Ziel der Arbeit ist die anschauliche Demonstration der Leistungsfähigkeit von Hardware- Systemen zur Regelung instabiler Systeme am Beispiel des Inversen Pendels. Dabei handelt es sich um das Balancieren eines Stabes, einem Standard-Problem der Regelungstechnik. Es wird die Konzeption und Implementierung einer Hardware-Regelung in einem FPGA-Prototypenboard zur Realisierung dieser Aufgabe beschrieben. Die Regelung basiert mit LQR-Entwurf und Kalman-Filter auf klassischen Methoden der Regelungstechnik. Zur Demonstration der Regelung wurde ein mechanischer Aufbau vorgenommen, an dem die Funktionsfähigkeit des Inversen Pendels praktisch gezeigt wurde.:1 Einleitung 11 1.1 Motivation.................................... 11 1.2 Analyse der Aufgabenstellung ......................... 11 1.3 Gliederung der Arbeit ............................. 12 2 Grundlagen 13 2.1 Referenzanwendung Inverses Pendel...................... 13 2.2 Aufbau des Regelsystems............................ 15 2.3 Verfahren zum Reglerentwurf ......................... 19 2.4 Verfahren zur Zustandsschätzung ....................... 22 2.5 Sensorik..................................... 26 2.6 Antrieb ..................................... 28 3 Inverse Pendel im Vergleich 33 3.1 Bauformen.................................... 33 3.2 Realisierungsbeispiele.............................. 34 3.3 Fazit der Recherche............................... 39 4 Elektromechanischer Aufbau 41 4.1 Mechanik .................................... 42 4.2 Sensorik..................................... 42 4.3 Antrieb ..................................... 44 4.4 FPGA-Board .................................. 47 5 Modellbildung 48 5.1 Herleitung der Systemgleichungen....................... 48 5.2 Anpassung an den Schrittmotor ........................ 51 5.3 Linearisiertes Modell im Zustandsraum.................... 51 5.4 Analyse der Modelleigenschaften........................ 52 6 Reglerentwurf 56 6.1 Einstellung des LQ-Reglers........................... 56 6.2 Einstellung des Kalman-Filters ........................ 57 6.3 Aufschwing- und Fangalgorithmus....................... 58 6.4 Simulation.................................... 60 6.5 Konsequenzen für die Realisierung....................... 63 7 Implementierung 65 7.1 Besonderheiten des Hardware-Entwurfs.................... 65 7.2 Systempartitionierung und Entwurfsstrategie . . . . . . . . . . . . . . . . . 66 7.3 Teilkomponenten ................................ 67 7.4 Modifizierung des Kalman-Filters ....................... 72 7.5 Probleme .................................... 78 8 Schluss 80 8.1 Zusammenfassung................................ 80 8.2 Ergebnisse.................................... 80 8.3 Ausblick..................................... 82 Literaturverzeichnis 84 A Details zum Projekt 87 A.1 Kurzdokumentation .............................. 87 A.2 Datei- und Verzeichnisstruktur......................... 88 A.3 Simulationsresultate .............................. 89

This master thesis project is focused on the development of an LQR controller and its comparison with other controllers (PID and MPC), in order to successfully control an Autonomous Underwater Vehicle manipulation system. The modelling of the manipulator was performed first in Matlab and later on in Simulink-Simscape. Once the manipulator was integrated with the AUV model, the LQR controller was also developed initially in Matlab and then in Simulink. The controller was then extracted from Simulink as a C-code and verified in Stonefish. After confirming that the LQR code was working in Stonefish, its results from Simulink were compared with PID and MPC results for two different trajectories. The data for comparison and statistical analysis were divided into the two trajectory scenarios (horizontal and vertical) since the weight matrices of both controllers were different. Looking at the system’s overall behavior the Model Predictive Control (MPC) and LQR had similar results, regarding the rise time, overshoot, steady-state error and robustness to disturbances. An anticipated fact for the MPC was that it takes the longest run time for both scenarios. Lastly, as expected the PID had the worst response of all three controllers, in both scenarios. Implementing a PID on a nonlinear system, produced many oscillations without being able to stabilize at the reference value, thus giving a large steady-state error. In addition, it could not counteract the noise disturbances in the signal. / Detta examensarbete är inriktat på utvecklingen av en LQR-styrenhet och dess jämförelse med andra kontroller (PID och MPC), för att framgångsrikt styra ett autonomt undervattensfordon-manipulationssystem. Modelleringen av manipulatorn utfördes först i Matlab och senare i Simulink-Simscape. När manipulatorn väl hade integrerats med AUV modellen, utvecklades LQR styrenheten också inledningsvis i Matlab och sedan i Simulink. Kontrollenheten extraherades sedan från Simulink som en C-kod och verifierades i Stonefish. Efter att ha bekräftat att LQR koden fungerade i Stonefish, jämfördes resultaten från Simulink med PID och MPC resultat för två olika banor. Data för jämförelse och statistisk analys delades in i de två bana-scenarierna (horisontella och vertikala), eftersom viktmatriserna för båda kontrollerna var olika. När man tittar på systemets övergripande beteende hade Model Predictive Controller (MPC) och LQR liknande resultat när det gäller stigningstid, överskott, steady-state fel och robusthet mot störningar. Ett förväntat faktum för MPC var att det tar den längsta körtiden för båda scenarierna. Slutligen, som väntat, hade PID det sämsta svaret av alla tre kontrollerna, i båda scenarierna. Implementering av ett PID på ett olinjärt system gav många oscillationer utan att kunna stabilisera sig vid referensvärdet, vilket gav ett stort steady-state fel. Dessutom kunde den inte motverka bullerstörningarna i signalen.

