Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Implementation of wind turbine controllers

Three of the important, generic, implementation issues encountered when developing controllers for pitch-regulated constant-speed wind turbines are considered, namely, (1) accommodation of the strongly nonlinear rotor aerodynamics; (2) automatic controller start-up/shut-down; and (3) accommodation of velocity and acceleration constraints within the actuator. Both direct linearisation and feedback linearisation methods for accommodating the nonlinear aerodynamics are investigated and compared. A widely employed technique for accommodating the nonlinear aerodynamics, originally developed on the basis of physical insight, is rigorously derived and extended to cater for all wind turbine configurations. A rigorous stability analysis of controller start-up is presented for the first time and novel design guidelines are proposed which can significantly reduce the power transients at controller start-up. The relation to anti-wind-up is noted and several aspects of an existing wind-turbine controller start-up strategy are observed to be novel in the anti-wind-up context. Restrictive position, velocity and acceleration constraints may all be present in wind turbines and the dynamic behaviour of the actuator cannot be neglected. A novel, and quite general, anti-wind-up method, based on the startup strategy, is proposed which caters for all these circumstances. The separate strategies for resolving the implementation issues are combined to achieve an elegant controller realisation which accommodates all the implementation issues in an integrated manner. The importance of adopting an appropriate controller realisation is considerable and is illustrated for a 300 kW wind turbine. The implementation issues encountered in this paper are, of course, not confined to wind turbines but are of wider concern

Adaptive control and parameter-dependent anti-windup compensation for inertia varying quadcopters.

A novel parameter-dependent anti-windup compensator is developed to improve the performance of a saturation constrained model reference adaptive controller. The combined control structure solves the input saturation and stability problem for inertia varying quadcopters. The control synthesis follows the conventional two-step anti-windup design paradigm where a nominal controller is designed without consideration of the input saturation, and the anti-windup compensator is designed to minimize deviations from nominal performance caused by saturated inputs. To account for varying inertia of the quadcopter during package retrieval/delivery routines, the inertia parameters of the vehicle/package are estimated with an online recursive system identification technique, and these estimates are used to schedule the parameter-dependent anti-windup compensator. The performance and stability conditions of the parameter-dependent anti-windup compensator are formulated as a set of parameter-dependent linear matrix inequalities. When solved, the linear matrix inequalities yield a gain-scheduled anti-windup compensator that ensures stability and minimizes the deviation from nominal model reference adaptive control performance when saturation occurs. The effectiveness of the combined control scheme is demonstrated by simulations of an input constrained quadcopter lifting a payload of unknown mass

