DOI: 10.3303/CET2188088 
 

 
 

 
 
 

 
 

 
 

 
 
 

 
 
 

 
 
 

 

 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

Paper Received: 16 June 2021; Revised: 3 September 2021; Accepted: 7 October 2021 
Please cite this article as: Vasičkaninová A., Bakošová M., Mészáros A., 2021, Fuzzy Control Design for Energy Efficient Heat Exchanger 
Network, Chemical Engineering Transactions, 88, 529-534  DOI:10.3303/CET2188088 

CHEMICAL ENGINEERING TRANSACTIONS

VOL. 88, 2021 

A publication of

The Italian Association
of Chemical Engineering
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš

Copyright © 2021, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-86-0; ISSN 2283-9216

Fuzzy Control Design for Energy Efficient Heat Exchanger
Network

Anna Vasičkaninová*, Monika Bakošová, Alajos Mészáros

Slovak University of Technology in Bratislava, Faculty of Chemical and Food Technology, Institute of Information
Engineering, Automation, and Mathematics, Radlinského 9, 81237 Bratislava, Slovak Republic
anna.vasickaninova@stuba.sk

Increasing energy efficiency and decreasing power consumption play a substantial role in the modern
industrial and technological world. Consequently, there are enhanced requirements on all production
processes and especially on energy intensive processes. Heat exchangers (HEs) and heat exchanger
networks (HENs) are very energy intensive processes and only their optimal operation assures efficient heat
recovery. Advanced optimization and advanced control are tools for assuring the energetic efficacy of HEs or
HENs. Between them, fuzzy logic control represents the advanced control strategy that has many applications
in industry and advantages as it can be used for control of strongly non-linear processes and processes that
are difficult to control because of asymmetric dynamics or uncertainties. The type-1 and type-2 fuzzy logic
controllers (FLCs) designed for a small heat exchanger network (HEN) are compared in this paper using
simulation results with the PI and PID controllers tuned by conventional methods. The controlled HEN was a
combination of two heat exchangers in series and one in parallel to them. The best controller was the type-2
fuzzy logic controller (FLC). This controller assured the most efficient operation of HEN measured by the
smallest coolant consumption. The coolant consumption increased exploiting the type-1 FLC by 2 %, the PI
controller by 3 %, and the PID controller by 5 %.

1. Introduction

In the modern industrial and technological world, where energy and its consumption represent the most
important global interests, the demands on the sustainability of all production processes for the next
generations are increasing. Klemeš et al. (2020) assessed recent developments in the field of improving heat 

transfer and modernizing heat exchanger networks and provided a critical analysis in terms of obtaining
practical solutions. Saranya et al. (2017) dealt with modeling and control of plate, spiral, and shell and tube
heat exchangers to achieve their more efficient control using integrated approaches. Kayabasi and Kurt (2018)
derived economic calculations of parallel, countercurrent, cross flow, and other heat exchangers based on the
relationships between efficiency and cost coefficients. Due to effectivennes and optimality, HEs are often
combined into networks. Short et al. (2015) presented a new algorithm for the synthesis of HENs. The method
combined two separate stages, namely the network topology optimization and the design stage that modeled
the individual HEs.
Fuzzy logic control is often found in applications where conventional control does not assure satisfactory
results because of non-linearity, asymmetric dynamics, and uncertainties in the controlled processes. Fuzzy
logic is based on the theory of fuzzy sets introduced by Zadeh (1965). Fuzzy PID controllers may have many
variants. Frequent versions are described by Pivoňka (2000). Shaheen et al. (2020) proposed a fuzzy 

controller for nonlinear systems with uncertainties. The controller combines the advantages of an adaptive
Takagi-Sugeno-Kang fuzzy PID controller and probability theory. The concept of the type-2 fuzzy logic was
introduced by Zadeh (1975). Mendel (2003) tried to motivate using the type-2 fuzzy sets. Tai et al. (2016)
described the methods used to calculate the type-2 FLC outputs. Zhao and Xiao (2015) proposed a new
interval type-2 fuzzy controller for the stabilization of nonlinear systems with parameter uncertainty. Begum
and Marutheeswar (2015) used the type-2 FLC for temperature control of a double pipe heat exchanger
system. Wati (2015) showed on air heater control that the type-2 fuzzy controller achieved better results

