Universal Design Equations for Fractional Order PID Control of Plants with Time Delay

Mehmet Emir Koksal

doi:10.21605/cukurovaummfd.609304

Research Article

Universal Design Equations for Fractional Order PID Control of Plants with Time Delay

Year 2019, Volume: 34 Issue: 2, 231 - 240, 30.06.2019

Mehmet Emir Koksal

https://doi.org/10.21605/cukurovaummfd.609304

Abstract

Some all-purpose design equations are derived for designing fractional order controllers for integer order plants with time delay. The results combine many design techniques appearing in the literature. In addition to plotting the global stability boundaries, they can be used to achieve desired gain and phase margins with a flat phase response near the gain cross over frequency. So, robustness can also be guaranteed. Further, satisfactory output disturbance and high frequency noise rejections can be realizable. An example is treated to make connections with the already existing results in the literature, which proves the usability of the obtained design equations.

Keywords

Control design, PID control, Stability

References

1. Astrom, K. J., Hagglund, T., 1995. PID Controllers: Theory, Design, and Tuning.
2. Ang, K. H., Chong, G., Li, Y., 2013. PID Control System Analysis, Design, and Technology, IEEE Trans. Control Syst. Technol. 13, 559–576.
3. Yamamoto, T., Takao, K., Yamada, T., 2009. Design of a Data-driven PID Controller, IEEE Trans. Control Syst. Technol. 17, 29-39.
4. Erenturk, K., 2013. Fractional-order PIλDµand Active Disturbance Rejection Control of Nonlinear Two-mass Drive System, IEEE Trans. Ind. Electron. 60, 3806-3813.
5. Yeroglu, C., Tan, N., 2011. Note on Fractionalorder Proportional-Integral-Differential Controller Design, IET Control Theory Appl., 5, 1978-1989.
6. Monje, C.A., Vinagreb, B.M., Feliuc, V., Chen, Y.Q., 2008. Tuning and Auto-tuning of Fractional Order Controllers for Industry Applications, Control Eng. Pract., 16, 798-812.
7. Chunna, Z., Xue, D., Chen, Y. Q., 2005. A Fractional Order PID Tuning Algorithm for a Class of Fractional Order Plants, IEEE Proc. of the Intern. Conf. Mechatronics & Automation, 216-221.
8. Cokmez, E., Atic, S., Peker, F., Kaya, I., 2018. Fractional-order PI Controller Design for Integrating Processes Based on Gain and Phase Margin Specifications, IFAC PapersOnLine, 51, 751-756.
9. Pullaguram, D., Mishra, S., Senroy, N., Mukherjee, M., 2018. Design and Tuning of Robust Fractional Order Controller for Autonomous Microgrid Vsc System, IEEE Transactions on Industry Applications, 54, 91-101.
10. Oustaloup, A., Cois, O., Lanusse, P., Melchior, P., Moreau, X., Sabatier, J., 2006. The Crone Aproach: Theoretical Developments and Major Applications, IFAC Proc., 39, 324-354.
11. Vinagre, B.M., Feliu, V., 2007. Optimal Fractional Controllers for Rational Order Systems, IEEE Trans. Autom. Control 52, 23852389.
12. Krishna, B.T., 2011. Studies on Fractional Order Differentiators and Integrators: a Survey, Signal Processing, 91, 386-426.
13. John, D.A., Biswas, K., 2018. Analysis of Disturbance Rejection by PIλ Controller Using Solid State Fractional Capacitor, IEEE Proc. of the International Symposiums of Circuits and Systems, 1-5.
14. Khurram, A., Rehman, H., Mukhopadhyay, S., 2018. Comparative Analysis of Integer-order and Fractional-order Proportional Integral Speed Controllers for Induction Motor Drive Systems, Journal of Power Electronics, 18, 723-735.
15. Dogruer, T., Tan, N., 2018. Design of PI Controller Using Optimization Method in Fractional Order Control Systems, IFAC PapersOnLine, 51, 841-846.
16. Raynaud, H.F., Zergainoh, A., 2000. State-space Representation for Fractional Order Controllers, Automatica, 36, 1017-1021.
17. Zagorowska, M., 2018. Analysis of Performance Indicators for Optimization of Noninteger-order Controllers, Journal of Circuits, Systems and Computers, 27.
