HUNGARIAN JOURNAL 
OF INDUSTRIAL CHEMISTRY 

VESZPREM 
Vol. 30. pp. 167- 170 (2002) 

A FUZZY LOGIC APPROACH TO THE CONTROL OF THE DRYING PROCESS 

M. BALDEA, V. M. CRISTEA andP. S. AGACHI 

(Department of Chemistry and Chemical Engineering, "Babes-Bolyai" University, 11, Arany Janos St., 3400 Cluj-
Napoca, ROMANIA) 

Received: March 8, 2002 

The paper presents the simulation results of an advanced control algorithm used for the control of the drying process of 
electric insulators. The industrial batch drier is modelled and three different approaches are taken for its control. In order 
to investigate its capabilities, Fuzzy Logic Control (FLC) is used for controlling the air temperature in the drying 
chamber. The results describing the controlled variables behaviour under the influence of some typical disturbances are 
compared with data obtained using Model Predictive Control (MPC) and traditional PID control. 
The requested drying program consists of a ramp-constant profile, obtained by manipulating the air and natural gas flow 
rate. Moisture content control is actually achieved by controlling the air temperature inside the drying chamber. 
Simulation results reveal clear benefits of the FLC approach over the other control methods subjected to our 
investigation, and prove real incentives for industrial implementation. 

Keywords: batch drying, fuzzy logic, model predictive control, non linear control 

Introduction 

The high-voltage electric insulator production implies a 
two-stage batch drying process. During the first step, the 
moisture content of the drying product is reduced from 
18-20% to 0.4% in special gas heated chambers. The 
second step is carried out in high temperature ovens, in 
order to achieve an even lower moisture content. 

Gas and air flow rates are controlled according to a 
special program, during a period of about 100 hours, in 
order to obtain the desired moisture content and 
avoiding the risk of unsafe tensions in the drying 
products. 

An analytical dynamic model of the process is 
derived for model predictive control purposes. 

Model description 

Mass and energy balance equations are used to describe 
the dynamic behaviour of the system. The main studied 
outputs of the model are: moisture content of the drying 
product X, outlet air temperature T0 and air humidity x0 ; 

the input variables: natural gas flow rate iF and mass . 
flow rate of fresh air m,1 • The chamber is divided into 
three sections as shown in Fig.l. Section 1 represents 

Contact information: E~mail: mbaldea@chem.ubbcluj.ro 

the air volume within the drying chamber, section 2 the 
direct surroundings of the drying product. Section 3 
represents the drying product itself. 

The mass balance of steam within section 1 is 
described by 

. . ( . . ) - V dxo (1) mal ·Xf +ma ·x- ma +mai ·xo- aCfl. Pa ·-
dt 

with Vach being the volume of the air in section 1. In 
section 2, the steam fluxes around the drying product 
are modelled by 

m ·(x -x)-m · dX ==.E_fy ·P ·x) (2) 
a o S dt dt \ 42 a 

with V a2 being the infinitesimal small volume of air in 
section 2. Due to this fact, the last term of the equation 
can be neglected, which results in the differential 
equation 

dX = (x -x)· ma. 
dt " ms 

(3) 

As a result of differentiation of Eq.(3) and assuming 
that, d!X!dr""' 0 the Eq.( 1) becomes: 

! = 1 ·(m"; ·x1 +m, ·x-(m .. +m"}x,}(4) 
V.,ch ·Pa 



168 

Fig. I Description of the drying chamber 

In section 3, the behaviour of the drying good itself 
is described with a normalised diagram by means of the 
following equation [1, 2]: 

dX __ m., ·A 
dt - m

5 
s · 

(5) 

The drying velocity for the three periods of the 
drying process of a hygroscopic material are 
characterised by the diagrams of Fig.2 [2]. 

This diagram a), only available by experiments and 
valid for the certain conditions can be normalized to b) 
according to: 

(6) 

It is assumed that X c is constant, not depending on 

the drying conditions, and that X equ only depends on 

relative air humidity, but no other factors. It is also 
assumed that all diagrams of the drying velocity for 
different drying conditions are geometrically similar. 

