Journal of Zhejiang University-SCIENCE A

, Volume 12, Issue 3, pp 190–200 | Cite as

Multi-loop adaptive internal model control based on a dynamic partial least squares model



A multi-loop adaptive internal model control (IMC) strategy based on a dynamic partial least squares (PLS) framework is proposed to account for plant model errors caused by slow aging, drift in operational conditions, or environmental changes. Since PLS decomposition structure enables multi-loop controller design within latent spaces, a multivariable adaptive control scheme can be converted easily into several independent univariable control loops in the PLS space. In each latent subspace, once the model error exceeds a specific threshold, online adaptation rules are implemented separately to correct the plant model mismatch via a recursive least squares (RLS) algorithm. Because the IMC extracts the inverse of the minimum part of the internal model as its structure, the IMC controller is self-tuned by explicitly updating the parameters, which are parts of the internal model. Both parameter convergence and system stability are briefly analyzed, and proved to be effective. Finally, the proposed control scheme is tested and evaluated using a widely-used benchmark of a multi-input multi-output (MIMO) system with pure delay.

Key words

Partial least squares (PLS) Adaptive internal model control (IMC) Recursive least squares (RLS) 

CLC number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdel-Rahman, A.I., Lim, G.J., 2009. A nonlinear partial least squares algorithm using quadratic fuzzy inference system. Journal of Chemometrics, 23(10):530–537. [doi:10.1002/cem.1249]CrossRefGoogle Scholar
  2. Astrom, K.J., Wittenmark, B., 1973. Self tuning regulators. Automatica, 9(2):185–199. [doi:10.1016/0005-1098(73)90073-3]CrossRefMATHGoogle Scholar
  3. Astrom, K.J., Borisson, U., Ljung, L., Wittenmark, B., 1977. Theory and applications of self-tuning regulators. Automatica, 13(5):457–476. [doi:10.1016/0005-1098(77)90067-X]CrossRefMATHGoogle Scholar
  4. Bang, Y.H., Yoo, C.K., Lee, I.B., 2002. Nonlinear PLS modeling with fuzzy inference system. Chemometrics and Intelligent Laboratory Systems, 64(2):137–155. [doi:10.1016/S0169-7439(02)00084-9]CrossRefGoogle Scholar
  5. Chen, J.H., Cheng, Y.C., 2004. Applying partial least squares based decomposition structure to multiloop adaptive proportional-integral-derivative controllers in nonlinear processes. Industrial & Engineering Chemistry Research, 43(18):5888–5898. [doi:10.1021/Ie040013b]CrossRefGoogle Scholar
  6. Chen, J.H., Cheng, Y.C., Yea, Y.Z., 2005. Multiloop PID controller design using partial least squares decoupling structure. Korean Journal of Chemical Engineering, 22(2):173–183. [doi:10.1007/BF02701481]CrossRefGoogle Scholar
  7. Datta, A., Ochoa, J., 1996. Adaptive internal model control design and stability analysis. Automatica, 32(2):261–266. [doi:10.1016/0005-1098(96)85557-9]MathSciNetCrossRefMATHGoogle Scholar
  8. Datta, A., Ochoa, J., 1998. Adaptive internal model control: H2 optimization for stable plants. Automatica, 34(1):75–82. [doi:10.1016/S0005-1098(97)00163-5]MathSciNetCrossRefMATHGoogle Scholar
  9. Datta, A., Xing, L., 1998. The Theory and Design of Adaptive Internal Model Control Schemes. Proceedings of the American Control Conference, Philadelphia, PA, USA, 6:3677–3684. [doi:10.1109/ACC.1998.703301]Google Scholar
