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International Journal of Engineering, Applied and Management Sciences Paradigms, Vol. 45, Issue 01
Publishing Month: March 2017
An Indexed and Referred Journal
ISSN (Online): 2320-6608
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Conventional Control of Continuous Fluidized Bed Dryers
for Pharmaceutical Products
Gurashi Abdullah Gasmelseed1 and Mahdi Mohammed2
1Department of Chemical Engineering, University of Science and Technology, Khartoum, Sudan
2Department of Chemical Engineering, University of Science and Technology, Khartoum, Sudan
Publishing Date: March 04, 2017
Abstract The dynamic response studies with step disturbances in the manipulated and load variables are investigated. These studies
are useful in control system identification schemes for fluidized
bed dryer. Both conventional and digital control strategies were
developed. Three loops were taken for comparison between the
methods of tuning and stability analysis for conventional and
digital control, each control loop was treated separately and its
transfer functions were developed .In conventional control the
characteristic equations were determined and used in Routh
array to determine the ultimate gain (Ku), the ultimate period
(Pu) was determined by using direct substitution. The OLTF's
were used by Root Locus and Bode plot methods using
MATLAB software to determine Ku and Pu. It is observed that
the three methods of investigating the stability gave optimum
and identical parameters Ku and Pu, and they were almost the
same. The average values of the ultimate gains and periods were
obtained and they were introduced in Zeigler – Nichols table to
get the adjustable parameters, however an average was taken to
give more précised and correct results. Also the offset was
investigated for P-controller, PI-controller and PID-controller. Keywords: Dynamic Response, Fluidization, Drying Control,
Automatic Control of Dryers, System Stability and Tuning,
Routh Hurwitz, Root Loucs Plot, Direct Substitution, Bode Plot
and System Stability.
Introduction
Drying means the removal of relatively small amounts of
water from wet material by the application of heat.
Drying is an energy-intensive operation that accounts for
up to 15% of the industrial energy usage. Moreover, conventional dryers often operate at low thermal
efficiency, typically between 25% and 50%, but it may be
as low as 10%. Fluidized bed dryer is used widely in
food, metallurgical, chemical and pharmaceutical industry, because of the shorter drying time required and
simple maintenance and operation. This type of dryers is
based on the phenomena of fluidization. Fluidization is the operation by which solid
particles are transformed into fluid-like state through
suspension in gas or liquid. When a gas is passed through
a layer of particles supported by a grid at low flow rate,
the fluid percolates through the void spaces between
stationary particles. As the fluid velocity increased, the void age increases, this resulting in an increase in pressure
drop on the particles.
The pressure drop across the particle layer will
continue to increase in proportion to the gas velocity till
the pressure drop reaches a constant value that is
equivalent to the weight of the particles in the bed divided
by the area of the bed, at this point the frictional force between particles and fluid counterbalances the weight of
the particles. At this stage the bed is to be incipiently
fluidized. Fluid velocity at this point is known as
minimum fluidization velocity. With an increase in flow
rates beyond minimum fluidization, large instabilities
with bubbling, channeling of gas and decrease in pressure
drop are observed. Fluidized bed dryers have some drawbacks.
Material with a wide particle-size distribution cannot be
handled satisfactorily, while at high temperatures the
melting and fusing of the material on the grid plate can
become a problem. To circumvent these difficulties,
dryers, originally developed for grain drying, have been
made with conical bottom sections which give a spouted
bed rather than a fully fluidized one. Deriving
mathematical models can be done by utilizing physical
laws to derive a mathematical model, this model must be
rigorous enough to give an accurate description of the process. In most cases they obtained models are set of
ordinary differential equations with one or more partial
differential equation, thus solving them requires powerful
mathematical solvers. Drying control is defined as the ability to dry a
product to a desired moisture content with acceptable
variation. Poor moisture content produces a distribution with a wide moisture content variation, whereas,
improved control results in narrow distribution.
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Automatic control of dryers is probably one of the least
studied areas of process control and has not progressed
with improvements in drying and dryer design. This may
be attributed to various factors, including:
1. The lack of direct, on-line and reliable methods for
sensing product moisture content.
2. The complex and highly nonlinear dynamics of drying
process, leading to difficulties in modeling process
adequately.
3. The lack of emphasis on product quality in the past.
4. An apparent lack of knowledge of the important role
that dryer control plays in product quality and drying
efficiency.
