The focus of the present master thesis is the automation of an existing controllerdesign for a missile using two aerodynamic actuating systems. The motivation isto evaluate more missile concepts in a shorter period of time.The option used is trimming and linearization of a highly nonlinear missile at specic conditions. According to these conditions, either a two-dimensional operatingpoint grid dened by Mach number and height or three-dimensional operatingpoint grid dened by Mach number, height and angle of attack is generated forthe whole operating range of the missile. The controllers are designed at thesepoints using convex optimization. The convex set denes the pole placement areawhich is constrained by linear matrix inequalities according to the dynamic behaviorof the missile at the operating point conditions. These controllers describea validity area where the missile can be stabilized. This area consists all neighboringoperating points and denes therefore the grid density which can dier atspecic regions of the operating range. Controlling the missile to the target makesit necessary to apply gain-scheduling in order to get the manipulated variable byinterpolation of adjacent operating points. During this blending of the controllersa problem called windup can occur when an actuator is saturated. This mightlead to instability in worst case but can be counteracted by a model-recovery antiwindupnetwork which guarantees stability in the presence of saturation. Thisanti-windup design is automated by an ane linear parameter dependency of thegrid parameters and has the same validity area like the controllers.The whole design was successfully developed and tested in MATLAB/Simulink onmissiles using one or two aerodynamic actuating systems. The controllers have agood performance at small and high acceleration steps and the anti-windup keepsthe missile stable even though the actuators are saturated. Stability and robustnessof the controllers and anti-windup networks was veried as well as an airdefense maneuver where the missile starts at the ground and intercepts a targetat high altitude was successfully simulated for dierent grids and missiles.

<p>This thesis studies the negative impact that control signal saturation may have on a controlled system. Different methods that are used to compensate for this problem are also studied and evaluated. Both sensitivity to disturbances and the effect the method has on the systems'ability to follow a reference signal will be examined. Stability will be discussed, but no conclusions whether the systems are stabilized or not can be drawn. </p><p>Control signal saturation will lead to a slower behavior in general. For controllers with integral action this performance degradation will cause an extended growth in the integrating part of the controller. This leads to large overshoots and possibly to instability. </p><p>As an alternative to the more ad-hoc based methods, model based predictive control is studied. This metod can explicitly handle constrained control signals. Here, too, sensitivity to disturbances and the effect the method has on the systems'ability to follow a reference signal is examined.</p>

This thesis studies the negative impact that control signal saturation may have on a controlled system. Different methods that are used to compensate for this problem are also studied and evaluated. Both sensitivity to disturbances and the effect the method has on the systems'ability to follow a reference signal will be examined. Stability will be discussed, but no conclusions whether the systems are stabilized or not can be drawn. Control signal saturation will lead to a slower behavior in general. For controllers with integral action this performance degradation will cause an extended growth in the integrating part of the controller. This leads to large overshoots and possibly to instability. As an alternative to the more ad-hoc based methods, model based predictive control is studied. This metod can explicitly handle constrained control signals. Here, too, sensitivity to disturbances and the effect the method has on the systems'ability to follow a reference signal is examined.