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.

As futuras utilizações de sistemas de controle em automóveis seguirão a tendência de integração, através do desenvolvimento de sistemas de controle integrados capazes de coordenar as ações dos vários subsistemas que compõem o veículo. Esta coordenação e integração requerem que as integrações entre os subsistemas sejam levadas em conta já nos primeiros estágios de projeto, levando ao desenvolvimento de modelos completos de veículos. Neste sentido, o comportamento dinâmico de um veículo de quatro rodas é analisado através de técnicas de modelagem de sistemas multicorpos utilizando-se o programa ADAMS. Posteriormente, são gerados modelos lineares obtidos através do Jacobiano das equações do modelo original, resultando em uma gama de equações na forma de espaço de estados. O modelo linearizado é então submetido a vários tipos de simulações e os resultados são comparados às respostas do modelo não linear de modo a validar as aproximações lineares em diferentes condições de operação do veículo. São também desenvolvidos dois sistemas de controle de suspensão baseados em técnicas de controle ótimo como duas diferentes abordagens: um controlador skyhook que foi implementado no modelo não linear desenvolvido no ADAMS e um controle de suspensão baseado em um controlador RLQ (Regulador Linear Quadrático), com realimentação de saída que utiliza os modelos linearizados na forma de espaço de estados, sendo este último implementado através da co-simulação ADAMS/Matlab. O sistema de controle de suspensão desenvolvido é um primeiro passo na tentativa de projeto de um sistema de controle integrado do movimento. / Future applications of control in automotive vehicles will follow a trend towards system integration, leading ultimately to the development of integrated vehicle control systems capable of coordinating the action of the various subsystems. The coordination and integration of automotive vehicle subsystems require the interaction amongst the various subsystems to be taken into consideration at the control design stages, resulting in full vehicle models. Therefore, a nonlinear 10 degree of freedom model is obtained through MBS modelling techniques present in ADAMS package software. Then, a linear model is obtained by linearization of the system equations through the Jacobian facility also present in ADAMS. The resulting linearised models are simulated and their response are compared to the previous non-linear one in order to validate the linear approximations. This work also presents two distincts suspension control systems based in optimal control theory: a skyhook controler designed at ADAMS (with the non-linear vehicle model) and a LQR (Linear Quadratic Regulator) with output feedback based on the state space linear vehicle model. This last one was designed through ADAMS/Matlab co-simulation facilities. This designed suspension control is a first attempt to future developments of integrated vehicle control.

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.

The popularity of distributed generating (DG) sources have been increasing over the past few years. With the increasing penetration of these DGs, the concept of micro grid is becoming popular. A micro grid is a small power system network with distributed generating sources which can operate seamlessly irrespective of the presence of the utility grid. Operating the micro grid in this manner increases system reliability and reduces power interruptions. However, it introduces several control challenges. This thesis aims at analysing the behaviour of a micro grid system during the transition between grid connected mode and islanded mode of operation and address the control challenges through novel schemes. With the presence of grid, the micro grid system variables, such as voltage and frequency, are strictly regulated by the grid. The local sources follow the voltage and frequency reference set by the grid and supply constant power. With the loss of grid, that is when the system is islanded, the network variables need to be regulated by the local sources. The control structures for the inverter-based sources during the two operating modes are detailed in the present work. With the loss of grid, the system should be able to transfer seamlessly to islanded mode without any transients. Similarly, when the grid supply is restored, the micro grid should seamlessly resynchronize to the grid without any transients. This thesis proposes two novel controller schemes for achieving seamless transfer between grid-connected and islanded mode in micro grids. The rst scheme uses an output feedback topology to reduce the transitions during mode transfer. The second scheme uses a Linear Quadratic Regulator (LQR) theory based compensator to achieve seamless transfer. The performance of the proposed schemes have been validated through simulations on a benchmark micro grid network for various operating conditions. An experimental micro grid set-up is developed with a single inverter based DG source. The droop control scheme for islanded mode of operation has been validated on hardware.

