeignete Sollwertführung der Stellaufwand positiv beeinflusst werden.The increasing feed-in of electrical power from renewable energy sources has a far-reaching impact on the entire energy supply. Most notably, conventional power plants need to adopt a more flexible mode of operation due to the increasingly fluctuating residual load. The notion of operational flexibility embraces several aspects; one of the most crucial of these is fast and precise load cycling operation. The focus of this thesis is on combined cycle gas turbine plants as this technology is widely used all over the world due to its high efficiencies and low specific emissions. Among the multitude of approaches towards increased operational flexibility of both new builds and existing units, improvements of the instrumentation and control system (I&C) are particularly advantageous. They require lower investments than constructional modifications and can be implemented and commissioned quickly. The extended unit control concept that is described in this thesis falls into this category. It aims at enabling faster load changes while allowing enhanced control performance. Furthermore, disturbances in subordinated control loops will be limited to a minimum, resulting in smoother overall process behaviour. From a control engineering perspective, load changes of power plants are best handled by feedforward control. Therefore, within the scope of this thesis, a feedforward control path is added to the feedback control structure of the existing unit control system of combined cycle gas turbine plants. This feedforward control path consists of two major components: At the core of this feedforward control path is a model-based feedforward control algorithm that has been calculated following the methodology of flatness based control. Knowledge of the dynamic behaviour of the power plant process is taken into account within the control algorithm by means of a dynamic model. The feedforward control enables faster load changes, leads to improved load tracking and thereby reduces feedback control action. Furthermore, the model based character of the feedforward control leads to improved coordination of all control variables which is relevant for multiple-input multiple-output type systems in the sense that undesired interaction between controlled variables are effectively reduced. The second crucial component that is closely related to the feedforward control algorithm is a new type of trajectory planning. Trajectory planning takes place before the control itself and consists of the planning of suitable set-point trajectories based on the target values of the controlled variables. Ansatz-functions for set-point trajectories that provide adequate degrees of freedom are required in order to take the process dynamics into account, as was done in the design of the feedforward control algorithm. Moreover, certain boundary conditions, imposed by the feedforward control, need to be considered. Both conditions are met by so-called Bézier-Curves which are additionally beneficial due to their simplicity and numerical stability. This thesis describes both the extended unit control concept in detail as well as the results of numerical simulations based on a nonlinear process model. The comparison between the extended unit control concept and the state-of-the-art one is particularly stressed in this context. Moreover, the impact of the new trajectory planning strategy is emphasized. This comprises both an optimal trajectory planning study for load changes as well as predictive online trajectory planning. The latter is necessary in order to also cover the provision of so-called Frequency Restoration Reserve (FRR) by the combined cycle gas turbine plant. The simulation results reveal the considerable foreseen improvements in terms of control performance as well as the positive impact of suitable set-point trajectories on the required control effort

Modeling and Control of the Paper Machine Drying Section

The topic of this thesis is modeling and control of the last part of the paper machine - the drying section. Paper is dried by letting it pass through a series of steam heated cylinders and the evaporation is thus powered by the latent heat of vaporization of the steam. The moisture in the paper is controlled by adjusting the set point of the steam pressure controllers. There exist several commercial incentives to focus on the performance of the moisture control. The time to perform a grade change is often limited by the moisture and shorter grade change time is directly correlated to economic profit. Studies have shown that the drying section uses 2/3 of the total energy requirement in paper making. Reduced variations in moisture gives opportunity for target shifts (changed set point) which reduces the amount of raw material and steam requirement. It also creates opportunity for increased production rate. The thesis is divided in two parts. The first part deals with the control of the steam pressure inside the cylinders. Both a black-box model and a physical model are given for the steam pressure process. A tuning rule for both PI and PID control is derived and various other controller structures are investigated. Many of the results are verified by experiments on paper machines at different paper mills. The second part of the thesis treats the moisture controller. The physical model from the first part is expanded with a model for the paper. This gives a complete simulation model for the drying section that is implemented in the object-oriented modeling language Modelica. Two new approaches to control the moisture by feedback are evaluated. The first utilizes the air around the paper in combination with the drying cylinders to improve the controller performance. The second uses only the last part of the drying section to control the moisture, while the first part is put at an appropriate level. Finally, feedforward of a surface temperature signal is examined

