Int. J. of Computers, Communications & Control, ISSN 1841-9836, E-ISSN 1841-9844
Vol. VI (2011), No. 3 (September), pp. 387-402

Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of
Nonlinear System considering Communication Time Delays on

Peripheral Elements

H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

Hector Benítez-Pérez, F. Cárdenas-Flores, Fabian García-Nocetti
Universidad Nacional Autónoma de México
Departamento de Ingeniería de Sistemas Computacionales y Automatización
Apdo. Postal 20-726., Admón. No. 20
Del. A. Obregón, México D. F., CP. 01000, México.
E-mail: hector@uxdea4.iimas.unam.mx

Abstract: Nowadays the study of faults and their consequences becomes an
issue into highly safety critical computer network systems. How to bound the
effects of a fault and how to tackle them into a dynamic system is still an open
field. In here an approach to tackle this problem is presented. The use of
Takagi-Sugeno fuzzy logic structure is given in order to accomplish two chal-
lenges, the presence of local faults and the respective time delays within a real-
time distributed system. This approach is pursued as reconfigurable strategy
according to communication time delays within a real-time distributed system.
This approach is pursued as reconfigurable strategy according to communica-
tion delays.
Keywords: fuzzy logic, network control.

1 Introduction

The emergence of smart sensor and actuator technology removes the need for centralized con-
trol with feedback loops to dumb peripheral actuators replacing it with a databus connection [1].
This gives an autonomous actuator installation [2] as well as local control, self-calibration, health
monitoring and reconfiguration availabilities. Several strategies for managing time delay within
control laws have been studied for different research groups. For instance [3] proposes the use
of a time delay scheme integrated to a reconfigurable control strategy based upon a stochastic
methodology. On the other hand, [4] proposes a reconfiguration strategy based upon a perfor-
mance measure from a parameter estimation fault diagnosis procedure. Another strategy has
been proposed by [5] where time delays are used as uncertainties, which modify pole placement
of a robust control law. In [6] presents an interesting view of fault tolerant control approach
related to time delay coupling. Reconfigurable control has been studied from the point of view of
structural modification since fault appearance as presented by [7] it performs a combined modi-
fication of system structure and dynamical systems as studied by [8–10]. Present approach takes
time delays due to communication as deterministic measured variables. As well as actuator fault
presence by modification of B matrix in order to propose a Takagi-Sugeno fuzzy control with two
conditions loose of local peripheral elements and the related time delays. In here fuzzy logic con-
trol (FLC) law [11] views time delays as a result of deterministic reconfigurable communications
based upon scheduling algorithm. These time delays are a structural consequence determined by
the insertion of new elements within communication channels due to fault appearance. In fact,
fault presence is taken into account as the lost of the related peripheral element, specifically,
sensor or actuator elements. The result of fault effects over the peripheral element is the lost
of the related measurement, in this case, the structure of the plant is modified in terms of the
lost of specific peripheral elements. As an obvious consequence control structure is modified.

Copyright c⃝ 2006-2011 by CCC Publications



388 H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

Fuzzy logic control engulf both undesirable situations by defining the time delays during fault
appearance as well as the related lost of the faulty peripheral element. The goal of this paper
is to define a strategy for control reconfiguration based upon communication system reconfigu-
ration. Some considerations need to be stated in order to define this approach. First, faults are
strictly local in peripheral elements, faults are tackled by just eliminating the faulty element. In
fact, faults are catastrophic and local. Time delays are bounded and restrictive to scheduling
algorithms. Global stability can be reached using Takagi-Sugeno fuzzy logic approach. Fuzzy
logic has been a very powerfull tool to systematic modelling an design complex nolinear systems
as presented by Zadeh in [23–26].

This paper is placed as a strategy for reconfigurable systems as shown in Figure 1. In fact,
this paper is focused into reconfigurable control law due to the presence of local faults and
time delays as consequences. Time delays are measurable and bounded according a real-time
scheduling algorithm. In this case scheduling algorithm is the well known earliest deadline first
algorithm (EDF). According to Figure 1, structural reconfiguration takes place as result of EDF
performance and related user request. This action provokes control law modification. How this
is modified is the scope of this paper by using Takagi-Sugeno approach.

