Skip to main content

IMC-PID Fractional Order Filter Multi-loop Controller Design for Multivariable Systems Based on Two Degrees of Freedom Control Scheme

International Journal of Control, Automation and Systems volume 16, pages 689–701 (2018)Cite this article

Abstract

An IMC-PID fractional order filter multi-loop controller design method based on two degrees of freedom paradigm is proposed for Multiple Input-Multiple Output systems with time delays. The interactions among the control loops are considered as disturbances. Thus, a two degrees of freedom control scheme, used for monovariable system to ensure the disturbance rejection, is extended to multivariable systems in order to reduce the effect of the coupling among the control loops. The proposed controller design method requires the control pairing selection with the least interactions and a set-point controller is calculated. An interactions reduction effect controller is calculated for each loop by defining a suitable complementary sensitivity function. The proposed controller design method is simple and systematic in relation with the desired closed loop specifications of each loop. The controllers obtained ensure robustness to process variations. Two illustrative examples are presented to show the merits of the proposed method.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. L. D. S. Coelho and V. C. Mariani, “Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controllers tuning,” computers & mathematics with applications, vol. 64, no. 8, pp. 2371–2382, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  2. X. Luan, Q. Chen, and F. Liu, “Centralized PIcontrol for high dimensional multivariable systems based on equivalent transfer function,” ISA Transactions, vol. 53, no. 5, pp. 1554–1561, 2014. [click]

    Article  Google Scholar 

  3. T. Liu, W. Zhang, and D. Gu, “Analytical design of decoupling internal model control (IMC) scheme for two-input two-output (TITO) processes with time delays,” Industrial & engineering chemistry research, vol. 45, no. 9, pp. 3149–3160, 2006.

    Article  Google Scholar 

  4. J. Garrido, F. Vázqueza, and F. Morrila, “Inverted decoupling internal model control for square stable multivariable time delay systems,” Journal of Process Control, vol. 24, no. 11, pp. 1710–1719, 2014. [click]

    Article  Google Scholar 

  5. W. Zhang, Y. Yang, T. liu, and W. Zhang, “Multivariable disturbance observer-based H2 analytical decoupling control design for multivariable systems,” International Journal of Systems Science, vol. 47, no. 1, pp. 179–193, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  6. D. K. Maghade and B. M. Patre, “Decentralized PI/PID controllers based on gain and phase margin specifications for TITO processes,” ISA Transactions, vol. 51, no. 4, pp. 550–558, 2012. [click]

    Article  Google Scholar 

  7. E. Bristol, “On a new measure of interaction for multivariable process control,” IEEE Transactions on automatic control, vol. 11, no. 1, pp. 133–134, 1966. [click]

    Article  Google Scholar 

  8. A. Niederlinski, “Two-variables distillation control: decouple or not decouple,” AICHE journal, vol. 17, no. 5, pp. 1261–1263, 1971. [click]

    Article  Google Scholar 

  9. T. O. Ajayi and I. S. Ogboh, “Determination of control pairing for higher order multivariable systems by the use of multi-ratios,” International Journal of Scientific and Engineering Research, vol. 3, no. 3, 2012.

    Google Scholar 

  10. R. H. Naik, D. V. A. Kumar, and K. S. R. Anjaneyulu, “Control configuration selection and controller design for multivariable processes using normalized gain,” International Journal of Electrical, Computer, Electronics and Communication Engineering, vol. 8, no. 10, pp. 1636–1640, 2014.

    Google Scholar 

  11. W. Luyben, “Simple method for tuning SISO controllers in multivariable systems,” Industrial & Engineering Chemistry Process Design and Development, vol. 25, no. 3, pp. 654–660, 1986. [click]

    Article  Google Scholar 

  12. B. C. Ji, E. M. Lee, Y. Han, and J. Lee, “Computation of multiloop controllers having desired closed loop responses,” Korean Journal of Chemical Engineering, vol. 24, no. 4, pp. 562–566, 2007. [click]

    Article  Google Scholar 

  13. C. G. Economou and M. Morari, “Internal model control: multiloop design,” Industrial & Engineering Chemistry Process Design and Development, vol. 25, no. 2, pp. 411–419, 1986.

    Article  Google Scholar 

  14. Z. Zhao, B. Hu, and J. Liang, “Multiloop adaptive internal model control based on a dynamic partial least squares model,” Journal of Zhejiang University-SCIENCE (Applied Physics and Engineering), vol. 12, no. 3, pp. 190–200, 2011.

    Article  Google Scholar 

  15. T. N. L. Vu, J. Lee, and M. Lee, “Design of Multiloop PID Controllers Based on the Generalized IMC-PID Method with Mp Criterion,” International Journal of Control, Automation, and Systems, vol. 5, no. 2, pp. 212–217, 2007.