Figure 1: Continuous Fluidized Bed Dryer
Prior to control system design, control synthesis must be
performed. The synthesis of control configurations for
multivariable system involves selection of controlled and manipulated variables, pairing manipulated inputs and
controlled outputs (loop pairing), and selection of the best
control configuration. Generally, input variables can be
classified into manipulated variables and disturbances or
load variables. In industrial drying systems the
manipulated variables typically include inlet air temperature, superficial air velocity, inlet solids flow rate
and dryer-wall temperature. Load variables include ambient air temperature, ambient air humidity, and feed
moisture content. The controlled variables in dryers are
dried product moisture content, exhaust air temperature
and exhaust air humidity. The most desirable drying
process output variable to control is product moisture
content, but this is difficult to measure directly. Often, the
moisture content of the dried product can be inferred from
the temperature and humidity of the exhaust gas. However, due to the weak correlation between the
temperature and the actual product moisture content,
using indirect control usually results in poor control of the
drying process. Multivariable control design must be
considered for fluidized bed dryers in order to account for
dynamic interactions between the control loops.
International Journal of Engineering, Applied and Management Sciences Paradigms, Vol. 45, Issue 01
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Research Objectives:
1/ Design of fluidized bed dryer for drying
pharmaceutical products.
2/ Design of conventional and digital control of fluidized
bed dryer.
3/ Comparison of performance between conventional and
digital control of fluidized bed dryer.
Methodology
System Stability and Tuning:
Stability:
System have several properties such as controllability,
stability, and invariability .which play a very decisive role
in their behavior. From these characteristic, stability plays
the most important role. The most basic practical control
problem is the design of a closed - loop system such that
its output follows its input as closely as possible , unstable
system cannot guarantee such behavior and therefore are
not useful in practice.
Stability Test:
The system is stable when all poles of the transfer
function have negative real parts. If any pole has a
positive real part, then the system is unstable. To ensure a
good performance of the system, each of the control loops
mentioned earlier should be analyzed for the stability,
separately .For the present work, we have four methods
used to check the stability of the system .Such methods
are:
1. Routh Hurwitz.
2. Root Loucs plot.
3. Direct Substitution.
4. Bode plot.
Routh Hurwitz (Routh’s Criterion):
One absolute method of determining whether complex or
real roots lie in the right hand plane is by use of Routh’s
criterion the method entails systematically generating a
column of numbers that are then analyzed for sign
variations .The first step is to arrange the denominator of
transfer function into descending powers of S. All terms
including those that are Zero should be included. The
stability is determined from the system characteristic
equation.
Root Loucs Plot:
It is one of the most powerful techniques in controller
design and analysis when there is no time delay .Root
locus is a graphical representation of the roots of the
closed – loop characteristic polynomial .The analysis
most commonly uses the proportional gain as the
parameter .A Root locus plot is a figure that shows how
the roots of the closed loop characteristic equation vary as
the gain of the feedback controller changes from zero to
infinity
Direct Substitution:
Determination of the ultimate period by direct
substitution method (ωco). By steps below:
G(s) = 𝑪(𝒔)
𝑹(𝒔)=
𝝅𝐟
𝟏+𝝅𝒍
Set s= iω in the characteristic equation.
Taking the real part.
Taking the imaginary part.
Substitute the value of cross over frequency.
The ultimate period {Pu =2π
ωco} .
Bode Plot and System Stability:
The Bode diagram in honour of H.W.Bode gives a
convenient method to represent the frequency response
characteristics of a system. It represents the amplitude
ratio and phase angle of the response of the system as the
function of the frequency. It shows the variation of the
logarithm of the amplitude ratios with the frequency and
the variation of the phase shift with the frequency. To
cover a large range of frequencies, the log scale is used
for the frequency.
