A parametric pole-matching approach to relative stability and system integrity
Abstract
This thesis is mainly concerned with developing simple geometrical and algebraic criteria for measuring the relative proximity of the poles and several other relevant invariants of any two linear, time-invariant systems. One should be able to use such criteria as optimization indices on any parametrized, linear system for the parameter-selection purpose, to match its transient performance and relative stability with those of a chosen model. The main invariant-matching indices introduced here are based upon the notion of aperture between two (backward-shift) invariant subspaces (of the systems in comparison). This aperture--in fact, a metric--is also the norm of a certain Hankel operator which arises from a generalized version of the Schur-Cohn stability test. A stability test of the Jury-Routh type, based on the Shur numbers, is also derived for this purpose. These invariant-matching criteria are justified not only for their natural origin, but also for their reliability as relative-proximity indicators for the invariants involved. Efficient algorithms are also provided for the computation of these indices, which make them particularly useful for large-order systems. In addition, for the M.I.M.O. integrity concern, we derive a complete description of the asymptotic behavior, near zero-gain, of the multiparameter root-locus of any system with some open-loop poles at the origin. This result gives rise to a practically minimum condition for multiparameter integral-controllability. In consequence, this mild robustness criterion allows much more freedom in control designs for system integrity. Our root-locus approach could also be adapted to systems with non-zero, marginally stable open-loop poles. In conclusion, besides the contributions to the understanding of some important geometrical aspects of the poles and other significant invariants of linear systems, this research provides control designers with a few most basic computer-aided-design tools in the form of optimization indices, and non-conservative robustness criteria, to assist them in the often indispensable parameter-selection tasks, for improving system performance, relative stability and integrity.
Degree
Ph.D.
Advisors
Frazho, Purdue University.
Subject Area
Systems design
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