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Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

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Kajal Kothari, Utkal Mehta, Vineet Prasad and Jito Vanualailai, "Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 882-891, May 2020. doi: 10.1109/JAS.2020.1003093
Citation: Kajal Kothari, Utkal Mehta, Vineet Prasad and Jito Vanualailai, "Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 882-891, May 2020. doi: 10.1109/JAS.2020.1003093

Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet

doi: 10.1109/JAS.2020.1003093
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  • The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix (HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.

     

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  • [1]
    J. Wang, Y. Wei, T. Liu, A. Li, and Y. Wang, “Fully parametric identification for continuous time fractional order Hammerstein systems,” J. Franklin I., 2019.
    [2]
    Y. Zhao, Y. Li, F. Zhou, Z. Zhou, and Y. Chen, “An iterative learning approach to identify fractional order KiBaM model,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 322–331, 2017. doi: 10.1109/JAS.2017.7510358
    [3]
    S. W. Sung, “System identification method for Hammerstein processes,” Industrial &Engineering Chemistry Research, vol. 41, no. 17, pp. 4295–4302, 2002.
    [4]
    Y. J. Lee, S. W. Sung, S. Park, and S. Park, “Input test signal design and parameter estimation method for the Hammerstein-Wiener processes,” Industrial &Engineering Chemistry Research, vol. 43, no. 23, pp. 7521–7530, 2004.
    [5]
    H. C. Park, S. W. Sung, and J. Lee, “Modeling of Hammerstein-Wiener processes with special input test signals,” Industrial &Engineering Chemistry Research, vol. 45, no. 3, pp. 1029–1038, 2006.
    [6]
    J.-C. Jeng, M.-W. Lee, and H.-P. Huang, “Identification of block-oriented nonlinear processes using designed relay feedback tests,” Industrial &Engineering Chemistry Research, vol. 44, no. 7, pp. 2145–2155, 2005.
    [7]
    U. Mehta and S. Majhi, “Identification of a class of Wiener and Hammerstein-type nonlinear processes with monotonic static gains,” ISA Trans., vol. 49, no. 4, pp. 501–509, 2010. doi: 10.1016/j.isatra.2010.04.006
    [8]
    S. Dong, T. Liu, and Q. Wang, “Identification of Hammerstein systems with time delay under load disturbance,” IET Control Theory Applications, vol. 12, no. 7, pp. 942–952, 2018.
    [9]
    S. Zhang, D. Wang, and F. Liu, “Separate block-based parameter estimation method for hammerstein systems,” Royal Society Open Science, vol. 5, no. 6, 2018. doi: 10.1098/rsos.172194
    [10]
    F. Li and L. Jia, “Parameter estimation of Hammerstein-Wiener nonlinear system with noise using special test signals,” Neurocomputing, vol. 344, pp. 37–48, 2019. doi: 10.1016/j.neucom.2018.02.108
    [11]
    M. Aoun, R. Malti, O. Cois, and A. Oustaloup, “System identification using fractional Hammerstein models, ” in Proc. 15th IFAC World Congr., Spain, pp. 264–268, 2002.
    [12]
    K. Hsu, K. Poolla, and T. L. Vincent, “Identification of structured nonlinear systems,” IEEE Trans. Automatic Control, vol. 53, no. 11, pp. 2497–2513, 2008. doi: 10.1109/TAC.2008.2006928
    [13]
    A. Maachou, R. Malti, P. Melchior, J.-L. Battaglia, A. Oustaloup, and B. Hay, “Nonlinear thermal system identification using fractional Volterra series,” Control Engineering Practice, vol. 29, pp. 50–60, 2014. doi: 10.1016/j.conengprac.2014.02.023
    [14]
    L. Vanbeylen, “A fractional approach to identify Wiener-Hammerstein systems,” Automatica, vol. 50, no. 3, pp. 903–909, 2014. doi: 10.1016/j.automatica.2013.12.013
    [15]
    G. Giordano and J. Sjoberg, “A time-domain fractional approach for Wiener-Hammerstein systems identification,” IFAC-PapersOnLine, vol. 48, no. 28, pp. 1232–1237, 2015. doi: 10.1016/j.ifacol.2015.12.300
    [16]