Second Reconfiguration State

Reconfiguration
Request Plan

Valid Plan
Database

Bus Controller
Node

Computer Network
(Sensor Network)

Cotrol Law
Database

Selection of the
Related Control

Law

Control Law
Node

Control Law is chosen )
(If the plan is valid, the 

Validation Plan
NOYES

First Reconfiguration Stage

Figure 1: General structure of Reconfigurable System over a Computer Network

The map of this paper is next, first section is current introduction, second section is scheduling
approach, third section is plant design, fourth section is control approach fifth section presents
a case study and finally some concluding remarks are given.

2 Scheduling aproach

The communication network plays a key role in order to define the behaviour of the dynamic
system in terms of time variance from communications and processing although it presents a
nonlinear behaviour. In order to understand such a nonlinear behaviour, time delays are incor-
porated by the use of real-time system theory that allows time delays to be bounded even in the
case of causal modifications due to external effects. Several algorithms can be pursued such as



Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of Nonlinear System considering
Communication Time Delays on Peripheral Elements 389

Rate Monotonic (RM), Deadline Monotonic or Earliest Deadline First (EDF) [15–17]. The use
of last algorithm is pursued in here due to flexibility of task reorganisation during online per-
formance. requires several characteristics from each task such as deadlines, consumption times
and priorities. For instance, consider three tasks with next characteristics (Table 1 and Figure
2) first section under EDF algorithm if a task changes its deadline at ∆t it would have a higher
priority than those tasks already defined (Table 2).

Table 1: Task used to exemplified EDF algorithm.

Task Consumption Periodic Deadline Priority
number Time (C) Time (P) (D)

1 C1 P1 D1 Pr2
2 C2 P2 D2 Pr3
3 C3 P3 D3 Pr1

From Figure 2 there are two scenarios, in the first task 3 has the smallest slack time (ts3)
therefore it has the highest priority Pr1 , thereafter, task 1 has next priority (Pr2 ) and task 2 has
the lowest priority Pr3 (Table 1).

3

2

1
ts1

ts2

ts3C3

t′s1C
′
1

t′s2

t′s3C
′
3

P1

P3

P2

C1

C2 C
′
2

tasks

∆t time

P ′2

P ′3

P ′1

Figure 2: Time Graph Related to Table 1.

Second scenario presents a different priority conformation according to slack times modifica-
tions. Thats it for the case of deadline modification as display in Figure 2 priorities are modified
as shown in Table 2 where task 2 has the smallest slack time (ts2) therefore it has the highest
priority Pr1 , task 3 has next priority and the task 1 has the lowest priority Pr3 . Therefore the
task that is going to be executed first is the one who has the shortest deadline in comparison
to the rest of alive tasks in a particular time. Since this algorithm is performed, two conditions
are stated upon this approach. Control law must be executed after all sensors have performed
their task and before any actuator takes an action over the plant, from these restriction system
performance has two main scenarios fault present and fault free situations. These scenarios are



390 H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

Table 2: New priority order after at reorganisation.

Task Consumption Periodic Deadline Priority
number Time (C) Time (P) (D)

1 C1 P ′1 D
′
1 Pr3

2 C2 P ′2 D
′
2 Pr1

3 C3 P ′3 D
′
3 Pr2

exposed in Figure 3, it shows a common configuration considering local time delays.

Sensors

time

τa

τs

τc

Control

Actuators

τcomc−a

τcoms−c

Figure 3: Related time delays from control configuration.

Related time delays are defined in terms of scheduling algorithm behaviour. Therefore time
delays are stated as:

delay sensor to controller τsc = τs + τcons−c

delay of the controller τc

delay controller actuator τca = τa + τcomc−a

where τcoms−c and τcomc−a are the source of variations due to communication variation between
elements.

3 Plant Approach

The proposed dynamic plant is based upon the following structure:

x(k + 1) = apx(k) + Bpu(k)

y = cpx(k),
(1)



Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of Nonlinear System considering
Communication Time Delays on Peripheral Elements 391

where ap ∈ ℜn×n, cp ∈ ℜn×1 and Bp ∈ ℜn×1 are matrices related to the plant. x(k), u(k) and
y(k) are the states, inputs and outputs respectively. Specially Bp is stated as:

Bp =
N∑
i=1

ρiBi

M∑
j=1

∫ τij−1
τij

e−a
p(t−τ)dτ, (2)

where ρi ∈ {0,1} and
∑N

i=1 ρi = 1 taking into account that N are the total number of possible
faults and M are the involved time delays from each fault. Current communication time delays
are expressed as tij−1 and t

i
j. Considering that

∑M
j=1 τ

i
j ≤ T , where T is the sampling period and

depends of the faults scenarios, then Bi is integrated as:

Bi =



b1

b2

0i
...


