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Robust adaptive neural network prescribed performance control for uncertain CSTR system with input nonlinearities and external disturbance

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Abstract

In this paper, the control problem for continuously stirred tank reactor (CSTR) systems with input nonlinearities and unknown disturbances is addressed. To ensure constraints satisfaction on the input and the output of CSTR, we employ a system transformation technique to transform the original constrained model of CSTR into an equivalent unconstrained model, whose stability is sufficient to achieve the tracking control of the original CSTR system with a priori prescribed performance. To deal with two kinds of input nonlinearities, two neural networks (NNs)-based adaptive controllers are proposed. In the first approach, a robust control term is introduced to overcome the effects of the unknown input dead zone; however, in the second approach, an anti-windup compensator is designed to reduce the influence of the actuator saturation. In the proposed control methods, NNs are employed to approximate the unknown dynamics of CSTR and additional adaptive compensators are introduced to cope with NNs approximation errors and external disturbance. The proposed adaptive neural tracking controllers are designed with only one adaptive parameter by using the second Lyapunov stability method. In comparison with the traditional back-stepping-based techniques, usually used in CSTR control, the structures of the proposed controllers are much simpler with few design parameters since the causes for the problem of complexity growing are completely eliminated. Simulation results are presented to show the effectiveness of the proposed controllers.

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References

  1. Alvarez-Ramirez J, Femat R (1999) Robust PI stabilization of a class of chemical reactors. Syst Control Lett 38(4–5):219–225

    MathSciNet  MATH  Google Scholar 

  2. Pérez M, Albertos P (2004) Self-oscillating and chaotic behaviour of a PI-controlled CSTR with control valve saturation. J Process Control 14(1):51–59

    Google Scholar 

  3. Viel F, Jadot F, Bastin G (1997) Robust feedback stabilization of chemical reactors. IEEE Trans Autom Control 42(4):473–481

    MathSciNet  MATH  Google Scholar 

  4. Antonelli R, Astolfi A (2003) Continuous stirred tank reactors: easy to stabilise? Automatica 39(10):1817–1827

    MathSciNet  MATH  Google Scholar 

  5. Biagiola SI, Figueroa JL (2004) A high gain nonlinear observer: application to the control of an unstable nonlinear process. Comput Chem Eng 28(9):1881–1898

    Google Scholar 

  6. Jana AK, Samanta AN, Ganguly S (2005) Globally linearized control on diabatic continuous stirred tank reactor: a case study. ISA Trans 44(3):423–444

    Google Scholar 

  7. Daaou B, Mansouri A, Bouhamida M, Chenafa M (2012) Development of linearizing feedback control with a variable structure observer for continuous stirred tank reactors. Chin J Chem Eng 20(3):567–571

    MATH  Google Scholar 

  8. So GB, Jin GG (2018) Fuzzy-based nonlinear PID controller and its application to CSTR. Korean J Chem Eng 35(4):819–825

    Google Scholar 

  9. Wang ZY, Wang GX (2017) Temperature fault-tolerant control system of CSTR with coil and jacket heat exchanger based on dual control and fault diagnosis. J Cent South Univ 24(3):655–664

    Google Scholar 

  10. Pratap A, Raja R, Rajchakit G, Cao J, Bagdasar O (2019) Mittag-Leffler state estimator design and synchronization analysis for fractional-order BAM neural networks with time delays. Int J Adapt Control Signal Process 33(5):855–874

    MathSciNet  MATH  Google Scholar 

  11. Pratap A, Raja R, Cao J, Rajchakit G, Fardoun HM (2019) Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of Mittag Leffler function. J Franklin Inst 356(4):2212–2239

    MathSciNet  MATH  Google Scholar 

  12. Anbalagan P, Ramachandran R, Cao J, Rajchakit G, Lim CP (2019) Global robust synchronization of fractional order complex valued neural networks with mixed time varying delays and impulses. Int J Control Autom Syst 17(2):509–520

    Google Scholar 

  13. Alamdar Ravari M, Yaghoobi M (2019) Optimum design of fractional order PID controller using chaotic firefly algorithms for a control CSTR system. Asian J Control 21:2245–2255

    MathSciNet  MATH  Google Scholar 

  14. Huaguang Z, Cai L (2002) Nonlinear adaptive control using the Fourier integral and its application to CSTR systems. IEEE Trans Syst Man Cybern Part B 32(3):367–372

    Google Scholar 

  15. Prakash J, Senthil R (2008) Design of observer based nonlinear model predictive controller for a continuous stirred tank reactor. J Process Control 18(5):504–514

    Google Scholar 

  16. Laurí D, Lennox B, Camacho J (2014) Model predictive control for batch processes: ensuring validity of predictions. J Process Control 24(1):239–249

    Google Scholar 

  17. Zerari N, Chemachema, M, Essounbouli N (2018) Adaptive neural-network output feedback control design for uncertain CSTR system with input saturation. In: 2018 international conference on electrical sciences and technologies in Maghreb (CISTEM). IEEE, pp 1–6

  18. Sowmiya C, Raja R, Cao J, Rajchakit G (2018) Enhanced result on stability analysis of randomly occurring uncertain parameters, leakage, and impulsive BAM neural networks with time-varying delays: discrete-time case. Int J Adapt Control Signal Process 32(7):1010–1039

    MathSciNet  MATH  Google Scholar 

  19. Sowmiya C, Raja R, Cao J, Rajchakit G, Alsaedi A (2018) Exponential stability of discrete-time cellular uncertain Bam neural networks with variable delays using Halanay-type inequality. Appl. Math 12(3):545–558

