In recent decades, MIMO (Multi-Input-Multi-Output) systems become more and more widely used in industrial applications. A variety of decoupling control algorithms have been studied in the literature. Therefore, a review of the most extensively applied coupling interaction analysis and decoupler design methods for industrial processes is necessary to be carried out. In this paper, in order to benefit researchers and engineers with different academic backgrounds, the scattered coupling interaction analysis and decoupling algorithms are collected and divided into different categories with their characteristics, application domains and informative comments for selection. Moveover, some frequently concerned problems of decoupling control are also discussed.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
A. S. Boksenbom and R. Hood, “General algebraic method applied to control analysis of complex engine types,” National Advisory Committee for Aeronautics, Techinical Report NCA-TR-980, Washington D.C., 1950.
K. V. Waller, “Impressions of chemical process control education and research in the USA,” Chemical Engineering Education, vol. 15, no. 1, p. 30, 1981.
H. Tsien, Engineering Cybernetics, McGraw-Hill Book Co., New York, 1954.
M. D. Mesarović, The Control of Multivariable Systems, no. 9, The MIT Press, 1960.
J. A. Sonquist and J. N. Morgan, A Detection of Interaction Effects: A Report on a Computer Program, Survey Research Centre Institute for Social Research, the University of Michigan, 1964.
P. L. Falb and W. A. Wolovich, “Decoupling in the design and synthesis of multivariable control systems,” IEEE Transactions on Automatic Control, vol. 12, no. 6, pp. 651–659, 1967.
E. G. Gilbert, “The decoupling of multivariable systems by state feedback,” SIAM Journal on Control, vol. 7, no. 1, pp. 50–63, 1969.
W. M. Wonham and A. S. Morse, “Decoupling and pole assignment in linear multivariable systems: a geometric approach,” SIAM Journal on Control, vol. 8, no. 1, pp. 1–18, 1970.
L. M. Silverman and H. Payne, “Input-output structure of linear systems with application to the decoupling problem,” SIAM Journal on Control, vol. 9, no. 2, pp. 199–233, 1971.
J. Descusse, “Block noninteracting control with (non) regular static state feedback: a complete solution,” Automatica, vol. 27, no. 5, pp. 883–886, 1991.
T. G. Koussiouris, “On the general problem of pole assignment,” International Journal of Control, vol. 30, no. 4, pp. 677–694, 1979.
V. Veselý, “On the subsystem level gain scheduled controller design for MIMO systems,” International Journal of Control Automation & Systems, no. 1, pp. 1–10, 2018.
W. L. Luyben, “Distillation decoupling,” AIChE Journal, vol. 16, no. 2, pp. 198–203, 1970.
M. Waller, J. B. Waller, and K. V. Waller, “Decoupling revisited,” Industrial & Engineering Chemistry Research, vol. 42, no. 20, pp. 4575–4577, 2003.
C. H. Liu, General Decoupling Theory of Multivariable Process Control Systems, Springer-Verlag, Berlin-New York, 1983.
Q. G. Wang, Decoupling Control, vol. 285, Springer Science & Business Media, 2002.
T. Chekari, R. Mansouri, and M. Bettayeb, “IMC-PID fractional order filter multi-loop controller design for multi-variable systems based on two degrees of freedom control scheme,” International Journal of Control Automation & Systems, vol. 16, no. 2, pp. 689–701, 2018.
M. Kim, T. Y. Kuc, H. Kim, and S. L. Jin, “Adaptive iterative learning controller with input learning technique for a class of uncertain MIMO nonlinear systems,” International Journal of Control Automation & Systems, vol. 15, no. 1, pp. 315–328, 2017.
E. Bristol, “On a new measure of interaction for multi-variable process control,” IEEE Transactions on Automatic Control, vol. 11, no. 1, pp. 133–134, 1966.
W. Zhang, Quantitative Process Control Theory, vol. 45, CRC Press, 2011.
T. McAvoy, “Interacting control systems: steady state and dynamic measurement of interaction,” ISA Transactions, vol. 16, no. 3, p. 35, 1978.
Q. Xiong, W. J. Cai, and M. J. He, “A practical loop pairing criterion for multivariable processes,” Journal of Process Control, vol. 15, no. 7, pp. 741–747, 2005.
J. L. Chang, “Discrete-time PID observer design for state and unknown input estimations in noisy measurements,” International Journal of Control Automation & Systems, vol. 13, no. 4, pp. 816–822, 2015.
F. Garelli, R. Mantz, and H. De Battista, “Limiting interactions in decentralized control of MIMO systems,” Journal of Process Control, vol. 16, no. 5, pp. 473–483, 2006.
