This thesis addresses robust stability, robust H¡Û and H2 performance and design of discrete-time polytopic systems with an LFT uncertainty assumed at each vertex. A sequence of relaxed sufficient analysis results based on the HPPDL matrix approach has been extended to cope with such more general uncertainty structure. The state feedback gain matrix to achieve robust H¡Û and H2 performance can be easily computed from the derived sufficient LMIs. The larger the degree of homogeneous polynomial is, the lower H¡Û and H2 norm are achieved. Numerical examples are included to illustrate the derived results.

For continuous-time descriptor systems with all system matrices incorporated with norm-bounded uncertainties, this thesis addresses robust admissibility and robust H¡Û analysis and the related state feedback design. The results are further extended to systems with time-varying state delay within a known interval. The former part of the thesis extends the current research of considering uncertainty only at the state derivative matrix to the case uncertainty being assumed at all system matrices. While the latter part of the thesis extends the current research in two folds: the state derivative matrix is allowed to be uncertain and the delay is allowed to be time-varying. Since all the results are derived in the LMI-based framework, examples with efficient numerical verifications are included to illustrate the derived results.

En este trabajo se presentó el análisis, diseño, e implementación analógica de estrategias de control robusto utilizando desigualdades matriciales lineales (LMI) en el mejoramiento de la dinámica de los convertidores conmutados de CC/CC. Inicialmente, se exponen aspectos básicos del control robusto LMI y el procedimiento general de la síntesis, que consiste en encontrar las ganancias de realimentación que maximice el rechazo a perturbaciones satisfaciendo especificaciones transitorias y limitación sobre el esfuerzo de control. Luego, se propone el diseño de dos controladores robustos LMIs para convertidores con dos etapas en cascada. El primer controlador robusto consiste de una ley monovariable, mientras que el segundo de una ley multivariable. Finalmente, se presenta un enfoque de diseño de controladores difusos LMIs para convertidores básicos de CC/CC bilineales, garantizando la estabilidad y unas determinadas prestaciones en un rango de operación mucho más amplio alrededor del punto de equilibrio. / This thesis describes the theoretical background necessary to design and implement of analog robust control strategies based on Linear Matrix Inequalities (LMI). The control strategies proposed has been used in basic and cascaded of dc-dc converters topologies. The robust control methods can simplify and systematize the choice of feedback gains, taking into account the converters nonlinearities and uncertainties. These control methods ensure some prescribed restrictions on the pole placement and the control effort are met, and optimize the load disturbance rejection. The first method consists of two different robust controllers for dc-dc converters with two stages in cascade. The first robust controller is monovariable, this means, the duty-cycle is the same for the two switches, while the second robust controller is multivariable robust controller, this means, with independent duty cycles in each switch. Finally, the second method is a synthesis of fuzzy control based on LM I that has been adapted to bilinears basic dc-dc converters. Concretely, this technique is a linear-piecewise continuous control which optimizes the load disturbance rejection under pole placement constraints and duty-cycle limitation.

For linear time-invariant descriptor models, this dissertation studies the extended strictly positive real (ESPR) design of continuous-time systems and the strictly positive real (SPR) analysis and design of discrete-time systems, respectively, all in the LMI framework. For a continuous-time system, by the LMI-based ESPR Lemma, a controller is designed such that the closed-loop system has its transfer matrix being ESPR while admissibility of the compensated descriptor system is guaranteed. Three forms of synthesis are considered, i.e. the static state feedback synthesis, estimated state feedback synthesis, and the dynamic output feedback synthesis. Moreover, design criterion of a dynamic output feedback controller in the state-space model is also addressed. For a discrete-time system, an LMI-based SPR characterization is developed. After giving the definition of SPR, the Cayley transformation is used to establish formulas bridging the admissible realizations for SPR and strictly bounded real (SBR) transfer matrices. Based on them, an LMI-based necessary and sufficient condition for a descriptor system to be, simultaneously, admissible and SPR is derived. When the descriptor variables are transformed into the SVD coordinate, it is shown that such a condition will have solution in the block diagonal form. Based on this result, the problem of static state feedback design to make transfer matrix of the closed-loop systems SPR is tackled. The problems of robust ESPR and SPR analysis and design when the considered systems have norm-bounded unstructured uncertainty are also addressed. Similarly, LMI-based conditions to guarantee robust admissibility with transfer matrices being ESPR for continuous systems or being SPR for discrete systems are proposed. Based on them, for continuous systems, a static state feedback controller and a dynamic output feedback controller are designed to make the entire family of uncertain closed-loop systems robustly admissible with transfer matrices being ESPR. While for discrete systems, only static state feedback controller is designed to achieve the robust admissibility and robust SPR property. Finally, based on ESPR lemma (or SPR lemma), we propose a new LMI-based robust admissibility analysis for a class of LTI continuous-time (or discrete-time) descriptor systems with convex polytopic uncertainties appearing on all the system matrices. Moreover, the development of state feedback controllers stemmed from these analysis results is also investigated. It is shown that the provided method has the capability to tackle the problem of computing a required feedback gain matrix for systems with either constant or polytopically dependent derivative (or advanced) state matrix in a unified way. Besides, the application of SPR property to absolute stability problem involving an LTI discrete-time descriptor system and a memoryless time-varying nonlinearity is also addressed. Since all conditions are expressed in LMIs, the obtained results are numerically tractable. It is illustrated by several numerical examples.

