This paper presents a new multimodel controller design approach incorporating stability and performance criteria. The gap metric is employed to measure the distance between local models. An efficient method based on state feedback strategy is introduced to improve the maximum stability margin of the local models. The proposed method avoids local model redundancy, simplifies the multimodel controller structure, and supports employing of many linear control techniques, while does not rely on a priori experience to choose the gridding threshold value. To evaluate the proposed method, three benchmark nonlinear systems are studied. Simulation results demonstrate that the method provides the closed-loop stability and performance via a simple multimodel structure in comparison with the opponents.

References

1.
Hosseini
,
S.
,
Fatehi
,
A.
,
Johansen
,
T. A.
, and
Sedigh
,
A. K.
,
2012
, “
Multiple Model Bank Selection Based on Nonlinearity Measure and H-Gap Metric
,”
J. Process Control
,
22
(
9
), pp.
1732
1742
.
2.
Kargar
,
S. M.
,
Salahshoor
,
K.
, and
Yazdanpanah
,
M. J.
,
2014
, “
Integrated Nonlinear Model Predictive Fault Tolerant Control and Multiple Model Based Fault Detection and Diagnosis
,”
Chem. Eng. Res. Des.
,
92
(
2
), pp.
340
349
.
3.
Liu
,
J.
,
Djurdjanovic
,
D.
,
Marko
,
K.
, and
Ni
,
J.
,
2009
, “
Growing Structure Multiple Model Systems for Anomaly Detection and Fault Diagnosis
,”
ASME J. Dyn. Syst. Meas. Control
,
131
(
5
), p.
051001
.
4.
Murray-Smith
,
R.
, and
Johansen
,
T.
,
1997
,
Multiple Model Approaches to Nonlinear Modelling and Control
,
Taylor & Francis
, London.
5.
Song
,
C.
,
Wu
,
B.
,
Zhao
,
J.
, and
Li
,
P.
,
2015
, “
An Integrated State Space Partition and Optimal Control Method of Multi-Model for Nonlinear Systems Based on Hybrid Systems
,”
J. Process Control
,
25
, pp.
59
69
.
6.
Zribi
,
A.
,
Chtourou
,
M.
, and
Djemal
,
M.
,
2016
, “
A Systematic Determination Approach of Model's Base Using Gap Metric for Nonlinear Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
138
(
3
), p.
031008
.
7.
Arslan
,
E.
,
Çamurdan
,
M. C.
,
Palazoglu
,
A.
, and
Arkun
,
Y.
,
2004
, “
Multimodel Scheduling Control of Nonlinear Systems Using Gap Metric
,”
Ind. Eng. Chem. Res.
,
43
(
26
), pp.
8275
8283
.
8.
Toscano
,
R.
, and
Lyonnet
,
P.
,
2009
, “
Robust PID Controller Tuning Based on the Heuristic Kalman Algorithm
,”
Automatica
,
45
(
9
), pp.
2099
2106
.
9.
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
.
10.
Martin
,
P. A.
,
Odloak
,
D.
, and
Kassab
,
F.
,
2013
, “
Robust Model Predictive Control of a Pilot Plant Distillation Column
,”
Control Eng. Pract.
,
21
(
3
), pp.
231
241
.
11.
Yang
,
Z.
,
Li
,
Y.
, and
Seem
,
J. E.
,
2015
, “
Multi-Model Predictive Control for Wind Turbine Operation Under Meandering Wake of Upstream Turbines
,”
Control Eng. Pract.
,
45
, pp.
37
45
.
12.
Du
,
J.
, and
Johansen
,
T. A.
,
2014
, “
Integrated Multimodel Control of Nonlinear Systems Based on Gap Metric and Stability Margin
,”
Ind. Eng. Chem. Res.
,
53
(
24
), pp.
10206
10215
.
13.
Du
,
J.
,
Song
,
C.
, and
Li
,
P.
,
2012
, “
Multimodel Control of Nonlinear Systems: An Integrated Design Procedure Based on Gap Metric and H∞ Loop Shaping
,”
Ind. Eng. Chem. Res.
,
51
(
9
), pp.
3722
3731
.
14.
Galán
,
O.
,
Romagnoli
,
J. A.
,
Palazočlu
,
A.
, and
Arkun
,
Y.
,
2003
, “
Gap Metric Concept and Implications for Multilinear Model-Based Controller Design
,”
Ind. Eng. Chem. Res
,
42
(
10
), pp.
2189
2197
.
15.
Haj Salah
,
A. A.
,
Garna
,
T.
,
Ragot
,
J.
, and
Messaoud
,
H.
,
2016
, “
Transition and Control of Nonlinear Systems by Combining the Loop Shaping Design Procedure and the Gap Metric Theory
,”
Trans. Inst. Meas. Control
,
38
(
8
), pp.
1004
1020
.
16.
