Quantitative Feedback Theory (QFT) method employs a two degree of freedom control configuration that includes a feedback controller and a prefilter in the feedforward path. When applied to multi-input multi-output (MIMO) systems, the QFT method calls for a special decomposition of the MIMO system. Specifically, the MIMO system is decomposed into multiple multi-input single-output (MISO) equivalent systems, and is followed by the single-input single-output (SISO) QFT design of each equivalent system. Depending on pole-zero structure of the equivalent SISO plants so obtained, the QFT design may become unnecessarily difficult/conservative or even infeasible. This situation is especially true for linear time invariant (LTI) systems with non-minimum phase (NMP) zero(s) and unstable pole(s). This unnecessary design difficulty and the challenge of dealing with MIMO systems that have unstable poles and NMP transmission zeros in undesirable locations, when MIMO QFT is considered, is investigated and addressed in this research. A new MIMO QFT design methodology was developed using the generalized formulation. The key idea of the generalized formulation is to utilize appropriate modifications at the plant input and/or the output to obtain a better conditioned plant that in turn can be used to execute a standard MIMO QFT design. The formulation is based on a more general control structure, where input and output transfer function matrices (TFM) are included to provide additional degrees of freedom in the typical decentralised MIMO QFT feedback structure, which facilitates the exploitation of directions in MIMO QFT designs. The formulation captures existing design approaches for a fully populated MIMO QFT controller design and provides for a directional design logic involving the plant and controller alignment and the directional properties of their multivariable poles and zeros. As a case in point Horowitz’s Singular-G design methodology is placed in the context of this generalized formulation, and the Singular-G design for the X-29 is analysed and redesigned using both non-sequential and sequential MIMO QFT demonstrating its utility. The results highlight a fundamental trade-off between multivariable controller directions for stability and performance in classically formulated MIMO QFT design methodologies, which elucidate the properties of Singular-G designed controllers for the X-29 and validate the developed new MIMO QFT design method.

The main focus of the work is the construction of a quantum spacetime emerging from theory.

Unmanned helicopters in recent years have gained much attention due to their potential in both civil as well as military applications. Helicopter is an inherently unstable system. As a result there is a growing need of developing a control structure that allows the helicopter to perform various applications while remaining stable throughout the flight. This thesis presents developments of a robust controller for the vertical channel of an unmanned helicopter while carrying and dropping a payload. In addition, a simulation platform is developed in Simulink that uses a nonlinear six degree of freedom helicopter model. Quantitative Feedback Theory, a frequency domain technique, is used to design a controller that meets specific performance criteria when uncertainties associated with different payload weights exist in the system. The controller performance is examined in simulation for an Xcell 60 helicopter for effective lifting and dropping of up to 10 lb payload. The performance is then compared with a traditional Proportional-Integral-Derivative controller. Further, the effect of actuator dynamics on the controller performance is also evaluated. Finally, a controller that is robust in minimizing the effect of actuator dynamics and the payload drop while keeping the helicopter stable in flight is designed.

Feynman graphs in perturbative quantum field theory are replete with infrared divergences caused by the presence of massless particles, how-ever these divergences are known to cancel order-by-order when all virtual and real contributions to a given cross section are summed and smeared against an experimental resolution. In this thesis we treat the infrared problem formally in the language of distribution theory so that we can remove the divergences with local momentum space subtractions using Hadamard's procedure. This is analogous with the BPHZ mechanism for removing UV divergences. Our aim is to show how it is possible to make both the real and virtual subtractions analytically such that we are left with manifestly finite integrands. For the virtual graphs we present a new decomposition of the integrand in momentum space and remove those terms that are divergent. For the real graphs we show how the Taylor expansion of the momentum conserving delta function allows the explicit removal of the divergent part; furthermore we show that the homogeneous properties of the soft structure greatly simplifies this procedure.

