Approximation methodologies for explicit model predictive control of complex systems

This thesis concerns the development of complexity reduction methodologies for the application of multi-parametric/explicit model predictive (mp-MPC) control to complex high fidelity models. The main advantage of mp-MPC is the offline relocation of the optimization task and the associated computational expense through the use of multi-parametric programming. This allows for the application of MPC to fast sampling systems or systems for which it is not possible to perform online optimization due to cycle time requirements. The application of mp-MPC to complex nonlinear systems is of critical importance and is the subject of the thesis. The first part is concerned with the adaptation and development of model order reduction (MOR) techniques for application in combination to mp-MPC algorithms. This first part includes the mp-MPC oriented use of existing MOR techniques as well as the development of new ones. The use of MOR for multi-parametric moving horizon estimation is also investigated. The second part of the thesis introduces a framework for the ‘equation free’ surrogate-model based design of explicit controllers as a possible alternative to multi-parametric based methods. The methodology relies upon the use of advanced data-classification approaches and surrogate modelling techniques, and is illustrated with different numerical examples.Open Acces

Application of optimal control to structural load alleviation control systems

Feedback laws based upon optimal control theory were derived. and these resulted in a reduction of the structural loads on the wing of a simulated aircraft. Various models of the aircraft dynamics were used. the most complete being of order 79. This model included rigid body motion, structural flexibility effects, unsteady aerodynamics, gust dynamics and actuator dynamics. The structural effects were characterised by the first fifteen bending modes. The subject aircraft studied, was considered to employ active ailerons and elevators and was subjected to manoeuvre commands and simulated atmospheric turbulence. Extensive numerical tests have shown that feedback laws derived from reduced dimension models performed comparably with the feedback law based on the most complete model. Tests were made on feedback laws ranging from order 79 to order 5. It was. however. not possible to reduce the number of feedback variables below five as this then affected the stability of the aircraft. The law based upon five state variable feedback was given the designation 'safety law'. One of the consequences of operating under the action of the 'safety law' was that the same level of load reduction could not be achieved as was obtained whenever a full state feedback law was employed. In addition 'safety law' operation was often marked by large transient oscillations of the wing root bending moment and it was considered that this would subsequently affect the fatigue life of the structure. An observer design was then investigated which reconstructed the complete state vector from a selection of measurements of the sensor signals appropriate to the 'safety law'. Results have shown that it is possible to achieve a practical implementation of such a scheme which will possess all the attendant advantages of full state feedback control. A consequence of reducing the strength of the wing of the aircraft as a result of employing an active load alleviation scheme is that a considerable degree of reliability of the control system, higher than that of both the basic airframe and its propulsive system, will be required. Because the use of hardware redundancy techniques as a means of providing the required degree of reliability would be expensive, software redundancy techniques suggest an attractive alternative. One example of how software redundancy may be employed is demonstrated in respect of , checking the analogue feedback gain controller used in the aircraft to implement linear feedback. It is shown how a-microprocessor may be effectively employed to introduce a surrogate gain should one or more of the channels of the controller fail

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Six Decades of Flight Research: An Annotated Bibliography of Technical Publications of NASA Dryden Flight Research Center, 1946-2006

Titles, authors, report numbers, and abstracts are given for nearly 2900 unclassified and unrestricted technical reports and papers published from September 1946 to December 2006 by the NASA Dryden Flight Research Center and its predecessor organizations. These technical reports and papers describe and give the results of 60 years of flight research performed by the NACA and NASA, from the X-1 and other early X-airplanes, to the X-15, Space Shuttle, X-29 Forward Swept Wing, X-31, and X-43 aircraft. Some of the other research airplanes tested were the D-558, phase 1 and 2; M-2, HL-10 and X-24 lifting bodies; Digital Fly-By-Wire and Supercritical Wing F-8; XB-70; YF-12; AFTI F-111 TACT and MAW; F-15 HiDEC; F-18 High Alpha Research Vehicle, F-18 Systems Research Aircraft and the NASA Landing Systems Research aircraft. The citations of reports and papers are listed in chronological order, with author and aircraft indices. In addition, in the appendices, citations of 270 contractor reports, more than 200 UCLA Flight System Research Center reports, nearly 200 Tech Briefs, 30 Dryden Historical Publications, and over 30 videotapes are included