The equilibrium humidity X equ in dependence of the 

relative air humidity <p , for clay, was considered by a 

correlation equation. The saturation humidity of the air, 
x,"u • is dependent of temperature TQ • For low partial 

pressures of steam a simple equation for mstl was 
considered: 

(7} 

with the mass transfer coefficient k determined by 
experiment data. 

Two energy balance equations, for the chamber: 

mal·(cpa ·(7; -T,)+xr·(h, +cpst ·1;)-x., ·{h,. +cpst·T,))+ 
(8) 

and for the burner: 

a) b) 

m:;tll 

X 

Fig.2 Drying rate in dependence of moisture content of drying 
product: a) absolute b) normalized 

(9) 

are used to describe the outlet temperature change. 
A dynamic sensitivity analysis was carried out on 

this model, indicating the most important parameters 
and manipulated variables. According to this analysis, 
they are: mass transfer coefficient k, heat transfer 
coefficient of chamber walls CA, heating power of 
natural gas HF, mass of the drying product ms (clay 
without humidity), environment temperature of the inlet 
air T., environment humidity of the inlet air x., volume 
of the drying chamber Vch, surface of the drying 
chamber Ach. surface of the drying product As, critical 
humidity of clay Xc and specific heat of natural gas cpF 
[3]. The scaled dynamic sensitivity analysis of the 
output variables with respect to the studied inputs 
pointed out the natural gas flow rate as the most 
important manipulated variable (about 10 times more 
important than the mass flow rate of fresh air). The 
control system was designed accordingly. 

Results and Discussion 

Any process controller's mission is to receive a number 
of inputs and compute the appropriate outputs in order 
to annihilate a possible error. The fuzzy controller is no 
exception: it receives a measured value from the system, 
if fuzzyfies it (assigns it a membership value), applies 
the system's rules, computes an overall result of all the 
rules and then defuzzyfies the result, converting it into a 
number which is an appropriate command for the 
system it controls. [4, 5]. The mission of the Model 
Predictive Controller [6] is accomplished by 
anticipating the outputs of the system with the aid of the 
mathematical model. The controller output is generated, 
based on the anticipated behavior of the system. 

All control methods investigated in this paper obey 
the current control practice [7], i.e. driving the evolution 
of the moisture content of the drying product in the 
desired way by means of controlling the air temperature 
inside the chamber. Usually, the desired decreasing 
profile of the drying product moisture content is 
obtained by imposing an increasing ramp-constant 



... -.-.·.·.····.·.·.·-·-

Fig.3 Structure of the control system 

Temperature [~C] 

90 

80 

70 

60 

50 

40 

30 

20 

10 
0 0.5 

A 

1.5 
Time[s) 

2.5 3.5 

X 10' 

Fig.4 Comparative behaviour of FL, MPC and PID control in 
the presence of the heating power disturbance 

45.2 

~44.8 
~ 
~44.6 

.li 
>--

44.4 

44.2 

44 

1

- Setpoint : 1 
-~-· Fuzzy logic 
-· MPC 
-- PID 

1.155 1.16 1.165 1.17 1.175 1.18 1.165 1.19 1.195 1.2 1.205 
Time [s) x 10' 

Fig.S Detailed presentation of the comparative behaviour of 
FL, MPC and PID control in the presence of the heating power 

disturbance 

profile on the air temperature. The setup of the 
simulated system is shown in Fig3. 

Performance testing was carried out for three 
significant disturbances typically occurring in the 
industrial practice: a 10 °C inlet air temperature T" drop 
(from 16 °C to 6 °C), a 10 %heating power capacity HF 
drop of natural gas and a 10% rise in the moisture 
content of the inlet air. The disturbances were 

169 

45.5 

l 
Se!point J 

··-· Fuzz.ylog[c 
-· MPC 
-- PID 

44 

• 1.155 1.16 1.185 1.17 1.175 1.18 1.185 1.19 1.195 1.2 1.205 
1irre [s] x to' 

Fig.6 Detailed presentation of the comparative behaviour of 
FL, MPC and PID control in the presence of the air inlet 

temperature drop disturbance 

45.6 

45.4 

44.8 I 
Setpoint l 

-··· Fuzzy !ogle 
-· MPC 
-- PID 

44.6 

1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 
1irne [s] xto' 

Fig. 7 Detailed presentation of the comparative behaviour of 
FL, MPC and PID control in the presence of the air inlet 

humidity increase disturbance 

introduced as steps at time t=l16000 s. The simulation 
results for case of the heating power disturbance are 
presented in Figs.4 and 5. 