Syftet med projektet är att konstruera en inverterad pendel som sedan med hjälp av reglertekniska metoder ska stabiliseras. De linjära regulatorer som prövats är Proportionell, Integrerande och Deriverande (PID) -regulatorn och Linnear Quadratic Gaussian (LQG) -regulatorn som båda är populära och beprövade i industrin. PID-regulatorn är den absolut mest använda regulatorn medan LQG-regulatorn är mer raffinerad och i vissa avseenden en optimal regulator. Regulatorerna programmerades in i mikrokontrollern Arduino Nano som skickar signaler till en motordrivare som styr den stegmotor som ska balansera pendeln. Mycket av arbetet har handlat om att skapa en uppställning som tillåter goda förutsättningar för att pröva regulatorerna. I uppställningen finns delar som utformats i Computor-Aided design (CAD) -verktyget OpenSCAD och skrivits ut på en 3D-skrivare. Den givare vi använt för att mäta pendelns vinkel är en potentiometer infäst i dessa 3D-utskrivna delar. Motorn kunde styras till sin maximala kapacitet och en uppställning har skapats. Dock skulle en starkare motor och en mer robust uppställning möjliggöra en avsevärt bättre reglering. Regulatorerna klarade inte av att stabilisera systemet mer än ett fåtal sekunder, detta bland annat pågrund av tidsbrist till att justera regleringsvariablerna.

As futuras utilizações de sistemas de controle em automóveis seguirão a tendência de integração, através do desenvolvimento de sistemas de controle integrados capazes de coordenar as ações dos vários subsistemas que compõem o veículo. Esta coordenação e integração requerem que as integrações entre os subsistemas sejam levadas em conta já nos primeiros estágios de projeto, levando ao desenvolvimento de modelos completos de veículos. Neste sentido, o comportamento dinâmico de um veículo de quatro rodas é analisado através de técnicas de modelagem de sistemas multicorpos utilizando-se o programa ADAMS. Posteriormente, são gerados modelos lineares obtidos através do Jacobiano das equações do modelo original, resultando em uma gama de equações na forma de espaço de estados. O modelo linearizado é então submetido a vários tipos de simulações e os resultados são comparados às respostas do modelo não linear de modo a validar as aproximações lineares em diferentes condições de operação do veículo. São também desenvolvidos dois sistemas de controle de suspensão baseados em técnicas de controle ótimo como duas diferentes abordagens: um controlador skyhook que foi implementado no modelo não linear desenvolvido no ADAMS e um controle de suspensão baseado em um controlador RLQ (Regulador Linear Quadrático), com realimentação de saída que utiliza os modelos linearizados na forma de espaço de estados, sendo este último implementado através da co-simulação ADAMS/Matlab. O sistema de controle de suspensão desenvolvido é um primeiro passo na tentativa de projeto de um sistema de controle integrado do movimento. / Future applications of control in automotive vehicles will follow a trend towards system integration, leading ultimately to the development of integrated vehicle control systems capable of coordinating the action of the various subsystems. The coordination and integration of automotive vehicle subsystems require the interaction amongst the various subsystems to be taken into consideration at the control design stages, resulting in full vehicle models. Therefore, a nonlinear 10 degree of freedom model is obtained through MBS modelling techniques present in ADAMS package software. Then, a linear model is obtained by linearization of the system equations through the Jacobian facility also present in ADAMS. The resulting linearised models are simulated and their response are compared to the previous non-linear one in order to validate the linear approximations. This work also presents two distincts suspension control systems based in optimal control theory: a skyhook controler designed at ADAMS (with the non-linear vehicle model) and a LQR (Linear Quadratic Regulator) with output feedback based on the state space linear vehicle model. This last one was designed through ADAMS/Matlab co-simulation facilities. This designed suspension control is a first attempt to future developments of integrated vehicle control.

This thesis deals with design of electronic laboratory model for teaching mechatronic subjects. The main part of the model consists of a RLC-circuit embedded in PCB. Other parts of PCB and data acquisition card mediate communication with Matlab environment. In the thesis the progress of design process, simulation, manufacture and model testing is described. The results are functioning educational model and several educational tasks, for which the solution are presented.

Master’s thesis deals with using a linear matrix inequality (LMI) in control of a dynamic systems. We can define a stability of a dynamic system with a LMI. We can use a LMI for research if the poles of a system are in a given regions in the left half-plane of the complex plane with a LMI or we can use a LMI for a state feedback control. In the work we describe a desing of a controller minimizing a norm from an input to an output of the system. There is also a desing of a LQ controller with a LMI. In the end of the work, there are two examples of a design a LQ controller, which minimize the norm from the input to the output of the system and moves a poles of a dynamic system in a given regions in the complex plane, with the LMI. We use a LMI for a design a continuos LQ controller in the first example. In the second example we use a LMI for a design a discrete LQ controller.