Results and Discussion
Based on operation conditions of the fluidized bed dryer
shown in table (4.1), control strategy was developed as shown
in figure (4.1). The block diagrams were constructed, the
transfer functions of loop1 through loop 3 were identified,
and the characteristic equations were calculated. Stability
analysis, tuning and simulation responses were obtained
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Table (1.1): Operating conditions of fluidized bed dryer:
Parameters Units Values
Inlet air temperature ℃ 65 – 75
Inlet air humidity %
Outlet air temperature ℃ 39 – 40
Outlet air humidity % 1
Height of dryer Cm 157
Fluidized bed height Cm 42
Diameter of the bed Cm 92
Thickness Mm 2
Material of construction 316 (product contact part)
304 (non-contact part)
Air pressure Bar 6
Type of steam used Saturated steam
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Control Strategy for Continuous System:
Figure (1.1): Physical Diagram of the Fluidized Bed Dryer, Continuous system
A. Control of the Furnace Temperature
(Loop 1):
Transfer Functions Identification:
Proportional controller:
G(c)=Kc
Valve transfer function:
G(v)=1
0.1𝑠+1
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Process transfer function:
G(p)= 1
(5𝑠+1)
Sensor transfer function :
G(m)= 1
(0.2𝑠+1)
Figure (1.2): Block diagram of loop (1) with identified transfer functions
Analysis of Stability and Tuning of Loop 1:
Routh-Hurwtz Analysis:
The characteristic equation:
Kc + (0.1𝑠 + 1)(5𝑠 + 1)(0.2𝑠 + 1) =0
0.1s3+1.52s2+5.3s+(1+ Kc)=0
The ultimate gain ku = 79.6
Determination of the ultimate period by direct substitution
method (ωco):
The ultimate period 𝑃𝑢 = 0.863 sec
Root Locus Method:
The OLTF of loop 1:
OLTF = Kc
(0.1𝑠+1)(5𝑠+1)(0.2𝑠+1)
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Figure (1.3): Root Locus plot of loop1
The ultimate gain ku = 78.5
𝑃𝑢 =2π
7.24= 0.868 𝑠𝑒𝑐
Bode Plot Method:
The OLTF of loop 1:
OLTF = Kc
(0.1𝑠+1)(5𝑠+1)(0.2𝑠+1)
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Figure (1.4): Bode plot of loop1
At -180
𝑃𝑢 = 0.855 sec
Ku = 78.13
The Average of Ultimate Gains and Ultimate
Periods:
Ku (average) =Ku(R) + Ku(R − L) + Ku (B)
3
Ku (average) =79.6 + 78.50 + 78.13
3= 78.74
Pu (average) =Pu(R) + Pu(R − L) + Pu (B)
3
Pu (average) =0.863 + 0.868 + 0.855
3= 0.862 𝑠𝑒𝑐
Table (1.2): (Ziegler-Nichols) Tuning parameters by
using 𝐊𝐮 (𝐚𝐯𝐞𝐫𝐚𝐠𝐞) and 𝐏𝐮 (𝐚𝐯𝐞𝐫𝐚𝐠𝐞) :
Type of
controller
Kc 𝛕i 𝛕d
P 39.370 - -
PI 35.433 0.718 -
PID 47.244 0.431 0.108
Simulation of the System for (loop 1):
System Response for P-Controller:
The overall transfer function:
G(s) =7.874𝑠 + 39.37
0.1s3 + 1.52s2 + 5.3s + 40.37
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Figure (1.5): System response of loop 1 using P- Controller
Offset investigation for P-controller:
Offset = C∞ - Cid
Cid = magnitude of unit step change = 1
C∞ = 𝑙𝑖𝑚𝑠→0[𝑠 ∗ 𝐶(𝑠)]
C∞ = 39.37
40.37 = 0.975
∴ offset = 0.8775 – 1 = - 0.025
System Response for PI-Controller:
The overall transfer function and the system response for PI-controller were determined using MATLAB software.
The overall transfer function:
G(s) =5.088𝑠2+32.53𝑠+35.43
0.0718s4+1.091s3+3.805s2+26.16s+35.43
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Figure (1.6): System response of loop 1 using PI-Controller
Offset investigation for PI-controller:
∴ G(s)= 𝐶(𝑠)
𝑅(𝑠)=
5.088𝑠2+32.53𝑠+35.43
0.0718s4+1.091s3+3.805s2+26.16s+35.43
Offset = C∞ - Cid
∴ offset = 1 – 1 = 0
System Response for PID-Controller:
The overall transfer function:
G(s) =0.4398𝑠3+6.271𝑠2+29.81𝑠+47.24
0.0431s4+0.6551s3+4.483s2+20.79s+47.24
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Figure (1.7): System response of loop 1 using PID-Controller
Offset investigation for PID-controller
∴ G(s)= 𝐶(𝑠)
𝑅(𝑠)=
0.4398𝑠3+6.271𝑠2+29.81𝑠+47.24
0.0431s4+0.6551s3+4.483s2+20.79s+47.24
r(t) = 1
R(S) = 1
𝑆
𝐶(𝑠) = [ 0.4398𝑠3+6.271𝑠2+29.81𝑠+47.24
0.0431s4+0.6551s3+4.483s2+20.79s+47.24] .
