This paper proposes a novel gap metric based fuzzy decomposition approach resulting in a reduced model bank that provides enough information to design controllers. It requires, first, the determination of the model base. For this, the number of initial models is obtained via fuzzy c-means (FCM) algorithm. Then, a gap metric based method which aims to get a reduced model bank is developed. Based on the linear models bank, a set of linear controllers are designed and combined into a global controller for setpoint tracking control.
Issue Section:
Research Papers
References
1.
Narendra
, K.
, and Balakrishnan
, J.
, 1997
, “Adaptive Control Using Multiple Models
,” IEEE Trans. Autom. Control
, 42
(2
), pp. 171
–187
.2.
Schorten
, R.
, MurrySmith
, R.
, Bjorgan
, R.
, and Gollee
, H.
, 1999
, “On the Interpretation of Local Models in Blended Multiple Structures
,” Int. J. Control
, 72
(7–8
), pp. 620
–628
.3.
Akar
, A.
, 2010
, “On Transient Improvement of Variable Structure Controlled Systems Using Multimodel Switching
,” ASME J. Dyn. Syst. Meas. Control
, 132
(3
), p. 034501
.4.
Galn
, O.
, Romagnoli
, J.
, Palazoglu
, A.
, and Arkun
, Y.
, 2003
, “Gap Metric Concept and Implications for Multilinear Model-Based Controller Design, Industrial
,” Ind. Eng. Chem. Res.
, 42
(10
), pp. 2189
–2197
.5.
Johansen
, T. A.
, and Foss
, B. A.
, 1993
, “Constructing NARMAX Models Using ARMAX Models
,” Int. J. Control
, 58
(5
), pp. 1125
–1153
.6.
Johansen
, T. A.
, and Foss
, B. A.
, 1995
, “Identification of Nonlinear System Structure and Parameters Using Regime Decomposition
,” Automatica
, 31
(2
), pp. 321
–326
.7.
Zribi
, A.
, Chtourou
, M.
, and Djemel
, M.
, 2011
, “Internal Multiple Models Control Based on Robust Clustering Algorithm
,” Nonlinear Dyn. Syst. Theory
, 11
(1), pp. 99
–112
.8.
Aswin
, N. V.
, and Ravindra
, D. G.
, 2002
, “A Fuzzy Segregation-Based Identification and Control of Nonlinear Dynamic Systems
,” Ind. Eng. Chem.
, 41
, pp. 538
–544
.9.
Elfelly
, N.
, Dieulot
, J.
, Benrejeb
, M.
, and Borne
, P.
, 2012
, “Multimodel Control Design Using Unsupervised Classifiers
,” Stud. Inf. Control
, 21
(1
), pp. 101
–108
.10.
Tan
, W.
, Marquez
, H.
, Chen
, T.
, and Liu
, J.
, 2004
, “Multimodel Analysis and Controller Design for Nonlinear Processes
,” Comput. Chem. Eng.
, 28
(12
), pp. 2667
–2675
.11.
Du
, J.
, Song
, C.
, and Li
, P.
, 2009
, “Application of Gap Metric to Model Bank Determination in Multilinear Model Approach
,” J. Process Control
, 19
(2
), pp. 231
–240
.12.
Du
, J.
, Song
, C.
, Yao
, Y.
, and Li
, P.
, 2013
, “Multilinear Model Decomposition of MIMO Nonlinear Systems and Its Implication for Multilinear Model-Based Control
,” J. Process Control
, 23
(3
), pp. 271
–281
.13.
Hossein
, S.
, Fatehi
, A.
, and Sedigh
, K.
, 2012
, “Multiple Model Bank Selection Based on Nonlinearity Measure and H-Gap Metric
,” J. Process Control
, 22
(9
), pp. 1732
–1742
.14.
Zribi
, A.
, Chtourou
, M.
, and Djemel
, M.
, 2012
, “Multiple Models Reduction Approach Using Gap Metric for Control of Uncertain Systems
,” Int. J. Modell., Identif. Control
, 17
(2
), p. 124.15.
Zames
, G.
, and El-Sakkary
, A.
, 1980
, “Unstable Systems and Feedback: The Gap Metric
,” Allerton Conference
, pp. 380
–385
.16.
El-Sakkary
, A.
, 1985
, “The Gap Metric: Robustness of Stabilization of Feedback Systems
,” IEEE Trans. Autom. Control
, 30
(3
), pp. 240
–247
.17.
Bezdek
, J.
, 1980
, “A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 2
(1
), pp. 1
–8
.18.
Ceylan
, R.
, and Ozbay
, Y.
, 2007
, “Comparison of FCM, PCA and WT Techniques for Classification ECG Arrhythmias Using Artificial Neural Networks
,” Expert Syst. Appl.
, 33
(2
), pp. 286
–295
.19.
Henson
, M. A.
, and Seborg
, D. E.
, 1990
, “Input-Output Linearization of General Nonlinear Processes
,” AIChE J.
, 36
(11
), pp. 1753
–1757
.20.
Doyle
, F. J.
, Kwatra
, H. S.
, and Schwaber
, J. S.
, 1998
, “Dynamic Gain Scheduled Process Control
,” Chem. Eng. Sci.
, 53
(15
), pp. 2675
–2690
.21.
Morarim
, M.
, and Zafiriou
, E.
, 1989
, Robust Process Control
, Prentice Hall, Englewood Cliffs
, NJ
.22.
Uppal
, A.
, Ray
, W.
, and Poore
, A.
, 1974
, “On the Dynamic Behavior of Continuous Stirred Tank Reactors
,” Chem. Eng. Sci.
, 29
(4
), pp. 967
–985
.23.
Panda
, R. C.
, 2009
, “Synthesis of PID Controller for Unstable and Integrating Processes
,” Chem. Eng. Sci.
, 64
(12
), pp. 2807
–2816
.24.
Koivo
, H.
, 2002
, “Fuzzy Gain Scheduling of MIMO PID Controllers for Nonlinear Multivariable Systems
,” IEEE
International Conference on Systems
, Man and Cybernetics, Yasmine Hammamet, Tunisia, Oct. 6–9, pp. 320–325.Copyright © 2016 by ASME
You do not currently have access to this content.