18. Sathishkumar, P., 2018. Fractional Controller Tuning Expressions for a Universal Plant Structure, IEEE Control Systems Letters, 2, 345-350.
19. Ranjbaran, K., Tabatabaei, M., 2018. Tuning PI and Fractional Order PI Controllers With an Additional Fractional Order Pole, Chemical Engineering Communications, 205, 207-225.
20. Xue, D., Chen, Y.Q., 2002. A Comparative Introduction of four Fractional Order Controllers, Proc. of the 4th World Congress on Intelligent Control and Automation, 3228-3235.
21. Kumar, L., Narang, D., 2018. Tuning of Fractional Order PIλDµ Controllers Using Evolutionary Optimization for Pid Tuned Synchronous Generator Excitation System, IFAC-PapersOnLine, 51, 859-864.
22. Dabiri, A., Moghaddam, B.P., Machado, J.A.T., 2018. Optimal Variable-order Fractional PID Controllers for Dynamical Systems, Journal of Comp. Appl. Math 339, 40-48.
23. Cao, J., Cao, B., 2006. Design of Fractional Order Controller Based on Particle Swarm Optimization, IEEE Conference on Industrial Electronics and Applications, 1-6.
24. Ranjan, J., Nayak, B.S., 2018. Application of Group Hunting Search Optimized Cascade Pdfractional Order PID Controller in Interconnected Thermal Power System, Trends in Renewable Energy, 4, 22-33.
25. Lu, K., Zhou, W., Zeng, G., Du, W., 2018. Design of PID Controller Based on a Selfadaptive State-space Predictive Functional Control Using Extremal Optimization Method, Journal of the Franklin Institute, 355, 2197-2220.
26. Shukla, M. K., Sharma, B. B., 2018. Control and Synchronization of a Class of Uncertain Fractional Order Chaotic Systems Via Adaptive Backstepping Control, Asian Journal of Control, 20, 707-720.
27. Ibraheem, L.K., Abdul-Adheem, W.R., 2016. On the Improved Nonlinear Tracking Differentiator Based Nonlinear Pid Controller Design, International Journal of Advanced Computer Science and Applications, 7, 234-241.
28. Li, L., 2018. Lebesgue-P NORM Convergence of Fractional-Order PID-Type Iterative Learning Control for Linear Systems, Asian Journal of Control, 20, 483-494.
29. Moradi, L., Mohammadi, F., Baleanu, D., 2018. A Hybrid Functions Numerical Scheme for Fractional Optimal Control Problems: Application to Nonanalytic Dynamic Systems, Journal of Vibration and Control, 22, 1-15.
30. Sharma, K.D., Sarkar, G., 2018. Stable Adaptive NSOF Domain FOPID Controller for a Class of Non-linear Systems, IET Control Theory & Applications.
31. De Keyser, R., Muresan, C.I., Ionescu, C.M., 2015. A Novel Auto-tuning Method for Fractional Order PI/PD Controllers, ISA Transactions, 62, 268-275.
32. Golnaraghi, F., Kuo, B.C., 2010. Automatic Control Systems, Wiley John Wiley & Sons, Inc.
33. Hamamci, S.E., 2007. An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers, IEEE Transactions on Automatic Control, 52, 1964-1969.
34. Tan, N., Kaya, I., Yeroglu, C., Atherton, D.P., 2006. Computation of Stabilizing PI and PID Controllers Using the Stability Boundary Locus, Energy Conversion and Management, 47, 3045-3058.
35. Monje, A., Blas, M., Vinagre, V., Chen, Y.Q., 2008. Tuning and Auto-tuning of Fractional Order Controllers for Industry Applications, Control Engineering Practice, 16, 798-812.
36. Wang, C.Y., Luo, Y., Chen, Y.Q., 2009. Tuning Fractional Order Proportional Integral Controllers for Fractional Order Systems, Chinese Control and Decision Conference, 329-334.
37. Franklin, G., Powell, J., Naeini, A., 2006. Feedback Control Of Dynamic Systems, Addison-Wesley.
38. Chen, Y.Q., Moore, K.L., 2005. Relay Feedback Tuning of Robust PID Controllers With Isodamping Property, IEEE Transactions on Systems, Man, and Cybernetics, 35, 23–31.
39. Tepljakov, A., Petlenkov, E., Belikov, J., 2014. Closed-loop Identification of Fractional-order Models Using FOMCON Toolbox for MATLAB, Proc. of the 14th Biennial Baltic Electronics Conference, 213-216.
40. Tepljakov, A., 2012. FONCON: Fractionalorder Modeling and Control.

