Dual estimation and combination of state and output feedback based robust adaptive NMBC control scheme on non-linear process

  • Atanu PandaEmail author
  • Shinjinee Goswami
  • Rames C. Panda


A robust adaptive non-linear model based control schemes have been carried out in this work. The control strategy has been implemented on various benchmark non-linear processes. The servo performance of the proposed control schemes were found satisfactory. In order to improve regulatory performance, both model state(s) and parameter(s) have been estimated on-line sequentially with the help of a derivative free Kalman filter and the predicted values of model state(s) have been used to formulate proposed control law. The performances and superiority of the proposed control schemes have been discussed and compared with conventional adaptive PI control scheme. From the extensive simulation studies, it can be concluded that proposed control schemes implemented on the non-linear processes are having better performance and goodness over conventional adaptive PI control scheme. It was also observed that proposed control schemes are able to eliminate measurement noise and also having good robustness features.


NMBC DUKF State and output feedback Conventional PI control 



Augmented unscented Kalman filter


Continuous stirred tank reactor


Conventional adaptive proportional and integral


Dual unscented Kalman filter


Extended Kalman filter




Integral squared error


Model based control


Model predictive control


Model reference adaptive control


Non-linear internal model based control


Non-linear model based control


Non-linear model predictive control


Neural network


Internal model control


Proportional integral derivative


Proposed scheme1


Proposed scheme2


Proposed scheme3


Self-tuning regulator


Total variation


Unscented Kalman filter


  1. 1.
    Astrom KJ, Hagglund T (1988) Automatic tuning of PID controllers. Instrument society of America, Research Triangle ParkGoogle Scholar
  2. 2.
    Nahas EP, Henson MA, Seborg DE (1992) Nonlinear internal model control strategy for neural network models. Comput Chem Eng 16(12):1039–1057CrossRefGoogle Scholar
  3. 3.
    Bequette BW (1991) Nonlinear control of chemical processes: a review. Ind Eng Chem Res 30(7):1391–1413CrossRefGoogle Scholar
  4. 4.
    Hu Q, Rangaiah GP (1999) Adaptive internal model control of nonlinear processes. Chem Eng Sci 54(9):1205–1220CrossRefGoogle Scholar
  5. 5.
    Findeisen R, Imsland L, Allgower F, Foss BA (2003) State and output feedback nonlinear model predictive control: an overview. Eur J Control 9(2–3):190–206CrossRefzbMATHGoogle Scholar
  6. 6.
    Doyle FJ, Ogunnaike BA, Pearson RK (1995) Nonlinear model-based control using second-order Volterra models. Automatica 31(5):697–714MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Edgar CR, Postlethwaite BE (2000) MIMO fuzzy internal model control. Automatica 34(6):867–877MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ling W-M, Rivera DE (2001) A methodology for control-relevant nonlinear system identification using restricted complexity models. J Process Control 11(2):209–222CrossRefGoogle Scholar
  9. 9.
    Hussain MA, Kittisupakorn P, Daosud W (2001) Implementation of neural-network-based inverse-model control strategies on an exothermic reactor. Sci Asia 27(8):41–50CrossRefGoogle Scholar
  10. 10.
    Niemiec MP, Kravaris C (2003) Nonlinear model-state feedback control for non minimum-phase processes. Automatica 39(7):1295–1302MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Panda RC, Yu C-C, Huang H-P (2004) PID tuning rules for SOPDT systems: review and some new results. ISA Trans 43(2):283–295CrossRefGoogle Scholar
  12. 12.
    Deng H, Xu Z, Li H-X (2009) A novel neural internal model control for multi-input multi-output nonlinear discrete-time processes. J Process Control 19(8):1392–1400CrossRefGoogle Scholar
  13. 13.
    Galan O, Romagnoli JA, Palazoglu A (2004) Real-time implementation of multi-linear model-based control strategies–an application to a bench-scale pH neutralization reactor. J Process Control 14(5):571–579CrossRefGoogle Scholar
  14. 14.
    Gomez JC, Jutan A, Baeyens E (2004) Wiener model identification and predictive control of a pH neutralisation process. IEE Proc Control Theory Appl 151(3):329–338CrossRefGoogle Scholar
  15. 15.
    Liu T, Jiang Z-P (2015) Event-based control of nonlinear systems with partial state and output feedback. Automatica 53(C):10–22MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Henson MA (1998) Nonlinear model predictive control: current status and future directions. Comput Chem Eng 23(2):187–202CrossRefGoogle Scholar
  17. 17.
    Economou CG (1986) An operator theory approach to nonlinear controller design. Ph.D. Dissertation, California Institute of Technology, PasadenaGoogle Scholar
  18. 18.
    Tsay TS (2014) Model based adaptive piecewise linear controller for complicated control systems. J Appl Math 120419(64):1–11CrossRefGoogle Scholar
  19. 19.
    Lu CH, Tsai HC (2007) Generalized predictive control using recurrent fuzzy neural networks for industrial processes. J Process Control 17(1):83–92CrossRefGoogle Scholar
  20. 20.
    Panda A, Panda RC (2018) Adaptive nonlinear model based control scheme implemented on the nonlinear processes. Nonlinear Dyn 91(4):2735–2753CrossRefGoogle Scholar
  21. 21.
    Anandanatarajan R, Chidambaram M, Jayasingh T (2006) Limitations of a PI controller for a first-order nonlinear process with dead time. ISA Trans 45(2):185–199CrossRefGoogle Scholar
  22. 22.
    Haykin S (ed) (2001) Kalman filtering and neural networks. Wiley, HobokenGoogle Scholar
  23. 23.
    Julier SJ, Uhlmann JK (2004) Unscented filtering and non linear estimation. Proc IEEE 92(3):401–422CrossRefGoogle Scholar
  24. 24.
    Misir D, Malki HA, Chen G (1996) Design and analysis of a fuzzy proportional-integral-derivative controller. Fuzzy Sets Syst 79(3):297–314MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Noriega JR, Wang H (1998) A direct adaptive neural-network control for unknown nonlinear systems and its application. IEEE Trans Neural Netw Learn Syst 9(1):27–34CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Atanu Panda
    • 1
    Email author
  • Shinjinee Goswami
    • 2
  • Rames C. Panda
    • 3
  1. 1.Department of Electronics and Communication EngineeringInstitute of Engineering and ManagementSalt Lake, KolkataIndia
  2. 2.Department of Electronics and Communication EngineeringNetaji Subhash Engineering CollegeGaria, KolkataIndia
  3. 3.Department of Chemical EngineeringCSIR-Central Leather Research InstituteChennaiIndia

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