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Mathematical Problems in Engineering
Volume 2011, Article ID 929430, 20 pages
Research Article

State-PID Feedback for Pole Placement of LTI Systems

School of Electrical Engineering, Institute of Engineering, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand

Received 3 February 2011; Revised 28 March 2011; Accepted 15 June 2011

Academic Editor: J. Rodellar

Copyright © 2011 Sarawut Sujitjorn and Witchupong Wiboonjaroen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Pole placement problems are especially important for disturbance rejection and stabilization of dynamical systems and regarded as algebraic inverse eigenvalue problems. In this paper, we propose gain formulae of state feedback through PID-elements to achieve desired pole placement for a delay-free LTI system with single input. Real and complex stable poles can be assigned with the proposed compact gain formulae. Numerical examples show that our proposed gain formulae can be used effectively resulting in very satisfactory responses.