 →, i fault element,

where bi → bn are the elements conformed at the input of the plant (such as actuators) and 0i
is the lost element due to local fault where Bp represents only one scenario following Equation
2. Therefore Bpi defined as:

B
p
i = Bi

M∑
j=1

∫ tij−1
tij

ea
p(t−τ)dτ, (3)

considers local faults and related time delays. For simplicity purposes Bpi is used in order to
depict local linear plants.

From this representation fuzzy plant is defined as follows, taking into each time delay and
fault cases:

r1 IF x1 is A1i and x2 is A2i and . . . and xℓ is Aℓi THEN a
p
i x(k) + B

p
i u(k), (4)

where x1 . . .xℓ are current state measures, ℓ is the number of states, i = 1, . . . ,N is one of the
fuzzy rules, N is the number of the rules which is equal to the number of possible faults and Aij
are the related membership functions which are gaussians defined as:

Aij(xi) = exp

(
−
(xi − cij)2

σ2ij

)
(5)

where cij and σij are constants to be tuned. Then it can be write hi as follows:

hi =
ℓ
Π
j=1

Aij(xj) (6)

The final representation of plant as integrated system is based upon center of area defuzzifi-
cation is expressed as:

xp(k + 1) =

∑N
i=1 hi(a

p
i x(k) + B

p
i u(k))∑N

i=1 hi
(7)

It is important to remember Equation 2 in order to pursue system response. From this rep-
resentation of a global nonlinear system, the integration of several linear systems, it is necessary
to define global stability as a result of this fuzzy system. This review is given in following section
considering fuzzy logic control approach. The result of this system representation allows the
integration of nonlinear stages and transitions to basically a group of linear plants.



392 H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

Fuzzy Logic Actuators
Foults-

u yref +

Control Plants

Figure 4: Plant Configuration using Fuzzy Logic Control.

4 Control Approach

From the representation of the plant as fuzzy system [18] it is considered to develop the
control law as a group of bounded local linear control laws related to each local linear system.
The structure of each fuzzy rule is:

r1 IF x1 is Ac1i and x2 is A
c
2i and . . . and xℓ is A

c
ℓi THEN u(k) = −gix(k), (8)

where i = 1, . . . ,N, N is the number of fuzzy rules which is the number of faults to be represented,
x1, . . . ,xℓ are current states of the plant, Acij are the gaussians members functions like:

Acij = exp

(
−
(xi − ccij)

2

(σcij)
2

)
(9)

where ccij and σ
c
ij are constants to be tuned. Furthermore gj represents the related control gain.

Similar to fuzzy system plant, fuzzy control representation is integrated as:

wi =
ℓ
Π
j=1

Acij(xj) (10)

and

u(k) =

∑N
j=1 wi(gix(k))∑N

i=1 wi
(11)

The configuration of FLC is integrated to the already explored plant where final representation
is given as closed loop system of linear feedback plant as shown in Figure 4.

x(k + 1) =

∑N
i=1,j=1 hiwj((ai − cigjB

p
i )x(k) + B

p
i gjref)∑N

i=1,j=1 hiwj

y = ciui = cigjBj

(12)

where ref is the reference to be followed by controller and the variables i and j are used due to
fuzzy rules interconnections as the representation of different linear plants and theirs controllers.
From this representation stability needs to be stated as the following Lyapunov function:

V (x(k)) = xT (k)Px(k) (13)

and
∆V (x(k)) = v(x(k + 1)) − v(x(k)), (14)



Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of Nonlinear System considering
Communication Time Delays on Peripheral Elements 393

where

V (k + 1) = x(k + 1)T Px(k + 1)

=

(∑N
i=1,j=1 hiwj((ai − cigjB

p
j )x(k + 1) + B

p
j gjref)∑N

i=1,j=1 hiwj

)T
P

(∑N
i=1,j=1 hiwj((aicigjB

p
j )x(k + 1) + B

p
j gjref)∑N

i=1,j=1 hiwj

)
.