Control and management of energy storage systems in microgrids

The rate of integration of the renewable energy sources in modern grids have significantly increased in the last decade. These intermittent, non-dispatchable renewable sources, though environment friendly tend to be grid unfriendly. This is precisely due to the issues pertaining to grid congestion, voltage regulation and stability of grids being reported as a result of the incorporation of renewable sources. In this scenario, the use of energy storage systems (ESS ) in electric grids is being widely proposed to overcome these issues. However, integrating energy storage systems alone will not compensate for the issue created by renewable generation. The control and management of the ESS should be done optimally so that their full capabilities are exploited to overcome the issues in the power grids and to ensure their lower cost of investment by prolonging ESS lifetime through minimising degradation. Motivated by this aspect this Ph.D work focusses on developing an efficient, optimal control and management strategy for ESS in a microgrid, especially hybrid ESS. The Ph.D work addresses this issue by proposing a hierarchical control scheme comprising of a lower power management and higher energy management stage with contributions in each stage. In the power management stage this work focusses on improving aspects of real time control of power converters interfacing ESS to grid and the microgrid system as whole. The work proposes control systems with improved dynamic behaviour for power converters based on the reset control framework. In the microgrid control the work presents a primary+secondary control scheme with improved voltage regulation performance under disturbances, using an observer. The real time power splitting strategies among hybrid ESS accounting for the ESS operating efficiencies and degradation mechanisms will also be addressed in the primary+secondary control of power management stage. The design criteria, stability and robustness analysis will be carried out, along with simulation or experimental verifications. In the higher level energy management stage, the contribution of this work involves application of an economic MPC framework for the management of ESS in microgrids. The work specifically addresses the problems of mitigating grid congestion from renewable power feed-in, minimising ESS degradation and maximising self consumption of generated renewable energy using the MPC based energy management system. A survey of the forecasting methods that can be used for MPC will be carried out and a neural network based forecasting unit for time series prediction will be developed. The practical issue of accounting for forecasting error in the decision making of MPC will be addressed and impact of the resulting conservative decision making on the system performance will be analysed. The improvement in performance with the proposed energy management scheme will be demonstrated and quantified.La integración de las fuentes de energía renovables en las redes modernas ha aumentado significativamente en la última década. Estas fuentes renovables, aunque muy convenientes para el medio ambiente son de naturaleza intermitente, y son no panificables, cosa que genera problemas en la red de distribución. Esto se debe precisamente a los problemas relacionados con la congestión de la red y la regulación del voltaje. En este escenario, el uso de sistemas de almacenamiento de energía (ESS) en redes eléctricas está siendo ampliamente propuesto para superar estos problemas. Sin embargo, la integración de sistemas de almacenamiento de energía por sí solos no compensará el problema creado por la generación renovable. El control y la gestión del ESS deben realizarse de manera óptima, de modo que se aprovechen al máximo sus capacidades para superar los problemas en las redes eléctricas, garantizar un coste de inversión razonable y prolongar la vida útil del ESS minimizando su degradación. Motivado por esta problemática, esta tesis doctoral se centra en desarrollar una estrategia de control y gestión eficiente para los ESS integrados en una microrred, especialmente cuando se trata de ESS de naturaleza. El trabajo de doctorado propone un esquema de control jerárquico compuesto por un control de bajo nivel y una parte de gestión de energía operando a más alto nivel. El trabajo realiza aportaciones en los dos campos. En el control de bajo nivel, este trabajo se centra en mejorar aspectos del control en tiempo real de los convertidores que interconectan el ESS con la red y el sistema de micro red en su conjunto. El trabajo propone sistemas de control con comportamiento dinámico mejorado para convertidores de potencia desarrollados en el marco del control de tipo reset. En el control de microrred, el trabajo presenta un esquema de control primario y uno secundario con un rendimiento de regulación de voltaje mejorado bajo perturbaciones, utilizando un observador. Además, el trabajo plantea estrategias de reparto del flujo de potencia entre los diferentes ESS. Durante el diseño de estos algoritmos de control se tienen en cuenta los mecanismos de degradación de los diferentes ESS. Los algoritmos diseñados se validarán mediante simulaciones y trabajos experimentales. En el apartado de gestión de energía, la contribución de este trabajo se centra en la aplicación del un control predictivo económico basado en modelo (EMPC) para la gestión de ESS en microrredes. El trabajo aborda específicamente los problemas de mitigar la congestión de la red a partir de la alimentación de energía