Stabilization of pan-tilt systems using acceleration based LMI-LQR controller

This paper extends the previous work on LPV modeling of a pan-tilt system [1] and tackles the robust stabilization problem by employing angular acceleration feedback in an LMI based optimal LQR controller. The state vector of the LPV model is augmented to include the integral of the position errors in addition to joint angles and velocities. Therefore, an extended polytopic quasi-LPV model of the pan tilt system is derived. The LMI based optimal LQR controller that utilizes acceleration feedback is synthesized based on the extended LPV model. Since the time varying parameter vector is 4 dimensional, the proposed controller is synthesized by interpolating LMIs at 16 vertices of the polytope. A cascaded nonlinear high gain observer is also designed to estimate reliable positions, velocities and accelerations from noisy encoder measurements. Simulation results show that the proposed LMI based optimal LQR controller outperforms the classical LMI based LQR controller

Parameter Varying Mode Decoupling for LPV systems

The paper presents the design of parameter varying input and output transformations for Linear Parameter Varying systems, which make possible the control of a selected subsystem. In order to achieve the desired decoupling the inputs and outputs of the plant are blended together, and so the MIMO control problem is reduced to a SISO one. The new input of the blended system will only interact with the selected subsystem, while the response of the undesired dynamical part is suppressed in the single output. Decoupling is achieved over the whole parameter range, and no further dynamics are introduced. Linear Matrix Inequality methods form the basis of the proposed approach, where the minimum sensitivity (denoted by the H − index) is maximized for the subsystem to be controlled, while the H∞ norm of the subsystem to be decoupled is minimized. The method is evaluated on a flexible wing aircraft model

A generalized framework for robust nonlinear compensation (application to an atmospheric reentry control problem)

Ce travail de thèse est consacré à l'extension de l'Inversion Dynamique non-linéaire (NDI-Nonlinear Dynamic Inversion) pour un ensemble plus grand de systèmes non-linéaires, tout en garantissant des conditions de stabilité suffisantes. La NDI a été étudiée dans le cas de diverses applications, y compris en aéronautique et en aérospatiale. Elle permet de calculer des lois de contrôle capables de linéariser et de découpler un modèle non-linéaire à tout point de fonctionnement de son enveloppe d'état. Cependant cette méthode est intrinsèquement non-robuste aux erreurs de modélisation et aux saturations en entrée. En outre, dans un contexte non-linéaire, l'obtention d'une garantie quantifiable du domaine de stabilité atteint reste à l'heure actuelle complexe. Contrairement aux approches classiques de la NDI, notre méthodologie peut être considérée comme un cadre de compensation non-linéaire généralisé qui permet d'intégrer les incertitudes et les saturations en entrée dans le processus de conception. En utilisant des stratégies de contrôle antiwindup, la loi de pilotage peut être calculée grâce à un simple processus en deux phases. Dans ce cadre de travail généralisé des transformations linéaires fractionnaires (LFT - Linear Fractional Transformations) de la boucle fermée non-linéaire peuvent être facilement déduites pour l'analyse de la stabilité robuste en utilisant des outils standards pour de systèmes linéaires. La méthode proposée est testée pour le pilotage d'un véhicule de rentrée atmosphérique de type aile delta lors de ses phases hypersonique, transsonique et subsonique. Pour cette thèse, un simulateur du vol incluant divers facteurs externes ainsi que des erreurs de modélisation a été développé dans Simulink.This thesis work is devoted to extending Nonlinear Dynamic Inversion (NDI) for a large scale of nonlinear systems while guaranteeing sufficient stability conditions. NDI has been studied in a wide range of applications, including aeronautics and aerospace. It allows to compute nonlinear control laws able to decouple and linearize a model at any operating point of its state envelope. However, this method is inherently non-robust to modelling errors and input saturations. Moreover, obtaining a quantifiable guarantee of the attained stability domain in a nonlinear control context is not a very straightforward task. Unlike standard NDI approaches, our methodology can be viewed as a generalized nonlinear compensation framework which allows to incorporate uncertainties and input saturations in the design process. Paralleling anti-windup strategies, the controller can be computed through a single multichannel optimization problem or through a simple two-step process. Within this framework, linear fractional transformations of the nonlinear closed-loop can be easily derived for robust stability analysis using standard tools for linear systems. The proposed method is tested for the flight control of a delta wing type reentry vehicle at hypersonic, transonic and subsonic phases of the atmospheric reentry. For this thesis work, a Flight Mechanics simulator including diverse external factors and modelling errors was developed in Simulink.TOULOUSE-ISAE (315552318) / SudocSudocFranceF

