Quasi-sliding mode control strategy based on multiple-linear models

In this paper, a multiple discrete quasi-sliding mode (QSM) control scheme is proposed for a general class of nonlinear discrete time systems with unknown dynamical equations, provided that input-output data is available for system identification. The self-organizing map (SOM) is employed to divide the state space into local regions such that it associates the operating region where a local linear model is the winner with a local quasi-sliding mode controller (QSMC). Switching of the controllers is done synchronously with the active local linear model that tracks the different operating conditions. The simulation results show that the proposed controller outperforms tracking the desired trajectory in noisy environments either with a global controller or simpler controllers based on multiple models.

[1]  Gail D. Baura,et al.  Nonlinear System Identification , 2002 .

[2]  Frank L. Lewis,et al.  Backlash compensation with filtered prediction in discrete time nonlinear systems by dynamic inversion using neural networks , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  Yixin Diao,et al.  Intelligent fault tolerant control using adaptive schemes and multiple models , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[4]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[5]  K. R. Goheen,et al.  Discrete Time Sliding Mode Control Via Input-Output Models , 1993, 1993 American Control Conference.

[6]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[7]  A. Packard Gain scheduling via linear fractional transformations , 1994 .

[8]  Toshio Fukuda,et al.  Adaptive quasi-sliding-mode tracking control for discrete uncertain input-output systems , 2001, IEEE Trans. Ind. Electron..

[9]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[10]  Kumpati S. Narendra,et al.  Adaptive control using multiple models , 1997, IEEE Trans. Autom. Control..

[11]  Kumpati S. Narendra,et al.  Adaptation and learning using multiple models, switching, and tuning , 1995 .

[12]  Richard D. Braatz,et al.  On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.

[13]  Katsuhisa Furuta,et al.  VSS type self-tuning control , 1993, IEEE Trans. Ind. Electron..

[14]  Arno Linnemann,et al.  Decoupling of structured systems , 1981 .

[15]  Atsushi Ishigame,et al.  Sliding mode controller design based on fuzzy inference for nonlinear systems [power systems] , 1993, IEEE Trans. Ind. Electron..

[16]  Kumpati S. Narendra,et al.  Adaptive control of discrete-time systems using multiple models , 2000, IEEE Trans. Autom. Control..

[17]  B. Widrow,et al.  Neural networks for self-learning control systems , 1990, IEEE Control Systems Magazine.

[18]  Juan R. Pimentel,et al.  A Real-Time Engine Simulator Using Multiple Microcomputers , 1983, IEEE Transactions on Industrial Electronics.

[19]  A. Jafari Koshkouei,et al.  Sliding Mode Control of Discrete-Time Systems , 2000 .

[20]  T. Johansen,et al.  Constructing NARMAX models using ARMAX models , 1993 .

[21]  Frank L. Lewis,et al.  BACKLASH COMPENSATION WITH FILTERED PREDICTION IN DISCRETE TIME NONLINEAR SYSTEMS BY DYNAMIC INVERSION USING NEURAL NETWORKS , 2008 .

[22]  Daniel G. Sbarbaro-Hofer,et al.  Self-tuning Control of Non-linear Systems Using Gaussian Process Prior Models , 2003, European Summer School on Multi-AgentControl.

[23]  Manesh J. Shah Use of hierarchical systems for automation of process analyzers in computer-controlled plants , 1972 .

[24]  H. Sira-Ramírez Non-linear discrete variable structure systems in quasi-sliding mode , 1991 .

[25]  Kenneth J. Hunt,et al.  Local Model Architectures for Nonlinear Modelling and Control , 1995 .

[26]  Wilson J. Rugh,et al.  Analytical Framework for Gain Scheduling , 1990, 1990 American Control Conference.

[27]  M. V. Velzen,et al.  Self-organizing maps , 2007 .

[28]  Deniz Erdoğmuş,et al.  Adaptive Inverse Control Using SOM based Multiple Models , 2002 .

[29]  Tor Arne Johansen,et al.  Non-linear predictive control using local models-applied to a batch fermentation process , 1995 .

[30]  J. A. Romagnoli,et al.  A nonlinear control design approach based on multi-linear models , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[31]  Andrzej Bartoszewicz,et al.  Discrete-time quasi-sliding-mode control strategies , 1998, IEEE Trans. Ind. Electron..

[32]  Xiangdong He,et al.  A New Method for Identifying Orders of Input-Output Models for Nonlinear Dynamic Systems , 1993, 1993 American Control Conference.

[33]  Andrew C. Singer,et al.  Codebook prediction: a nonlinear signal modeling paradigm , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[34]  A. Ishigame,et al.  Sliding mode controller design based on fuzzy inference for non-linear systems , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[35]  Tor Arne Johansen,et al.  Nonlinear Multiple Model Predictive Control in a FED-Batch Reactor , 2000 .

[36]  K. Furuta Sliding mode control of a discrete system , 1990 .

[37]  Jeongho Cho,et al.  Multiple model based flight control design , 2002, The 2002 45th Midwest Symposium on Circuits and Systems, 2002. MWSCAS-2002..

[38]  O. Kaynak,et al.  On the stability of discrete-time sliding mode control systems , 1987 .

[39]  J. Príncipe,et al.  Local dynamic modeling with self-organizing maps and applications to nonlinear system identification and control , 1998, Proc. IEEE.

[40]  C. Y. Chan Robust discrete quasi-sliding mode tracking controller , 1995, Autom..

[41]  Jun-Ho Oh,et al.  Improvements on VSS-type self-tuning control for a tracking controller , 1998, IEEE Trans. Ind. Electron..

[42]  Kumpati S. Narendra,et al.  Intelligent control using neural networks and multiple models , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[43]  W. Rugh,et al.  Feedback linearization families for nonlinear systems , 1987 .

[44]  Jeongho Cho,et al.  Modeling and inverse controller design for an unmanned aerial vehicle based on the self-organizing map , 2006, IEEE Transactions on Neural Networks.

[45]  Peter J. Gawthrop,et al.  Local Model Networks and Self-Tuning Predictive Control , 1999 .

[46]  M. Athans,et al.  Gain Scheduling: Potential Hazards and Possible Remedies , 1992, 1991 American Control Conference.

[47]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[48]  Jörg A. Walter,et al.  Nonlinear prediction with self-organizing maps , 1990, 1990 IJCNN International Joint Conference on Neural Networks.