A Novel Design of Fractional PI/PID Controllers for Two-Input-Two-Output Processes
Abstract
:1. Introduction
2. Materials and Methods
2.1. Fractional Order Calculus
2.2. Simplified Decoupling Smith Predictor Structure based on FO (F-SDSP) for TITO Processes
2.3. IMC-Fractional PI/PID Controller Design
2.4. System Performance and Robustness Analysis
2.4.1. Integral Absolute Error Index
2.4.2. Integral of Time-Weighted Absolute Error (ITAE)
2.4.3. Total Variation (TV)
2.4.4. Robust Stability Analysis
3. Results
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Podlubny, I. Fractional-Order Systems and PIλDμ-Controllers. IEEE Trans. Autom. Control 1999, 44, 208–214. [Google Scholar] [CrossRef]
- Chen, Y.; Bhaskaran, T.; Xue, D. Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers. J. Comput. Nonlinear Dyn. 2008, 3, 021403. [Google Scholar] [CrossRef] [Green Version]
- Monje, C.A.; Chen, Y.; Vinagre, B.M.; Xue, D.; Feliu-Batlle, V. Fractional-Order Systems and Controls, Fundamentals and Applications; Springer: London, UK, 2010. [Google Scholar]
- Rabah, K.; Ladaci, S.; Lashab, M. Bifurcation-based Fractional Order PIλ Dμ Controller Design Approach for Nonlinear Chaotic Systems. Front. Inf. Technol. Electron. Eng. 2018, 19, 180–191. [Google Scholar] [CrossRef]
- Luo, Y.; Chen, Y.Q.; Wang, C.Y.; Pi, Y.G. Tuning fractional order proportional integral controllers for fractional order systems. J. Process Control 2010, 20, 823–831. [Google Scholar] [CrossRef]
- Beschi, M.; Padula, F.; Visioli, A. Fractional robust PID control of a solar furnace. Control Eng. Pract. 2016, 60, 190–199. [Google Scholar] [CrossRef]
- De Keyser, R.; Muresan, C.I.; Ionescu, C.M. A novel auto-tuning method for fractional order PI/PD controllers. ISA Trans. 2016, 62, 268–275. [Google Scholar] [CrossRef]
- Padula, F.; Visioli, A. Tuning rules for optimal PID and fractional-order PID controllers. J. Process Control 2011, 21, 69–81. [Google Scholar] [CrossRef]
- Vu, T.N.; Lee, M. Analytical design of fractional-order proportional-integral controllers for time-delay processes. ISA Trans. 2013, 52, 583–591. [Google Scholar] [CrossRef]
- Vu, T.N.; Lee, M. Smith predictor based fractional-order PI control for time-delay processes. Korean J. Chem. Eng. 2014, 31, 1321–1329. [Google Scholar] [CrossRef]
- Li, D.; Liu, L.; Jin, Q.; Hirasawa, K. Maximum sensitivity based fractional IMC-PID controller design for non-integer order system with time delay. J. Process Control 2015, 31, 17–29. [Google Scholar] [CrossRef]
- Amoura, K.; Mansouri, R.; Bettayeb, M.; Al-Saggaf, U.M. Closed-loop step response for tuning PID-fractional-order-filter controllers. ISA Trans. 2016, 64, 247–257. [Google Scholar] [CrossRef]
- Li, M.; Zhou, P.; Zhao, Z.; Zhang, J. Two-degree-of-freedom fractional order-PID controllers design for fractional order processes with dead-time. ISA Trans. 2016, 61, 147–154. [Google Scholar] [CrossRef] [Green Version]
- Bouyedda, H.; Ladaci, S.; Sedraoui, M.; Lashab, M. Identification and Control design for a class of non-minimum Phase dead-time Systems based on fractional-order Smith Predictor and Genetic Algorithm Technique. Int. J. Dyn. Control 2019, 7, 914–925. [Google Scholar] [CrossRef]
