Abstract
For Wiener distributed parameter systems (DPS), a spatio-temporal Wiener model (a linear DPS followed by a static nonlinearity) is constructed in this chapter. After the time/space separation, it can be represented by the traditional Wiener system with a set of spatial basis functions. To achieve a low-order model, the Karhunen-Loève (KL) method is used for the time/space separation and dimension reduction. Finally, unknown parameters of the Wiener system are estimated with the least-squares estimation and the instrumental variables method to achieve consistent estimation under noisy measurements. The simulation on the catalytic rod and the experiment on snap curing oven are presented to illustrate the effectiveness of this modeling method.
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References
Armaou, A., Christofides, P.D.: Dynamic optimization of dissipative PDE systems using nonlinear order reduction. Chemical Engineering Science 57(24), 5083–5114 (2002)
Baker, J., Christofides, P.D.: Finite-dimensional approximation and control of non-linear parabolic PDE systems. International Journal of Control 73(5), 439–456 (2000)
Bloemen, H.H.J., Chou, C.T., van den Boom, T.J.J., Verdult, V., Verhaegen, M., Backx, T.C.: Wiener model identification and predictive control for dual composition control of a distillation column. Journal of Process Control 11(6), 601–620 (2001)
Campello, R.J.G.B., Favier, G., Amaral, W.C.: Optimal expansions of discrete-time Volterra models using Laguerre functions. Automatica 40(5), 815–822 (2004)
Cervantes, A.L., Agamennoni, O.E., Figueroa, J.L.: A nonlinear model predictive control system based on Wiener piecewise linear models. Journal of Process Control 13(7), 655–666 (2003)
Christofides, P.D.: Nonlinear and robust control of PDE systems: Methods and applications to transport-reaction processes. Birkhäuser, Boston (2001b)
Christofides, P.D., Daoutidis, P.: Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds. Journal of Mathematical Analysis and Applications 216(2), 398–420 (1997)
Coca, D., Billings, S.A.: Identification of finite dimensional models of infinite dimensional dynamical systems. Automatica 38(11), 1851–1865 (2002)
Deng, H., Li, H.-X., Chen, G.: Spectral-approximation-based intelligent modeling for distributed thermal processes. IEEE Transactions on Control Systems Technology 13(5), 686–700 (2005)
Dierckx, P.: Curve and surface fitting with splines. Clarendon, Oxford (1993)
Fu, Y., Dumont, G.A.: An optimum time scale for discrete Laguerre network. IEEE Transactions on Automatic Control 38(6), 934–938 (1993)
Gerksic, S., Juricic, D., Strmcnik, S., Matko, D.: Wiener model based nonlinear predictive control. International Journal of Systems Science 31(2), 189–202 (2000)
Gómez, J.C.: Analysis of dynamic system identification using rational orthonormal bases. PhD Thesis, The University of Newcastle, Australia (1998)
Gómez, J.C., Baeyens, E.: Identification of block-oriented nonlinear systems using orthonormal bases. Journal of Process Control 14(6), 685–697 (2004)
Gómez, J.C., Jutan, A., Baeyens, E.: Wiener model identification and predictive control of a pH neutralisation process. IEE Proceedings-Control Theory and Applications 151(3), 329–338 (2004)
Greblicki, W.: Nonparametric identification of Wiener systems by orthogonal series. IEEE Transactions on Automatic Control 39(10), 2077–2086 (1994)
Hagenblad, A.: Aspects of the identification of Wiener models. Thesis No.793, Linköping University, Sweden (1999)
Hagenblad, A., Ljung, L.: Maximum likelihood identification of Wiener models with a linear regression initialization. In: Proceedings of the 37th IEEE Conference Decision & Control, Tampa, Fourida, USA, pp. 712–713 (1998)
