An improved constrained model predictive control approach for Hammerstein-Wiener nonlinear systems

Abstract

Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.

Keywords

Hammerstein-Wiener nonlinear systems / model predictive control / parameter-dependent Lyapunov functions / stability / linear matrix inequalities (LMIs)

References

[1] WangD, DingF. Hierarchical least squares estimation algorithm for Hammerstein-Wiener systems [J]. IEEE Signal Processing Letters, 2012, 19(12): 825-827

[2] TervoK, ManninenA. Analysis of model orders in human dynamics identification using linear polynomial and Hammerstein-Wiener structures [C]. 2010 International Conference on Networking, Sensing and Control (ICNSC), 2010614-620

[3] WangD, DingF. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems [J]. Computers & Mathematics with Applications, 2008, 56(12): 3157-3164

[4] WillsA, NinnessB. Estimation of generalised Hammerstein-Wiener systems [C]. Proceedings of the 15th IFAC Symposium on System Identification (SYSID 2009), 20091104-1109

[5] PatcharaprakitiN, KirtikaraK, MonyakulV, ChenvidhyaD, ThongpronJ, SangswangA, MuenpinijB. Modeling of single phase inverter of photovoltaic system using Hammerstein-Wiener nonlinear system identification [J]. Current Applied Physics, 2010, 10(3): 532-536

[6] SungS W, JeC H, LeeJ, LeeD H. Improved system identification method for Hammerstein-Wiener processes [J]. Korean Journal of Chemical Engineering, 2008, 25(4): 631-636

[7] PatikirikoralaT, WangL, ColmanA, HanJ. Hammerstein-Wiener nonlinear model based predictive control for relative QoS performance and resource management of software systems [J]. Control Engineering Practice, 2012, 20(1): 49-61

[8] SentoniG, AgamennoniO, DesagesA, RomagnoliJ. Approximate models for nonlinear process control [J]. Aiche Journal, 1996, 42(8): 2240-2250

[9] GerksicS, JuricicD, StrmcnikS, MatkoD. Wiener model based nonlinear predictive control [J]. International Journal of Systems Science, 2000, 31(2): 189-202

[10] FruzzettiK P, PalazogluA, McdonaldK A. Nonlinear model predictive control using Hammerstein models [J]. Journal of Process Control, 1997, 7(1): 31-41

[11] DingB, HuangB. Output feedback model predictive control for nonlinear systems represented by Hammerstein-Wiener model [J]. IET Control Theory and Applications, 2007, 1(5): 1302-1310

[12] BloemenH H J, van Den BoomT J J, VerbruggenH B. Model-based predictive control for Hammerstein-Wiener systems [J]. International Journal of Control, 2001, 74(5): 482-495

[13] LiY, MaoZ-z, WangY, YuanP, JiaM-xing. Model predictive control synthesis approach of electrode regulator system for electric arc furnace [J]. Journal of Iron and Steel Research, International, 2011, 18(11): 20-25

[14] YauH T. Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs [J]. Physics Letters A, 2008, 372(14): 2380-2385

[15] WangD, ChuY, YangG, DingF. Auxiliary model based recursive generalized least squares parameter estimation for Hammerstein OEAR systems [J]. Mathematical and Computer Modelling, 2010, 52(1): 309-317

[16] ZhangY-w, GuiW-hua. Compensation for secondary uncertainty in electro-hydraulic servo system by gain adaptive sliding mode variable structure control [J]. Journal of Central South University of Technology, 2008, 15(2): 256-263