In this paper, an attempt is made to generalize the analytical structures of Takagi-Sugeno (TS) fuzzy two-input two-output (TITO) proportional-integral (PI)/proportional-derivative (PD) controllers using multiple input fuzzy sets. Two models of fuzzy TITO PI/PD controllers are proposed based on two distinct control strategies. The inputs are fuzzified by multiple fuzzy sets with trapezoidal/triangular membership functions. The generalized rule base consists of nine control rules imbibing the complete control strategy and is closer in spirit to the original TS rule base. Algebraic product (AP) triangular norm, bounded sum (BS) triangular conorm, and center of gravity (CoG) defuzzifier are applied to derive the models. The models of the fuzzy TITO PI/PD controllers with multiple input fuzzy sets are (nonlinear) variable gain/structure controllers. Also, each output of the fuzzy controller is the sum of two nonlinear PI/PD controllers with variable gains. The gain variation and properties of the proposed controllers are studied. Two examples of nonlinear dynamic processes are considered to demonstrate the applicability of the proposed controllers.

References

References
1.
Chien
,
I. L.
,
Hung
,
H. P.
, and
Yang
,
J. C.
,
2000
, “
A Simple TITO PI Tuning Method Suitable for Industrial Applications
,”
Chem. Eng. Commun.
,
182
(
1
), pp.
181
196
.
2.
Tavakoli
,
S.
,
Griffin
,
I.
, and
Flemming
,
P. J.
,
2006
, “
Tuning of Decentralized PI (PID) Controllers for TITO Processes
,”
Control Eng. Pract.
,
14
(
9
), pp.
1069
1080
.
3.
Mokadam
,
H. R.
,
Patre
,
B. M.
, and
Maghade
,
D. K.
,
2013
, “
Tuning of Multivariable PI/PID Controllers for TITO Processes Using Dominant Pole Placement Approach
,”
Int. J. Autom. Control
,
7
(
1/2
), pp.
21
41
.
4.
Roy
,
P.
, and
Roy
,
B. K.
,
2016
, “
Fractional Order PI Control Applied to Level Control in Coupled Two-Tank MIMO System With Experimental Validation
,”
Control Eng. Pract.
,
48
, pp.
119
135
.
5.
Zadeh
,
L. A.
,
1965
, “
Fuzzy Sets
,”
Inf. Control
,
8
(
3
), pp.
338
353
.
6.
Mamdani
,
E. H.
,
1974
, “
Application of Fuzzy Algorithms for Control of Simple Dynamic Plant
,”
Proc. Inst. Electr. Eng.
,
121
(
12
), pp.
1585
1588
.
7.
Takagi
,
T.
, and
Sugeno
,
M.
,
1985
, “
Fuzzy Identification of Systems and Its Applications to Modeling and Control
,”
IEEE Trans. Syst., Man Cybern.
,
SMC-15
(
1
), pp.
116
132
.
8.
Gupta
,
M. M.
,
Kiszka
,
J. B.
, and
Trojan
,
G. M.
,
1986
, “
Multivariable Structure of Fuzzy Control Systems
,”
IEEE Trans. Syst., Man, Cybern.
,
16
(
5
), pp.
638
656
.
9.
Xu
,
C. W.
,
1991
, “
Linguistic Decoupling Control of Fuzzy Multivariable Processes
,”
Fuzzy Sets Syst.
,
44
(
2
), pp.
209
217
.
10.
Ying
,
H.
,
1994
, “
Analytical Structure of a Two-Input Two-Output Fuzzy Controller and Its Relation to PI and Multilevel Relay Controllers
,”
Fuzzy Sets Syst.
,
63
(
1
), pp.
21
33
.
11.
Park
,
H. W.
, and
Park
,
G. T.
,
1998
, “
Design of a Robust Adaptive Fuzzy Controller Globally Stabilizing the Multi-Input Nonlinear System With State-Dependent Uncertainty
,”
Control Cybern.
,
27
(
4
), pp.
613
629
.
12.
Shaocheng
,
T.
,
Jiantao
,
T.
, and
Tao
,
W.
,
2000
, “
Fuzzy Adaptive Control of Multivariable Nonlinear Systems
,”
Fuzzy Sets Syst.
,
111
(
2
), pp.
153
167
.
13.
Zhang
,
H.
, and
Bien
,
Z.
