Modeling and identification of a fractional-order discrete-time SISO Laguerre-Wiener system

On Digital Realizations of Non-integer Order Filters

“…As it can be seen in Lemma 1, the closed-loop realization of filter (6) with Oustaloup integrators is quite complicated and closed-loop eigenvalues are not easily available for analysis. In case of LIRA, eigenvalues of filter are not only available, but also state matrix in (38) has n identical eigenvalues and their value can be regulated (moved away from right half plane) and their discrete form is naturally more robust toward rounding errors. It should be also noted that this approximation leads to effective approximation of any order, whereas Oustaloup approximation allows only even values (because two integrators have to be realized).…”

“…For example, in Stanislawski et al [37,38] use Grünwald-Letnikow difference to design discrete filters. Another proposition of non-integer order discrete filter can be found in [13].…”

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

“…It is well known that many industrial processes are inherently nonlinear and when the operating point changes it is difficult to represent adequately a given process by means of a linear model. Therefore, to achieve the required system performance, advanced control methods based on nonlinear process models are identification of Wiener systems, and many different identification methods have been developed that are based on correlation analysis (e.g., Billings and Fakhouri, 1987;1982;Van Vaerenbergh et al, 2013), frequency analysis (Giri et al, 2014;Brouri and Slassi, 2015), nonlinear optimization (Wigren, 1993;Al-Duwaish et al, 1996;Janczak, 2005;Vörös, 2007;Ławryńczuk, 2013;Zhou et al, 2013), linear regression (Janczak, 2005;2018;Stanisławski et al, 2014), nonparametric regression (Greblicki, 1997;2001), and subspace approach (Westwick and Verhaegen, 1996;Baeyens, 2002, 2005;Ase and Katayama, 2015).…”

“…Polynomials (Westwick and Verhaegen, 1996;Janczak, 2005;Stanisławski et al, 2014;Tiels and Schoukens, 2014;Ding et al, 2015;Jansson and Medvedev, 2015;Xiong et al, 2015;Mahataa et al, 2016;Bottegal et al, 2017;Kazemi and Arefi, 2017;Schoukens and Tiels, 2017;Janczak, 2018), Legendre polynomials (Ase and Katayama, 2015), piecewise-linear functions (Dong et al, 2009;Fan and Lo, 2009), cubic splines (Aljamaan et al, 2016), least-squares support vector machine models (Ławryńczuk, 2016), sets of basis functions (Gómez and Baeyens, 2002;2005;Schoukens and Tiels, 2011;Yang et al, 2017), multilayer perceptrons (Al-Duwaish et al, 1996;Janczak, 2005;Ławryńczuk, 2013), kernel expansions (Van Vaerenbergh et al, 2013), or nonparametric representations (Greblicki, 1997;2001) are commonly used for modeling the static nonlinear element or its inverse. The linear dynamic subsystem is usually represented by a transfer function (Janczak, 2005;Dong et al, 2009;Schoukens and Tiels, 2011;Ławryńczuk, 2013;2016;Ding et al, 2015;Xiong et al, 2015;Mahataa et al, 2016;Bottegal et al, 2017;Kazemi and Arefi, 2017;Yang et al, 2001)…”

Fractional order state space canonical model identification using fractional order information filter

“…Due to their long-term memory behaviour, the identification of fractional-order models are more difficult than for integer-order models; therefore, different algorithms have been proposed in the frequency domain to solve this problem. In recent years many investigations are performed in this field [13][14][15][16][17][18][19][20], but there are no reports on recursive identification of fractional order state space system parameters. The hierarchical identification approach proposed in this paper has less computational overhead compared to the previous methods.…”