Regular Papers

International Journal of Control, Automation and Systems 2014; 12(6): 1197-1206

Published online October 9, 2014

https://doi.org/10.1007/s12555-013-0341-0

© The International Journal of Control, Automation, and Systems

Proportional-Integral Controller for Stabilization of Second-Order Delay Processes

Honghai Wang, Jianchang Liu, Feisheng Yang*, and Yu Zhang

Northwestern Polytechnical University

Abstract

This paper considers the problem of determining the complete stabilizing set of proportional-integral (PI) controllers for a second-order process with time delay by employing a version of the Hermite-Biehler theorem applicable to quasipolynomials. With the poles of open-loop system being complex, we first provide the result to find the admissible range of the proportional gain. Then by choosing a fixed proportional gain in this range, we can ascertain the complete region of integral gain which can stabilize the second-order delay process. Similarly, the result for the case of open-loop real poles is also obtained. It is mentioned that the condition to obtain the parameter set for stabilizing the given plant is sufficient and necessary.

Keywords Proportional-integral (PI) controller, second-order process, stabilization, time delay.

Article

Regular Papers

International Journal of Control, Automation and Systems 2014; 12(6): 1197-1206

Published online December 1, 2014 https://doi.org/10.1007/s12555-013-0341-0

Copyright © The International Journal of Control, Automation, and Systems.

Proportional-Integral Controller for Stabilization of Second-Order Delay Processes

Honghai Wang, Jianchang Liu, Feisheng Yang*, and Yu Zhang

Northwestern Polytechnical University

Abstract

This paper considers the problem of determining the complete stabilizing set of proportional-integral (PI) controllers for a second-order process with time delay by employing a version of the Hermite-Biehler theorem applicable to quasipolynomials. With the poles of open-loop system being complex, we first provide the result to find the admissible range of the proportional gain. Then by choosing a fixed proportional gain in this range, we can ascertain the complete region of integral gain which can stabilize the second-order delay process. Similarly, the result for the case of open-loop real poles is also obtained. It is mentioned that the condition to obtain the parameter set for stabilizing the given plant is sufficient and necessary.

Keywords: Proportional-integral (PI) controller, second-order process, stabilization, time delay.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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