The research described in this dissertation deals with an open problem concerning
the synthesis of controllers of xed order and structure. This problem is encountered
in a variety of applications. Simply put, the problem may be put as the
determination of the set, S of controller parameter vectors, K = (k1; k2; : : : ; kl),
that render Hurwitz a family (indexed by F) of complex polynomials of the form
fP0(s; ) + Pl
i=1 Pi(s; )ki; 2 Fg, where the polynomials Pj(s; ); j = 0; : : : ; l
are given data. They are specied by the plant to be controlled, the structure of the
controller desired and the performance that the controllers are expected to achieve.
Simple examples indicate that the set S can be non-convex and even be disconnected.
While the determination of the non-emptiness of S is decidable and amenable
to methods such as the quantier elimination scheme, such methods have not been
computationally tractable and more importantly, do not provide a reasonable approximation
for the set of controllers. Practical applications require the construction of a
set of controllers that will enable a control engineer to check the satisfaction of performance
criteria that may not be mathematically well characterized. The transient
performance criteria often fall into this category. From the practical viewpoint of the construction of approximations for S, this
dissertation is dierent from earlier work in the literature on this problem. A novel
feature of the proposed algorithm is the exploitation of the interlacing property of
Hurwitz polynomials to provide arbitrarily tight outer and inner approximation to
S. The approximation is given in terms of the union of polyhedral sets which are
constructed systematically using the Hermite-Biehler theorem and the generalizations
of the Descartes' rule of signs.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2089 |
| Date | 15 May 2009 |
| Creators | Malik, Waqar Ahmad |
| Contributors | Rajagopal, Kumbakonam, Swaroop, Darbha |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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