Output regulation of rational nonlinear systems with input saturation

This thesis deals with the output regulation of rational nonlinear systems with input saturation. The output regulation problem considers a controlled plant subject to non-vanishing perturbations or reference signals produced by an exogenous autonomous system, where the goal is to ensure asymptotic convergence to zero of the plant output error. This work develops systematic methodologies for stability analysis and design of anti-windup compensated dynamic output feedback stabilizing controllers able to solve the output regulation problem for rational nonlinear systems with saturating inputs. In order to obtain these results, the proposed method employs the differential-algebraic representation, a theoretical framework that treats rational nonlinear systems by a differential equation combined with an equality relation. This tool is utilized in order to cast the stability analysis and control synthesis into optimization problems subject to linear matrix inequality constraints. Towards ensuring asymptotic output regulation, it is initially assumed the prior knowledge of an exact solution to the regulator equations, which represent an invariant and zero-error steady-state manifold. This assumption is later relaxed, where the results are extended for the practical regulation problem. In this last scenario, any numerically approximated solution to the regulator equations may be considered and the devised methodology ensures ultimate boundedness of the output error. Overall, the main innovation of this thesis is the application of the differential-algebraic representation into the nonlinear output regulation context, in turn providing a solution to a new set of problems intractable by state-of-the-art nonlinear methods.Esta tese trata da regulação de saída de sistemas não-lineares racionais com saturação na entrada. O problema de regulação de saída considera uma planta sujeita a sinais persistentes de distúrbio ou referência produzidos por um sistema exógeno autônomo, onde o objetivo é garantir a convergência assintótica do erro de saída da planta para zero. Este trabalho desenvolve metodologias sistemáticas para análise de estabilidade e projeto de controladores estabilizantes dinâmicos de realimentação de saída com compensadores anti-windup para sistemas não-lineares racionais com saturação no contexto de regulação de saída. O método proposto utiliza principalmente a representação algébrico-diferencial, uma abordagem teórica que trata sistemas não-lineares racionais por meio de uma equação diferencial combinada com uma igualdade algébrica. Para assegurar a regulação assintótica de saída, inicialmente assume-se o conhecimento de um modelo interno e uma solução exata para as equações do regulador, que representa um conjunto invariante de regime permanente onde o erro de saída é zero. Esta suposição é posteriormente relaxada, onde os resultados são estendidos para o contexto de regulação de saída prática. Os desenvolvimentos principais desta tese estão divididos nos seguintes capítulos: Regulação de Saída de Sistemas Não-Lineares Racionais; Regulação de Saída de Sistemas Não-Lineares Racionais com Saturação de Entrada e Extensão para Regulação de Saída Prática. O primeiro capítulo mencionado introduz a proposta de base deste trabalho, que consiste no emprego da representação algébrico-diferencial para a dinâmica do erro de regulação entorno do conjunto invariante descrito pelas equações do regulador. Com base nesta formulação, teoremas de estabilidade e desempenho são obtidos com condições na forma de desigualdades matriciais, permitindo o uso de otimização numérica para análise e síntese de controladores estabilizantes. No próximo capítulo, a formulação é estendida para a presença de saturação no sinal de controle, onde uma nova condição de setor é proposta para tratar esta não-linearidade adicional. Desta forma, novos teoremas são obtidos tanto para análise quanto para síntese de controladores estabilizantes incluindo compensadores anti-windup. No capítulo final da metodologia, considera-se uma abordagem de regulação prática onde soluções numéricas aproximadas podem ser consideradas para as equações do regulador. Novos teoremas de estabilidade voltados para análise e síntese também são obtidos dentro deste panorama prático, onde garante-se um conjunto terminal para a trajetória do erro de saída. Em geral, a grande importância deste trabalho é a possibilidade de solucionar um novo conjunto de problemas de regulação de saída não-linear, anteriormente intratáveis por métodos do estado-da-arte

Control of Systems with Limited Capacity

Virtually all real life systems are such that they present some kind of limitation on one or many of its variables, physical quantities. These systems are designated in this thesis as systems with limited capacity. This work is treating control related problems of a subclass of such systems, where the limitation is a critical factor. The thesis is composed of four parts. The first part is treating the control of tire slip in a braking car. The Anti-lock Braking System (ABS) is an important component of a complex steering system for the modern car. In the latest generation of brake-by-wire systems, the controllers have to maintain a specified tire slip for each wheel during braking. This thesis proposes a design model and based on that a hybrid controller that regulates the tire-slip. Simulation and results from drive tests are presented. In the second part, a design method for robust PID controllers is presented for a class of systems with limited capacity. Robustness is ensured with respect to a cone bounded static nonlinearity acting on the plant. Additional constraints on maximum sensitivity are also considered. The design procedure has been successfully applied in the synthesis of the proposed ABS controller. The third part studies the trajectory convergence for a general class of nonlinear systems. The servo problem for piecewise linear systems is presented. Convex optimization is used to describe the behavior of system trajectories of a piecewise linear system with respect to some input signals. The obtained results are then applied for the study of anti-windup compensators. The last part of the thesis is treating the problem of voltage stability in power systems. Voltage at the load end of a power system has to be controlled within prescribed tolerances. In case of emergencies such as sudden line failures, this task ca n be very challenging. The main contribution of this chapter is a method for improving the stability properties of the power system by dynamic compensation of the reference load voltage. Moreover, a complete compensation scheme is proposed where load shedding is the secondary control variable. This control scheme is shown to stabilize different power system models

