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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 316827, 8 pages
Research Article

On PID Controller Design by Combining Pole Placement Technique with Symmetrical Optimum Criterion

“Dunarea de Jos” University of Galati, 47 Domneasca Street, 800008 Galati, Romania

Received 10 April 2013; Revised 8 July 2013; Accepted 8 July 2013

Academic Editor: Cristian Toma

Copyright © 2013 Viorel Nicolau. 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.


In this paper, aspects of analytical design of PID controllers are studied, by combining pole placement technique with symmetrical optimum criterion. The proposed method is based on low-order plant model with pure integrator, and it can be used for both fast and slow processes. Starting from the desired closed-loop transfer function, which contains a second-order oscillating system and a lead-lag compensator, it is shown that the zero value depends on the real-pole value of closed-loop transfer function. In addition, there is only one pole value, which satisfies the assumptions of symmetrical optimum criterion imposed to open-loop transfer function. In these conditions, by combining the pole placement technique with symmetrical optimum criterion, the analytical expressions of the controller parameters can be simplified. For simulations, PID autopilot design for heading control problem of a conventional ship is considered.