529



compared to the type-1 FLC. Mendel (2018) covered rule-based systems from type-1 through interval type-2
to general type-2 fuzzy systems. Debnath et al. (2018) used a weighted interval type-2 fuzzy inference system
for air quality assessment. Wu et al. (2019) assessed the performance of wind power coupling hydrogen
storage projects from the perspective of sustainability using the interval type-2 fuzzy technique. As a part of
future application work, new applications in the real world will be explored, e.g. hardware implementations,
applications in medical diagnostics, big data, applications in robotics (Mittal et al., 2020).
Despite intensive research and promising applications in various fields, there is a lack of publications devoted
to the implementation of the type-1 and type-2 FLCs to HENs. The main goal of this paper is to show that
fuzzy controllers and especially the type-2 FLCs can guarantee energy savings and better performance
compared to conventional PID controllers when controlling a small HEN. The presented comparative study of
the type-1 FLC, type-2 FLC, PI controller, and PID controller is based on simulation results.

2. Fuzzy control

2.1 Type-1 fuzzy control 

The design of a simple type-1 fuzzy controller (Figure 1) can be based on a procedure that is built on PID
control. The algorithm is as follows: start with a PID controller, insert an equivalent linear fuzzy controller, and
make it gradually nonlinear. A fuzzy controller can include empirical rules that are called a rule base.
A dynamic controller would have additional inputs, for example, derivatives, integrals, or previous values of
measurements backward in time. The block fuzzification converts each piece of input data to degrees of
membership by a lookup in one or several membership functions. The rules may use several variables, both in
the condition and the conclusion of the rules.

Figure 1: Feedback control structure with a type-1 fuzzy controller 

Basically, a linguistic controller contains rules in the if-then format, but it can be presented in different formats.
The resulting fuzzy set must be converted to a number that can be sent to the process as a control signal.
This operation is called defuzzification. There are several defuzzification methods. Output scaling is also
relevant. In the case the output is defined on a standard universe, it must be scaled to engineering units.

2.2 Interval type-2 fuzzy control 

The rule base for the interval type-2 fuzzy controller (Figure 2) remains the same as for the type-1 FLC, but its
membership functions are represented by type-2 interval fuzzy sets instead of type-1 fuzzy sets and some
type of reducer is used prior defuzzification (Kumbasar, 2014).

Figure 2: Interval type-2 fuzzy controller block diagram 

The advantage of using type-2 fuzzy logic over type-1 is that type-2 can handle the inherent uncertainty in
control, which can be due to noise, dynamic changes in the environment, or imprecision in the models (Mittal
et al., 2020).

3. Process description and control design

The investigated HEN composed of two HEs in series parallel to one HE is presented in Figure 3.

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Figure 3: Scheme of the heat exchanger network 

Kerosene flows in the inner tubes. Water is used as a cooling fluid and it flows in the shell of each heat
exchanger. The objective is to decrease the kerosene temperature Thot out in the mixed outlet stream. The
manipulated variable is the coolant flow rate. The simplified nonlinear dynamic mathematical model of the HEs
has the form of six first-order ordinary differential equations (Oravec et al., 2016). Parameters and steady-
state inputs of the HEs are given in Vasičkaninová et al. (2017).

 3.1 Identification of the heat exchanger network 

The explored HEN (Figure 3) was identified using the Strejc method (Mikleš and Fikar, 2007) in the form of
a second order transfer function with a time delay Eq(1), where s represents the Laplace transform argument.
The process model in Eq(1) was needed for PI and PID controller tuning. As several step responses were
identified, intervals were obtained for the gain K, the time delay D and the time constant . The nominal values
of the parameters are the mean values. The resulting nominal values of the transfer function parameters are
Kmean =  50.1 °C min m-3, mean = 1.8 min and Dmean = 0.1 min and the order is n = 2.

𝑆 =
𝐾

(𝑠 + 1)𝑛
e−𝐷𝑠 =

−50.1

3.24 𝑠2 + 3.6𝑠 + 1
e−0.1𝑠 (1)

3.2 Conventional PID control of the heat exchanger network 

The nominal plant model Eq(1) was used to design the parameters of PID and PI controllers. The PID
controller was tuned using the Chien-Hrones-Reswick method and PI controller was tuned using minimum
ITAE method (Corriou, 2004). The transfer function of the PID controller C with a filtered derivative part was
considered in the form:

𝐶 = 𝑘𝑝 (1 +
1

𝑡𝑖 𝑠
+

𝑡𝑑 𝑠
𝑡𝑑 𝑠
𝑁

+ 1
) (2)

where kp is the proportional gain, ti the integral time, td the derivative time and N is a constant. The PID
controller parameters are presented in Table 1 and N = 20. The negative value of the controller gain kp
expresses the fact that the higher cooling agent flow rate is applied, the lower temperature of the outlet stream
Thot out is reached.