    MathSciNet  Google Scholar 

  20. Zerari N, Chemachema M, Essounbouli N (2018) Neural network based adaptive tracking control for a class of pure feedback nonlinear systems with input saturation. IEEE/CAA J Autom Sin 6(1):278–290

    MathSciNet  Google Scholar 

  21. Zerari N, Chemachema M, Essounbouli, N. (2017, November). Adaptive neural control design of MIMO nonaffine nonlinear systems with input saturation. In: International conference on electrical engineering and control applications. Springer, Cham, pp 155–167

  22. Chemachema M (2012) Output feedback direct adaptive neural network control for uncertain SISO nonlinear systems using a fuzzy estimator of the control error. Neural Netw 36:25–34

    MATH  Google Scholar 

  23. Bounemeur A, Chemachema M, Essounbouli N (2018) Indirect adaptive fuzzy fault-tolerant tracking control for MIMO nonlinear systems with actuator and sensor failures. ISA Trans 79:45–61

    Google Scholar 

  24. Wang LX, Ying H (1995) Adaptive fuzzy systems and control: design and stability analysis. J Intell Fuzzy Syst Appl Eng Technol 3(2):187

    Google Scholar 

  25. Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257

    Google Scholar 

  26. Salehi S, Shahrokhi M (2008) Adaptive fuzzy approach for H∞ temperature tracking control of continuous stirred tank reactors. Control Eng Pract 16(9):1101–1108

    Google Scholar 

  27. Salehi S, Shahrokhi M (2009) Adaptive fuzzy backstepping approach for temperature control of continuous stirred tank reactors. Fuzzy Sets Syst 160(12):1804–1818

    MathSciNet  MATH  Google Scholar 

  28. Li Z, Xiao H, Yang C, Zhao Y (2015) Model predictive control of nonholonomic chained systems using general projection neural networks optimization. IEEE Trans Syst Man Cybern Syst 45(10):1313–1321

    Google Scholar 

  29. Li D (2014) Adaptive neural network control for a class of continuous stirred tank reactor systems. Sci China Inf Sci 57(10):1–8

    MathSciNet  Google Scholar 

  30. Li S, Gong M, Liu Y (2016) Neural network-based adaptive control for a class of chemical reactor systems with non-symmetric dead-zone. Neurocomputing 174:597–604

    Google Scholar 

  31. Li DJ, Tang L (2014) Adaptive control for a class of chemical reactor systems in discrete-time form. Neural Comput Appl 24(7–8):1807–1814

    Google Scholar 

  32. Wu W (2003) Adaptive-like control methodologies for a CSTR system with dynamic actuator constraints. J Process Control 13(6):525–537

    Google Scholar 

  33. Wu F (2001) LMI-based robust model predictive control and its application to an industrial CSTR problem. J Process Control 11(6):649–659

    Google Scholar 

  34. Li DJ, Li DP (2015) Adaptive controller design-based neural networks for output constraint continuous stirred tank reactor. Neurocomputing 153:159–163

    Google Scholar 

  35. Li DJ (2015) Adaptive neural network control for a two continuously stirred tank reactor with output constraints. Neurocomputing 167:451–458

    Google Scholar 

  36. Bechlioulis CP, Rovithakis GA (2008) Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans Autom Control 53(9):2090–2099

    MathSciNet  MATH  Google Scholar 

  37. Bechlioulis CP, Rovithakis GA (2009) Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems. Automatica 45(2):532–538

    MathSciNet  MATH  Google Scholar 

  38. Henson MA, Seborg DE (1990) Input-output linearization of general nonlinear processes. AIChE J 36(11):1753–1757

    Google Scholar 

  39. Chang WD (2013) Nonlinear CSTR control system design using an artificial bee colony algorithm. Simul Model Pract Theory 31:1–9

    Google Scholar 

  40. Uppal A, Ray WH, Poore AB (1974) On the dynamic behavior of continuous stirred tank reactors. Chem Eng Sci 29(4):967–985

    Google Scholar 

  41. Polycarpou MM, Ioannou PA (1993) A robust adaptive nonlinear control design. In: 1993 American Control Conference. IEEE, pp 1365–1369

  42. Deng H, Krstić M (1997) Stochastic nonlinear stabilization—I: a backstepping design. Syst Control Lett 32(3):143–150

    MathSciNet  MATH  Google Scholar 

  43. White DA, Sofge DA (eds) (1992) Handbook of intelligent control: neural, fuzzy, and adaptative approaches. Van Nostrand Reinhold Company, New York

    Google Scholar 

  44. Gupta MM, Rao DH (1994) Neuro-control systems: theory and applications. IEEE Press, Piscataway

    Google Scholar 

  45. Wang XS, Su CY, Hong H (2004) Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica 40(3):407–413

    MathSciNet  MATH  Google Scholar 

  46. Galeani S, Tarbouriech S, Turner M, Zaccarian L (2009) A tutorial on modern anti-windup design. Eur J Control 15(3–4):418–440

    MathSciNet  MATH  Google Scholar 

  47. Do HM, Basar T, Choi, JY (2004) An anti-windup design for single input adaptive control systems in strict feedback form. In: Proceedings of the 2004 American Control Conference, vol 3. IEEE, pp. 2551–2556

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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  1. Signal Processing Laboratory, Department of Electronics, Faculty of Technology Sciences, Constantine 1 University, 2500, Constantine, Algeria

    Nassira Zerari & Mohamed Chemachema

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  1. Nassira Zerari
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  2. Mohamed Chemachema
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Correspondence to Nassira Zerari.

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Zerari, N., Chemachema, M. Robust adaptive neural network prescribed performance control for uncertain CSTR system with input nonlinearities and external disturbance. Neural Comput & Applic 32, 10541–10554 (2020). https://doi.org/10.1007/s00521-019-04591-1

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