(15)

Therefore

∆V (x(k)) =

(∑N
i=1,j=1 hiwj((ai − cigjB

p
j )x(k + 1) + B

p
j gjref)∑N

i=1,j=1 hiwj

)T
P

(∑N
i=1,j=1 hiwj((aicigjB

p
j )x(k + 1) + B

p
j gjref)∑N

i=1,j=1 hiwj

)
− XT PX,

(16)

and

∆V (x(k)) =

∑N
i=1,j=1



(hiwj)

2xT




− (aTi PcigjB
P
j ) + a

T
i P(B

P
j giref)−

(cigjB
P
j )

T Pai−
(cigjB

P
j )P(B

P
j gjref)+

(giB
P
j ref)

T Pai−
(gjB

P
j ref)

T P(cigjB
P
j )+

aTi Pai + (cigjB
P
j )P(cigjB

P
j )+

BPj gjrefP(gjB
P
j ref)



x − xPx




∑N
i=1,j=1(hiwj)

2
,

(17)
then by considering ref=0

∆V (x(k)) =

∑N
i=1,j=1

(
(hiwj)

2xT

[
− (aTi PcigjB

P
j ) − (cigjB

p
j )

T ai

+ aTi Pai + (cigjB
P
j )P(cigjB

P
j )

]
x − xPx

)
∑N

i=1,j=1(hiwj)
2

. (18)

It is important to remember that:

∆V (x(k)) ≤ 0, (19)

and [
− (aTi PcigjB

P
j ) − (cigjB

p
j )

T ai

+ aTi Pai + (cigjB
P
j )P(cigjB

P
j )

]
< 0, (20)

where P > 0, || • || is the Euclidean norm and it is possible to define:

gj > ||BPj ||. (21)
This condition has to be given for every single time delay and local fault appearance. Fur-

thermore the stability and the convergence of states should be assured by the adequate selection
of matrices gi (Equation 8) and the related parameters from both fuzzy systems. In this case rec-
ommendable procedure to follow is multi-objective optimisation in order to define those suitable
values.



394 H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

I1 I2 I3
q13

q1

q20

q2
Section A

Section A2

q32

Figure 5: Three tanks representation.

I1 I2 I3
q13 q32

q1

q20

Section A
q2

Sensor Sensor Sensor

Actuator Actuator

Controller

Figure 6: Three Tanks Representation based upon Computer Network.

5 Case of Study

Case study is based upon three tanks approach following Figure 5. This is composed by three
tanks with identical cross section A. The tanks are coupled by two pipes with cross section of A2.
Two pumps are driven by DC motors who supply two inflows q1 and q2. Liquid level in each tank
is measured and reported as I1, I2 and I3. The computer network integration is shown in Figure
6. This system has a sampling period of 80 ms and nominal communication time delay of 20
ms. Common representation of this system is stated in Eq. 22 as state space representation [19].
This representation takes into account the inherent non-linearities of the model represented as:

x(k + 1) =




−
ql3
A
q32x − q20x

A
ql3x − q32x

A


 +




1
A

0

0 1
A

0 0


U, (22)

where x = [l1 l2 l3]T , y = [l1 l2]T and u = [q1 q2]T and

qij = µijA ∗ signum(li − lj)
√

2g|li − lj|

q20 = µ20A
√

2gl2.
(23)



Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of Nonlinear System considering
Communication Time Delays on Peripheral Elements 395

Here µij are the outflow coefficients. In terms of fuzzy representation, three rules are given due
the possible number of faults which are two due to just two actuators are available.

ri IF x1 is AC11 and x2 is X
c
21 and x3 is A

c
31 THEN a

p
1x(k) + B

p
1u(k),

r2 IF x1 is Ac12 and x2 is A
c
22 and x3 is A

c
32 THEN a

p
2x(k) + B

p
2u(k),

r3 IF x1 is Ac13 and x2 is A
c
23 and x3 is A

c
33 THEN a

p
3x(k) + B

p
3u(k),

In this case Bp1, B
p
2 and B

p
3 are defined as:

B
p
1 = B1

(∫ 0.03
0.0

e−a
p
1(t−τ)dτ +

∫ 0.08
0.03

e−a
p
1(t−τ)dτ

)
,

B
p
2 = B2

(∫ 0.04
0.0

e−a
p
2(t−τ)dτ +

∫ 0.08
0.04

e−a
p
2(t−τ)dτ

)
,

B
p
3 = B3

(∫ 0.05
0.0

e−a
p
3(t−τ)dτ +

∫ 0.08
0.05

e−a
p
3(t−τ)dτ

)
.