Haj Salah
,
A. A.
,
Garna
,
T.
,
Ragot
,
J.
, and
Messaoud
,
H.
,
2016
, “
Synthesis of a Robust Controller With Reduced Dimension by the Loop Shaping Design Procedure and Decomposition Based on Laguerre Functions
,”
Trans. Inst. Meas. Control
,
38
(
10
), pp.
1236
1260
.
17.
Zhang
,
R.
,
Alleyne
,
A. G.
, and
Carter
,
D. E.
,
2005
, “
Generalized Multivariable Gain Scheduling With Robust Stability Analysis
,”
ASME J. Dyn. Syst. Meas. Control
,
127
(
4
), pp.
668
687
.
18.
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
.
19.
Tao
,
X.
,
Li
,
D.
,
Wang
,
Y.
,
Li
,
N.
, and
Li
,
S.
,
2015
, “
Gap Metric Based Multiple-Model Predictive Control With Polyhedral Stability Region
,”
Ind. Eng. Chem. Res.
,
54
(
45
), pp.
11319
11329
.
20.
Du
,
J.
,
Song
,
C.
, and
Li
,
P.
,
2009
, “
Multilinear Model Control of Hammerstein-like Systems Based on an Included Angle Dividing Method and the MLD-MPC Strategy
,”
Ind. Eng. Chem. Res.
,
48
(
8
), pp.
3934
3943
.
21.
Jalali
,
A. A.
, and
Golmohammad
,
H.
,
2012
, “
An Optimal Multiple-Model Strategy to Design a Controller for Nonlinear Processes: A Boiler-Turbine Unit
,”
Comput. Chem. Eng.
,
46
, pp.
48
58
.
22.
Mahdianfar
,
S. O. H.
, and
Momeni
,
H. R.
,
2011
, “
Robust Multiple Model Adaptive Control: Modified Using v-Gap Metric
,”
Int. J. Robust Nonlinear Control
,
21
(
18
), pp.
2027
2063
.
23.
Shaghaghi
,
D.
,
Fatehi
,
A.
, and
Khaki-Sedigh
,
A.
,
2017
, “
Multi-Linear Model Set Design Based on the Nonlinearity Measure and H-Gap Metric
,”
ISA Trans.
,
68
, pp.
1
13
.
24.
Zribi
,
A.
,
Chtourou
,
M.
, and
Djemel
,
M.
,
2017
, “
Multiple Model Reduction Approach Using Gap Metric and Stability Margin for Control Nonlinear Systems
,”
Int. J. Control, Autom. Syst.
,
15
(
1
), pp.
267
273
.
25.
Tan
,
W.
,
Marquez
,
H. J.
,
Chen
,
T.
, and
Liu
,
J.
,
2004
, “
Multimodel Analysis and Controller Design for Nonlinear Processes
,”
Comput. Chem. Eng.
,
28
(
12
), pp.
2667
2675
.
26.
Wang
,
F. Y.
,
Bahri
,
P.
,
Lee
,
P. L.
, and
Cameron
,
I. T.
,
2007
, “
A Multiple Model, State Feedback Strategy for Robust Control of Non-Linear Processes
,”
Comput. Chem. Eng.
,
31
(
5–6
), pp.
410
418
.
27.
Du
,
J.
, and
Johansen
,
T. A.
,
2017
, “
Control-Relevant Nonlinearity Measure and Integrated Multi-Model Control
,”
J. Process Control
,
57
, pp.
127
139
.
28.
Du
,
J.
, and
Johansen
,
T. A.
,
2015
, “
Integrated Multilinear Model Predictive Control of Nonlinear Systems Based on Gap Metric
,”
Ind. Eng. Chem. Res.
,
54
(
22
), pp.
6002
6011
.
29.
Ahmadi
,
M.
, and
Haeri
,
M.
,
2017
, “
A New Structured Multimodel Control of Nonlinear Systems by Integrating Stability Margin and Performance
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
9
), p.
091014
.
30.
Du
,
J.
, and
Johansen
,
T. A.
,
2014
, “
A Gap Metric Based Weighting Method for Multimodel Predictive Control of MIMO Nonlinear Systems
,”
J. Process Control
,
24
(
9
), pp.
1346
1357
.
31.
El-Sakkary
,
A.
,
1985
, “
The Gap Metric: Robustness of Stabilization of Feedback Systems
,”
IEEE Trans. Autom. Control
,
30
(
3
), pp.
240
247
.
32.
Zhou
,
K.
, and
Doyle
,
J. C.
,
1998
,
Essentials of Robust Control
,
Prentice Hall
, Upper Saddle River, NJ.
33.
Hajjaji
,
A. E.
, and
Ouladsine
,
M.
,
2001
, “
Modeling and Nonlinear Control of Magnetic Levitation Systems
,”
IEEE Trans. Ind. Electron.
,
48
(
4
), pp.
831
838
.
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