    Google Scholar 

  16. M. Morari and E. Zafiriou, Robust Process Control, Prentice hall, Englewood Cliffs, NJ, 1989.

    MATH  Google Scholar 

  17. T. N. L. Vu and M. Lee, “Independent design of multi-loop PI/PID controllers for interacting multivariable processes,” Journal of Process Control, vol. 40, no. 8, pp. 922–933, 2010. [click]

    Article  Google Scholar 

  18. H. P. Huang, J. C. Jeng, C. H. Chiang, and W. Pan, “A direct method for multi-loop PI/PID controller design,” Journal of Process Control, vol. 13, no. 8, pp. 769–786, 2003. [click]

    Article  Google Scholar 

  19. X. Luan, Q. Chen, and F. Liu, “Equivalent transfer function based multiloop PIcontrol for high dimensional multivariable systems,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 1–7, 2015.

    Article  Google Scholar 

  20. Y. Wei, J. Qiu, H. R. Karimi, and M. Wang, “New results on H ∞ dynamic output feedback control for Markovian jump systems with time varying delay and defective mode information,” Optimal Control Applications and Methods, vol. 35, no. 6, pp. 656–675, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. Y. Wei, J. Qiu, and S. Fu, “Mode-dependent nonrational output feedback control for continuous time semi Markovian jump systems with time varying delay,” Non linear Analysis: Hybrid Systems, vol. 16, pp. 51–71, 2015.

    MathSciNet  MATH  Google Scholar 

  22. Y. Wei, X. Peng, and J. Qiu, “Robust and non-fragile static output feedback control for continuous-time semi- Markovian jump systems,” Transactions of the Institute of Measurement and Control, vol. 38, no. 9, pp. 1136–1150, 2016.

    Article  Google Scholar 

  23. Y. Wei, J. Qiu, P. Shi, and H. K. Lam, “A new design of H-infinity piecewise filtering for Discrete-time nonlinear time-varying delay systems via TSfuzzy affine models,” IEEE Transactions on Systems, Man, and Cybernetics: systems, 2016.

    Google Scholar 

  24. Y. Wei, J. Qiu, H. K. Lam, and L. Wu, “Approaches to TSfuzzy-affine-model-based reliable output feedback control for nonlinear Itô stochastic systems,” IEEE Transactions on Fuzzy Systems, 2016.

    Google Scholar 

  25. I. Podlubny, “Fractional-order-systems and PIaDm controller,” IEEE Transactions on automatic control, vol. 44, no. 1, pp. 208–214, 1999. [click]

    Article  MathSciNet  MATH  Google Scholar 

  26. R. S. Barbosa, J. A. T. Machado, and I. M. Ferreira, “Tuning of PID controllers based on Bode’s ideal transfer function,” Nonlinear Dynamics, vol. 38, no. 1-4, pp. 305–321, 2004. [click]

    Article  MATH  Google Scholar 

  27. J. Yi and B. G. Cao, “Design of fractional order controller based on particle swarm optimisation,” International Journal of Control, Automation, and Systems, vol. 4, no. 6, pp. 775–781, 2006.

    Google Scholar 

  28. M. Bettayeb and R. Mansouri, “IMC-PID-fractional-orderfilter controller design for integer order systems,” ISA Transactions, vol. 53, no. 5, pp. 1620–1628, 2014. [click]

    Article  Google Scholar 

  29. M. Bettayeb and R. Mansouri, “Fractional IMC-PID-filter controllers design for non integer order systems,” Journal of Process Control, vol. 24, no. 4, pp. 261–271, 2014.

    Article  Google Scholar 

  30. K. Titouche, R. Mansouri, M. Bettayeb, and U. M. Al-Saggaf, “Internal model control proportional integral derivative fractional-order filter controllers design for unstable delay systems,” Journal of Dynamic Systems, Measurement and Control, vol. 138, no. 2, pp. 451–461, 2016.

    Google Scholar 

  31. D. N. Gruel, P. Lanusse, and A. Oustaloup, “Robust control design for multivariable plants with time-delay,” Chemical Engeneering Journal, vol. 146, no. 3, pp. 414–427, 2009. [click]

    Article  Google Scholar 

  32. D. N. Gruel, P. Lanusse, and A. Oustaloup, “Commande CRONE des systemes multi-entrés multi-sorties non carrés retardés,” e-STA Sciences et Technologies de l’Automatique, vol. 6, no. 1, pp. 21–28, 2009.

    Google Scholar 

  33. P. Lanusse, D. N. Gruel, A. Lamara, A. Lesobre, X. Wang, Y. Chamaillard, and A. Oustaloup, “Development of a fractional order based MIMO controller for high dynamic engine testbeds,” Control Engineering Practice, vol. 56, pp. 174–189, 2016.

    Article  Google Scholar 

  34. C. I. Muresan, A. Dutta, E. H. Dulf, Z. Pinar, A. Maxim, and C. M. Ionescu, “Tuning algorithms for fractional order internal model controllers for time delay processes,” International Journal of Control, vol. 89, no. 3, pp. 579–593, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  35. C. I. Muresan, R. De Keyser, and C. M. Ionescu, “Autotuning method for a fractional order controllers for a multivariable 13C isotope separation column,” Proc. of European Control Conference, Denmark, pp. 358–363, 2016.