Gerçek Zaman Gecikmeli Rasyonel Transfer Fonksiyonuna Sahip Sistemlerin Kontrolü için Kesirli Mertebeden Oransal-Entegral-Türevsel (PID) Bir Kontrol Edicinin Genel Tasarım Denklemleri

Year 2019, Volume: 34 Issue: 2, 231 - 240, 30.06.2019

Mehmet Emir Koksal

https://doi.org/10.21605/cukurovaummfd.609304

Abstract

Herhangi bir gerçek zaman gecikmeli rasyonel transfer fonksiyonuna sahip sistemin kontrolü için kesirli mertebeden oransal-entegral-türevsel (PID) kontrol edicinin tasarımı için çok amaçlı tasarım denklemleri türetilmiştir. Sonuçlar literatürde mevcut birçok tasarım metodunu birleştirmektedir. Özellikle genel kararlılık sınırlarının çiziminde kullanılmakta, istenilen kazanç ve faz aralıklarının kazanç-kesim frekansında yatay bir faz karakteritiği ile birlikte tasarımını sağlamaktadır. Dolayısıyla dayanıklılık da garanti edilmektedir. Ayrıca, tatminkar çıkış bozulması karakteristiği ve yüksek frekans gürültü engellenmesi gerçekleştirilmesine imkan sağlamaktadır. Literatürde mevcut metodlarla ilişkileri göstermek için bir örnek ele alınmıştır, ki böylece elde edilen tasarım denklemlerinin faydası gösterilmiştir.