Made available in DSpace on 2016-12-12T17:38:37Z (GMT). No. of bitstreams: 1 CLAUDIO EDUARDO SOARES.pdf: 20046362 bytes, checksum: 135e6d7d3a6f98bef9152afe645904c4 (MD5) Previous issue date: 2011-04-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The controllers based on the internal model principle have found emphasis on control systems due to its ability to perform robust tracking of signals whose generator models are embedded in their internal structures. Controllers with integral, resonant and repetitive terms are examples of this principle. However, the control systems are subject to physical limitations that restrict their operation under certain conditions. The amplitude saturation of the control action is the most common type of restriction found in real systems. The impacts of the saturation of control action are known as windup and its consequences for systems with integral action have already been exhaustive examined. However, the impacts of saturation of control action are not restricted to this type of controller. Other controllers based on the internal model principle are also affected by the windup phenomenon due to saturation of the action control. The impacts of the windup phenomenon for resonant, multi-resonant and repetitive controllers are investigated in this dissertation and an anti-windup technique is suggested to mitigate the impacts of the control saturation on these controllers. The proposed anti-windup technique is based on the conditional integration technique, originally developed for the controllers with integral action, and it is named conditional update. Simulation results are presented to validate the proposed technique. / Os controladores baseados no princípio do modelo interno têm encontrado destaque no controle de sistemas devido a sua capacidade de realizar o rastreamento robusto dos sinais cujos modelos geradores estejam embutidos nas suas estruturas internas. Os controladores com ação integral, ressonantes e repetitivos são exemplos da aplicação deste princípio. Contudo, os sistemas de controle estão sujeitos a limitações físicas que restringem suas condições de operação. A saturação da amplitude da ação de controle é o tipo de limitação mais comum encontrada nos sistemas reais. Os impactos da saturação da ação de controle são conhecidos como windup e suas consequências para os sistemas com ação integral já foram exaustivamente analisadas. Porém, os impactos da saturação da ação de controle não se restringem a este tipo de controlador. Outros controladores baseados no princípio do modelo interno também são afetados pelo fenômeno windup decorrente da saturação da ação de controle. Os impactos do fenômeno windup sobre os controladores ressonantes, multiressonantes e repetitivos são investigados nesta dissertação e uma técnica anti-windup é sugerida para atenuar os impactos da saturação da ação de controle sobre estes controladores. A técnica anti-windup proposta é baseada na técnica da integração condicional, originalmente desenvolvida para os controladores com ação integral e, por isso, denominada de atualização condicional. Resultados de simulação são apresentados para validação da técnica proposta.

Most practical control problems must deal with constraints imposed by equipment limitations, safety considerations or environmental regulations. While it is often beneficial to maintain operation close to the limits in order to maximize profit or meet stringent product specifications, the violation of actuator constraints during normal operation can result in serious performance degradation (sometimes instability) and economic losses. This thesis is concerned with the development of control strategies for multivariable systems which systematically account for actuator constraints while guaranteeing closed-loop stability as well as graceful degradation of non-linear performance. A novel anti-windup structure is proposed which combines the efficiency of conventional anti-windup schemes with the optimality of model predictive control (MPC) algorithms. In particular, the classical internal model control (IMC) law is enhanced for optimal performance by incorporating an on-line optimization. The resulting control scheme offers both stability and performance guarantees with moderate computational expense. The proposed optimizing scheme has prospects for industrial applications as it can be implemented easily and efficiently on programmable logic controllers (PLC).

Cette thèse s’inscrit dans le domaine de l’automatique, et a pour but de fournir des outils utiles à l’atterrissage en mer d’hélicoptères (sur navire ou plateforme) et employés dans le cadre d’un potentiel pilotage automatique. L’objectif a donc été de développer une série de lois de commande pilotées manuellement, puis commandées de façon autonome à l’aide d’informations caméra. Les lois ainsi développées à l’aide de modèles dynamiques d’hélicoptères, limitations mécaniques incluses, se basent sur les critères de Qualité de Vol issus de la norme ADS-33. L’ensemble a fait appel à une approche anti-windup pour améliorer la robustesse face aux situations d’actionneurs en saturation. Enfin les lois issues de ces travaux ont été testées en temps-réel sur le banc de pilotage d’hélicoptères de l’ONERA Salon-de-Provence. / This thesis is related to the automatic & control engineering field, and itsmain goal is to provide useful tools for ship landing missions, tools that can be used fora potential autopilot. The objective has been to develop a series of control laws manuallypiloted, then automatically controlled by visual servoing using identified image features. Thelaws developped thanks to helicopter models with mechanical limitations were based on flyingqualities criteria from the ADS-33 standard. The process also defines an anti-windup approachto cope with actuator saturations. Finally the main results were assessed in real time withthe ONERA rotorcraft flight test bench at ONERA Salon-de-Provence.