Linear Parameter-Varying Control of Full-Vehicle Vertical Dynamics using Semi-Active Dampers

Semi-aktive Fahrwerke bergen im Vergleich zu passiven großes Potential zur Verbesserung wesentlicher Fahrzeugeigenschaften, wie Fahrkomfort, Straßenhaftung und Fahrverhalten. Die Ausnutzung dieses Potentials verlangt nach geeigneten Regelungsalgorithmen,welche das nichtlineare Eingangssignal-zu-Dämpferkraft Verhalten und die Passivitätsbeschränkung semi-aktiver Dämpfer berücksichtigen. Im Besonderen die Passivitätsbeschränkung impliziert enge, zustandsabhängige Aktuatorkraftbegrenzungen und sollte daher im Regelungsentwurf direkt berücksichtigt werden. Der Entwurf performanter semi-aktiver Fahrwerkregelungen stellt eine große Herausforderung dar, da Störungen aufgrund von Straßenunebenheiten und Lastwechseln unterschiedliche Anforderungen an die Regelung stellen, und zusätzlich in einer Gesamtfahrzeuganwendung auch ein Regelungsentwurf basierend auf einem Gesamtfahrzeugmodell benötigt wird. Im Gegensatz zu konventionellen viertelfahrzeug-basierten Fahrwerkregelungsansätzen, welche häufig in der Literatur zu finden sind, zielt der Gesamtfahrzeugregelungsansatz dieser Dissertation auf die explizite Berücksichtigung der Hub-, Wank und Nickbewegung des Aufbaus. Darüber hinaus ermöglicht der Gesamtfahrzeugansatz die Entwicklung von fehlertoleranten Reglern, welche die schwache Aktuatorredundanz der vier Dämpfer nutzen. Die vorliegende Dissertation befasst sich mit linear parameter-variablen (LPV) Regelungsmethoden zur Lösung des oben beschriebenen komplexen Regelungsproblems. Die Kraftbegrenzungen der semi-aktiven Dämpfer werden mittels Sättigungsindikatoren modelliert und diese dann als variable Parameter in den LPV Regelungsentwurf integriert. Zusätzlich wird der LPV Regler um eine Dämpferkraftrekonfiguration erweitert, so dass der Regler den Dämpferkraftverlust im Falle einer Dämpferfehlfunktion mit den verbleibenden gesunden Dämpfern kompensiert. Der Regelungsentwurf begegnet den unterschiedlichen Anforderungen von Straßen- und Lastwechselstörungen durch eine Zweifreiheitsgradregelung bestehend aus einem LPV Regler und einer LPV Vorsteuerung.Dabei fokussiert sich der LPV Regler auf die Verminderung des Effekts der Straßenunebenheiten und die LPV Vorsteuerung verringert den Effekt der Lastwechselstörungen. Auf diese Weise zeigt die Zweifreiheitsgradregelung das gewünschte Verhalten trotz dieser beiden konträren Störungen. Die Wirksamkeit der vorgeschlagenen Zweifreiheitsgradregelung wird durch Experimente auf einem Stempelprüfstand und durch Straßenversuche validiert. Die Ergebnisse zeigen eine Verbesserung des klassischen Zielkonflikts der Fahrwerksregelung zwischen Fahrkomfort und Straßenhaftung durch die LPV Gesamtfahrzeugregelung. Insbesondere erzielt die LPV Gesamtfahrzeugregelung eine 10 % ige Verbesserung von Fahrkomfort und Straßenhaftung im Vergleich zu einer Skyhook-Groundhook Gesamtfahrzeugregelung. Des Weiteren verdeutlicht ein Experiment mit einem simulierten Dämpferfehler die Vorteile der fehlertoleranten LPV Regelung. Abschließend wird anhand von Spurwechselversuchen die Wirksamkeit der LPV Vorsteuerung zur Verbesserung von Fahrkomfort, Straßenhaftung und Fahrverhalten bei dynamischen Lenkwinkeleingaben des Fahrers demonstriert