(24)

These three plant representations are modified just as B matrix where the reconfiguration is
performed. In here two integrals are presented due to important time delays of related faults.
For instance, Bp2 has a time delay of 0.04 and B

p
3 has a time delay of 0.05 seconds. In the same

way control laws are represented, where three control laws are presented.

ri IF x1 is AC11 and x2 is X
c
21 and x3 is A

c
31 THEN u(k) = −g1x(k),

r2 IF x1 is Ac12 and x2 is A
c
22 and x3 is A

c
32 THEN u(k) = −g2x(k),

r3 IF x1 is Ac13 and x2 is A
c
23 and x3 is A

c
33 THEN u(k) = −g3x(k).

Based upon this equation, final closed loop equation is:

x(k + 1) =

∑3
i=1,j=1 hiwj((ai − cigjB

k
j )x(k) + B

k
j gjref)∑3

i=1,j=1 hiwj
. (25)

Since this representation is given and based upon stability proposal in last section, optimi-
sation toolbox from MATLAB [20] is used to define current values of g matrices.

6 Implementing Approach

Following the review of case study, this is implemented over a computer network simulation
[8,21,22] based upon True-Time strategy. This simulation consists of a CSMA/CA CAN network
integrated over ten nodes, where the typical time diagram is presented in Figure 7.

Inconsistencies appear during communication and consumption times as well as the jitter
play an important role.

Table 3 shows the consumptions, periods and variations of the involved nodes where sensors
and actuators are organised according to EDF algorithm. Moreover, Table 4 shows the related
time delays according to Figure 6. Based upon these conditions, scheduling modifications are
performed. This scheduling modification affects performance response of peripheral elements
where Bpi (Equation 3) and cij (Equation 5) matrices are altered as where time delays are
defined as follows (Table 5):



396 H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

tps1

S1 S1

S2

S3 S3

tps3

C

tcs1

tcs2

C

A1

tps2

S2

Cs2

Cs1

Cs3

Cc

A2

CA1

tcca1

CA2

time

tcs3

tcpp

tcca2

Figure 7: Time Diagram Representation based upon Computer Network.

Table 3: Consumption times and periods from tasks. (in seconds)

Component Consumption Variation Time Variation
time % deadlines %

S1 Cs1 = 0.03 6-8 0.08 2-3
S2 Cs2 = 0.03 6-8 0.08 2-3
S3 Cs3 = 0.03 6-8 0.08 2-3
C Cc = 0.05 7-9 0.08 2-3
A1 CA1 = 0.045 5-7 0.08 2-3
A2 CA2 = 0.045 5-7 0.08 2-3



Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of Nonlinear System considering
Communication Time Delays on Peripheral Elements 397

Table 4: Communication Times needed (in seconds)

Communication Spent
time time
tcs1 0.02
tcs2 0.02
tcs3 0.02
tcca1 0.02
tcca2 0.02
jitter 0.015

τ11 = 0,τ
1
2 = tcca1 + jitter + variation, and τ

1
3 = 0.08

τ21 = 0,τ
2
2 = tcca2 + jitter + variation, and τ

2
3 = 0.08

Therefore control reconfiguration becomes necessary in order to keep certain response level.
For this case study three different control laws are proposed as shown in Table 6. The type of
membership functions are gaussians normally distributed over the rank of each state as shown in
Figure 8. In the case that any state is gone further its effected are reduced through the related
control law.

Minimum
Allowed
Value

Maximum
Allowed
Value

State
Variable

A11 A21 A31

Figure 8: State Variable.

Table 5: Fuzzy logic rules considering the related plant.

Rule Linearised Plant
if x1 is A11 and x2 is A12 and x3 and A13 x(k + 1) = a

p
1x(k) + B

p
1u

if x1 is A21 and x2 is A22 and x3 and A23 x(k + 1) = a
p
2x(k) + B

p
2u

if x1 is A31 and x2 is A32 and x3 and A33 x(k + 1) = a
p
3x(k) + B

p
3u



398 H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

Table 6: Fuzzy logic rules considering the related control law.