D. Maghade and B. 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.
J. Lee, D. H. Kim, and T. F. Edgar, “Static decouplers for control of multivariable processes,” AIChE Journal, vol. 51, no. 10, pp. 2712–2720, 2005.
E. Gagnon, A. Pomerleau, and A. Desbiens, “Simplified, ideal or inverted decoupling?” ISA Transactions, vol. 37, no. 4, pp. 265–276, 1998.
G. Acioli Jr and P. R. Barros, “Evaluation and redesign of decouplers for TITO processes using relay experiment,” Proceedings of IEEE International Conference on Control Applications (CCA), pp. 1145–1150, 2011.
B. T. Jevtovic and M. R. Matausek, “PID controller design of TITO system based on ideal decoupler,” Journal of Process Control, vol. 20, no. 7, pp. 869–876, 2010.
L. Yunhui, L. Hongbo, and J. Lei, “Improved inverted decoupling control using dead-time compensator for MIMO processes,” Proceedings of 29th Chinese Control Conference (CCC) IEEE, pp. 3548–3553, 2010.
F. G. Shinskey, Process Control Systems: Application, Design, and Tuning, McGraw-Hill, Inc., 1990.
H. L. Wade, “Inverted decoupling: a neglected technique,” ISA Transactions, vol. 36, no. 1, pp. 3–10, 1997.
J. Garrido, F Vazquez, and F. Morula, “An extended approach of inverted decoupling,” Journal of Process Control, vol. 21, no. 1, pp. 55–68, 2011.
P. Chen and W. Zhang, “Improvement on an inverted decoupling technique for a class of stable linear multivariable processes,” ISA Transactions, vol. 46, no. 2, pp. 199–210, 2007.
Y. Arkun, B. Manousiouthakis, and A. Palazoglu, “Robustness analysis of process control systems. A case study of decoupling control in distillation,” Industrial & Engineering Chemistry Process Design and Development, vol. 23, no. 1, pp. 93–101, 1984.
Q. C. Zhong, Robust Control of Time-delay Systems, Springer Science & Business Media, 2006.
O. Smith, “Closer control of loops with dead time,” Chemical Engineering Progress, vol. 53, no. 5, pp. 217–219, 1957.
B. Ogunnaike and W. Ray, “Multivariable controller design for linear systems having multiple time delays,” AIChE Journal, vol. 25, no. 6, pp. 1043–1057, 1979.
C. Huang, W. H. Gui, C. Yang, and Y Xie, “Design of decoupling smith control for multivariable system with time delays,” Journal of Central South University of Technology, vol. 18, no. 2, pp. 473–478, 2011.
R. S. Sánchez-Pena, Y. Bolea, and V. Puig, “MIMO smith predictor: global and structured robust performance analysis,” Journal of Process Control, vol. 19, no. 1, pp. 163–177, 2009.
T. Liu, W. Zhang, and F. Gao, “Analytical decoupling control strategy using a unity feedback control structure for MIMO processes with time delays,” Journal of Process Control, vol. 17, no. 2, pp. 173–186, 2007.
P. Nordfeldt and T. Hägglund, “Decoupler and PID controller design of TITO systems,” Journal of Process Control, vol. 16, no. 9, pp. 923–936, 2006.
C. H. Lee, M. H. Shin, and M. J. Chung, “A design of gain-scheduled control for a linear parameter varying system: an application to flight control,” Control Engineering Practice, vol. 9, no. 1, pp. 11–21, 2001.
X. Wei and L. Del Re, “Gain scheduled control for air path systems of diesel engines using LPV techniques,” IEEE Transactions on Control Systems Technology, vol. 15, no. 3, pp. 406–415, 2007.
N. V. Chi, “Adaptive feedback linearization control for twin rotor multiple-input multiple-output system,” International Journal of Control Automation & Systems, vol. 15, no. 2, pp. 1–8, 2017.
S. A. C. Giraldo, R. C. C. Flesch, J. E. Normey-Rico, and M. Z. P. Sejas, “A method for designing decoupled filtered smith predictors for square MIMO systems with multiple time delays,” IEEE Transactions on Industry Applications, vol. PP, no. 99, pp. 1–1, 2018.
Y. Weng and X. Gao, “Adaptive sliding mode decoupling control with data-driven sliding surface for unknown MIMO nonlinear discrete systems,” Circuits Systems & Signal Processing, vol. 36, no. 3, pp. 969–997, 2017.
U. Borison, “Self-tuning regulators for a class of multi-variable systems,” Automatica, vol. 15, no. 2, pp. 209–215, 1979.
C. Ran, G. Tao, J. Liu, and Z. Deng, “Self-tuning decoupled fusion kalman predictor and its convergence analysis,” Sensors Journal, vol. 9, no. 12, pp. 2024–2032, 2009.