Robust model-based fault estimation and fault-tolerant control : towards an integration

To maintain robustly acceptable system performance, fault estimation (FE) is adopted to reconstruct fault signals and a fault-tolerant control (FTC) controller is employed to compensate for the fault effects. The inevitably existing system and estimation uncertainties result in the so-called bi-directional robustness interactions defined in this work between the FE and FTC functions, which gives rise to an important and challenging yet open integrated FE/FTC design problem concerned in this thesis. An example of fault-tolerant wind turbine pitch control is provided as a practical motivation for integrated FE/FTC design.To achieve the integrated FE/FTC design for linear systems, two strategies are proposed. A H∞ optimization based approach is first proposed for linear systems with differentiable matched faults, using augmented state unknown input observer FE and adaptive sliding mode FTC. The integrated design is converted into an observer-based robust control problem solved via a single-step linear matrix inequality formulation.With the purpose of an integrated design with more freedom and also applicable for a range of general fault scenarios, a decoupling approach is further proposed. This approach can estimate and compensate unmatched non-differentiable faults and perturbations by combined adaptive sliding mode augmented state unknown input observer and backstepping FTC controller. The observer structure renders a recovery of the Separation Principle and allows great freedom for the FE/FTC designs.Integrated FE/FTC design strategies are also developed for Takagi-Sugeno fuzzy modelling nonlinear systems, Lipschitz nonlinear systems, and large-scale interconnected systems, based on extensions of the H∞ optimization approach for linear systems.Tutorial examples are used to illustrate the design strategies for each approach. Physical systems, a 3-DOF (degree-of-freedom) helicopter and a 3-machine power system, are used to provide further evaluation of the proposed integrated FE/FTC strategies. Future research on this subject is also outlined

Fault tolerant flight control system design for unmanned aerial vehicles

Safety and reliability of air vehicles is of the utmost importance. This is particularly true for large civil transport aircraft where a large number of human lives depend on safety critical design. With the increase in the use of unmanned aerial vehicles (UAVs) in our airspace it is essential that UAV safety is also given attention to prevent devastating failures which could ultimately lead to loss of human lives. While civil aircraft have human operators, the pilot, to counteract any unforeseen faults, autonomous UAVs are only as good as the on board flight computer. Large civil aircraft also have the luxury of weight hence redundant actuators (control surfaces) can be installed and in the event of a faulty set of actuators the redundant actuators can be brought into action to negate the effects of any faults. Again weight is a luxury that UAVs do not have. The main objective of this research is to study the design of a fault tolerant flight controller that can exploit the mathematical redundancies in the flight dynamic equations as opposed to adding hardware redundancies that would result in significant weight increase. This thesis presents new research into fault tolerant control for flight vehicles. Upon examining the flight dynamic equations it can be seen, for example, that an aileron, which is primarily used to perform a roll manoeuvre, can be used to execute a limited pitch moment. Hence a control method is required that moves away from the traditional fixed structure model where control surface roles are clearly defined. For this reason, in this thesis, I have chosen to study the application of model predictive control (MPC) to fault tolerant control systems. MPC is a model based method where a model of the plant forms an integral part of the controller. An optimisation is performed based on model estimations of the plant and the inputs are chosen via an optimisation process. One of the main contributions of this thesis is the development of a nonlinear model predictive controller for fault tolerant flight control. An aircraft is a highly nonlinear system hence if a nonlinear model can be integrated into the control process the cross-coupling effects of the control surface contributions can be easily exploited. An active fault tolerant control system comprises not only of the fault tolerant controller but also a fault detection and isolation subsystem. A common fault detection method is based on parameter estimation using filtering techniques. The solution proposed in this thesis uses an unscented Kalman filter (UKF) for parameter estimation and controller updates. In summary the main contribution of this thesis is the development of a new active fault tolerant flight control system. This new innovative controller exploits the idea of analytical redundancy as opposed to hardware redundancy. It comprises of a nonlinear model predictive based controller using pseudospectral discretisation to solve the nonlinear optimal control problem. Furthermore a UKF is incorporated into the design of the active fault tolerant flight control system

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools