Significant research has been initiated recently to devise control strategies that could predict and compensate manufacturing errors using so called explicit Stream-of-Variation(SoV) models that relate process parameters in a Multistage Manufacturing Process (MMP) with product quality. This doctoral dissertation addresses several important scientific and engineering problems that will significantly advance the model-based, active control of quality in MMPs. First, we will formally introduce and study the new concept of compensability in MMPs, analogous to the concept of controllability in the traditional control theory. The compensability in an MMP is introduced as the property denoting one’s ability to compensate the errors in quality characteristics of the workpiece, given the allocation and character of measurements and controllable tooling. The notions of “within-station” and “between-station” compensability are also introduced to describe the ability to compensate upstream product errors within a given operation or between arbitrarily selected operations, respectively. The previous research also failed to concurrently utilize the historical and on-line measurements of product key characteristics for active model-based quality control. This dissertation will explore the possibilities of merging the well-known Run-to-Run (RtR) quality control methods with the model-based feed-forward process control methods. The novel method is applied to the problem of control of multi-layer overlay errors in lithography processes in semiconductor manufacturing. In this work, we first devised a multi-layer overlay model to describe the introduction and flow of overlay errors from one layer to the next, which was then used to pursue a unified approach to RtR and feedforward compensation of overlay errors in the wafer. At last, we extended the existing methodologies by considering inaccurately indentified noise characteristics in the underlying error flow model. This is also a very common situation, since noise characteristics are rarely known with absolute accuracy. We formulated the uncertainty in process noise characteristics using Linear Fractional Transformation (LFT) representation and solved the problem by deriving a robust control law that guaranties the product quality even under the worst case scenario of parametric uncertainties. Theoretical results have been evaluated and demonstrated using a linear state-space model of an actual industrial process for automotive cylinder head machining. / text

<p>Flight Control Systems are often designed in linearization points over a flight envelope and it must be proven to clearance authorities that the system works for different parameter variations and failures all over this envelope. </p><p>In this thesis µ-analysis is tried as a complement for linear analysis in the frequency plane. Using this method stability can be guaranteed for all static parameter combinations modelled and linear criteria such as phase and gain margins and most unstable eigenvalue can be included in the analysis. A way of including bounds on the parameter variations using parameter dependent Lyapunov functions is also tried. </p><p>To perform µ-analysis the system must be described as a Linear Fractional Transformation (LFT). This is a way of reformulating a parameter dependent system description as an interconnection of a nominal linear time invariant system and a structured parameter block. </p><p>A linear and a rational approximation of the system are used to make LFTs. These methods are compared. Four algorithms for calculation of the upper and lower bounds of µ are evaluated. The methods are tried on VEGAS, a SAAB research aircraft model. </p><p>µ-analysis works quite well for linear clearance. The rational approximation LFT gives best results and can be cleared for the criteria mentioned above. A combination of the algorithms is used for best results. When the Lyapunov based method is used the size of the problem grows quite fast and, due to numerical problems, stability can only be guaranteed for a reduced model.</p>

Flight Control Systems are often designed in linearization points over a flight envelope and it must be proven to clearance authorities that the system works for different parameter variations and failures all over this envelope. In this thesis µ-analysis is tried as a complement for linear analysis in the frequency plane. Using this method stability can be guaranteed for all static parameter combinations modelled and linear criteria such as phase and gain margins and most unstable eigenvalue can be included in the analysis. A way of including bounds on the parameter variations using parameter dependent Lyapunov functions is also tried. To perform µ-analysis the system must be described as a Linear Fractional Transformation (LFT). This is a way of reformulating a parameter dependent system description as an interconnection of a nominal linear time invariant system and a structured parameter block. A linear and a rational approximation of the system are used to make LFTs. These methods are compared. Four algorithms for calculation of the upper and lower bounds of µ are evaluated. The methods are tried on VEGAS, a SAAB research aircraft model. µ-analysis works quite well for linear clearance. The rational approximation LFT gives best results and can be cleared for the criteria mentioned above. A combination of the algorithms is used for best results. When the Lyapunov based method is used the size of the problem grows quite fast and, due to numerical problems, stability can only be guaranteed for a reduced model.

This thesis develops theoretical and computational methods for the robustness analysis of uncertain systems. The considered systems are linearized and depend rationally on random parameters with an associated probability distribution. The uncertainty is tackled by applying a polynomial chaos expansion (PCE), a series expansion for random variables similar to the well-known Fourier series for periodic time signals. We consider the linear perturbations around a system's operating point, i.e., reference trajectory, both from a probabilistic and worst-case point of view. A chief contribution is the polynomial chaos series expansion of uncertain linear systems in linear fractional representation (LFR). This leads to significant computational benefits when analyzing the probabilistic perturbations around a system's reference trajectory. The series expansion of uncertain interconnections in LFR further delivers important theoretical insights. For instance, it is shown that the PCE of rational parameter-dependent linear systems in LFR is equivalent to applying Gaussian quadrature for numerical integration. We further approximate the worst-case performance of uncertain linear systems with respect to quadratic performance metrics. This is achieved by approximately solving the underlying parametric Riccati differential equation after applying a polynomial chaos series expansion. The utility of the proposed probabilistic robustness analysis is demonstrated on the example of an industry-sized autolanding system for an Airbus A330 aircraft. Mean and standard deviation of the stochastic perturbations are quantified efficiently by applying a PCE to a linearization of the system along the nominal approach trajectory. Random uncertainty in the aerodynamic coefficients and mass parameters are considered, as well as atmospheric turbulence and static wind shear. The approximate worst-case analysis is compared with Monte Carlo simulations of the complete nonlinear model. The methods proposed throughout the thesis rapidly provide analysis results in good agreement with the Monte Carlo benchmark, at reduced computational cost.

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.