This thesis develops techniques for the design and analysis of controllers to achieve sub-micron accuracy on the position of electron beams for the optimal performance of synchrotrons. The techniques have been applied to Diamond Light Source, the UK's national synchrotron facility. Electron beam motion in synchrotrons is considered as a large-scale, two-dimensional process and by using basis functions, controllable modes of the process are identified which are independent and allow the design to be approached in terms of a family of single-input, single-output transfer functions. This thesis develops techniques for the design and analysis of controllers to achieve sub-micron accuracy on the position of electron beams for the optimal performance of synchrotrons. The techniques have been applied to Diamond Light Source, the UK's national synchrotron facility. Electron beam motion in synchrotrons is considered as a large-scale, two-dimensional process and by using basis functions, controllable modes of the process are identified which are independent and allow the design to be approached in terms of a family of single-input, single-output transfer functions. In this thesis, loop shaping concepts for dynamical systems are applied to the two-dimensional frequency domain to meet closed loop specifications. Spatial uncertainties are modelled by complex Fourier matrices and the closed loop robust stability, in the presence of spatial uncertainties is analysed within an Integral Quadratic Constraint framework. Two extensions to the unconstrained, single-actuator array controller design are considered. The first being anti-windup augmentation to give satisfactory performance when rate limit constraints are imposed on the actuators and the second being a strategy to account for two arrays of actuators with different dynamics. The resulting control schemes offer both stability and performance guarantees within structures that are feasible for online computation in real time.

Esta dissertação aborda a síntese de leis de controle baseadas em compensação dinâmica de saída para sistemas lineares contínuos invariantes no tempo, sujeitos a restrições no atuador. Baseados em condições suficientes expressas em LMIs, obtidas a partir de uma nova condição de setor para a função zona-morta, dois métodos são propostos. O primeiro método propõe a síntese de compensadores dinâmicos de anti-windup de ordem plena e reduzida para um sistema com um controlador dado a priori desprezando limites do atuador. A síntese dos compensadores considera um atuador restrito em amplitude e o sistema sujeito a perturbações limitadas em norma L2. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, ganho L2 limitado da perturbação à saída controlada do sistema, e um conjunto de inicialização dos estados do sistema tolerante à perturbação de norma L2 máxima, conhecida. Na ausência de perturbação a origem é garantida assintoticamente estável. Para o compensador de ordem plena, condições em LMIs garantem a estabilidade local e global da origem. Para o caso de ordem reduzida, inicialmente obtém-se estas condições expressas em termos de BMIs, sobre as quais aplica-se o Lema de Finsler, e pela escolha apropriada de seus multiplicadores, condições expressas em LMIs são obtidas. Dois métodos baseados em BMIs são propostos para estender os resultados obtidos das otimizações, em esquemas de relaxação. O segundométodo proposto aborda a síntese de controladores dinâmicos, para um atuador restrito em amplitude e taxa de variação, sujeito a perturbações limitadas em norma L2. Propõe-se um controlador dinâmico não-linear, composto por um compensador dinâmico linear, um integrador saturante e laços anti-windup. Esta metodologia possibilita a síntese simultânea de um controlador, e da malha de compensação anti-windup. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, ganho L2 limitado da perturbação à saída controlada do sistema, e um conjunto de inicialização do sistema tolerante à perturbação de norma L2 máxima, conhecida. Na ausência de perturbação a origem é garantida assintoticamente estável. As condições para estabilidade local e global são formuladas em LMIs a partir da aplicação do lema de Finsler e da escolha apropriada de multiplicadores. Dois métodos também baseados em BMIs podem estender os resultados obtidos das otimizações em esquemas de relaxação. Casos especiais são propostos a partir do método geral obtido; nestes casos condições diretamente em LMI podem ser obtidas. Problemas de otimização são propostos para ambos os métodos para maximizar a tolerância à perturbação e a minimização do ganho L2 da perturbação à saída controlada. Exemplos numéricos são apresentados para ilustrar o efeito de cada método na solução do problema de máxima tolerância à perturbação. / This thesis addresses control law synthesis based upon dynamic output compensation of continuous time invariant linear systems. By sufficient conditions expressed in LMIs, obtained from a new sector condition to the dead-zone function, two methods are proposed. The first one, comprises the synthesis of full and reduced order dynamic antiwindup compensators for a system with a linear controller a priori given, regardless the actuators limits. The compensator synthesis considers an amplitude limited actuator and a system subjected to L2-norm limited perturbation. The verification of the announced conditions assures the closed-loop origin stability, limited L2 gain for the perturbation at the system controlled output, and a system states initialization set tolerating the known L2-norm disturbance. In the absence of disturbance the origin is asymptotically stable guaranteed. For the full-order compensator, LMI conditions assure the local and global origin closed-loop stability. For the reduced order case, at first, BMI conditions are obtained, which, by the Finsler Lemma and proper choosing of itsmultipliers, become LMIs. Two methods are presented based on BMIs in order to improve the obtained results, by relaxation schemes. The second method addresses the synthesis of dynamic controllers considering a linear plant with the actuator restricted both in amplitude and rate, the system is meant to be subjected to L2 norm disturbances. The proposed methodology issues a non-linear dynamic controller, composed by a dynamic linear compensator, a saturating integrator and anti-windup loops. This approach allows the simultaneous synthesis of both the controller and the anti-windup loops. The validity of its announced conditions guarantees the closedloop origin stability, an upper-bound to the disturbances L2 gain on the plant’s controlled output, and an initialization set for the system that stands the specified disturbance. In the absence of disturbances the system’s origin is asymptotically stable guaranteed. Both local and global stability conditions are given in terms of LMIs. Two BMI-based methods arise in order to improve the results obtained on the referred optimizations problems by relaxation schemes. Special cases are derived from the general method; in these cases directly LMI conditions may be obtained. Optimization problems arise in both methods in order to maximize disturbance tolerance and rejection, by means of respectively its L2-norm, and L2-gain at the controlled output. Numerical Examples are presented in order to illustrate the effect of each method in the solution of the disturbance toleration problem.