Hagenblad, A., Ljung, L.: Maximum likelihood estimation of Wiener models. Report no.: LiTH-ISY-R-2308, Linköping University, Sweden (2000)
Heuberger, P.S.C., Van den Hof, P.M.J., Bosgra, O.H.: A generalized orthonormal basis for linear dynamical systems. IEEE Transactions on Automatic Control 40(3), 451–465 (1995)
Holmes, P., Lumley, J.L., Berkooz, G.: Turbulence, coherent structures, dynamical systems, and symmetry. Cambridge University Press, New York (1996)
Janczak, A.: Instrumental variables approach to identification of a class of MIMO Wiener systems. Nonlinear Dynamics 48(3), 275–284 (2007)
Jeong, B.-G., Yoo, K.-Y., Rhee, H.-K.: Nonlinear model predictive control using a Wiener model of a continuous methyl methacrylate polymerization reactor. Industrial and Engineering Chemistry Research 40(25), 5968–5977 (2001)
Lacy, S.L., Bernstein, D.S.: Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities. International Journal of Control 76(15), 1500–1507 (2003)
Lancaster, P., Salkauskas, K.: Curve and surface fitting: An introduction. Academic Press, London (1986)
Newman, A.J.: Model reduction via the Karhunen-Loève expansion part I: An exposition. Technical Report T.R.96-32, University of Maryland, College Park, Maryland (1996a)
Newman, A.J.: Model reduction via the Karhunen-Loève expansion part II: Some elementary examples. Technical Report T.R.96-33, University of Maryland, College Park, Maryland (1996b)
Pawlak, M., Hasiewicz, Z., Wachel, P.: On nonparametric identification of Wiener systems. IEEE Transactions on Signal Processing 55(2), 482–492 (2007)
Raich, R., Zhou, G.T., Viberg, M.: Subspace based approaches for Wiener system identification. IEEE Transactions on Automatic Control 50(10), 1629–1634 (2005)
Sahan, R.A., Koc-Sahan, N., Albin, D.C., Liakopoulos, A.: Artificial neural network-based modeling and intelligent control of transitional flows. In: Proceeding of the 1997 IEEE International Conference on Control Applications, Hartford, CT, pp. 359–364 (1997)
Shikin, E.V., Plis, A.I.: Handbook on splines for the user. CRC Press, Boca Raton (1995)
Sirovich, L.: New perspectives in turbulence, 1st edn. Springer, New York (1991)
Sjöberg, J., Zhang, Q., Ljung, L., Benveniste, A., Delyon, B., Glorennec, P., Hjalmarsson, H., Juditsky, A.: Nonlinear black-box modeling in system identification: A unified approach. Automatica 31(12), 1691–1724 (1995)
Strikwerda, J.C.: Finite difference schemes and partial differential equations. Wads. & Brooks/Cole Adv. Bks. & S.W., Pacific Grove (1989)
Wahlberg, B.: System identification using Laguerre models. IEEE Transactions on Automatic Control 36(5), 551–562 (1991)
Wahlberg, B.: System identification using Kautz models. IEEE Transactions on Automatic Control 39(6), 1276–1282 (1994)
Westwick, D., Verhaegen, M.: Identifying MIMO Wiener systems using subspace model identification methods. Signal Processing 52(2), 235–258 (1996)
Wigren, T.: Recursive prediction error identification using the nonlinear Wiener model. Automatica 29(4), 1011–1025 (1993)
Wigren, T.: Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model. IEEE Transactions on Automatic Control 39(11), 2191–2206 (1994)
Zhu, Y.C.: Estimation of an N-L-N Hammerstein-Wiener model. Automatica 38(9), 1607–1614 (2002)
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Li, HX., Qi, C. (2011). Spatio-Temporal Modeling for Wiener Distributed Parameter Systems. In: Spatio-Temporal Modeling of Nonlinear Distributed Parameter Systems. Intelligent Systems, Control and Automation: Science and Engineering, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0741-2_3
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DOI: https://doi.org/10.1007/978-94-007-0741-2_3
Publisher Name: Springer, Dordrecht
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