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.

References

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.
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