This paper presents a method for online identification of non-linear dynamic systems using the Wiener model. For the linear dynamic part the subspace identification method with the multivariable output-error state-space algorithm is employed, whereas for the non-linear static part the multi-layer perceptron neural network with Levenberg–Marquardt algorithm is used. The stability and convergence of the proposed method is shown using the Lyapunov direct method and the region solution of the linear matrix inequality (LMI) approach. The proposed method is tested by simulations performed on the continuous stirred tank reactor (CSTR) plant, which is presented by non-linear differential equations. Moreover, the method is applied on the input–output data that are obtained from a practical system of the CSTR plant as well as the pH neutralization plant. The results show significant improvements in online identification of the non-linear dynamic systems compared with the recently reported methods in literature.
AadaleesanPMiglanNSharmaRet al. (2008) Nonlinear system identification using Wiener type Laguerre–wavelet network model. Chemical Engineering Science63(15): 3932–3941.
2.
AlwakeelMShaabanZ (2010) Face recognition based on Haar wavelet transform and principal component analysis via Levenberg–Marquardt backpropagation neural network. European Journal of Scientific Research42(1): 25–31.
3.
ArefiMMMontazeriAPoshtanJet al. (2008) Wiener-neural identification and predictive control of a more realistic plug-flow tubular reactor. Chemical Engineering Journal138(1): 274–282.
4.
Ashtari MahiniMTeshnehlabMAhmadieh khanehsarM (2015) Nonlinear system identification using Hammerstein–Wiener neural network and subspace algorithms. Journal of Advances in Computer Engineering and Technology1(2): 9–16.
5.
BoydSChuaLO (1985) Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Transactions on Circuits and Systems32(11): 1150–1161.
6.
ChenSHongXGongYet al. (2013) Digital predistorter design using B-spline neural network and inverse of De Boor algorithm. IEEE Transactions on Circuits and Systems60(6): 1584–1594.
7.
De MoorBDe GersemPDe SchutterBet al. (1997) DAISY: a database for identification of systems. Journal A, Special Issue on CACSD (Computer Aided Control Systems Design)38(3): 4–5.
8.
EfeMÖDebiasiMYanPet al. (2009) Seven tuning schemes for an ADALINE model to predict floor pressures in a subsonic cavity flow. Transactions of the Institute of Measurement and Control31(1): 97–112.
9.
GiriFBaiE-W (2010) Block-oriented Nonlinear System Identification. Berlin: Springer.
10.
GoethalsIPelckmansKSuykensJAet al. (2005) Subspace identification of Hammerstein systems using least squares support vector machines. IEEE Transactions on Automatic Control50(10): 1509–1519.
11.
GómezJCBaeyensE (2005) Subspace-based identification algorithms for Hammerstein and Wiener models. European Journal of Control11(2): 127–136.
12.
HachichaSKharratMChaariA (2014) N4SID and MOESP algorithms to highlight the ill-conditioning into subspace identification. International Journal of Automation and Computing11(1): 30–38.
13.
HongXChenS (2011) Modeling of complex-valued Wiener systems using B-spline neural network. IEEE Transactions on Neural Networks22(5): 818–825.
14.
HongXMitchellRJChenS (2013) System identification of Wiener systems with B-spline functions using De Boor recursion. International Journal of Systems Science44(9): 1666–1674.
15.
HsuY-LWangJ-S (2009) A Wiener-type recurrent neural network and its control strategy for nonlinear dynamic applications. Journal of Process Control19(6): 942–953.
16.
InghamJDunnIJHeinzleEet al. (2008) Chemical Engineering Dynamics: An Introduction to Modelling and Computer Simulation. New York: John Wiley & Sons.
17.
JalaleddiniKKearneyRE (2013) Subspace identification of SISO Hammerstein systems: application to stretch reflex identification. IEEE Transactions on Biomedical Engineering60(10): 2725–2734.
18.
KalafatisADWangLCluettWR (2005) Identification of time-varying pH processes using sinusoidal signals. Automatica41(4): 685–691.
19.
KatayamaT (2006) Subspace Methods for System Identification. London: Springer.
20.
LacySLBernsteinDS (2003) Subspace identification with guaranteed stability using constrained optimization. IEEE Transactions on Automatic Control48(7): 1259–1263.
21.
MaciejowskiJM (1995) Guaranteed stability with subspace methods. Systems & Control Letters26(2): 153–156.
22.
MeyerCD (2000) Matrix Analysis and Applied Linear Algebra. Philadelphia. PA: SIAM.
23.
MillerDNDe CallafonRA (2013) Subspace identification with eigenvalue constraints. Automatica49(8): 2468–2473.
24.
PaduartJLauwersLPintelonRet al. (2012) Identification of a Wiener–Hammerstein system using the polynomial nonlinear state space approach. Control Engineering Practice20(11): 1133–1139.
25.
PengJDubayR (2011) Identification and adaptive neural network control of a DC motor system with dead-zone characteristics. ISA Transactions50(4): 588–598.
26.
SastryS (1999) Nonlinear Systems: Analysis, Stability, and Control. New York: Springer.
27.
SchönTBWillsANinnessB (2011) System identification of nonlinear state-space models. Automatica47(1): 39–49.
TanWLuFLohAet al. (2005) Modeling and control of a pilot pH plant using genetic algorithm. Engineering Applications of Artificial Intelligence18(4): 485–494.
30.
TöttermanSToivonenHT (2009) Support vector method for identification of Wiener models. Journal of Process Control19(7): 1174–1181.
31.
Van GestelTSuykensJAVan DoorenPet al. (2001) Identification of stable models in subspace identification by using regularization. IEEE Transactions on Automatic Control46(9): 1416–1420.
32.
Van OverscheePDe MoorB (1996) Subspace Identification for Linear Systems: Theory, Implementation, Applications. Boston, MA: Kluwer Academic.
33.
VerhaegenM (2014) Subspace Techniques in System Identification. London: Springer.
34.
ZhangLXuQYBaoZJ (2015) Study on the MOESP subspace identification method and its simulation. Applied Mechanics and Materials. Pfaffikon, Switzerland: Trans Tech Publications, pp. 358–361.