- Chuong, V.L.; Vu, T.N.L.; Truong, N.T.N.; Jung, J.H. An Analytical Design of Simplified Decoupling Smith Predictors for Multivariable Processes. Appl. Sci. 2019, 9, 2487. [Google Scholar] [CrossRef] [Green Version]
- Garrido, J.; Vázquez, F.; Morilla, F. Centralized multivariable control by simplified decoupling. J. Process Control 2012, 22, 1044–1062. [Google Scholar] [CrossRef] [Green Version]
- Truong, N.L.V.; Lee, M. Independent design of multi-loop PI/PID controllers for interacting multivariable processes. J. Process Control 2010, 20, 922–933. [Google Scholar]
- Truong, N.L.V.; Lee, M. An extended method of simplified decoupling for multivariable processes with multiple time delays. J. Chem. Eng. Jpn. 2013, 46, 279–293. [Google Scholar]
- Skogestad, S.; Postlethwaithe, I. Multivariable Feedback Control Analysis and Design, 1st ed.; John Wiley & Sons: Hoboken, NJ, USA, 1996. [Google Scholar]
- Garrido, J.; Vázquez, F.; Morilla, F. Inverted decoupling internal model control for square stable multivariable time delay systems. J. Process Control 2014, 24, 1710–1719. [Google Scholar] [CrossRef] [Green Version]
- Garrido, J.; Vázquez, F.; Morilla, F. Centralized Inverted Decoupling Control. Ind. Eng. Chem. Res 2013, 52, 7854–7866. [Google Scholar] [CrossRef] [Green Version]
- Santos, T.L.; Torrico, B.C.; Normey-Rico, J.E. Simplified filtered Smith predictor for MIMO processes with multiple time delays. ISA Trans. 2016, 65, 339–349. [Google Scholar] [CrossRef]
- Morari, M.; Zafiriou, E. Robust Process Control; Prentice Hall: Englewood Cliffs, NJ, USA, 1989. [Google Scholar]
- Wood, R.K.; Berry, M.W. Terminal composition control of binary distillation column. Chem. Eng. Sci. 1973, 28, 1707–1717. [Google Scholar] [CrossRef]
- Luyben, W.L. Simple method for tuning SISO controllers in multivariable systems. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 654–660. [Google Scholar] [CrossRef]
Models | Tuning Rules |
---|---|
; ; ; ; | |
| ; ; ; ; |
Tuning Method | IAE | ITAE | TV | |
---|---|---|---|---|
F-SDSP | 57.824 | 10173 | 1.4838 | 0.200 |
IDIMC-F | 750.00 | 218750 | 1.7289 | 0.7068 |
ID-K | 95.521 | 14561 | 14.678 | 0.3880 |
Tuning Method | IAE | ITAE | TV | |
---|---|---|---|---|
F-SDSP | 9.221 | 631.207 | 0.9587 | 0.2291 |
SDSP | 10.963 | 667.088 | 0.7720 | 0.3091 |
Santos | 13.294 | 881.098 | 1.2976 | 0.5750 |
Tuning Method | IAE | ITAE | TV | |
---|---|---|---|---|
F-SDSP | 3.7490 | 101.66 | 10.838 | 0.2974 |
SDSP | 3.4382 | 102.83 | 8.7549 | 0.3046 |
Garrido | 4.5255 | 126.04 | 11.295 | 0.4107 |
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Chuong, V.L.; Vu, T.N.L.; Truong, N.T.N.; Jung, J.H. A Novel Design of Fractional PI/PID Controllers for Two-Input-Two-Output Processes. Appl. Sci. 2019, 9, 5262. https://doi.org/10.3390/app9235262
Chuong VL, Vu TNL, Truong NTN, Jung JH. A Novel Design of Fractional PI/PID Controllers for Two-Input-Two-Output Processes. Applied Sciences. 2019; 9(23):5262. https://doi.org/10.3390/app9235262
Chicago/Turabian StyleChuong, Vo Lam, Truong Nguyen Luan Vu, Nguyen Tam Nguyen Truong, and Jae Hak Jung. 2019. "A Novel Design of Fractional PI/PID Controllers for Two-Input-Two-Output Processes" Applied Sciences 9, no. 23: 5262. https://doi.org/10.3390/app9235262