renovable, minimizando la degradación de ESS y maximizando el autoconsumo de energía renovable generada. Se ha realizado una revisión de los métodos de predicción del consumo/generación que pueden usarse en el marco del EMPC y se ha desarrollado un mecanismo de predicción basado en el uso de las redes neuronales. Se ha abordado el análisis del efecto del error de predicción sobre el EMPC y el impacto que la toma de decisiones conservadoras produce en el rendimiento del sistema. La mejora en el rendimiento del esquema de gestión energética propuesto se ha cuantificado.La integració de les fonts d'energia renovables a les xarxes modernes ha augmentat significativament en l’última dècada. Aquestes fonts renovables, encara que molt convenients per al medi ambient són de naturalesa intermitent, i són no panificables, cosa que genera problemes a la xarxa de distribució. Això es deu precisament als problemes relacionats amb la congestió de la xarxa i la regulació de la tensió. En aquest escenari, l’ús de sistemes d'emmagatzematge d'energia (ESS) en xarxes elèctriques està sent àmpliament proposat per superar aquests problemes. No obstant això, la integració de sistemes d'emmagatzematge d'energia per si sols no compensarà el problema creat per la generació renovable. El control i la gestió de l'ESS s'han de fer de manera _optima, de manera que s'aprofitin al màxim les seves capacitats per superar els problemes en les xarxes elèctriques, garantir un cost d’inversió raonable i allargar la vida útil de l'ESS minimitzant la seva degradació. Motivat per aquesta problemàtica, aquesta tesi doctoral es centra a desenvolupar una estratègia de control i gestió eficient per als ESS integrats en una microxarxa, especialment quan es tracta d'ESS de natura híbrida. El treball de doctorat proposa un esquema de control jeràrquic compost per un control de baix nivell i una part de gestió d'energia operant a més alt nivell. El treball realitza aportacions en els dos camps. En el control de baix nivell, aquest treball es centra a millorar aspectes del control en temps real dels convertidors que interconnecten el ESS amb la xarxa i el sistema de microxarxa en el seu conjunt. El treball proposa sistemes de control amb comportament dinàmic millorat per a convertidors de potència desenvolupats en el marc del control de tipus reset. En el control de micro-xarxa, el treball presenta un esquema de control primari i un de secundari de regulació de voltatge millorat sota pertorbacions, utilitzant un observador. A més, el treball planteja estratègies de repartiment de el flux de potència entre els diferents ESS. Durant el disseny d'aquests algoritmes de control es tenen en compte els mecanismes de degradació dels diferents ESS. Els algoritmes dissenyats es validaran mitjanant simulacions i treballs experimentals. En l'apartat de gestió d'energia, la contribució d'aquest treball se centra en l’aplicació de l'un control predictiu econòmic basat en model (EMPC) per a la gestió d'ESS en microxarxes. El treball aborda específicament els problemes de mitigar la congestió de la xarxa a partir de l’alimentació d'energia renovable, minimitzant la degradació d'ESS i maximitzant l'autoconsum d'energia renovable generada. S'ha realitzat una revisió dels mètodes de predicció del consum/generació que poden usar-se en el marc de l'EMPC i s'ha desenvolupat un mecanisme de predicció basat en l’ús de les xarxes neuronals. S'ha abordat l’anàlisi de l'efecte de l'error de predicció sobre el EMPC i l'impacte que la presa de decisions conservadores produeix en el rendiment de el sistema. La millora en el rendiment de l'esquema de gestió energètica proposat s'ha quantificat

Energy efficient control of electrostatically actuated MEMS

Plenty of Micro-electro-mechanical Systems (MEMS) devices are actuated using electrostatic forces, and specially, parallel-plate actuators are extensively used, due to the simplicity of their design. Nevertheless, parallel-plate actuators have some limitations due to the nonlinearity of the generated force. The dissertation analyzes the dynamics of the lumped electrostatically actuated nonlinear system, in order to obtain insight on its characteristics, define desired performance goals and implement a controller for energy efficient robustly stable actuation of MEMS resonators. In the first part of the dissertation, the modeling of the electromechanical lumped system is developed. From a complete distributed parameters model for MEMS devices which rely on electrostatic actuation, a concentrated parameters simplification is derived to be used for analysis and control design. Based on the model, energy analysis of the pull-in instability is performed. The classic approach is revisited to extend the results to models with a nonlinear springs. Analysis of the effect of dynamics is studied as an important factor for the stability of the system. From this study, the Resonant Pull-in Condition for parallel-plate electrostatically actuated MEMS resonators is defined and experimentally validated. Given the importance of the nonlinear dynamics and its richness in behaviors, Harmonic Balance is chosen as a tool to characterize the steady-state oscillation of the resonators. This characterization leads to the understanding of the key factors for large and stable oscillation of resonators. An important conclusion is reached, Harmonic Balance predicts that any oscillation amplitude is possible for any desired frequency if the appropriate voltage is applied to the resonator. And the energy consumption is dependent on this chosen oscillation frequency. Based on Harmonic Balance results, four main goals are defined for the control strategy: Stable oscillation with large amplitudes of motion; Robust oscillation independently of MEMS imperfections; Pure sinus-like