<p>A modern fighter aircraft is exposed to very different flight conditions and must despite that perform infallibly in every single situation. Several variables like center of gravity, speed, altitude and weight vary during a standard mission flight or</p><p>between flights. For the aircraft to be able to perform effectively, superior manoeuvrability is vital. Hence it is of great importance that the flight control system is capable to cope with these different variations.</p><p>In the 1960s professor Isaac Horowitz presented the method Quantitative feedback theory (QFT) which is a method whose aim is to manage system variations. The method can be useful in the construction of the control system for a fighter aircraft. QFT is a frequency based method whose main objective is to shape the</p><p>open loop gain in a Nicholschart to meet the required closed loop demands. A prefilter is then applied to achieve correct reference tracking.</p><p>This thesis is divided into two parts, where the first part presents the method QFT for both the SISO-systems and for the MIMO-systems. For the MIMOsystems several design techniques are presented, the chapter also includes a method on the implementation of state feedback. Furthermore statements of how nonlinear and unstable systems are handled with the QFT is included.</p><p>The second part of the thesis presents the design of a control system for an unstable fighter aircraft. The design is constructed for the SISO longitudinal dynamics as well as for the MIMO lateral dynamics, where the design must be robust against variations in speed, altitude and center of gravity.</p><p>The flight control system that is implemented meets almost all requirements and gives good preformance and this is achieved with only a few regulators. Proposals of possible solutions to those requirements note yet reached are discusssed.</p>

Considered in this thesis is multi-input multi-output (MIMO) systems with non-minimum phase (NMP) zeros and unstable poles where some of the unstable poles are located to the right of the NMP zeros. In the single-input single-output (SISO) case such systems pose serious difficulties in controller synthesis for performance and stability. In spite of the added degrees of freedom the MIMO case also poses difficulties as has been shown in the stabilization of the X-29 aircraft. When using the MIMO QFT technique the synthesis starts by considering a set of equivalent SISO plants derived from the plant transfer function matrix that are used to develop a controller. In effect the design problem is reduced to several MISO designs with the diagonal entries of as the equivalent SISO plants. Developed is a transformation scheme that can be used to condition the resulting equivalent SISO plants so that the difficult problem of NMP zeros lying to the left of unstable poles is avoided. Examples illustrate the use of the proposed transformation.

A modern fighter aircraft is exposed to very different flight conditions and must despite that perform infallibly in every single situation. Several variables like center of gravity, speed, altitude and weight vary during a standard mission flight or between flights. For the aircraft to be able to perform effectively, superior manoeuvrability is vital. Hence it is of great importance that the flight control system is capable to cope with these different variations. In the 1960s professor Isaac Horowitz presented the method Quantitative feedback theory (QFT) which is a method whose aim is to manage system variations. The method can be useful in the construction of the control system for a fighter aircraft. QFT is a frequency based method whose main objective is to shape the open loop gain in a Nicholschart to meet the required closed loop demands. A prefilter is then applied to achieve correct reference tracking. This thesis is divided into two parts, where the first part presents the method QFT for both the SISO-systems and for the MIMO-systems. For the MIMOsystems several design techniques are presented, the chapter also includes a method on the implementation of state feedback. Furthermore statements of how nonlinear and unstable systems are handled with the QFT is included. The second part of the thesis presents the design of a control system for an unstable fighter aircraft. The design is constructed for the SISO longitudinal dynamics as well as for the MIMO lateral dynamics, where the design must be robust against variations in speed, altitude and center of gravity. The flight control system that is implemented meets almost all requirements and gives good preformance and this is achieved with only a few regulators. Proposals of possible solutions to those requirements note yet reached are discusssed.

In this thesis I present a nonequilibrium quantum field theory that describes the production of molecular dimers from a two-component quantum-degenerate atomic Fermi gas, via a linear downward sweep of a magnetic field across an s-wave Feshbach resonance. This problem raises interest because it is presently unclear as to why deviations from the universal Landau-Zener formula for the transition probability at two-level crossing are observed in the experimentally measured production efficiencies. The approach is based on evaluating real-time Green functions within the Keldysh- Schwinger formalism. The effects of quantum statistics associated with Pauli blocking for fermions and induced emission for bosons, characteristic of particle scattering in a quantum-degenerate many-body medium, are fully accounted for. I show that the molecular conversion efficiency is represented by a power series in terms of a dimensionless parameter which, in the zero-temperature limit, depends solely on the initial gas density and the Landau-Zener parameter. This result reveals a hindrance of the canonical Landau-Zener transition probability due to many-body effects, and presents an explanation for the experimentally observed deviations. A second topic treated in this thesis concerns the study of non-adiabatic transitions in N-state Landau-Zener systems. In connection to this, I provide a proof of the conjecture put forth by Brundobler and Elser, regarding the survival probability on the diabatic levels with maximum/minimum slope.

