In this article, the Meixner-like model is used to represent the linear discrete-time system in comparison with the Laguerre model. Furthermore, we propose from input/output measurements a new recursive representation of the Meixner-like model. However, a significant approximation of this model is subject to an optimal choice of Meixner-like parameters: pole, order of generalization and Fourier coefficients. The present research yields a series of computational experiments, through a simulation example of a linear parameter varying (LPV) system. This study tests this approach, verifies the theoretical results and points out the positive outcomes of using the Meixner-like model in comparison with the Laguerre model.
AsyaliMHJuusolaM (2005) Use of Meixner functions in estimation of Volterra kernels of nonlinear systems with delay. IEEE Transactions on Biomedical Engineering52(2).
3.
BeltHJWDen BrinkerAC (1997) Optimal parameterization of truncated generalized Laguerre series. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol. 5, pp. 3805–3808.
4.
BeltHJWDen BrinkerAC (1995) Optimality condition for truncated generalized Laguerre networks. International Journal of Circuit Theory and Applications23: 227–235.
5.
BjörsellNIsakssonMHändelPet al. (2007) Kautz–Volterra modelling of an analogue-to-digital converter using a stepped three-tone excitation. In: Proceedings of the IMEKO 12th Workshop on ADC Modelling and Testing, Iasi, Romania, September.
6.
BokorJSchippF (1998) Approximate identification in Laguerre and Kautz bases. Automatica34(4): 463–468.
7.
BoleaYPuigVBlesaJ (2014) Gain-scheduled smith predictor PID-based LPV controller for open-flow canal control. IEEE Transactions on Control Systems Technology22(2): 468–477.
8.
BouzraraKGarnaTRagotJet al. (2013) Online identification of the ARX model expansion on Laguerre orthonormal bases with filters on model input and output. International Journal of Control86(3): 369–385.
9.
CaoLSchwartzH (1999) A novel recursive algorithm for directional forgetting. Proceedings of the American Control Conference, pp. 1334–1338.
10.
Den BrinkerAC (1995) Meixner-Like functions having a rational z-transform. International Journal of Circuit Theory and Applications23: 237–246.
11.
Den BrinkerACBendersFPASilvaTO (1996) Optimality conditions for truncated Kautz series. IEEE Transactions on Circuits Systems11(43): 117–122.
12.
GarnaTBouzraraKRagotJet al. (2014) Optimal expansions of discrete-time bilinear models using Laguerre functions. IMA Journal of Mathematical Control and Information31(3): 313–343.
13.
HeubergerPSCVan den HofPMJBosgraOH (1995) A generalized orthonormal basis for linear dynamical systems. IEEE Transactions on Automatic Control40(3): 451–465.
14.
HiramaY (2011) Identification method for commercialized PI control using Laguerre function. In: SICE Annual Conference, 13–18 September, Tokyo, Japan, pp. 2955–2960.
15.
LiPShiG (2011) Closed-loop identification using Laguerre orthogonal functions for a virtual diesel engine. International Journal of Computer Applications in Technology41: 34–39.
16.
MarouaniGMbarekAGarnaTet al. (2015) Nonlinear model based predictive control using multiple models approach expanded on Laguerre bases. WSEAS Transactions on Systems and Control10: 113–126.
17.
ProkhorovSAKulikovskikhIM (2015) Unique condition for generalized Laguerre functions to solve pole position problem. Signal Processing108: 25–29.
18.
ProkhorovSAKulikovskikhIM (2016) Pole position problem for Meixner filters. Signal Processing120: 8–12.
19.
ShammaJSAthansM (1990) Analysis of gain scheduled control for nonlinear plants. IEEE Transactions on Automatic Control35(8): 898–907.
20.
ShammaJSAthansM (1991) Guaranteed properties of gain scheduled control for linear parameter-varying plants. Automatica27(3): 559–564.
21.
ShaoHYangZYuY (2014) LPV model-based temperature control of thermoelectric device. In: International Conference on Mechatronics and Control (ICMC), 3–5 July, Jinzhou, China.
22.
VahidiAStefanopoulouAPengH (2005) Recursive least squares with forgetting for online estimation of vehicle mass and road grade: theory and experiments. Vehicle System Dynamics43(1): 31–55.
23.
Van den HofPMJHeubergerPSCBokorJ (1994) System identification with generalized orthonormal basis functions. In: Proceedings of the 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, 3382–3387.
24.
WahlbergB (1991) System identification using Laguerre models. IEEE Transactions on Automatic Control36(5): 551–562.
25.
WahlbergB (1994) System identification using kautz models. IEEE Transactions on Automatic Control39(6): 1276–1281.
26.
YoshitaniNHasegawaA (1998) Model-based control of strip temperature for the heating furnace in continuous annealing. IEEE Transactions on Control Systems Technology6(2): 146–156.
27.
YuSBöhmCChenHet al. (2012) Model predictive control of constrained LPV systems. International Journal of Control85(6): 671–683.
