DocumentCode :
857925
Title :
On closed-form expressions for mean squares in discrete-continuous systems
Author :
Sklansky, Jack
Author_Institution :
RCA Laboraories, Princeton, NJ, USA
Volume :
4
Issue :
1
fYear :
1958
fDate :
3/1/1958 12:00:00 AM
Firstpage :
21
Lastpage :
27
Abstract :
When a system is to be optimized with respect to the mean square of some variable, a closed-form expression for that mean square is usually desired. The problem of obtaining such expressions for discrete-continuous systems-i.e., systems made up of both sampled-data and continuous subsystems-has been a difficulty in the past. The reason for this is that the spectral densities of the variables of interest often contain rational functions of \\exp (j2\\pi fT) combined multiplicatively with rational functions of f, f being the frequency coordinate of the spectral densities, and T the sampling period. Presented here is a technique for finding the desired closed-form expressions. It is based on the relation int\\min{-j\\infty }\\max {j\\infty } P^{\\ast }(e^{s^{T}})Q(s)ds = \\oint P^{\\ast }(z)Q^{\\ast }(z)z^{-1}dz , where Q^{\\ast } (z) is the " Z -transform" of Q (s) , To illustrate the technique, closed-form formulas for the output and ripple of discrete-continuous systems and for the control error of sampled-data feedback systems are derived, and an application to a "track-while-scan" system is given.
Keywords :
Closed-form solution; Communication system control; Control systems; Error correction; Frequency; Integral equations; Mean square error methods; Output feedback; Sampling methods; Transfer functions;
fLanguage :
English
Journal_Title :
Automatic Control, IRE Transactions on
Publisher :
ieee
ISSN :
0096-199X
Type :
jour
DOI :
10.1109/TAC.1958.1104837
Filename :
1104837
Link To Document :
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