Skip to main content
SpringerLink
Log in

Adaptive control for a class of chemical reactor systems in discrete-time form

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, an adaptive predictive control algorithm is applied to control a class of SISO continuous stirred tank reactor (CSTR) system in discrete time. The main contribution of the paper is that the considered systems belong to pure-feedback form where the unknown dead-zone is considered in the in-fan, and dead-zone is nonsymmetric, and it is first to control this class of systems. Radial basis function neural networks are used to approximate the unknown functions, and the mean value theorem is exploited in the design. Based on the Lyapunov analysis method, it is proven that all the signals of the resulting closed-loop system are guaranteed to be semi-global uniformly ultimately bounded, and the tracking error can be reduced to a small compact set. A simulation example for CSTR systems is studied to verify the effectiveness of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Klatt KU, Engell S (1998) Gain-scheduling trajectory control of a continuous stirred tank reactor. Comput Chem Eng 22:491–502

    Article  Google Scholar 

  2. Wu F (2001) LMI-based robust model predictive control and its application to an industrial CSTR problem. J Process Control 11:649–659

    Article  Google Scholar 

  3. Aguilar R (2007) Sliding-mode observer for uncertainty estimation in a class of chemical reactor: a differential-algebraic approach. Chem Prod Process Model 2:1934–2689

    MathSciNet  Google Scholar 

  4. Chen CP, LeClair SR, Pao YH (1998) An incremental adaptive implementation of functional-link processing for function approximation, time-series prediction, and system identification. Neurocompting 18(1–3):11–31

    Article  Google Scholar 

  5. Ge SS, Wang C (2002) Adaptive NN of uncertain nonlinear pure-feedback systems. Automatica 38:671–682

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu YJ, Wang W (2007) Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf Sci 177:3901–3917

    Article  MATH  Google Scholar 

  7. Liu YJ, Tong SC, Wang W (2009) Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst 160:2727–2754

    Article  MathSciNet  MATH  Google Scholar 

  8. Tong SC, Li CY, Li YM (2009) Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst 60:2755–2775

    MathSciNet  Google Scholar 

  9. Liu YJ, Tong SC, Li TS (2011) Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems. Fuzzy Sets Syst 164(1):25–44

    Article  MathSciNet  MATH  Google Scholar 

  10. Tong SC, He XL, Zhang HG (2009) A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans Fuzzy Syst 17:1059–1069

    Article  Google Scholar 

  11. Chen WS, Li JM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern Part B Cybern 38:258–266

    Article  Google Scholar 

  12. Li TS, Wang D, Feng G (2010) A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans Syst Man Cybern Part B Cybern 40:915–927

    Article  Google Scholar 

  13. Liu YJ, Tong SC, Wang D, Li TS, Chen CLP (2011) Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear SISO systems. IEEE Trans Neural Netw 22(8):1328–1334

    Article  Google Scholar 

  14. Li HY, Yu J, Hilton C, Liu H (2012) Adaptive sliding mode control for nonlinear active suspension systems using T-S fuzzy model. IEEE Trans Industr Electron. doi:10.1109/TIE.2012.2202354

    Google Scholar 

  15. Chen M, Ge SS, Ren BB (2010) Robust attitude control of helicopters with actuator dynamics using neural networks. IET Control Theory Appl 4:2837–2854

    Article  MathSciNet  Google Scholar 

  16. Li ZJ, Xu CQ (2009) Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums. Fuzzy Sets Syst 160:1787–1803

    Article  MATH  Google Scholar 

  17. Tong SC, Liu CL, Li YM (2010) Fuzzy adaptive decentralized control for large-scale nonlinear systems with dynamical uncertainties. IEEE Trans Fuzzy Syst 18(5):845–861

    Article  Google Scholar 

  18. Zhang HG, Luo YH, Liu DR (2009) Neural network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraint. IEEE Trans Neural Netw 20:1490–1503

    Article  Google Scholar 

  19. Liu YJ, Wang W, Tong SC, Liu YS (2010) Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans Syst Man Cybern Part A Syst Hum 40:170–184

    Article  Google Scholar 

  20. Zhou Q, Shi P, Lu J, Xu S (2011) Adaptive output feedback fuzzy tracking control for a class of nonlinear systems. IEEE Trans Fuzzy Syst 19(5):972–982

    Article  Google Scholar 

  21. Tong SC, Li Y, Li YM, Liu YJ (2011) Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans Syst Man Cybern B Cybern 41(6):1693–1704

