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

Honghai Wang, Jianchang Liu, Feisheng Yang*, and Yu Zhang
International Journal of Control, Automation, and Systems, vol. 12, no. 6, pp.1197-1206, 2014

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.

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

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