Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes
Abstract
:1. Introduction
2. PI, PID, and PIDA Controller for the IPDT Plant Tuned with the MRDP Method
2.1. Optimal “Ideal” Controller Design
2.2. PID Controllers with Proper Transfer Functions and the Delay Equivalence
3. Robustness Issues
Robust Stability Analysis
4. Robust Stability of PI Controllers
4.1. Unfiltered PI Controllers
4.2. Filtered PI Controller with the First-Order Filter
4.3. Filtered PI Controller with the Second-Order Filter
4.4. Discussion on the Filtered PI Control
5. Robust Stability of Filtered PID Control
5.1. PID with the First-Order Filters
5.2. PID with the Second-Order Filter
5.3. PID with the Third-Order Filter
5.4. Discussion about Filtered PID Control
6. Robust Stability of PIDA Controller
6.1. PIDA with the Second-Order Filters
6.2. PIDA with the Third-Order Filters
6.3. PIDA with the Fourth-Order Filters
6.4. Discussion on the Filtered PIDA Control
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Boundary Point | |
Integral Absolute Error | |
IPDT | Integrator Plus Dead-Time |
MRDP | Multiple Real Dominant Pole |
PI | Proportional-Integral |
PID | Proportional-Integral-Derivative |
PIDA | Proportional-Integral-Derivative-Accelerative |
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K | 0.4612 | 0.78361 | 1.08268 |
5.8284 | 3.73205 | 3.00000 | |
0 | 0.26289 | 0.37500 | |
0 | 0 | 0.04167 |
- | |||
---|---|---|---|
12.639 | 4.763 | 2.771 |
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Huba, M.; Bistak, P.; Vrancic, D. Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes. Mathematics 2023, 11, 30. https://doi.org/10.3390/math11010030
Huba M, Bistak P, Vrancic D. Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes. Mathematics. 2023; 11(1):30. https://doi.org/10.3390/math11010030
Chicago/Turabian StyleHuba, Mikulas, Pavol Bistak, and Damir Vrancic. 2023. "Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes" Mathematics 11, no. 1: 30. https://doi.org/10.3390/math11010030
APA StyleHuba, M., Bistak, P., & Vrancic, D. (2023). Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes. Mathematics, 11(1), 30. https://doi.org/10.3390/math11010030