1
𝑠
Offset = C∞ - Cid
Cid = magnitude of unit step change = 1
C∞ = 𝑙𝑖𝑚𝑠→0[𝑠 ∗ 𝐶(𝑠)]
C∞ = 47.24
47.24 = 1
∴ offset = 1 – 1 = 0
Table (1.3): Characteristics of closed loop
Value Characteristic
87.3 Over shoot(%)
0.154 Rise time(sec)
4.7 Settling time(sec)
7621.29 Decay ratio
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The system is under damped.
ƺ < 1
Table (1.4): Characteristics of closed loop response with PI-controller
Value Characteristic
126 Over shoot(%)
0.156 Rise time(sec)
14 Settling time(sec)
15876 Decay ratio
0.574 Dampness coefficient (ξ)
1 Final value
ƺ < 1
The system is underdamped overshoots.
Table (1.5): Characteristics of closed loop response with PID-controller
Value Characteristic
94.8 Over shoot(%)
0.0863 Rise time(sec)
2.82 Settling time(sec)
8987.04 Decay ratio
0.6124 Dampness coefficient (ξ)
1 Final value
ƺ < 1
The system is under damped overshoots
0.559 Dampness coefficient (ξ)
0.975 Final value
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Figure (1.8): The comparison between different type of controllers (P, PI and PID)
Due to the minimum overshoot the PI-controller is selected, this because high overshoot in temperature will damage the
products.
Table (1.6): The overshoot of different types of controllers
Type of controller Overshoot (%)
P 87.3
PI 126
PID 94.8
B. Control of the Fluidized Bed Pressure (Loop 2):
Transfer Functions Identification:
G(c)=Kc
G(v)= 1
0.3𝑠+1
G(p)= 1
(10𝑠+1)
G(m)= 1
(0.2𝑠+1)
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The Average of Ultimate Gains and Ultimate Periods:
Ku (average) =Ku(R) + Ku(R − L) + Ku (B)
3
Ku (average) =87.55 + 87.30 + 86.23
3= 87.03
Pu (average) =Pu(R) + Pu(R − L) + Pu (B)
3
Pu (average) =1.502 + 1.503 + 1.512
3= 1.506 𝑠𝑒𝑐
Table (1.7): (Ziegler-Nichols) Tuning parameters by using 𝐊𝐮 and 𝐏𝐮 (soourse)
Type of controller Kc 𝛕i 𝛕d
P 43.515 - -
PI 39.164 1.255 -
PID 52.218 0.753 0.188
Simulation of the System for (loop 2):
Figure (1.9): The comparison between the three types of controllers
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Table (1.8): The overshoot of different types of controllers
Type of controller Overshoot(%)
P 65.6
PI 103
PID 69.8
Due to the minimum overshoot the P-controller is selected.
C. Control of the Outlet Air Humidity (Loop 3):
G(c)=Kc
G(v)= 1
G(p)= 1
𝑠2+2𝑠+1
G(m)= 1
(0.1𝑠+1)
The Average of Ultimate Gains and Ultimate
Periods:
Ku (average) =Ku(R) + Ku(R − L) + Ku (B)
3
Ku (average) =24.2 + 24 + 23.7
3= 23.97
Pu (average) =Pu(R) + Pu(R − L) + Pu (B)
3
Pu (average) =1.371 + 1.381 + 1.381
3= 1.38 𝑠𝑒𝑐
Table (1.9): (Ziegler-Nichols) Tuning parameters
Type of
controller
Kc 𝝉i 𝝉d
P 11.985 - -
PI 10.787 1.15 -
PID 14.382 0.690 0.173
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Simulation of the System for (loop 3):
Figure (1.10): The comparison between the three types of controllers
Table (1.10): The overshoot of different types of controllers
Type of controller Overshoot (%)
P 68.5
PI 93.9
PID 58.7
Due to the maximum overshoot the PI-controller is selected.
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Conclusions
The stability and tuning are different giving different
parameters, the root locus and bode plots are also
different with different parameters and stability limits. It
may be concluded that the digital controller (PLC) itself
tune to stable perform.
Recommendations
There for it is recommended that continuous control
system should be replaced by discrete control system.
Acknowledgement
The authors wish to thank the graduate college of the
Karary University for Help and registration of this work
for PhD in chemical engineering.
References
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[3] Jumah, R. Y., Mujumdar, A. S. and Raghavan, G. S.,
"Control of Industrial Dryers", Handbook of
Industrial Drying, 2nded, (A.S.Mujumdar, ed.),
Marcel Dekker, New York, (1995), pp. 1343-1368.
[4] Strumillo, C., Jones, P., and Zulla, R., "Energy
Aspects in Drying", Handbook of Industrial Drying,
2nded, (A.S.Mujumdar, ed.), Marcel Dekker, New
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