    Article  MathSciNet  Google Scholar 

  22. Liu YJ, Tong SC, Chen CLP (2013) Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics. IEEE Trans Fuzzy Syst 21(2):275–288

    Article  Google Scholar 

  23. Ge SS, Hang CC, Zhang T (1999) Nonlinear adaptive control using neural networks and its application to CSTR systems. J Process Control 9:313–323

    Article  Google Scholar 

  24. Zhang HG, Cai LL (2002) Nonlinear adaptive control using the Fourier integral and its application to CSTR systems. IEEE Trans Syst Man Cybern B Cybern 32:367–372

    Article  Google Scholar 

  25. Salehi S, Shahrokhi M (2008) Adaptive fuzzy approach for H∞ temperature tracking control of continuous stirred tank reactors. Control Eng Pract 16:1101–1108

    Article  Google Scholar 

  26. Salehi S, Shahrokhi M (2009) Adaptive fuzzy backstepping approach for temperature control of continuous stirred tank reactors. Fuzzy Sets Syst 160:1804–1818

    Article  MathSciNet  MATH  Google Scholar 

  27. Ge SS, Li GY, Lee TH (2003) Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems. Automatica 39:807–819

    Article  MathSciNet  MATH  Google Scholar 

  28. Ge SS, Zhang J, Lee TH (2004) State feedback neural network control of a class of discrete MIMO nonlinear systems with disturbances. IEEE Trans Sys Man Cybern B 34:1630–1645

    Article  Google Scholar 

  29. Ge SS, Yang CG, Lee TH (2008) Adaptive predictive control using neural network for a class of pure-feedback systems in discrete time. IEEE Trans Neural Netw 19(9):1599–1614

    Article  Google Scholar 

  30. Liu YJ, Chen CLP, Wen GX, Tong SC (2011) Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans Neural Netw 22:1162–1167

    Article  Google Scholar 

  31. Yang CG, Ge SS, Xiang C, Chai T, Lee TH (2008) Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans Neural Netw 19:1873–1886

    Article  Google Scholar 

  32. Chen M, Ge SS, Ren BB (2010) Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans Neural Netw 21:796–812

    Article  Google Scholar 

  33. Tong SC, Li YM (2012) Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans Fuzzy Syst 20:168–180

    Article  Google Scholar 

  34. Chen M, Ge SS, Ren BB (2011) Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica 47:452–465

    Article  MathSciNet  MATH  Google Scholar 

  35. Campos J, Lewis FL (1999) Dead-zone compensation in discrete-time using adaptive fuzzy logic. IEEE Trans Fuzzy Syst 7:697–707

    Article  Google Scholar 

  36. Zhang X, Zhang HG, Liu DR, Kim YS (2009) Neural-network-based reinforcement learning controller for nonlinear systems with non-symmetric dead-zone inputs. IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning Nashville, pp 124–129

  37. Deolia VK, Purwar S, Sharma TN (2011) Backstepping control of discrete-time nonlinear system under unknown dead-zone constraint. International Conference on Communication Systems and Network Technologies, pp 344–349

  38. Liu YJ, Liu L, Tong SC (2013) Adaptive neural network tracking design for a class of uncertain nonlinear discrete-time systems with dead-zone. Sci China Inf Sci. doi:10.1007/s11432-012-4779-0

    Google Scholar 

Download references

Acknowledgments

This work was supported by the Natural Science Foundation of China [Grant Nos. 61071014 and 61104017] and Program for Liaoning Innovative Research Team in University [Grant No. LT2012013]; the Program for Liaoning Excellent Talents in University [Grant No. LJQ2011064]; Liaoning Bai QianWan Talent Program [Grant No. 2012921055]; The Foundation of Educational Department of Liaoning Province [Grant No. L2013].

Author information

Authors and Affiliations

  1. School of Chemical and Environmental Engineering, Liaoning University of Technology, Jinzhou, 121001, Liaoning, China

    Dong-Juan Li

  2. College of Science, Liaoning University of Technology, Jinzhou, 121001, Liaoning, China

    Li Tang

Authors
  1. Dong-Juan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong-Juan Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, DJ., Tang, L. Adaptive control for a class of chemical reactor systems in discrete-time form. Neural Comput & Applic 24, 1807–1814 (2014). https://doi.org/10.1007/s00521-013-1420-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-013-1420-0

Keywords

Search

Navigation