Open Access Open Access  Restricted Access Subscription or Fee Access

Decoupled Fractional Order Filter with PID Controller Design for Multivariable Distillation Column System

(*) Corresponding author

Authors' affiliations



The main objective of this research work is the design of decentralized PID controller with fractional order filter for strongly connected multivariable distillation column system. Wherein, the major contribution of this paper is the proposition of compensators for the decoupling process, in addition to extending the application of the proposed approach from Single-Input Single-Output (SISO) systems into Multi-Input Multi-Output (MIMO) systems. More precisely, the proposed idea is based on eliminating the strongly interactive terms between the inputs and outputs of the multivariable distillation column systems so that, the separated multi-loop parts can be treated as a set of SISO subsystems, which have an equivalent dynamic of the whole original system. Thereafter, a PID controller with a fractional filter has been introduced to the decoupled subsystems in decentralized scheme in order to improve the control system robustness. Two multivariable systems have been carefully considered in this paper; the first is a theoretical Two-Input Two-Output (TITO) system while the second is the Wood and Berry distillation column. The obtained results have confirmed the superiority of the proposed approach over the two degrees of freedom technique, which is based on Internal Model Control method. Indeed, the proposed approach has reduced the dynamic error, the settling time, and the rise time. Furthermore, the designed decentralized PID controller with fractional filter has demonstrated rejection to structured perturbation from one loop to another.
Copyright © 2022 Praise Worthy Prize - All rights reserved.


Decentralized PID Controller; Fractional Order Filter; Decoupling Process; IMC; Interaction; Distillation Column

Full Text:



Tzanev, A., Tzvetkov, K., Vasilev, P., Design of Property Shifts in V-Interconnected Hydraulic Systems, (2021) International Review of Automatic Control (IREACO), 14 (2), pp. 61-75.

E. Bristol, On a new measure of interaction for multivariable process control, IEEE Transactions on Automatic Control, vol. 11, pp. 133-134, 1966.

Fattahi, F., Lahlouh, I., Elakkary, A., Sefiani, N., Grey Wolf Optimizer Based PID/Multi-Loop Controller for the Egg Incubator System, (2021) International Review of Automatic Control (IREACO), 14 (4), pp. 233-241.

Palacios, A., Amaya, D., Ramos, O., Solar Tracking Control of a Parabolic Trough Collector by Traditional PID, Fuzzy Sets and Particle Swarm Optimization Algorithm, (2021) International Review of Automatic Control (IREACO), 14 (3), pp. 124-134.

Tahir, T., Al-Samarraie, S., The Application of Extremum Seeking Algorithms in PID Tuning for Continuous Stirred Tank Reactor, (2021) International Review of Automatic Control (IREACO), 14 (1), pp. 28-38.

J. Ziegler et N. Nichols, Optimum setting for automatic controllers, Trans.ASME, vol. 64, pp. 759-768, 1942.

W. Luyben, Simple method for tuning SISO controllers in multivariable systems, Industrial&Engeneering Chemistry Process Design and Developpement , vol. 25, pp. 654-660, 1986.

C. Economou et M. Morari, internal model control: multiloop design., Industriel&Engineering Chemistry Process Design and Developpement , vol. 25, pp. 411-419, 1986.

D.Y. Kiran Kumar, S Shravya Geethika, P.Bharat Kumar, Design and implementation of performance enhanced IMC-PI controller for large scale industrial processes, International Research Journal of Modernization in Engineering Technology and Science, vol. 03, pp. 1036-1043, 2021.

H. L. Wade, Inverted decoupling: a neglected technique, Elsevier Science Ltd, vol. 36, pp. 3-10, 1997.

G. Gurumurthy and D. k. das, A proportional integral (PI) controller design and implimentation for decoupled two-input two-output coupled tank system with dead time, in 2019 Six Indian Control Conference (ICC), Hyderabad, 2019.

L. Sun, J. Dong, d. li and k. y. lee, A pratical multivariable control approach based on inverted decoupling and decentralized active disturbance rejection control, Industrial & Engennering Chemistry Research, pp. 2008-2019, 2016.

S. Nasseri, M. R. Khalesi, A. Ramezani, M. Abdollahi M. Mohseni, An Adaptive Decoupling Control Design for Flotation Column: A Comparative Study Against Model Predictive Control, IETE Journal of Research, pp. 1-14, 2020.

J. Lee, H. K. Dong , T. F. Edgar, Static decouplers for control of multivariable processes, AICHE Journal, vol. 51, pp. 2712-2720, 2005.

P. Chen, and W. Zhang, Improvement on an inverted decoupling technique for a class of stable linear multivariable processes, ISA Transactions, vol. 46, pp. 199-210, Apr 2007.