Keywords

Kontrol dizayn, PID kontrol, Kararlılık

References

1. Astrom, K. J., Hagglund, T., 1995. PID Controllers: Theory, Design, and Tuning.
2. Ang, K. H., Chong, G., Li, Y., 2013. PID Control System Analysis, Design, and Technology, IEEE Trans. Control Syst. Technol. 13, 559–576.
3. Yamamoto, T., Takao, K., Yamada, T., 2009. Design of a Data-driven PID Controller, IEEE Trans. Control Syst. Technol. 17, 29-39.
4. Erenturk, K., 2013. Fractional-order PIλDµand Active Disturbance Rejection Control of Nonlinear Two-mass Drive System, IEEE Trans. Ind. Electron. 60, 3806-3813.
5. Yeroglu, C., Tan, N., 2011. Note on Fractionalorder Proportional-Integral-Differential Controller Design, IET Control Theory Appl., 5, 1978-1989.
6. Monje, C.A., Vinagreb, B.M., Feliuc, V., Chen, Y.Q., 2008. Tuning and Auto-tuning of Fractional Order Controllers for Industry Applications, Control Eng. Pract., 16, 798-812.
7. Chunna, Z., Xue, D., Chen, Y. Q., 2005. A Fractional Order PID Tuning Algorithm for a Class of Fractional Order Plants, IEEE Proc. of the Intern. Conf. Mechatronics & Automation, 216-221.
8. Cokmez, E., Atic, S., Peker, F., Kaya, I., 2018. Fractional-order PI Controller Design for Integrating Processes Based on Gain and Phase Margin Specifications, IFAC PapersOnLine, 51, 751-756.
9. Pullaguram, D., Mishra, S., Senroy, N., Mukherjee, M., 2018. Design and Tuning of Robust Fractional Order Controller for Autonomous Microgrid Vsc System, IEEE Transactions on Industry Applications, 54, 91-101.
10. Oustaloup, A., Cois, O., Lanusse, P., Melchior, P., Moreau, X., Sabatier, J., 2006. The Crone Aproach: Theoretical Developments and Major Applications, IFAC Proc., 39, 324-354.
11. Vinagre, B.M., Feliu, V., 2007. Optimal Fractional Controllers for Rational Order Systems, IEEE Trans. Autom. Control 52, 23852389.
12. Krishna, B.T., 2011. Studies on Fractional Order Differentiators and Integrators: a Survey, Signal Processing, 91, 386-426.
13. John, D.A., Biswas, K., 2018. Analysis of Disturbance Rejection by PIλ Controller Using Solid State Fractional Capacitor, IEEE Proc. of the International Symposiums of Circuits and Systems, 1-5.
14. Khurram, A., Rehman, H., Mukhopadhyay, S., 2018. Comparative Analysis of Integer-order and Fractional-order Proportional Integral Speed Controllers for Induction Motor Drive Systems, Journal of Power Electronics, 18, 723-735.
15. Dogruer, T., Tan, N., 2018. Design of PI Controller Using Optimization Method in Fractional Order Control Systems, IFAC PapersOnLine, 51, 841-846.
16. Raynaud, H.F., Zergainoh, A., 2000. State-space Representation for Fractional Order Controllers, Automatica, 36, 1017-1021.
17. Zagorowska, M., 2018. Analysis of Performance Indicators for Optimization of Noninteger-order Controllers, Journal of Circuits, Systems and Computers, 27.
18. Sathishkumar, P., 2018. Fractional Controller Tuning Expressions for a Universal Plant Structure, IEEE Control Systems Letters, 2, 345-350.
19. Ranjbaran, K., Tabatabaei, M., 2018. Tuning PI and Fractional Order PI Controllers With an Additional Fractional Order Pole, Chemical Engineering Communications, 205, 207-225.
20. Xue, D., Chen, Y.Q., 2002. A Comparative Introduction of four Fractional Order Controllers, Proc. of the 4th World Congress on Intelligent Control and Automation, 3228-3235.
21. Kumar, L., Narang, D., 2018. Tuning of Fractional Order PIλDµ Controllers Using Evolutionary Optimization for Pid Tuned Synchronous Generator Excitation System, IFAC-PapersOnLine, 51, 859-864.
22. Dabiri, A., Moghaddam, B.P., Machado, J.A.T., 2018. Optimal Variable-order Fractional PID Controllers for Dynamical Systems, Journal of Comp. Appl. Math 339, 40-48.
23. Cao, J., Cao, B., 2006. Design of Fractional Order Controller Based on Particle Swarm Optimization, IEEE Conference on Industrial Electronics and Applications, 1-6.
24. Ranjan, J., Nayak, B.S., 2018. Application of Group Hunting Search Optimized Cascade Pdfractional Order PID Controller in Interconnected Thermal Power System, Trends in Renewable Energy, 4, 22-33.
25. Lu, K., Zhou, W., Zeng, G., Du, W., 2018. Design of PID Controller Based on a Selfadaptive State-space Predictive Functional Control Using Extremal Optimization Method, Journal of the Franklin Institute, 355, 2197-2220.
26. Shukla, M. K., Sharma, B. B., 2018. Control and Synchronization of a Class of Uncertain Fractional Order Chaotic Systems Via Adaptive Backstepping Control, Asian Journal of Control, 20, 707-720.
27. Ibraheem, L.K., Abdul-Adheem, W.R., 2016. On the Improved Nonlinear Tracking Differentiator Based Nonlinear Pid Controller Design, International Journal of Advanced Computer Science and Applications, 7, 234-241.
28. Li, L., 2018. Lebesgue-P NORM Convergence of Fractional-Order PID-Type Iterative Learning Control for Linear Systems, Asian Journal of Control, 20, 483-494.
29. Moradi, L., Mohammadi, F., Baleanu, D., 2018. A Hybrid Functions Numerical Scheme for Fractional Optimal Control Problems: Application to Nonanalytic Dynamic Systems, Journal of Vibration and Control, 22, 1-15.
30. Sharma, K.D., Sarkar, G., 2018. Stable Adaptive NSOF Domain FOPID Controller for a Class of Non-linear Systems, IET Control Theory & Applications.
31. De Keyser, R., Muresan, C.I., Ionescu, C.M., 2015. A Novel Auto-tuning Method for Fractional Order PI/PD Controllers, ISA Transactions, 62, 268-275.
32. Golnaraghi, F., Kuo, B.C., 2010. Automatic Control Systems, Wiley John Wiley & Sons, Inc.
33. Hamamci, S.E., 2007. An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers, IEEE Transactions on Automatic Control, 52, 1964-1969.
34. Tan, N., Kaya, I., Yeroglu, C., Atherton, D.P., 2006. Computation of Stabilizing PI and PID Controllers Using the Stability Boundary Locus, Energy Conversion and Management, 47, 3045-3058.
35. Monje, A., Blas, M., Vinagre, V., Chen, Y.Q., 2008. Tuning and Auto-tuning of Fractional Order Controllers for Industry Applications, Control Engineering Practice, 16, 798-812.
36. Wang, C.Y., Luo, Y., Chen, Y.Q., 2009. Tuning Fractional Order Proportional Integral Controllers for Fractional Order Systems, Chinese Control and Decision Conference, 329-334.
37. Franklin, G., Powell, J., Naeini, A., 2006. Feedback Control Of Dynamic Systems, Addison-Wesley.
38. Chen, Y.Q., Moore, K.L., 2005. Relay Feedback Tuning of Robust PID Controllers With Isodamping Property, IEEE Transactions on Systems, Man, and Cybernetics, 35, 23–31.
39. Tepljakov, A., Petlenkov, E., Belikov, J., 2014. Closed-loop Identification of Fractional-order Models Using FOMCON Toolbox for MATLAB, Proc. of the 14th Biennial Baltic Electronics Conference, 213-216.
40. Tepljakov, A., 2012. FONCON: Fractionalorder Modeling and Control.