Rule Control Law
if x1 is A11 and x2 is A12 and x3 and A13 U = g1X
if x1 is A21 and x2 is A22 and x3 and A23 U = g2X
if x1 is A31 and x2 is A32 and x3 and A33 U = g3X

7 Results

Following the response of the case study, some interesting results are given related to three
different scenarios named reconfiguration (stages) 1, 2 and 3 (Figure 9a), where each stage is
20 ms long. And for each of the those cases three different responses like: dynamic response,
consumption and communication times are given. The response shown, corresponds to three
tanks performance during three different dynamic conditions with respect to communication time
behaviour. The local response presented in the third scenario is performed due to modification
of the response and dynamic conditions with respect to communication time delays. Figure
10) presents communication system response of each element involved on the system. In this
case, periodic activation per task and node is presented. Where free time needs to be reorder
to be more efficient. Figure 10a) presents periodic time modification when reconfiguration was
necessary and second graphic presents time used to communicate elements through the network.
For instance, at first 20 seconds every period of activated task are relatively similar. From 20-40
seconds those modified periodic tasks change the relatively. Similar situation is presented from
40-60 seconds. The reader may realize that some tasks reduce their periodic consumption times
while others tends to spend more time.

8 Concluding Remarks

As has been shown in this work, fuzzy logic control based upon Takagi-Sugeno structure
allows the possibility of control reconfiguration as long as linear models based representation
of the plant are available. Despite of local faults and bounded time delays appearance, several
conditions should be fulfil in order to be able to follow this proposal, for instance, plant should
be observable and controllable during the whole nonlinear behaviour as well as the states should
be present during undesirable situations. Several approaches can be pursued such as robustness
study during variations from one to another scenarios as well as further work is needed when not
every state is available during fault conditions which is a realistic condition. In this case observer
design under fault scenario need to be defined looking for smooth transitions between fault and
fault free status. Stability conditions are reached as long as system design is pursued by Equations
15-19, where fuzzy logic variables and local control laws are established. Following future work,
a non-desirable drawback is related to a peripheral element fault without any propagation to the
rest of the system. This can be possible by just considering some specific scenarios during fault
propagation from local to general catastrophic faults.

Acknowledgements

The authors would like to thank the financial support of DISCA-IIMAS-UNAM, and UNAM-
PAPIIT (IN106100, IN103310 and IN101307), ICyTDF PICCO10-53 México in connection with
this work.



Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of Nonlinear System considering
Communication Time Delays on Peripheral Elements 399

0 10 20 30 40 50 60 70
−0.5

0

0.5

1

1.5

2
a) Error

Time
0 10 20 30 40 50 60

−1

0

1

Time

b) Current States response

 

 

State 1
State 2
State 3

0 10 20 30 40 50 60
−0.5

0

0.5

1

1.5

Time

c) Current Control response

0 10 20 30 40 50 60

−1

0

1

2

Time

d) Current Values to Plant

 

 

Value 1
Value 2

0 10 20 30 40 50 60
0

0.2

0.4

0.6

0.8

Time

e) Periodical Time Modifications

0 10 20 30 40 50 60
0

5

10

Time

f) Communication Network Response

Figure 9: Dynamic Response of Case Study Following Three Scenarios.



400 H. Benítez-Pérez, F. Cárdenas-Flores, F. García-Nocetti

0 10 20 30 40 50 60 70 80 90
−0.5

0

0.5

1

1.5

a) Error

Time
0 10 20 30 40 50 60 70 80 90

−1

0

1

2

Time

b) Current States response

 

 
State 1
State 2
State 3

0 10 20 30 40 50 60 70 80 90
−0.5

0

0.5

1

1.5

Time

c) Current Control response

0 10 20 30 40 50 60 70 80 90

−1

0

1

2

Time

d) Current Values to Plant

 

 

Value 1
Value 2

0 10 20 30 40 50 60 70 80 90
−0.2

0

0.2

0.4

0.6

0.8

Time

e) Periodical Time Modifications

0 10 20 30 40 50 60 70 80 90
0

5

10

Time

f) Communication Network Response

Figure 10: Dynamic Response of Case Study Following Three Scenarios considering periodic
communication.



Reconfigurable Takagi-Sugeno Fuzzy Logic Control for a Class of Nonlinear System considering
Communication Time Delays on Peripheral Elements 401

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