Table 1: Parameters of the conventionally tuned PID and PI controllers 

Controller kp  (m3 min-1 °C-1) ti  (min-1) td (min)
PID Chien-Hrones-Reswick 0.3413 2.52 0.047
PI minimum ITAE method 0.1565 1.56 0

3.3 Fuzzy control of the heat exchanger network 

The type-1 fuzzy controller was designed as the Sugeno-type fuzzy inference system (FIS) in Eq(3),

If 𝑒 is 𝐴1 and 𝑑𝑒/𝑑𝑡 is 𝐵1 Then 𝑓1 =  𝑝1𝑒 +  𝑞1 𝑑𝑒/𝑑𝑡 +  𝑟1 

If 𝑒 is 𝐴1 and 𝑑𝑒/𝑑𝑡 is 𝐵2 Then 𝑓2 =  𝑝2𝑒 +  𝑞2 𝑑𝑒/𝑑𝑡 +  𝑟2 

If 𝑒 is 𝐴2 and 𝑑𝑒/𝑑𝑡 is 𝐵1 Then 𝑓3 =  𝑝3𝑒 +  𝑞3 𝑑𝑒/𝑑𝑡 +  𝑟3 

If 𝑒 is 𝐴2 and 𝑑𝑒/𝑑𝑡 is 𝐵2 Then 𝑓4 =  𝑝4𝑒 +  𝑞4 𝑑𝑒/𝑑𝑡 +  𝑟4 

If 𝑒 is 𝐴3 and 𝑑𝑒/𝑑𝑡 is 𝐵1 Then 𝑓5 =  𝑝5𝑒 +  𝑞5 𝑑𝑒/𝑑𝑡 +  𝑟5 

If 𝑒 is 𝐴1 and 𝑑𝑒/𝑑𝑡 is 𝐵3 Then 𝑓6 =  𝑝6𝑒 +  𝑞6 𝑑𝑒/𝑑𝑡 +  𝑟6 

(3)

531



where e is the control error, de/dt is the derivative of error, pi, qi, ri are the consequent parameters. Sugeno-
type FIS was generated using a subtractive clustering method. The symmetric Gaussian function was used for
the fuzzification of inputs. Figure 4 shows three Gaussian membership functions for the input e and two
membership functions for the input de/dt. Figure 4 also shows three input interval type-2 fuzzy sets for the
input e and two interval type-2 fuzzy sets for the input de/dt (Wu and Mendel, 2009). An interval type-2
membership function is represented by an upper and a lower membership function. The area enclosed by
these membership functions is the footprint of uncertainty. The type-2 reducer uses the Karnik-Mendel
algorithm (Karnik and Mendel, 2001).

Figure 4: Gaussian membership functions: (a) – input e, (b) - input de/dt; interval type-2 membership 

functions: (c) – input e, (d) – input de/dt 

4. Simulation results

The simulation results were attained using the MATLAB/Simulink R2020b programming environment. The
Control and Fuzzy toolboxes were used for the implementation of PID and fuzzy controllers. The simulation
results in reference tracking and disturbance rejection with measurement noise are presented in Figure 5. The
reference temperature r = 80 °C was set at time t = 0 min and changed to 77 °C at t = 60 min. The
disturbances were represented by the coolant temperature changes in the inlet stream to the HEN and they
were as follows: the temperature increased by 4 °C at t = 30 min and decreased by 3 °C at t = 90 min.

Figure 5: Control responses of the kerosene temperature Thot out 

The results were compared numerically assessing the total consumption of cooling water V consumed during
control, the integral quality criteria IAE (integrated absolute error), and ISE (integrated squared error) defined
e. g. in Corriou (2004). Table 2 summarizes these numerical results.

