Arbitrary Pole Placement With Limited Number of Inputs and Outputs

[+] Author and Article Information
W. V. Loscutoff

Engineering Technology Department, Battelle-Northwest, Richland, Wash.

J. Dyn. Sys., Meas., Control 96(3), 322-326 (Sep 01, 1974) (5 pages) doi:10.1115/1.3426809 History: Received April 08, 1974; Online July 13, 2010


In controller design problems, the quantitative description of the desired controlled system behavior is often given by specifying the closed loop poles. An output-variable, feedback control policy for a linear system of order n, with m outputs and p inputs, is described by u = −Gy . Matrix G contains p × m parameters which may be used to dictate the locations of the closed loop poles. The limiting condition for arbitrary pole placement, without some form of state estimation, is p × m = n since the p × m independent controller parameters may be used to specify the n poles. However, there is no systematic procedure for the design of controllers subject to limiting condition. In this paper, a technique based on modal system description is used to design static output-variable feedback controllers with limited number of inputs and outputs. It is shown that arbitrary closed loop pole placement is possible if p + m ≥ n + 1 for sufficiently well coupled systems.

Copyright © 1974 by ASME
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