  10. Datta, A., Xing, L., 1999. Adaptive internal model control: H infinity optimization for stable plants. IEEE Transactions on Automatic Control, 44(11):2130–2134. [doi:10.1109/9.802930]MathSciNetCrossRefMATHGoogle Scholar
  11. Doymaz, F., Palazoglu, A., Romagnoli, J.A., 2003. Orthogonal nonlinear partial least-squares regression. Industrial & Engineering Chemistry Research, 42(23):5836–5849. [doi:10.1021/ie0109051]CrossRefGoogle Scholar
  12. Garcia, C.E., Morari, M., 1982. Internal model control. A unifying review and some new results. Industrial & Engineering Chemistry Process Design and Development, 21(2):308–323. [doi:10.1021/i200017a016]CrossRefGoogle Scholar
  13. Geladi, P., Kowalski, B.R., 1986. Partial least-squares regression: a tutorial. Analytica Chimica Acta, 185:1–17. [doi: 10.1016/0003-2670(86)80028-9]CrossRefGoogle Scholar
  14. Goodwin, G.C., Ramadge, P.J., Caines, P.E., 1980. Discrete-time multivariable adaptive control. IEEE Transactions on Automatic Control, 25(3):449–456. [doi:10.1109/TAC.1980.1102363]MathSciNetCrossRefMATHGoogle Scholar
  15. Hu, B., Zheng, P.Y., Liang, J., 2010. Multi-loop internal model controller design based on a dynamic PLS framework. Chinese Journal of Chemical Engineering, 18(2):277–285. [doi:10.1016/S1004-9541(08)60353-5]CrossRefGoogle Scholar
  16. Kaspar, M.H., Ray, W.H., 1992. Chemometric methods for process monitoring and high-performance controller-design. AIChE Journal, 38(10):1593–1608. [doi:10.1002/aic.690381010]CrossRefGoogle Scholar
  17. Kaspar, M.H., Ray, W.H., 1993. Dynamic PLS modeling for process control. Chemical Engineering Science 48(20): 3447–3461. [doi:10.1016/0009-2509(93)85001-6]CrossRefGoogle Scholar
  18. Qi, D.L., Yao, L.B., 2004. Hybrid internal model control and proportional control of chaotic dynamical systems. Journal of Zhejiang University-SCIENCE, 5(1):62–67. [doi:10.1631/jzus.2004.0062]CrossRefGoogle Scholar
  19. Qin, S.J., Mcavoy, T.J., 1992. Nonlinear PLS modeling using neural networks. Computers & Chemical Engineering, 16(4):379–391. [doi:10.1016/0098-1354(92)80055-E]CrossRefGoogle Scholar
  20. Sastry, S.M.B., 1994. Adaptive Control: Stability, Convergence, and Robustness. Prentice Hall, New Jersey, USA.Google Scholar
  21. Su, C.L., Wang, S.Q., 2006. Robust model predictive control for discrete uncertain nonlinear systems with time-delay via fuzzy model. Journal of Zhejiang University-SCIENCE A, 7(10):1723–1732. [doi:10.1631/jzus.2006.A1723]MathSciNetCrossRefMATHGoogle Scholar
  22. Wold, S., 1992. Nonlinear partial least-squares modeling II. Spline inner relation. Chemometrics and Intelligent Laboratory Systems, 14(1–3):71–84. [doi:10.1016/0169-7439(92)80093-J]CrossRefGoogle Scholar
  23. Wold, S., Kettanehwold, N., Skagerberg, B., 1989. Nonlinear PLS modeling. Chemometrics and Intelligent Laboratory Systems, 7(1–2):53–65. [doi:10.1016/0169-7439(89)80111-X].CrossRefGoogle Scholar
  24. Wold, S., Sjostrom, M., Eriksson, L., 2001. PLS-regression: a basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems, 58(2):109–130. [doi:10.1016/S0169-7439(01)00155-1]CrossRefGoogle Scholar
  25. Xie, W.F., Rad, A.B., 2000. Fuzzy adaptive internal model control. IEEE Transactions on Industrial Electronics, 47(1):193–202. [doi:10.1109/41.824142]CrossRefGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.State Key Lab of Industrial Control Technology, Department of Control Science & EngineeringZhejiang UniversityHangzhouChina

Personalised recommendations