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

Proton beam steering control system for high precision radiotherapy at iThemba LABS : an investigation on actuator saturation constraints

Includes abstract.Includes bibliographical references (leaves 101-106).This thesis aims at studying some of the techniques used to deal with constraints with special application to the Proton beam steering control at iThemba LABS. The steering of charged particles occurring in research plants is one of the interests of control systems. In this work an investigation of the algorithm for the control of the proton beam steering system in the radiotherapy treatment facility at iThemba LABS is conducted. This algorithm is intended to autonomously maintain the beam centered with reference to the axis of the beamline, and keep the beam front parallel to the central axis of the beamline as stated by van Tubbergh and De Kock, 2006. Furthermore, the algorithm is responsible for monitoring the distribution of the proton beam, in a plane normal to the beam travel direction

New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book

Design and application of advanced disturbance rejection control for small fixed-wing UAVs

Small Unmanned Aerial Vehicles (UAVs) have seen continual growth in both research and commercial applications. Attractive features such as their small size, light weight and low cost are a strong driver of this growth. However, these factors also bring about some drawbacks. The light weight and small size means that small UAVs are far more susceptible to performance degradation from factors such as wind gusts. Due to the generally low cost, available sensors are somewhat limited in both quality and available measurements. For example, it is very unlikely that angle of attack is sensed by a small UAV. These aircraft are usually constructed by the end user, so a tangible amount of variation will exist between different aircraft of the same type. Depending on application, additional variation between flights from factors such as battery placement or additional sensors may exist. This makes the application of optimal model based control methods difficult. Research literature on the topic of small UAV control is very rich in regard to high level control, such as path planning in wind. A common assumption in such literature is the existence of a low level control method which is able to track demanded aircraft attitudes to complete a task. Design of such controllers in the presence of significant wind or modelling errors (factors collectively addressed as lumped disturbances herein) is rarely considered. Disturbance Observer Based Control (DOBC) is a means of improving the robustness of a baseline feedback control scheme in the presence of lumped disturbances. The method allows for the rejection of the influence of unmeasurable disturbances much more quickly than traditional integral control, while also enabling recovery of nominal feedback con- trol performance. The separation principle of DOBC allows for the design of a nominal feedback controller, which does not need to be robust against disturbances. A DOBC augmentation can then be applied to ensure this nominal performance is maintained even in the presence of disturbances. This method offers highly attractive properties for control design, and has seen a large rise in popularity in recent years. Current literature on this subject is very often conducted purely in simulation. Ad- ditionally, very advanced versions of DOBC control are now being researched. To make the method attractive to small UAV operators, it would be beneficial if a simple DOBC design could be used to realise the benefits of this method, as it would be more accessible and applicable by many. This thesis investigates the application of a linear state space disturbance observer to low level flight control of a small UAV, along with developments of the method needed to achieve good performance in flight testing. Had this work been conducted purely in simulation, it is likely many of the difficulties encountered would not have been addressed or discovered. This thesis presents four main contributions. An anti-windup method has been devel- oped which is able to alleviate the effect of control saturation on the disturbance observer dynamics. An observer is designed which explicitly considers actuator dynamics. This development was shown to enable faster observer estimation dynamics, yielding better disturbance rejection performance. During initial flight testing, a significant aeroelastic oscillation mode was discovered. This issue was studied in detail theoretically, with a pro- posed solution developed and applied. The solution was able to fully alleviate the effect in flight. Finally, design and development of an over-actuated DOBC method is presented. A method for design of DOBC for over actuated systems was developed and studied. The majority of results in this thesis are demonstrated with flight test data