NDLI: Stabilization of discrete time systems by first order controllers

Content Provider	IEEE Xplore Digital Library
Author	Tantaris, R.N. Keel, L.H. Bhattacharyya, S.P.
Copyright Year	2002
Description	Author affiliation: Center of Excellence in Inf. Syst., Tennessee State Univ., Nashville, TN, USA (Tantaris, R.N.)
Abstract	We consider the problem of stabilizing a given but arbitrary linear time invariant discrete time system with transfer function P(z), by a first order discrete time feedback controller. The complete set of stabilizing controllers is determined in the controller parameter space [x/sub 1/, x/sub 2/, x/sub 3/]. The solution involves the Tchebyshev representation of the characteristic equation on the unit circle. The set is shown to be computable explicitly, for fixed x/sub 3/ by solving linear equations involving the Tchebyshev polynomials in closed form, and the three dimensional set is recovered by sweeping over the scalar parameter x/sub 3/. This result gives a constructive solution of a) the problem of "first order stabilizability" of a given plant b) simultaneous stabilization of a set of plants P/sub i/(z) and c) stable or minimum phase first order stabilization of a plant. The solution is facilitated by the fact that it is based on linear equations and the intersection of sets can be found by adding more equations. In each case the complete set of solutions is found and this feature is essential and important for imposing further design requirements. Illustrative examples are included. They demonstrate that the shape of the stabilizing set in the controller parameter space is quite different and much more complicated compared to that of digital MID controllers despite the fact that both are "three term controllers". Extensions and applications to design are discussed.
Sponsorship	IEEE Control Syst. Soc
Starting Page	1084
Ending Page	1089
File Size	383523
Page Count	6
File Format	PDF
ISBN	0780375165
ISSN	01912216
DOI	10.1109/CDC.2002.1184656
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-12-10
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Discrete time systems Control systems Equations Three-term control Optimal control Shape control Pi control Proportional control Information systems Transfer functions
Content Type	Text
Resource Type	Article

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