    Google Scholar 

  36. C. I. Muresan, E. H. Dulf, and C. M. Ionescu, “Robustness evaluation of a multivariable fractional order PIcontroller for time delay processes,” Control and Intelligent Systems, vol. 42, no. 2, pp. 112–118, 2014.

    Article  Google Scholar 

  37. Z. Li and Y. Q. Chen, “Ideal simplified and inverted decoupling of fractional order TITO processes,” IFAC Proceedings, vol. 47, no. 3, pp. 2897–2902, 2014. [click]

    Article  Google Scholar 

  38. U. S. Banu and S. K. Lakshmanaprabu, “Adaptive multiloop fractional order PID controller tuning using bat colony optimization for quadruple tank process,” Proc. of International Conference on Robotics, Automation, Control and Embedded Systems (RACE), 18-20 February, Chennai, India, pp. 1–8, 2015.

    Google Scholar 

  39. F. G. Prakash and V. Alamelumangai, “Design of predictive fractional order PIcontroller for the quadruple tank process,” WSEAS, Transactions on Systems and Control, vol. 10, pp. 85–94, 2015

    Google Scholar 

  40. D. E. Rivera, M. Morari, and S. Skogestad, “Internal model control: PID controller design,” Industrial & Engineering Chemistry Process Design and Development, vol. 25, no. 1, pp. 252–265, 1986. [click]

    Article  Google Scholar 

  41. J. E. Normey-Rico and E. F. Camacho, Control of Deadtime Processes, Springer Science & Business Media, 2007.

    Google Scholar 

  42. T. Hélie, “Simulation of fractional-order low-pass filters,” IEEE/ACM Transactions on Audio, Speech and Language Processing (TASLP), vol. 22, no. 11, pp. 1636–1647, 2014. [click]

    Article  Google Scholar 

  43. I. Petras, “The fractional-order controllers: methods for their synthesis and application,” arXiv preprint math/0004064, 2000.

    Google Scholar 

  44. B. A. Orgunaike, J. P. Lemaire, M. Morari, and W. H. Ray, “Advanced multivariable control of a pilot plant distillation column,” AICHE Journal, vol. 29, no. 4, pp. 632–640, 1983. [click]

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. L2CSP Laboratory, Mouloud Mammeri University, Tizi Ouzou, Algeria

    Tassadit Chekari & Rachid Mansouri

  2. Electrical and Computer Engineering Department, University of Sharjah, United Arab Emirates and Distinguished Adjunct Professor, Center of Excellence in Intelligent Engineering Systems (CEIES) King Abdulaziz University, Jeddah, Saudi Arabia

    Maamar Bettayeb

Authors
  1. Tassadit Chekari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rachid Mansouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maamar Bettayeb
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tassadit Chekari.

Additional information

Recommended by Associate Editor Kyoungchul Kong under the direction of Editor Yoshito Ohta.

Tassadit Chekari received the B.S. and M.S. degrees in Electrical Engineering from University of Tizi-Ouzou, in 2009 and 2011, respectively. She is actually a Ph.D. student at the same University (L2CSP Laboratory). Her research interests include multi-loop control, multivariable systems control, fractional order control, Compensation interactions in multivariable systems

Rachid Mansouri received the B.S. and M.S. degrees in Electrical Engineering from Ecole Nationale Polytechnique d’Alger, Algiers, Algeria in 1990, and 1993, respectively and the Ph.D. degrees in Electrical Engineering from University of Tizi-Ouzou Algeria in 2008. He has been a Professor at University of of Tizi-Ouzou since June 2015. His research interests include H∞ optimization, Electrical machine control, order model reduction, structured system, and fractional order systems control

Maamar Bettayeb received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from University of Southern California, Los Angeles, in 1976, 1978 and 1981, respectively. He worked as a Research Scientist at the Bellaire Research Center at Shell Oil Development Company, Houston, Texas, USA, in the development of seismic signal processing deconvolution algorithms for the purpose of Gas and Oil exploration during 1981/1982. From 1982 to 1988, He directed the Instrumentation and Control Laboratory of High Commission for Research in Algeria. In 1988, He joined the Electrical Engineering Department at King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. He has been Professor at University of Sharjah UAE since August 2000. He is presently the Vice Chancellor for Research and Graduate Studies at University of Sharjah. He has published over 300 journal and conference papers in the fields of control and signal processing. He has also supervised over 50 M. Sc. and Ph. D. students. His recent research interest is in H∞ optimal control, model reduction, signal and image processing, process control, networked control systems, fractional dynamics and control, nonlinear estimation and filtering, soft computing, wavelets, renewable energies and engineering education.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chekari, T., Mansouri, R. & Bettayeb, M. IMC-PID Fractional Order Filter Multi-loop Controller Design for Multivariable Systems Based on Two Degrees of Freedom Control Scheme. Int. J. Control Autom. Syst. 16, 689–701 (2018). https://doi.org/10.1007/s12555-016-0699-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0699-x

Keywords

  • Bode’s ideal transfer function
  • IMC control
  • MIMO systems
  • multiloop control
  • 2DOF structure