Conventional Control of Continuous Fluidized Bed Dryers ...ijeam.com/Published Paper/Volume 45/Issue...

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

[email protected]

2Department of Chemical Engineering, University of Science and Technology, Khartoum, Sudan

[email protected]

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.

mailto:[email protected]

mailto:[email protected]





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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.





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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.


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:


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


126 Over shoot(%)


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


94.8 Over shoot(%)


2.82 Settling time(sec)

8987.04 Decay ratio


1 Final value

ƺ < 1

The system is under damped overshoots


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:


3

Ku (average) =87.55 + 87.30 + 86.23

3= 87.03


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


Figure (1.9): The comparison between the three types of controllers





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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:


3

Ku (average) =24.2 + 24 + 23.7

3= 23.97


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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Figure (1.10): The comparison between the three 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

[1] Gasmelseed, G, A, A Text Book of Engineering

Process Control, G. Town, Khartoum, (2015).

[2] Robinson, J. W., "Improved Moisture Content

Control Saves Energy", Internet: www.process-

heating.com (2000).

[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

York, (1995), pp.1343-1368.

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