Optimal control with structure constraints and its application to the design of passive mechanical systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Page 214 blank.Includes bibliographical references.Structured control (static output feedback, reduced-order control, and decentralized feedback) is one of the most important open problems in control theory and practice. In this thesis, various techniques for synthesis of structured controllers are surveyed and investigated, including H2 optimization, H[infinity] optimization, L1 control, eigenvalue and eigenstructure treatment, and multiobjective control. Unstructured control-full- state feedback and full-order control-is also discussed. Riccati-based synthesis, linear matrix inequalities (LMI), homotopy methods, gradient- and subgradientbased optimization are used. Some new algorithms and extensions are proposed, such as a subgradient-based method to maximize the minimal damping with structured feedback, a multiplier method for structured optimal H2 control with pole regional placement, and the LMI-based H2/H[infinity]/pole suboptimal synthesis with static output feedback. Recent advances in related areas are comprehensively surveyed and future research directions are suggested. In this thesis we cast the parameter optimization of passive mechanical systems as a decentralized control problem in state space, so that we can apply various decentralized control techniques to the parameter design which might be very hard traditionally. More practical constraints for mechanical system design are considered; for example, the parameters are restricted to be nonnegative, symmetric, or within some physically-achievable ranges. Marginally statable systems and hysterically damped systems are also discussed. Numerical examples and experimental results are given to illustrate the successful application of decentralized control techniques to the design of passive mechanical systems, such as multi-degree-of-freedom tuned-mass dampers, passive vehicle suspensions, and others.by Lei Zuo.S.M

Performance Parameters of Micromechanical Resonators

Ph.DDOCTOR OF PHILOSOPH

Selective detection for gas chromatography by ultraviolet spectrometry

Spectrometric detection systems for gas chromatography (GC) based on gas phase ultraviolet absorbance and fluorescence measurements have been developed and evaluated in this research. Polynuclear aromatic compounds (PNAs) are selectively detected by these systems. Limits of detection for PNAs range from 4 ng to 90 ng for absorbance determinations, and from 3 ng to 400 ng for fluorescence determinations made at a fixed waveband. The spacial design and optical components have been carefully selected to be compatible with hightemperature gas-phase measurements (ca. 250°C) while preserving the resolution of the chromatographic separation and enhancing the sensitivity of the multimode spectrometric determinations. Vapor-phase determinations of GC eluates are made directly as they leave the GC column in specially designed, heated flow-through detector cells with low volume and dead space. A long pathlength cell of 167 mm was used to enhance the sensitivity of the absorbance measurements. High-temperature, quartz fiber optic bundles transmit light to and from the detector cell, thus thermally isolating optical components. There are two configurations for these GC detection systems, each advantageous for either quantitative or qualitative determinations, respectively. In the first, waveband selection is accomplished via optical filters. These simple and compact systems are particularly suited to precise and sensitive determinations of polynuclear aromatic compounds. The sensitivity and selectivity of the absorbance and fluorescence measurements vary with individual compounds. These differences also provide some qualitative information about eluates. The second detection system configuration provides repetitive UV spectral information of GC eluates. This computer-controlled system scans a modified Czerny- Turner monochromator and can acquire up to two 62-nm spectra of eluates per second. Spectral information thus obtained may be used for identification purposes and to locate unresolved GC eluates. After compounds have been separated and identified, fixed waveband spectrometric data acquired at an absorption maximum may be used to determine concentrations