A Review of Industrial MIMO Decoupling Control

  • Lu Liu
  • Siyuan Tian
  • Dingyu Xue
  • Tao Zhang
  • YangQuan Chen
  • Shuo ZhangEmail author
Regular Papers Control Theory and Applications


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.


Decoupling control industrial application interaction analysis MIMO system 


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  1. [1]
    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.Google Scholar
  2. [2]
    K. V. Waller, “Impressions of chemical process control education and research in the USA,” Chemical Engineering Education, vol. 15, no. 1, p. 30, 1981.Google Scholar
  3. [3]
    H. Tsien, Engineering Cybernetics, McGraw-Hill Book Co., New York, 1954.Google Scholar
  4. [4]
    M. D. Mesarović, The Control of Multivariable Systems, no. 9, The MIT Press, 1960.CrossRefGoogle Scholar
  5. [5]
    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.Google Scholar
  6. [6]
    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.CrossRefGoogle Scholar
  7. [7]
    E. G. Gilbert, “The decoupling of multivariable systems by state feedback,” SIAM Journal on Control, vol. 7, no. 1, pp. 50–63, 1969.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    J. Descusse, “Block noninteracting control with (non) regular static state feedback: a complete solution,” Automatica, vol. 27, no. 5, pp. 883–886, 1991.MathSciNetCrossRefGoogle Scholar
  11. [11]
    T. G. Koussiouris, “On the general problem of pole assignment,” International Journal of Control, vol. 30, no. 4, pp. 677–694, 1979.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    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.Google Scholar
  13. [13]
    W. L. Luyben, “Distillation decoupling,” AIChE Journal, vol. 16, no. 2, pp. 198–203, 1970.CrossRefGoogle Scholar
  14. [14]
    M. Waller, J. B. Waller, and K. V. Waller, “Decoupling revisited,” Industrial & Engineering Chemistry Research, vol. 42, no. 20, pp. 4575–4577, 2003.CrossRefGoogle Scholar
  15. [15]
    C. H. Liu, General Decoupling Theory of Multivariable Process Control Systems, Springer-Verlag, Berlin-New York, 1983.CrossRefzbMATHGoogle Scholar
  16. [16]
    Q. G. Wang, Decoupling Control, vol. 285, Springer Science & Business Media, 2002.Google Scholar
  17. [17]
    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.CrossRefGoogle Scholar
  18. [18]
    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.CrossRefGoogle Scholar
  19. [19]
    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.CrossRefGoogle Scholar
  20. [20]
    W. Zhang, Quantitative Process Control Theory, vol. 45, CRC Press, 2011.Google Scholar
  21. [21]
    T. McAvoy, “Interacting control systems: steady state and dynamic measurement of interaction,” ISA Transactions, vol. 16, no. 3, p. 35, 1978.Google Scholar
  22. [22]
    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.CrossRefGoogle Scholar
  23. [23]
    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.CrossRefGoogle Scholar
  24. [24]
    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.CrossRefGoogle Scholar
  25. [25]
    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.CrossRefGoogle Scholar
  26. [26]
    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.CrossRefGoogle Scholar
  27. [27]
    E. Gagnon, A. Pomerleau, and A. Desbiens, “Simplified, ideal or inverted decoupling?” ISA Transactions, vol. 37, no. 4, pp. 265–276, 1998.CrossRefGoogle Scholar
  28. [28]
    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.Google Scholar
  29. [29]
    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.CrossRefGoogle Scholar
  30. [30]
    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.Google Scholar
  31. [31]
    F. G. Shinskey, Process Control Systems: Application, Design, and Tuning, McGraw-Hill, Inc., 1990.Google Scholar
  32. [32]
    H. L. Wade, “Inverted decoupling: a neglected technique,” ISA Transactions, vol. 36, no. 1, pp. 3–10, 1997.CrossRefGoogle Scholar
  33. [33]
    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.CrossRefGoogle Scholar
  34. [34]
    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.CrossRefGoogle Scholar
  35. [35]
    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.CrossRefGoogle Scholar
  36. [36]
    Q. C. Zhong, Robust Control of Time-delay Systems, Springer Science & Business Media, 2006.zbMATHGoogle Scholar
  37. [37]
    O. Smith, “Closer control of loops with dead time,” Chemical Engineering Progress, vol. 53, no. 5, pp. 217–219, 1957.Google Scholar
  38. [38]
    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.CrossRefGoogle Scholar
  39. [39]
    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.CrossRefGoogle Scholar
  40. [40]
    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.CrossRefGoogle Scholar
  41. [41]
    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.CrossRefGoogle Scholar
  42. [42]
    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.CrossRefGoogle Scholar
  43. [43]
    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.CrossRefGoogle Scholar
  44. [44]
    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.CrossRefGoogle Scholar
  45. [45]
    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.Google Scholar
  46. [46]
    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.Google Scholar
  47. [47]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    U. Borison, “Self-tuning regulators for a class of multi-variable systems,” Automatica, vol. 15, no. 2, pp. 209–215, 1979.CrossRefzbMATHGoogle Scholar
  49. [49]
    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.CrossRefGoogle Scholar
  50. [50]
    P. Daoutidis, M. Soroush, and C. Kravaris, “Feedforward/feedback control of multivariable nonlinear processes,” AIChE Journal, vol. 36, no. 10, pp. 1471–1484, 1990.CrossRefGoogle Scholar
  51. [51]
    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.CrossRefGoogle Scholar
  52. [52]
    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.CrossRefGoogle Scholar
  53. [53]
    T. Yue and C. H. You, “Multivariable intelligent decoupling control system and its application,” Acta Automatica Sinica, vol. 1, p. 013, 2005.Google Scholar
  54. [54]
    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.CrossRefGoogle Scholar
  55. [55]
    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.CrossRefGoogle Scholar
  56. [56]
    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.CrossRefGoogle Scholar
  57. [57]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    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.CrossRefGoogle Scholar
  59. [59]
    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.Google Scholar
  60. [60]
    H. Demirciolu and P. J. Gawthrop, “Multivariable continuous-time generalized predictive control (MCGPC),” Automatica, vol. 28, no. 4, pp. 697–713, 1992.MathSciNetCrossRefzbMATHGoogle Scholar
  61. [61]
    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.CrossRefGoogle Scholar
  62. [62]
    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.CrossRefGoogle Scholar
  63. [63]
    M. A. Smith, “For coupling a turbofan engine to airplane structure,”, US Patent 4,458,863, Jul. 10 1984.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Marine Science and TechnologyNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Lam Research CorporationFremontUSA
  3. 3.School of Information Science and EngineeringNortheastern UniversityShenyangChina
  4. 4.School of Science and EngineeringUniversity of CaliforniaMercedUSA
  5. 5.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina

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