The figures show the response of the controlled 
variable over the entire time interval and a detailed 
representation of the period when the disturbance acts 
and is eliminated. The behaviour of three investigated 
control methods (Fuzzy Logic Control- FLC, Model 
Predictive Control-MPC and PID control) is presented 
comparatively. Figs.S-7 are magnifications of the area 
marked as detail A on Fig.4. 

Fig.6 presents a detail of the controlled output 
temperature for the air inlet temperature drop 
disturbance and Fig. 7 represents in the same manner the 
case of the disturbance consisting in a humidity increase 
of the inlet air. 

With respect to setpoint tracking performance, the 
. results reveal a good behaviour in case of PID and 
MPC, FL control featuring superior abilities. As it can 
be seen, FLC is very accurate, following with precision 
both the constant and the ramp sections of the 
temperature setpoint scheduling· function. 



170 

63 

2.755 2.76 2.755 2.77 2.775 2.78 2.785 2.79 2.795 
Time [s[ x 10s 

Fig.8 Detailed presentation of the ramp setpoint following 
performance of FLC, MPC and PID control 

All control methods exhibit a low offset behaviour 
f?r the constant parts of the setpoint function. For the 
ramp sections, as in Fig.8 (detail B on Fig.4), the MPC 
and PID control proved to be less accurate than FL 
showing a larger offset. 

This accuracy of the FL control is largely due to the 
asymmetrical membership function definition. The 
definition takes into account the need for an asymmetric 
amplitude of the manipulated variable change (i.e. a 
controller response of higher amplitude to a negative 
error compared to a lower amplitude response for a 
positive error) in the ramp section of the setpoint 
function. . 

With respect to disturbance rejection performance, 
FL control showed a considerably shorter (more than 10 
times) response time and smaller (more than five times) 
overshoot than the other control strategies. 

Conclusions 

A comparative study of three control methods for the 
process of drying high voltage ceramic insulators (FLC, 

MPC and PID) was carried out. Setpoint tracking and 
disturbance rejection were investigated for disturbances 
typically occurring in the industrial practice. Fuzzy 
Logic clearly stands out as the preferable control 
method for the considered process, due to the good 
setpoint tracking performance, low overshoot and short 
settling time. FLC is easy to implement and adapt in 
case of process modification due to its similarity with 
natural language. Also, the controller's simple structure 
is another argument in favour of the industrial 
implementation of this control method. Further research 
is envisioned for the control of the inferred moisture 
content of the drying product, with the implementation 
of an artificial intelligence based method for tuning the 
FL controller. 

REFERENCES 

1. VAN MEEL D. A.: Chern. Engng. Sci., 1958, 9, 36-
44 

2. KRISCHER 0. and KAsT W.: Die wissenschaftlichen 
Grundlagen der Trocknungstechnik, Springer-
Verlag, 1992 

3. PERRY R. and CHILTON C.: Chemical Engineers' 
Handbook, 5. Edition, Me Graw Hill,l973 

4. Fuzzy Logic Toolbox, For Use with Matlab®, 
User's Guide v. 2.0, The Mathworks, Inc. Natick, 
MA, 1999 

5. RussoM.: IEEE Trans. Fuzzy Systems, 1998, 6(3), 
372-388 

6. GARCIA C. E., PREIT M. P. and MORARI M.: 
Automatica, 1989, 25(3), 335-348 

7. CRISTEA V. M., BALDEA M. and AGACIIT S. P.: 
Model Predictive Control of an Industrial Dryer, 
European Symposium on Computer Aided Process 
Engineering-10, Florence 2000 


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