Inverse problems in 2-norm and infinity-norm controller synthesis

This paper studies certain inverse problems in the optimal frequency-domain synthesis of robust controllers, in both the 2-norm and the infinity-norm. These inverse problems identify the class of controllers which are optimal for some choice of weights. Their implications for loopshaping are discussed. \u

Supplementing Frequency Domain Interpolation Methods for Character Animation

The animation of human characters entails difficulties exceeding those met simulating objects, machines or plants. A person's gait is a product of nature affected by mood and physical condition. Small deviations from natural movement are perceived with ease by an unforgiving audience. Motion capture technology is frequently employed to record human movement. Subsequent playback on a skeleton underlying the character being animated conveys many of the subtleties of the original motion. Played-back recordings are of limited value, however, when integration in a virtual environment requires movements beyond those in the motion library, creating a need for the synthesis of new motion from pre-recorded sequences. An existing approach involves interpolation between motions in the frequency domain, with a blending space defined by a triangle network whose vertices represent input motions. It is this branch of character animation which is supplemented by the methods presented in this thesis, with work undertaken in three distinct areas. The first is a streamlined approach to previous work. It provides benefits including an efficiency gain in certain contexts, and a very different perspective on triangle network construction in which they become adjustable and intuitive user-interface devices with an increased flexibility allowing a greater range of motions to be blended than was possible with previous networks. Interpolation-based synthesis can never exhibit the same motion variety as can animation methods based on the playback of rearranged frame sequences. Limitations such as this were addressed by the second phase of work, with the creation of hybrid networks. These novel structures use properties of frequency domain triangle blending networks to seamlessly integrate playback-based animation within them. The third area focussed on was distortion found in both frequency- and time-domain blending. A new technique, single-source harmonic switching, was devised which greatly reduces it, and adds to the benefits of blending in the frequency domain

Multifrequency Aperture-Synthesizing Microwave Radiometer System (MFASMR). Volume 1

Background material and a systems analysis of a multifrequency aperture - synthesizing microwave radiometer system is presented. It was found that the system does not exhibit high performance because much of the available thermal power is not used in the construction of the image and because the image that can be formed has a resolution of only ten lines. An analysis of image reconstruction is given. The system is compared with conventional aperture synthesis systems

Radio Astronomy Image Reconstruction in the Big Data Era

Next generation radio interferometric telescopes pave the way for the future of radio astronomy with extremely wide-fields of view and precision polarimetry not possible at other optical wavelengths, with the required cost of image reconstruction. These instruments will be used to map large scale Galactic and extra-galactic structures at higher resolution and fidelity than ever before. However, radio astronomy has entered the era of big data, limiting the expected sensitivity and fidelity of the instruments due to the large amounts of data. New image reconstruction methods are critical to meet the data requirements needed to obtain new scientific discoveries in radio astronomy. To meet this need, this work takes traditional radio astronomical imaging and introduces new of state-of-the-art image reconstruction frameworks of sparse image reconstruction algorithms. The software package PURIFY, developed in this work, uses convex optimization algorithms (i.e. alternating direction method of multipliers) to solve for the reconstructed image. We design, implement, and apply distributed radio interferometric image reconstruction methods for the message passing interface (MPI), showing that PURIFY scales to big data image reconstruction on computing clusters. We design a distributed wide-field imaging algorithm for non-coplanar arrays, while providing new theoretical insights for wide-field imaging. It is shown that PURIFY’s methods provide higher dynamic range than traditional image reconstruction methods, providing a more accurate and detailed sky model for real observations. This sets the stage for state-of-the-art image reconstruction methods to be distributed and applied to next generation interferometric telescopes, where they can be used to meet big data challenges and to make new scientific discoveries in radio astronomy and astrophysics

Analysis and synthesis of SISO H[subscript infinity] controllers

Classical feedback control theories are traditionally concerned with issues like stability and performance, however, they typically fail to address issues such as robustness and plant perturbation. This thesis is concerned with the robust stability and the robust performance of single-input single-output plants. The basic issue under analysis is how to realize the benefits of the usual feedback control structure in the presence of model uncertainty. This is accomplished by seeking feedback controllers providing robust stability and performance by minimizing weighted sensitivity functions of a linear system represented by its transfer function. A characterization of models for plants with unstructured uncertainty is introduced. Specifications and measures of stability and performance for robust controllers and the necessary and sufficient conditions to test the robust stability and the robust performance conditions of a control design are explored. A parametrization of feedback controllers that guarantee closed loop stability for both stable and unstable plants is shown and a systematic procedure for synthesizing robust controllers, known in the literature as HK controllers, is presented. These systematic algorithms are based on the theory of interpolation by analytic functions and the solution to the model matching problem. A case study of the inverted pendulum positioning system is developed to illustrate the concepts of robust analysis and the design algorithms. The controller is compared to a classic state variable feedback solution

Air-breathing hypersonic vehicle guidance and control studies; An integrated trajectory/control analysis methodology: Phase 1

A tool which generates optimal trajectory/control histories in an integrated manner is generically adapted to the treatment of single-stage-to-orbit air-breathing hypersonic vehicles. The methodology is implemented as a two point boundary value problem solution technique. Its use permits an assessment of an entire near-minimum-fuel trajectory and desired control strategy from takeoff to orbit while satisfying physically derived inequality constraints and while achieving efficient propulsive mode phasing. A simpler analysis strategy that partitions the trajectory into several boundary condition matched segments is also included to construct preliminary trajectory and control history representations with less computational burden than is required for the overall flight profile assessment. A demonstration was accomplished using a tabulated example (winged-cone accelerator) vehicle model that is combined with a newly developed multidimensional cubic spline data smoothing routine. A constrained near-fuel-optimal trajectory, imposing a dynamic pressure limit of 1000 psf, was developed from horizontal takeoff to 20,000 ft/sec relative air speed while aiming for a polar orbit. Previously unspecified propulsive discontinuities were located. Flight regimes demanding rapid attitude changes were identified, dictating control effector and closed-loop controller authority was ascertained after evaluating effector use for vehicle trim. Also, inadequacies in vehicle model representations and specific subsystem models with insufficient fidelity were determined based on unusual control characteristics and/or excessive sensitivity to uncertainty