,
2000
, “
Adaptive Fuzzy Control of MIMO Nonlinear Systems
,”
Fuzzy Sets Syst.
,
115
(
2
), pp.
191
204
.
14.
Saravanan
,
S.
, and
Kher
,
S.
,
2002
, “
Fuzzy Control of Multivariable Process by Modified Error Coupling
,”
ISA Trans.
,
41
(
4
), pp.
437
444
.
15.
Lian
,
R. J.
, and
Lin
,
B. F.
,
2005
, “
Design of a Mixed Fuzzy Controller for Multiple-Input Multiple-Output Systems
,”
Mechatronics
,
15
(
10
), pp.
1225
1252
.
16.
Lin
,
T. C.
,
Liu
,
H. L.
, and
Kuo
,
M. J.
,
2009
, “
Direct Adaptive Interval Type-2 Fuzzy Control of Multivariable Nonlinear Systems
,”
Eng. Appl. Artif. Intell.
,
22
(
3
), pp.
420
430
.
17.
Xu
,
C.
, and
Shin
,
Y. C.
,
2011
, “
A Self Tuning Fuzzy Controller for a Class of Multi-Input Multi-Output Nonlinear Systems
,”
Eng. Appl. Artif. Intell.
,
24
(
2
), pp.
238
250
.
18.
Boulkroune
,
A.
,
M'saad
,
M.
, and
Farza
,
M.
,
2012
, “
Fuzzy Approximation Based Indirect Adaptive Controller for Multi-Input Multi-Output Non-Affine Systems With Unknown Control Direction
,”
IET Control Theory Appl.
,
6
(
17
), pp.
2619
2629
.
19.
Shi
,
W.
,
Luo
,
R.
, and
Li
,
B.
,
2017
, “
Adaptive Fuzzy Prescribed Performance Control for MIMO Nonlinear Systems With Unknown Control Direction and Unknown Dead-Zone Inputs
,”
ISA Trans.
,
66
, pp.
86
95
.
20.
Ying
,
H.
,
2000
, “
TITO Mamdani Fuzzy PI/PD Controllers as Nonlinear, Variable Gain PI/PD Controllers
,”
Int. J. Fuzzy Syst.
,
2
(
3
), pp.
191
196
.
21.
Arun
,
N. K.
, and
Mohan
,
B. M.
,
2016
, “
Mathematical Modelling of the Simplest Fuzzy Two-Input Two-Output Proportional-Integral or Proportional-Derivative Controller Via Larsen Product Inference
,”
Int. J. Autom. Control
,
10
(
1
), pp.
34
51
.
22.
Alwadie
,
A.
,
Ying
,
H.
, and
Shah
,
H.
,
2003
, “
Practical Two-Input Two-Output Takagi-Sugeno Fuzzy Controller
,”
Int. J. Fuzzy Syst.
,
5
(
2
), pp.
123
130
.
23.
Raj
,
R.
, and
Mohan
,
B. M.
,
2018
, “
An Analytical Structure of the Simplest Takagi-Sugeno TITO PI/PD Controller
,”
IFAC-PapersOnline
,
51
(
1
), pp.
19
24
.
24.
Raj
,
R.
, and
Mohan
,
B. M.
,
2018
, “
Stability Analysis of General Takagi-Sugeno Fuzzy Two-Term Controllers
,”
Fuzzy Inf. Eng.
,
10
(
2
), pp.
196
212
.
25.
Johnson
,
M. A.
, and
Moradi
,
M. H.
,
2005
,
PID Control: New Identification and Design Methods
,
Springer-Verlag
,
London
.
26.
Lygouras
,
J. N.
,
Kodogiannis
,
V. S.
,
Pachidis
,
T.
,
Tarchanidis
,
K. N.
, and
Koukourlis
,
C. S.
,
2008
, “
Variable Structure TITO Fuzzy-Logic Controller Implementation for a Solar Air-Conditioning System
,”
Appl. Energy
,
85
(
4
), pp.
190
203
.
27.
Driankov
,
D.
,
Hellendoorn
,
H.
, and
Reinfrank
,
M.
,
1993
,
An Introduction to Fuzzy Control
,
Narosa Publishing House
,
New Delhi, India
.
28.
Spong
,
M. W.
, and
Vidyasagar
,
M.
,
1989
,
Robot Dynamics and Control
,
Wiley
,
New York
.
You do not currently have access to this content.