There are 40 citations in total.

Details

Primary Language	English
Journal Section	Articles
Authors	Mehmet Emir Koksal This is me
Publication Date	June 30, 2019
Published in Issue	Year 2019 Volume: 34 Issue: 2

Cite

APA	Koksal, M. E. (2019). Universal Design Equations for Fractional Order PID Control of Plants with Time Delay. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 34(2), 231-240. https://doi.org/10.21605/cukurovaummfd.609304
AMA	Koksal ME. Universal Design Equations for Fractional Order PID Control of Plants with Time Delay. cukurovaummfd. June 2019;34(2):231-240. doi:10.21605/cukurovaummfd.609304
Chicago	Koksal, Mehmet Emir. “Universal Design Equations for Fractional Order PID Control of Plants With Time Delay”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 34, no. 2 (June 2019): 231-40. https://doi.org/10.21605/cukurovaummfd.609304.
EndNote	Koksal ME (June 1, 2019) Universal Design Equations for Fractional Order PID Control of Plants with Time Delay. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 34 2 231–240.
IEEE	M. E. Koksal, “Universal Design Equations for Fractional Order PID Control of Plants with Time Delay”, cukurovaummfd, vol. 34, no. 2, pp. 231–240, 2019, doi: 10.21605/cukurovaummfd.609304.
ISNAD	Koksal, Mehmet Emir. “Universal Design Equations for Fractional Order PID Control of Plants With Time Delay”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 34/2 (June 2019), 231-240. https://doi.org/10.21605/cukurovaummfd.609304.
JAMA	Koksal ME. Universal Design Equations for Fractional Order PID Control of Plants with Time Delay. cukurovaummfd. 2019;34:231–240.
MLA	Koksal, Mehmet Emir. “Universal Design Equations for Fractional Order PID Control of Plants With Time Delay”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, vol. 34, no. 2, 2019, pp. 231-40, doi:10.21605/cukurovaummfd.609304.
Vancouver	Koksal ME. Universal Design Equations for Fractional Order PID Control of Plants with Time Delay. cukurovaummfd. 2019;34(2):231-40.

Article Files

Full Text