Este trabalho apresenta uma nova metodologia para a síntese simultânea de controlador e laço anti-windup visando o problema de seguimento de referências em sistemas sujeitos à saturação. Além do projeto dos controladores, será apresentada uma estimativa dos domínios de estabilidade e do conjunto de referências admissíveis. O seguimento de referências constantes e a rejeição de perturbações, também constantes, será garantido pelo princípio do modelo interno, ou seja, uma ação integral será adicionada a uma malha de controle com realimentação de saída. Além da adição desta ação integral, uma mudança de coordenadas será aplicada ao sistema, onde será garantido que o único ponto de equilíbrio que garante erro nulo de seguimento está no interior da sua região de linearidade. Os efeitos da saturação no sistema serão considerados através de condições de setor modificadas, as quais introduzem novos graus de liberdade ao projeto. Em um primeiro momento, a metodologia será aplicada para sistemas de tempo contínuo, considerando um esquema de controle conhecido como “integradores inteligentes”. Posteriormente, este esquema será simplificado, no que foi chamado de solução “clássica”. Além de apresentar um esquema de controle mais simples e um número menor de condições, estas condições são obtidas diretamente na forma de LMIs, evitando assim, a utilização de esquemas iterativos. Alguns problemas de otimização serão apresentados, podendo levar a três objetivos de controle distintos: maximização da referência admissível, maximização da condição inicial e maximização da perturbação admissível. Por meio de exemplos, será mostrado que esta solução apresenta resultados menos conservativos do que os apresentados na literatura corrente, além de chamar a atenção para um problema ignorado por outros autores. Este problema se refere à existência de pontos de equilíbrio dentro dos domínios de estabilidade mas fora da região linear, o que impossibilita a garantia de erro de seguimento nulo. Num segundo momento, esta metodologia será estendida para sistemas de tempo discreto. Mais uma vez, condições LMI serão obtidas a fim de projetar os controladores e oferecer estimativas dos domínios de estabilidade. Por não haver uma referência direta para comparação dos resultados, a metodologia será aplicada para exemplos estáveis, instáveis e com integradores, tanto no caso monovariável quanto no caso multivariável. Finalmente, será apresentado um estudo dos pontos de equilíbrio fora da região de linearidade, como mencionado anteriormente, considerando tanto sistemas de tempo contínuo quanto em tempo discreto. Este estudo será realizado para alguns tipos de sistemas, considerando apenas o caso monovariável. Será provado que estes equilíbrios só são possíveis em plantas assintoticamente estáveis, exigindo a consideração de uma condição extra na solução do problema de otimização. / This work addresses the problem of tracking constant references for linear systems subject to control saturation. The main idea is to present LMI conditions in order to design both a stabilizing controller and an anti-windup gain. These conditions ensure that the trajectories of the closed-loop system are bounded by an invariant ellipsoidal set, provided that the initial conditions are taken in this set and the references and the disturbances belong to a certain admissible set. The constant reference tracking and constant disturbance rejection is taken into account by the internal model principle, i. e., considering the introduction of an integral action in a unitary output feedback scheme. We also introduce the error co-ordinate representation, where is proved that there exists only one equilibrium point inside the linearity region and that this equilibrium point ensures perfect reference tracking. In order to consider the saturation effects, we use a modified sector condition, introducing new degrees of freedom to the synthesis problem. In a first step, the proposed framework was applied to the control scheme called “intelligent integrators”, regarding continuous-time systems. However, this control scheme does not allow the simultaneous synthesis so it is simplified to the so called “classical” anti-windup scheme. Based on this simplified control structure, LMI conditions are directly derived, avoiding therefore the necessity of applying iterative schemes. Convex optimization problems aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances are proposed. We show, by means of an example, that the obtained results are less conservative than the ones previously presented in related works. In these examples, we also show that a study about the existence of other equilibria inside the invariant set is worthwhile. Later, the proposed framework is extended to discrete-time systems, where new LMI conditions are presented in order to synthesize the controller and present an estimate of the stability domains. Due to a lack of related works, our framework is applied to stable, unstable and integrator examples. These examples consider both single and multi-variable systems. Finally, we conclude this work with a study about the possibility of existence of other equilibria inside the invariant set. For the single-input case, we show that this is only possible if the open-loop system is asymptotically stable. In this case, in order to avoid convergence to these points, additional constraints on the admissible references to be tracked should be considered. It is worth to emphasize that such kind of analysis has not been performed in previous works.