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.

In this thesis, LMI approach is employed to design a static output feedback controller so that all poles of the considered closed-loop continuous-time system are located within a prescribed LMI region, named D region. Based on the coordinate transformation, an analysis about the derived LMI-based sufficient condition is also established. The result is, moreover, extended to treat pole placement in the generalized LMI region, denoted by DR region. In addition to the requirement on pole location, two commonly exploited system performances in robust control, i.e. the H2 and Hinf designs, are also considered so that the multiobjective control by static output feedback is investigated in this thesis. To address robustness issue of the designed controllers, three different uncertainty descriptions, i.e. norm bounded uncertainty, positive real uncertainty, and polytopic uncertainty, are considered and LMI conditions for quadratic D stabilization by static output feedback have been derived. The bounded realness and positive realness with respect to an LMI D region are studied as well. Numerical examples are provided in the end of chapters 3, 4, and 5 to illustrate the obtained results there.

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Made available in DSpace on 2014-06-11T19:22:35Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-02-16Bitstream added on 2014-06-13T20:47:11Z : No. of bitstreams: 1 mendes_rat_me_ilha.pdf: 974679 bytes, checksum: 258abcb7515fb2e2e389d313c9dbcf4c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho é proposta uma metodologia de modificação de zeros para solucionar o problema do rastreamento do sinal de referência em sistemas discretos considerando-se uma entrada de perturbação na planta. Em um primeiro momento é projetado um controlador discreto para minimizar a norma H8 entre a entrada exógena e o sinal de saída com o objetivo de reduzir o efeito da perturbação sobre a saída do sistema. Posteriormente, minimiza-se a norma H8 entre o sinal de referência e o erro de rastreamento através da modificação de zeros do sistema discreto, constituindo desta maneira o rastreador de sinal de referência. A formulação do projeto é descrita na forma de inequações matriciais lineares, pois estas permitem a descrição de problemas de otimização convexa. Por fim, são apresentados três exemplos numéricos que ilustram a viabilidade da metodologia proposta. / The tracking problem in discrete time systems, with the presence of a disturbance signal in the plant, is solved using a zero variation methodology. This methodology is proposed in this work. A discrete state feedback controller is designed in order to minimize the H8-norm between the exogen input and the output signal, such that the effect of the disturbance is attenuated. After, a discrete state estimator is designed for the tracking problem and the variation of the zeros is used to minimize the H8-norm from the reference input signal to the error tracking signal. The error is taking as the difference between the reference and the output signal, and so it is a tracking problem. The design is formulated in the Linear Matrix Inequalities (LMI) framework, such that the optimal solution of the stated control problem is obtained. Three numerical examples illustrate the proposed methodology viability.

Feedback is used to control systems whose open-loop behaviour is uncertain. Over the last twenty years a mature theory of robust control has been developed for linear multivariable systems in continuous time. But most practical control systems have constraints such as saturation limits on the actuators, which render the closed-loop nonlinear. Most of the modern controllers are also implemented digitally using computers.The study of this research is divided in two directions: the stability analysis of discrete-time Lur’e systems and the synthesis of static discrete-time anti-windup schemes. With respect to stability analysis, the main contributions of this thesis are the derivations of new LMI-based stability criteria for the discrete-time Lur’e systems with monotonic, slope-restricted nonlinearities via the Lyapunov method. The criteria provide convex stability conditions via LMIs, which can be efficiently computed via convex optimization methods. They are also extended to the general case that includes the non-diagonal MIMO nonlinearities. The importance of extending them to the general case is that it can eventually be applied to the stability analysis of several optimization-based controllers such as an input-constrainedmodel predictive control (MPC), which is inherently discrete. With respect to synthesis, the contribution is the convex formulation of a static discrete-time anti-windup scheme via one of the Jury-Lee criteria (a discrete-time counterpart of Popov criterion), which was previously conjectured to be unachievable. The result is also in the form of LMI, and is extended to several existing static anti-windup schemes with open-loop stable plants.

The need to design a controller that self-schedules itself during the flight of an aircraft has been an active area of research. New methods have been developed beyond the traditional gain-scheduling approach. One such design method leads to a linear parameter varying (LPV) controller that changes based on the real-time variation of system dynamics. Before such a controller can be designed, the system has to also be represented as an LPV system. The current effort proposes a LPV modeling technique that is inspired by an affine LPV modeling techniques found in recent research. The properties of the proposed modeling method are investigated and compared to the affine modeling technique. It is shown that the proposed modeling technique represents the actual system behavior more closely than the existing affine modeling technique. To study the effect of the two LPV modeling techniques on controller design, a linear quadratic regulator (LQR) controller using linear matrix inequality (LMI) formulation is designed. This control design method provides a measure of conservatism that is used to compare the controllers based on the different modeling techniques. An F-16 short-period model is used to implement the modeling techniques and design the controllers. It was found that the controller based on the proposed LPV modeling method is less conservative than the controller based on the existing LPV method. Interesting features of LMI formulation for multiple plant models were also discovered during the exercise. A stability robustness analysis was also conducted as an additional comparison of the performance of the controllers designed using the two modeling methods. A scalar measure, called the probability of instability, is used as a measure of robustness. It was found that the controller based on the proposed modeling technique has the necessary robustness properties even though it is less conservative than the controller designed based on the existing modeling approach. / Master of Science