## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 926430, 9 pages.

### Characterization of the Stabilizing PID Controller Region for the Model-Free Time-Delay System

#### Abstract

For model-free time-delay systems, an analytical method is proposed to characterize the stabilizing PID region based on the frequency response data. Such characterization uses linear programming which is computationally efficient. The characteristic parameters of the controller are first extracted from the frequency response data. Subsequently, by employing an extended Hermite-Biehler theorem on quasipolynomials, the stabilizing polygon region with respect to the integral and derivative gains $({k}_{i}$ and ${k}_{d})$ is described for a given proportional gain $({k}_{p})$ in term of the frequency response data. Simultaneously, the allowable stabilizing range of ${k}_{p}$ is derived such that the complete stabilizing set of the PID controller can be obtained easily. The proposed method avoids the complexity and inaccuracy of the model identification and thus provides a convenient approach for the design and tuning of the PID controller in practice. The advantage of the proposed algorithm lies in that the boundaries of the stabilizing region consist of several simple straight lines, the complete stabilizing set can be obtained efficiently, and it can be implemented automatically in computers.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 926430, 9 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807781

Digital Object Identifier
doi:10.1155/2013/926430

Mathematical Reviews number (MathSciNet)
MR3064961

Zentralblatt MATH identifier
1271.93103

#### Citation

Ou, Linlin; Su, Yuan; Chen, Xuanguang. Characterization of the Stabilizing PID Controller Region for the Model-Free Time-Delay System. J. Appl. Math. 2013, Special Issue (2013), Article ID 926430, 9 pages. doi:10.1155/2013/926430. https://projecteuclid.org/euclid.jam/1394807781

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