Table 2: Values of V, ISE, IAE 

Controller V (m3) ISE (°C2 min) IAE (°C min) 
PID Chien-Hrones-Reswick  78.81 30.2 23.1
PI minimum ITAE method 77.22 41.8 31.8
Type-1 FLC 76.28 28.2 21.1
Type-2 FLC 75.01 27.6 20.2

The type-2 FLC (FLC2) guaranteed the lowest coolant consumption with 5 % reduction in comparison with the
highest consumption reached by the PID controller. The type-1 FLC (FLC1) increased the coolant
consumption by 2 % compared to FLC2. Evaluating the ISE and IAE values, the best controller was FLC2.
FLC1 increased the ISE value by 2 % and the IAE value by 4 % compared to FLC2. The ISE value increased
by 51 % and the IAE value by 57 % when the PI controller was used. Exploiting the PID controller, the ISE

532



value increased by 9 % and the IAE value by 14 %. Comparing the coolant consumption and the ISE and IAE
values, FLC2 was the best controller.
The maximum overshoots and settling times were evaluated for the setpoint changes at t = 0 min (case 1
(C1)) and at t = 60 min (case 3 (C3)) and also for loaded disturbances at t = 30 min (case 2 (C2)) and at
t = 90 min (case 4 (C4)). Overshoot percentage measures the closeness of the response to the desired
response. The settling time is the time taken for the system to converge to its steady state (Skogestad, 2003).
Table 3 and Table 4 contain these numerical results.

Table 3: Values of overshoots and settling times in setpoint tracking 

Controller Overshoot (C1)
(%)

Settling Time (C1)
(min)

Overshoot (C3)
(%)

Settling Time (C3)
(min)

PID Chien-Hrones-Reswick  49.48 17.4 13.55 42
PI minimum ITAE method 56.46 24.1 21.17 42
Type-1 FLC 25.41 12.3 14.12 38
Type-2 FLC 34.72 12.3 14.68 38

Table 4: Values of overshoots and settling times in disturbance rejection 

Controller Overshoot (C2)
(%)

Settling Time (C2)
(min)

Overshoot (C4)
(%)

Settling Time (C4)
(min)

PID Chien-Hrones-Reswick  24.10 70 20.67 100
PI minimum ITAE method 22.67 72 31.67 104
Type-1 FLC 3.00 64 25.00 105
Type-2 FLC 10.01 68 23.33 102

In setpoint tracking, FLC1 compared to FLC2 decreased the overshoots by 27 % (C1) and by 4 % (C3). The
settling times were the same using both FLCs. The worst results were achieved by the PI controller. In
comparison with FLC2, the overshoots increased by 63 % (C1) and by 44 % (C3) and the settling times
increased by 96 % (C1) and by 11 % (C3). In disturbance rejection, FLC1 compared to FLC2 decreased the
overshoot by 70 % and the settling time by 6 % in C2 but increased the overshoot by 7 % and the settling time
by 3 % in C3. The worst results were achieved again using the PI controller. In comparison with FLC2, the
overshoots increased by 126 % (C2) and by 36 % (C4) and the settling times increased by 6 % (C2) and
by 2 % (C4). PID controller guaranteed the best control performance according to the overshoots when the
setpoint and the disturbance decreased (C3 and C4). Comparing the overshoots and settling times, the best
controller was FLC1.

5. Conclusions

Fuzzy control of a small HEN was studied. The type-1 FLC, type-2 FLC, and conventional PID and PI
controllers were used for temperature control of the HEN. The type-2 FLC assured the most efficient operation
of HEN measured by the lowest coolant consumption. The consumption of cooling agent increased by 2 %
using FLC1, by 3 % using the PI controller, and by 5 % using the PID controller. Based on the maximum
overshoots and settling times evaluated for the setpoint changes and loaded disturbances, the best results
were obtained using FLC1 followed by FLC2. Judging the settling times in setpoint tracking, FLC1 reached the
same results as FLC2 in C1 and C3 and compared to FLC2 decreased the settling time by 6 % in C2 and
increased the settling time by 3 % in C4. The worst results were reached exploiting PI controller tuned by the
minimum ITAE method and in comparison with FLC2, the settling times increased from 2 % (C4) to 96 % (C1).
Evaluating the overshoots, FLC1 assured the smallest overshoots in C1 and C2, and these overshoots were
25.41 % and 3.00 %. In C3 and C4, the best controller was the PID controller with overshoots of 13.55 % and
20.67 % followed by FLC1 with the overshoot of 14.12 % in C3 and by FLC2 with the overshoot of 23.33 % in
C4. Based on the comparison of all results, it can be stated that both types of FLCs could be used
successfully for reaching the goals of control. Application of more complicated fuzzy type-2 controllers helped
to improve the energetic efficiency of the studied heat exchanger network measured by coolant consumption.
This strategy is promising for implementation in practice. Further research in this field will continue in the
future.

533



Acknowledgements  

The authors gratefully acknowledge the contribution of the Scientific Grant Agency of the Slovak Republic
under the grants 1/0545/20 and 1/0691/21.

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