P-D Feedback for Decoupling and Pole Assignment of Singular Systems

[+] Author and Article Information
F. N. Koumboulis

University of Thessaly, School of Technological Sciences, Department of Mechanical and Industrial Engineering, 38334 Volos, Greece

B. G. Mertzios

Democritus University of Thrace, Department of Electrical and Computer Engineering, 67100, Xanthi, Greece

J. Dyn. Sys., Meas., Control 120(3), 378-388 (Sep 01, 1998) (11 pages) doi:10.1115/1.2805412 History: Received November 05, 1996; Online December 03, 2007


The problem of reducing a multi input-multi output system to many single input-single output systems, namely the problem of input-output decoupling, is studied for the case of singular systems i.e., for systems described by dynamic and algebraic equations. The problem of input-output decoupling with simultaneous arbitrary pole assignment, via proportional plus derivative (P-D) state feedback, is extensively solved. The general explicit expression of all P-D controllers solving the decoupling problem is determined. The general form of the diagonal elements of the decoupled closed-loop system is proven to be in a form having a fixed numerator polynomial and an arbitrary denominator polynomial. The necessary and sufficient conditions for the solvability of the problem of decoupling with simultaneous asymptotic stabilizability or arbitrary pole assignment are established. Furthermore, the necessary and sufficient conditions for decoupling with simultaneous impulse elimination, as well as the necessary and sufficient conditions for decoupling with arbitrary assignment of the finite and infinite poles of the closed-loop system, are established.

Copyright © 1998 by The American Society of Mechanical Engineers
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