oscillation for high-grade sensing; and Low energy consumption. The second part of the dissertation deals with the controller selection, design and verification. A survey of prior work on MEMS control confirms that existing control approaches cannot provide the desired performance. Consequently, a new three-stage controller is proposed to obtain the desired oscillation with the expected stability and energy efficiency. The controller has three different control loops. The first control loop includes a Robust controller designed using on µ-synthesis, to deal with MEMS resonators uncertainties. The second control loop includes an Internal-Model-Principle Resonant controller, to generate the desired control action to obtain the desired oscillation. And the third control loop handles the energy consumption minimization through an Extremum Seeking Controller, which selects the most efficient working frequency for the desired oscillation. The proposed controller is able to automatically generate the needed control voltage, as predicted by the Harmonic Balance analysis, to operate the parallel-plate electrostatically actuated MEMS resonator at the desired oscillation. Performance verification of stability, robustness, sinus-like oscillation and energy efficiency is carried out through simulation. Finally, the needed steps for a real implementation are analyzed. Independent two-sided actuation for full-range amplitude oscillation is introduced to overcome the limitations of one-sided actuation. And a modification of standard Electromechanical Amplitude Modulation is analyzed and validated for position feedback implementation. With these improvements, a MEMS resonator with the desired specifications for testing the proposed control is designed for fabrication. Based on this design, testing procedure is discussed as future work.Molts microsistemes (MEMS) són actuats amb forces electrostàtiques, i especialment, els actuadors electrostàtics de plaques paral.leles són molt usats, degut a la simplicitat del seu disseny. Tot i això, aquests actuadors tenen limitacions degut a la no-linealitat de les forces generades. La tesi analitza el sistema mecànic no-lineal actuat electrostàticament que forma el MEMS, per tal d'entendre'n les característiques, definir objectius de control de l'oscil.lació, i implementar un controlador robust, estable i eficient energèticament. A la primera part de la tesi es desenvolupa el modelat del sistema electromecànic complert. A partir de la formulació de paràmetres distribuïts aplicada a dispositius MEMS amb actuació electrostàtica, es deriva una formulació de paràmetres concentrats per a l'anàlisi i el disseny del control. Basat en aquest model, s'analitza energèticament la inestabilitat anomenada Pull-in, ampliant els resultats de l'enfocament clàssic al model amb motlles no-lineals. Dins de l'anàlisi, l'evolució dinàmica s'estudia per ser un factor important per a l'estabilitat. D'aquest estudi, la Resonant Pull-in Condition per a actuadors electrostàtics de plaques paral.leles es defineix i es valida experimentalment. Donada la importància de la dinàmica no-lineal del sistema i la seva riquesa de comportaments, s'utilitza Balanç d'Harmònics per tal de caracteritzar les oscil.lacions en estacionari. Aquesta caracterització permet entendre els factors claus per a obtenir oscil.lacions estables i d'amplitud elevada. El Balanç d'Harmònics dóna una conclusió important: qualsevol amplitud d'oscil.lació és possible per a qualsevol freqüència desitjada si s'aplica el voltatge adequat al ressonador. I el consum energètic associat a aquesta oscil.lació depèn de la freqüència triada. Llavors, basat en aquests resultats, quatre objectius es plantegen per a l'estratègia de control: oscil.lació estable amb amplituds elevades; robustesa de l'oscil.lació independentment de les imperfeccions dels MEMS; oscil.lació sinusoïdal sense harmònics per a aplicacions d'alta precisió; i baix consum energètic. La segona part de la tesi tracta la selecció, disseny i verificació dun controlador adequat per a aquests objectius. La revisió dels treballs existents en control de MEMS confirma que cap dels enfocaments actuals permet obtenir els objectius desitjats. En conseqüència, es proposa el disseny d'un nou controlador amb tres etapes per tal d'obtenir l'oscil.lació desitjada amb estabilitat i eficiència energètica. El controlador té tres llaços de control. Al primer llaç, un controlador robust dissenyat amb µ-síntesis gestiona les incertes es dels MEMS. El segon llaç inclou un controlador Ressonant, basat en el Principi del Model Intern, per a generar l'acció de control necessària per a obtenir l'oscil.lació desitjada. I el tercer llaç de control gestiona la minimització de l'energia consumida mitjançant un controlador basat en Extremum Seeking, el qual selecciona la freqüència de treball més eficient energèticament per a l'oscil.lació triada. El controlador proposat és capaç de generar automàticament el voltatge necessari, igual al previst pel Balanç d'Harmònics, per tal d'operar electrostàticament amb plaques paral.leles els ressonadors MEMS. Mitjançant simulació se'n verifica l'estabilitat, robustesa, inexistència d'harmònics i eficiència energètica de l'oscil.lació. Finalment, la implementació real és analitzada. En primer lloc, un nou esquema d'actuació per dos costats amb voltatges independents es proposa per aconseguir l'oscil.lació del ressonador en tot el rang d'amplituds. I en segon lloc, una modificació del sensat amb Modulació d'Amplitud Electromecànica s'utilitza per tancar el llaç de control de posició. Amb aquestes millores, un ressonador MEMS es dissenya per a ser fabricat i validar el control. Basat en aquest disseny, es proposa un procediment de test plantejat com a treball futur.Postprint (published version