I. Kasireddy, A. W. Nasir, A.. Singh, IMC based controller design for automatic generation control of multi area power system via simplified decoupling, International Journal of Control, Automation and Systems, vol. 16, pp. 994-1010, 2018.

T. Liu, W. Zhang, D. Gu, Analytical Design of Decoupling Internal Model Control (IMC) Scheme for Two-Input-Two-Output (TITO) Processes with Time Delays, Industriel Engeneering Chemistry Research, vol. 45, pp. 3149-3160, 2006.

N. N. Nedić, S. L. Prodanović, L. M. Dubonjić, Decoupling control of the TITO system supported by the dominant pole placement method, Facta Universitatis ,Series: Mechanical Engineering, vol. 15, pp. 245-256, 2017.

Z. Azizah, J. P Sutikno, R Handogo, R.A Hikmadiyar,"inverted decoupling MIMO internal model control using Mp tuning, Energy Security and Chemical Engineering Congress, pp. 1-14, 2020.

I. Podlubny, Fractional-order systems and piλdµ controller, IEEE Transactions on Automatic Control, pp. 208-214, 1999.

Puangdownreong, D., A Novel Fractional-Order PIλDμAν Controller and Its Design Optimization Based on Spiritual Search, (2019) International Review of Automatic Control (IREACO), 12 (6), pp. 271-280.

P. R. Hemavathy, S. Y. Mohamed, S. Lakshmanaprabu, Internal model controller based PID with fractional filter design for a nonlinear process, International Journal of Electrical and Computer Engineering, vol. 10, pp. 243-254, 2020.

S. Sen, C. dey et U. mondal, IMC based fractional-order controller for a level process, International Conference on Opto-Electronics and Applied Optics (optronix), 2019.

T. Chekari, R. Mansouri et M. Bettayeb, 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, vol. 16, pp. 689-701, 2018.

C. I. Muresan, E. H. Dulf, C. M. Ionescu, robustness evaluation of a multivariable fractionall order PI controller for time delay processes, Control and Intelligent Systems, 2014.

N. Fartas, A. Khelassi, The impact of fractional order control on multiariable systems, Algerian Journal of Signals and Systems, vol.7, pp. 7-12, 2022.

H. Senberber, A. Bagis, Fractional PID Controller Design for Fractional Order Systems using ABC Algorithm, IEEE, 2017.

D. Li, L. Liu, Q. Jin, K. Hirasawa, Maximum sensitivity based fractional IMC-PID controller design for non-integer order system with time delay, Journal of Process Control, vol. 31, pp. 17-29, 2015.

T. Chekari, R. Mansouri, M. Bettayeb, improved internal model control-proportional-integral-derivative fractional-order multiloop controller design for non integer order multivariable systems, Journal of Dynamics Systems, Measurement and Control, vol. 141, 2019.

N. Zhuong, W. Qingguo, R. Liu, L. Yonghong, identification and PID control of delay fractional-order systems, IEEE/CAA Journal of Automatica Sinica, vol. 3, pp. 463-476, 2016.

F. Bengtsson, T. Wik, E. Svensson, Resolving issues of scaling for gramian-based input-output pairing methods, International Journal of Control, pp. 1-13, 2020.

C. Bouyahiaoui, L. I. Grigoriev, F. Laaouad, A. Khelassi, Optimal fuzzy control to reduce energy consumption in distillation columns, Automation and Remote Control, vol. 66, pp. 200-208, 2005.

K.S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, New York, 1993.

B.M Vinaigre, I. Podlubny, A. Hernandez, V. Feliu, some approximations of fractional order operators used in control theory and application, Fractional Calculus and Applied Analysis, vol.3, pp.231-248,2000.

M. Z. Doghmane, M. Kidouche, A. Ahriche, Decentralized Overlapping Control Design with Application to Rotary Drilling System, IETE Journal of Research.

M. Z. Doghmane, M. Kidouche, Decentralized controller robustness improvement using longitudinal overlapping decomposition-Application to web winding system, Elektronika ir Elektronika, vol. 24, pp. 10-18, 2018.

Orjuela, A., Ramos, O., Amaya, D., Design and Development of a Multivariable Control for a Distillation System Using Fuzzy Logic, (2016) International Review of Automatic Control (IREACO), 9 (2), pp. 122-127.

A. Khelassi, R. Bendib, A. Benhalla, Configurations of binary distillation column for optimal control, in Proceedings of the International Conference on Control, Cardiff, UK, pp.793-797, 2012.

R. wood, M. berry, terminal compostion control of a binary distillation column, Chemical Engineering Science, vol. 28, pp. 1707-1717, 1973.

Sabry, W., Eliwa, A., New Design of a Fractional Order Controller Based on Padé Approximation to Enhance a Stable Power System Load Frequency, (2018) International Review of Automatic Control (IREACO), 11 (5), pp. 241-247.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2023 Praise Worthy Prize