    W. Allafi, I. Zajic, K. Uddin, and K. J. Burnham, “Parameter estimation of the fractional-order Hammerstein-Wiener model using simplified refined instrumental variable fractional-order continuous time,” IET Control Theory Applications, vol. 11, no. 15, pp. 2591–2598, 2017. doi: 10.1049/iet-cta.2017.0284
    [17]
    V. S. Krishnasamy, S. Mashayekhi, and M. Razzaghi, “Numerical solutions of fractional differential equations by using fractional Taylor basis,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 98–106, 2017. doi: 10.1109/JAS.2017.7510337
    [18]
    W. Gu, Y. Yu, and W. Hu, “Artificial bee colony algorithmbased parameter estimation of fractional-order chaotic system with time delay,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 107–113, 2017. doi: 10.1109/JAS.2017.7510340
    [19]
    N. I. Chaudhary, M. S. Aslam, and M. A. Z. Raja, “Modified volterra lms algorithm to fractional order for identification of Hammerstein nonlinear system,” IET Signal Processing, vol. 11, no. 8, pp. 975–985, 2017. doi: 10.1049/iet-spr.2016.0578
    [20]
    D. Cai, Y. Yu, and J. Wei, “A modified artificial Bee colony algorithm for parameter estimation of fractional-order nonlinear systems,” IEEE Access, vol. 6, pp. 48600–48610, 2018. doi: 10.1109/ACCESS.2018.2859978
    [21]
    M. J. Moghaddam, H. Mojallali, and M. Teshnehlab, “Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay,” Applied Soft Computing, vol. 70, pp. 486–500, 2018. doi: 10.1016/j.asoc.2018.05.046
    [22]
    S. Cheng, Y. Wei, D. Sheng, Y. Chen, and Y. Wang, “Identification for Hammerstein nonlinear ARMAX systems based on multi-innovation fractional order stochastic gradient,” Signal Processing, vol. 142, pp. 1–10, 2018. doi: 10.1016/j.sigpro.2017.06.025
    [23]
    M.-R. Rahmani and M. Farrokhi, “Fractional-order Hammerstein statespace modeling of nonlinear dynamic systems from input-output measurements,” ISA Trans., 2019.
    [24]
    Z. Aslipour and A. Yazdizadeh, “Identification of nonlinear systems using adaptive variable-order fractional neural networks (case study: a wind turbine with practical results),” Engineering Applications of Artificial Intelligence, vol. 85, pp. 462–473, 2019. doi: 10.1016/j.engappai.2019.06.025
    [25]
    S. Cheng, Y. Wei, D. Sheng, and Y. Wang, “Identification for Hammerstein nonlinear systems based on universal spline fractional order LMS algorithm,” Communications in Nonlinear Science and Numerical Simulation, vol. 79, pp. 104901, 2019. doi: 10.1016/j.cnsns.2019.104901
    [26]
    Y. Li, X. Meng, and Y.-Q. Ding, “Using wavelet multi-resolution nature to accelerate the identification of fractional order system,” Chinese Physics B, vol. 26, no. 5, pp. 050201, 2017. doi: 10.1088/1674-1056/26/5/050201
    [27]
    Y. Li, X. Meng, B. Zheng, and Y. Ding, “Parameter identification of fractional order linear system based on Haar wavelet operational matrix,” ISA Trans., vol. 59, pp. 79–84, 2015. doi: 10.1016/j.isatra.2015.08.011
    [28]
    Y. Tang, N. Li, M. Liu, Y. Lu, and W. Wang, “Identification of fractionalorder systems with time delays using block pulse functions,” Mechanical Systems and Signal Processing, vol. 91, pp. 382–394, 2017. doi: 10.1016/j.ymssp.2017.01.008
    [29]
    K. Kothari, U. Mehta, and J. Vanualailai, “A novel approach of fractional-order time delay system modeling based on Haar wavelet,” ISA Trans., vol. 80, pp. 371–380, 2018. doi: 10.1016/j.isatra.2018.07.019
    [30]
    X.-L. Luo, L.-Z. Liao, and H. W. Tam, “Convergence analysis of the Levenberg-Marquardt method,” Optimization Methods and Software, vol. 22, no. 4, pp. 659–678, 2007. doi: 10.1080/10556780601079233
    [31]
    M. A. Demetriou and I. G. Rosen, “On the persistence of excitation in the adaptive estimation of distributed parameter systems,” IEEE Trans. Automatic Control, vol. 39, no. 5, pp. 1117–1123, 1994. doi: 10.1109/9.284907

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