P. Daoutidis, M. Soroush, and C. Kravaris, “Feedforward/feedback control of multivariable nonlinear processes,” AIChE Journal, vol. 36, no. 10, pp. 1471–1484, 1990.
X. Wang, S. Li, W. Cai, H. Yue, X. Zhou, and T. Chai, “Multi-model direct adaptive decoupling control with application to the wind tunnel system,” ISA Transactions, vol. 44, no. 1, pp. 131–143, 2005.
H. Medhaffar, N. Derbel, and T. Damak, “A decoupled fuzzy indirect adaptive sliding mode controller with application to robot manipulator,” International Journal of Modelling, Identification and Control, vol. 1, no. 1, pp. 23–29. 2006.
T. Yue and C. H. You, “Multivariable intelligent decoupling control system and its application,” Acta Automatica Sinica, vol. 1, p. 013, 2005.
Y. Fu and T. Chai, “Neural-network-based nonlinear adaptive dynamical decoupling control,” IEEE Transactions on Neural Networks, vol. 18, no. 3, pp. 921–925, 2007.
Z. Deng, Y. Wang, F. Gu, and C. Li, “Robust decoupling control of BTT vehicle based on PSO,” International Journal of Bio-Inspired Computation, vol. 2, no. 1, pp. 42–50, 2009.
Y. Shen, Y. Sun, and S. Li, “Adjoint transfer matrix based decoupling control for multivariable processes,” Industrial & Engineering Chemistry Research, vol. 51, no. 50, pp. 16419–16426, 2012.
C. Commault, J. M. Dion, and V. Hovelaque, “A geometric approach for structured systems: Application to disturbance decoupling,” Automatica, vol. 33, no. 3, pp. 403–409, 1997.
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.
H. Wang, Y. Q. Zhu, and J. Chen, “A design method of decoupling IMC controller for multi-variable system based on Butterworth filter,” Proceedings of the American Control Conference, pp. 5714–5719, 2017.
H. Demirciolu and P. J. Gawthrop, “Multivariable continuous-time generalized predictive control (MCGPC),” Automatica, vol. 28, no. 4, pp. 697–713, 1992.
S. Ochs, S. Engell, and A. Draeger, “Decentralized vs. model predictive control of an industrial glass tube manufacturing process,” Proceedings of the 1998 IEEE International Conference on Control Applications, vol. 1, IEEE, pp. 16–20, 1998.
R. Middleton and G. J. Adams, “Modification of model predictive control to reduce cross-coupling,” IFAC Proceedings Volumes, vol. 41, no. 2, pp. 9940–9945, 2008.
M. A. Smith, “For coupling a turbofan engine to airplane structure,”, US Patent 4,458,863, Jul. 10 1984.
Recommended by Associate Editor Jong Min Lee under the direction of Editor Jay H. Lee. This work was supported by the National Natural Science Foundation of China under grant No. 61673094, and the Fundamental Research Funds for the Central Universities of China under grants No. G2018KY0305 and No. G2018KY0302.
Lu Liu received her Ph.D. degree in automation from Northeastern University, China, in 2017. From 2015 to 2017, she was a visiting Ph.D. student in Univercity of California, Merced, USA. Her current research interests include control system analysis, controller design, process control and so on.
Siyuan Tian received his Ph.D. degree in chemical engineering from University of Houston, USA in 2015. He joined Lam Research Corporation since 2015, works in etch product development group.
Dingyu Xue received his Ph.D. degree from Sussex University, United Kingdom, in 1992. His current research interests include fractional order control system, auxiliary control system design and so on.
Tao Zhang received his Ph.D. degree in the Department of Electrical Engineering, the National University of Singapore in 2000. His research interests include nonlinear control, adaptive control, neural networks, and control applications.
YangQuan Chen received his Ph.D. degree in advanced control and instrumentation from Nanyang Technological University, Singapore, in 1998. His current research interests include unmanned aerial systems, applied fractional calculus, mechatronics, cyber-physical systems and so on.
Shuo Zhang received his Ph.D. degree from Beijing Jiaotong University, China, in 2017. From 2015 to 2016, he was a research scholar in Univercity of California, Merced, USA. His current research interests include neural networks, chaos synchronization, complex networks, nonlinear dynamics and control.
About this article
Cite this article
Liu, L., Tian, S., Xue, D. et al. A Review of Industrial MIMO Decoupling Control. Int. J. Control Autom. Syst. 17, 1246–1254 (2019). https://doi.org/10.1007/s12555-018-0367-4
- Decoupling control
- industrial application
- interaction analysis
- MIMO system