Considered in this thesis is multi-input multi-output (MIMO) systems with non-minimum phase (NMP) zeros and unstable poles where some of the unstable poles are located to the right of the NMP zeros. In the single-input single-output (SISO) case such systems pose serious difficulties in controller synthesis for performance and stability. In spite of the added degrees of freedom the MIMO case also poses difficulties as has been shown in the stabilization of the X-29 aircraft. When using the MIMO QFT technique the synthesis starts by considering a set of equivalent SISO plants derived from the plant transfer function matrix that are used to develop a controller. In effect the design problem is reduced to several MISO designs with the diagonal entries of as the equivalent SISO plants. Developed is a transformation scheme that can be used to condition the resulting equivalent SISO plants so that the difficult problem of NMP zeros lying to the left of unstable poles is avoided. Examples illustrate the use of the proposed transformation.

Dans ce projet de thèse, nous étudions le rôle joué par l'anomalie dû à la connexion composée dans les théories de supergravités dans l'espace-temps à huit dimensions. Ce genre d'anomalie est en effet engendrée par la structure quotient d'espace des champs moduli de la supergravité là où le nombre des super-charges posent des contraintes rigoureux. Notre accomplissement principal est de proposer des termes supplémentaires pour annuler cette anomalie dans la théorie de supergravité en huit dimensions avec seize supercharges. Ces termes, en outre, peuvent être considérés comme une manifestation des corrections provenant de la théorie de super-cordes et nous montrons par des calculs explicites qu'une amplitude sur une boucle dans la théorie de cordes correspondante reproduit ces termes. Motivés par cette démonstration de la cohérence entre la supergravité et la théorie de cordes, nous proposons un seuil mathématique pour la compactification de ces théories dans huit dimensions vers six dimensions sur une sphère en présence des branes de co-dimension 2. Ceci est une simulation de compactification sur une surface K3 à l'aide des branes. Nous montrons que la présence d'anomalie composé ne peut être justifiée que par des branes de co-dimensions deux. Nous discutons la dualité entre la théorie Heterotic et la théorie-F sous la lumière de 7-branes et puis la compactification des supergravités de dix dimensions sur K3 en présence des 5-branes. Tous cela nous ouvrent nouvelles voies pour étudier des aspects non-perturbatives de la théorie de cordes. Nous concluons avec un calcul sur deux boucles dans la théorie de cordes Heterotic de dix dimensions qui n'ont pas été beaucoup exploré dans la littérature. / We examine the structure of composite anomaly in maximal and half-maximal supergravity theories especially in eight space-time dimensions. The number of super-charges dictates the structure of the coset space of the moduli fields of the theory which in turn engenders the composite anomaly in such theories. Our main achievement lies in proposing counter-terms for such anomalies. These terms are of stringy nature and we show by explicit 1-loop amplitude calculations in corresponding string theories that those counter-terms are consistently provided by string amplitude. In the light of non-perturbative higher dimensional theories like F-theory, the anomaly cancelling counter-terms are seen to be related to co-dimension two branes e.g. 7-branes. We then use these results of 8-dimensional theories to provide for supergravity theories in six-dimensions by compactifying on a sphere in the presence of 5-branes. This is in fact a simulation of K3 compactification and our knowledge of composite connection provide us with threshold conditions to achieve such compactifications. All these analysis provide for greater insight into the non-perturbative regime of string theory. We then conclude with a calculation of 2-loop Heterotic string amplitude which has been very less explored in the literature.