O presente trabalho aborda o problema de estabilização local de sistemas não lineares quadráticos contínuos no tempo (possivelmente instáveis em malha aberta) e sujeitos a saturação de atuadores. Além disso o trabalho apresenta um estudo de técnicas de síntese de compensadores de anti-windup para sistemas quadráticos sujeitos à saturação de atuadores. A abordagem do estudo é comparativa em relação a duas formas de representação dos sistemas quadráticos. A primeira forma de abordagem é a Representação Algébrico-Diferencial — DAR (do inglês, Differential Algebraic Representation), aplicável a toda a classe de sistemas racionais. A segunda forma, por sua vez, consiste em uma decomposição quadrática, particular para sistemas quadráticos. Em ambos os casos, utiliza-se a não linearidade de zona morta e uma condição generalizada de setor para tratar da saturação. Para ambas representações, condições baseadas em Desigualdades Matriciais Lineares — LMIs (do inglês, Linear Matrix Inequalities) dependentes dos estados são obtidas para fornecer uma lei de controle linear, com o objetivo de estabilizar o sistema em malha fechada enquanto fornece uma região maximizada de estabilidade garantida associada a uma função de Lyapunov. A partir da mesma metodologia, são propostas técnicas de síntese de compensadores de anti-windup estáticos e dinâmicos. Exemplos numéricos são apresentados para verificar a eficácia dos métodos propostos. / This work addresses the problem of local stabilization of continuous-time quadratic systems (possibly open-loop unstable) and subject to actuator saturation. Furthermore, the work addresses a study of techniques for synthesis of anti-windup compensators for quadratic systems subject to actuator saturation. The study approach is comparative in the sense of considering two representations of quadratic systems. The first one is the Differential Algebraic Representation — DAR, suitable for the entire class of rational systems. The second representation consists in a quadratic decomposition, particular for quadratic systems. In both cases, it is used the deadzone nonlinearity and the generalized sector condition in order to deal with the saturation. For both representations, state-dependent Linear Matrix Inequalities — LMIs conditions are obtained to provide a control law with the aim of stabilize the closed-loop system while providing a region of guaranteed stability, associated to a Lyapunov function. Based on the same methodology, techniques are proposed for the synthesis of static and dynamic anti-windup compensators. Numerical examples are presented to verify the effectiveness of proposed methods.