On Reduced Input-Output Dynamic Mode Decomposition

The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate the input-output behavior of the data source. In this work, we consider the input-output dynamic mode decomposition method for system identification. We compare excitation approaches for the data-driven identification process and describe an optimization-based stabilization strategy for the identified systems

Evaluation of process systems operating envelopes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 229-238).This thesis addresses the problem of worst-case steady-state design of process systems under uncertainty, also known as robust design. Designing for the worst case is of great importance when considering systems for deployment in extreme and hostile environments, where operational failures cannot be risked due to extraordinarily high economic and/or environmental expense. For this unique scenario, the cost of "over-designing" the process far outweighs the cost associated with operational failure. Hence, it must be guaranteed that the process is sufficiently robust in order to avoid operational failures. Many engineering, economic, and operations research applications are concerned with worst-case scenarios. Classically, these problems give rise to a type of leader-follower game, or Stackelberg game, commonly known as the "minimax" problem, or more precisely as a max-min or min-max optimization problem. However, since the application here is to steady-state design, the problem formulation results in a more general nonconvex equality-constrained min-max program, for which no previously available algorithm can solve effectively. Under certain assumptions, the equality constraints, which correspond to the steady-state model, can be eliminated from the problem by solving them for the state variables as implicit functions of the control variables and uncertainty parameters. This approach eliminates explicit functional dependence on the state variables, and in turn reduces the dimensionality of the original problem. However, this embeds implicit functions in the program, which have no explicit algebraic form and can only be approximated using numerical methods. By doing this, the max-min program can be reformulated as a more computationally tractable semi-infinite program, with the caveat that there are embedded implicit functions. Semi-infinite programming with embedded implicit functions is a new approach to modeling worst-case design problems. Furthermore, modeling process systems--especially those associated with chemical engineering--often results in highly nonconvex functions. The primary contribution of this thesis is a mathematical tool for solving implicit semi-infinite programs and assessing robust feasibility of process systems using a rigorous model-based approach. This tool has the ability to determine, with mathematical certainty, whether or not a physical process system based on the proposed design will fail in the worst case by taking into account uncertainty in the model parameters and uncertainty in the environment.by Matthew David Stuber.Ph.D

Contrôle du vol longitudinal d'un avion civil avec satisfaction de qualités de manoeuvrabilité

RÉSUMÉ Satisfaire les qualités de manœuvrabilité demeure toujours une contrainte essentielle lors de la conception des commandes de vol. Ces critères de différentes natures sont le fruit d'une longue expérience d'essais en vol et d'analyse de données et il convient de les considérer pour espérer un bon comportement de l'appareil en vol. Dans ce cadre, l'enjeu de cette thèse est d'élaborer des méthodes de synthèse capables de satisfaire au mieux ces critères en respectant d'une part des architectures classiques imposées par le constructeur et, d'autre part, en adoptant une nouvelle architecture de contrôle. Le travail est effectué sur le vol longitudinal d'un avion d'affaire de Bombardier Inc., le Challenger 604. Une première étape consiste à rassembler les qualités de manœuvrabilité les plus souvent utilisées et de les confronter. Nous étudions plus particulièrement le critère du dropback pour lequel une analyse théorique permet d'établir une formulation pratique utilisable lors d'une synthèse. De plus, la confrontation de ces critères sur un modèle standard met en évidence des critères dominants, qui, une fois satisfaits, impliquent que d'autres critères le sont aussi. Nous pouvons dès lors considérer le problème de satisfaction de ces critères dominants dans le cadre d'une loi de contrôle dont l'architecture est imposée. Nous nous tournons alors du côté des applications gardiennes (Saydy et al., 1990). Initialement destinées à l'étude de la robustesse, elles sont intégrées dans différents algorithmes pour la synthèse de correcteur. Ce problème s'inscrit dans le cadre plus général de stabilisation par retour de sortie et de synthèse de correcteurs d'ordre réduit. Il en ressort des algorithmes permettant la stabilisation de système et le placement de pôles dans une région du plan complexe. Ceux-ci sont étendus dans le cadre du séquencement du contrôleur sur toute l'enveloppe de vol en fonction de certains paramètres. Nous faisons ensuite fi de la structure du correcteur en conservant seulement les mêmes sorties. L'idée est à présent d'utiliser une synthèse H pour obtenir un correcteur satisfaisant les qualités de manœuvrabilité grâce à l'appariement avec un modèle de référence et robuste à des variations de masse et de centrage de l'avion. Grâce aux travaux sur la commande modale robuste (Magni, 2002), nous pouvons réduire substantiellement l'ordre de ce correcteur ainsi que le structurer afin de nous rapprocher d'une architecture classique. Une méthode d'auto-séquencement de correcteurs, nous permet finalement de séquencer ce correcteur à travers toute l'enveloppe de vol. Deux voies différentes sont donc empruntées pour la résolution du même problème; chacune montre ses avantages et ses inconvénients.----------ABSTRACT Fulfilling handling qualities still remains a challenging problem during flight control design. These criteria of different nature are derived from a wide experience based upon flight tests and data analysis, and they have to be considered if one expects a good behavior of the aircraft. The goal of this thesis is to develop synthesis methods able to satisfy these criteria with fixed classical architectures imposed by the manufacturer or with a new flight control architecture. This is applied to the longitudinal flight model of a Bombardier Inc. business jet aircraft, namely the Challenger 604. A first step of our work consists in compiling the most commonly used handling qualities in order to compare them. A special attention is devoted to the dropback criterion for which theoretical analysis leads us to establish a practical formulation for synthesis purpose. Moreover, the comparison of the criteria through a reference model highlighted dominant criteria that, once satisfied, ensure that other ones are satisfied too.Consequently, we are able to consider the fulfillment of these criteria in the fixed control architecture framework. Guardian maps (Saydy et al., 1990) are then considered to handle the problem. Initially for robustness study, they are integrated in various algorithms for controller synthesis. Incidently, this fixed architecture problem is similar to the static output feedback stabilization problem and reduced-order controller synthesis. Algorithms performing stabilization and pole assignment in a specific region of the complex plane are then proposed. Afterwards, they are extended to handle the gain-scheduling problem. The controller is then scheduled through the entire flight envelope with respect to scheduling parameters. Thereafter, the fixed architecture is put aside while only conserving the same output signals. The main idea is to use H synthesis to obtain an initial controller satisfying handling qualities thanks to reference model pairing and robust versus mass and center of gravity variations. Using robust modal control (Magni, 2002), we are able to reduce substantially the controller order and to structure it in order to come close to a classical architecture. An auto-scheduling method finally allows us to schedule the controller with respect to scheduling parameters. Two different paths are used to solve the same problem; each one exhibits its own advantages and disadvantages