Digital Control of Continuous Fluidized Bed Dryers for ...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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34

Digital 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 05, 2017

Abstract For continuous system, we know that certain behaviors results

from different pole location in the s-plane. For instance, a

system in unstable when any pole is located to the right of the

imaginary axis. For discrete system, we can analyze the system

behaviors from different pole location in the z-plane. The

characteristic in the z-pole can be related to those in the s-plane

by the expression:

Z=e ST

T = Sampling time (Sec \ Sample)

S = Location in the s-plane

Z = Location in the z-plane

The stability of any system is determined by the location of the

roots its characteristic equation of the transfer function. The

characteristic equation of the continuous system is a polynomial

in the complex variable S. If all the roots of the polynomial lie

in the LHP of the S-plane, the system is stable. The stability of a

sampled-data system is determined by the location of the roots

of the characteristic equation that is polynomial in the complex

variable Z. The region of stability in the Z-plane can be found

directly from the region of stability in the s-plane using the basic

relationship between the complex variable S and Z: Z = e -TS Keywords: Continuous System, Discrete System, Stability

of any System, Stability and Transient Response,

Fluidized Bed Dryers, Drying, Moisture Content, The

Computer System, Discrete-Time Response of Dynamic

Systems, Digital Control.

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 the obtained

models are set of ordinary differential equations. 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





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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. The most

desirable drying process output variable to control is

product moisture content, but this is difficult to measure

directly

Figure 1: Flow sheet of Fluidized Bed Dryer





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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.

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

Digital Control:

The computer system collects data from the process

measurements and calculates the values of the manipulated

variable and implements the control action on the process,

based on the control algorithm that is already programmed

and stored in the memory of the computer. Signals are

converted by digital to analog (D/A) and analog to digital

(A/D) converters.

Z-Transforms play the same role for discrete-time

systems as that played by Laplace transforms for dynamic

analysis and design of continuous open or closed loops

systems.

Block Diagram:

Tuning of the level in the continuous fluidized bed

dryer from the physical diagram:

Figure 2: Block diagram of the discrete-digital control loop (DDC)

Discrete-time Response of Dynamic Systems:

In continuous analog systems, we get the overall

transfer in Laplace or time-domain and we make our

analysis of the system such as stability, controller settings

and design. The above methodology cannot be used for

dynamic analysis of digital control-loop as these poses

discrete element (Digital-Control algorithm) and discrete

time signals. These are two primary distinct components

whose responses are very important in the dynamic

analysis of control systems:

This is a discrete element of the DDC-Loop with discrete-time input and output signal.





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Conversion to z-transform (Using c2d):

There is a MATLAB function called c2d that converts a

given continuous system (either in transfer or state – space

form) to a discrete system using the zero order hold

operation explained above. The basic command for this in

MATLAB is the sampling time (Ts in sec /sample) should

be smaller than 1/30*BW), where BW is the closed- loop

bandwidth frequency.

Stability and transient response:

For continuous system , we know that certain behaviors

results from different pole location in the s-plane .For

instance , a system is un stable when any pole is located to

the right of the imaginary axis .For discrete system , we

can analyze the system behaviors from different pole

location in z-plane . The characteristics in the z-plane can

be related to those in s-plane by the expression:

z = eST

T = Sampling time (sec /sample)

S = Location in the s-plane

Z = Location in the z-plane

Stability in the Z-plane:

The stability of any system is determined by the location

of the roots of its characteristic equation of its transfer

function. The characteristic equation of the continuous

system is a polynomial in the complex variable S. If all the

roots of this polynomial lie in the LHP of the S-plane, the

system is stable. The stability of a sampled-data system is

determined by the location of the roots of a characteristic

equation that is polynomial in the complex variable Z. The

region of stability in the Z-plane can be found directly

from the region of stability in the s-plane using the basic

relationship between the complex variable S and Z:

Z = e-TS

Tuning:

Discrete Root Locus:

The root Locus is the locus of points where roots of

characteristic equation can be found as a single gain is

varied from zero to infinity. The characteristic equation of

a unity feedback system is:

1 + KG(z) Hzoh (z) = 0

Where G(z) is the compensator implemented in the digital

controller and Hzoh (z) is the plant transfer function in z .

Bode Plot:

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 determine the Amplitude ratio

value AR should be converted from decibels to absolute.

This can be done using one of the following:

1. Double click on bode diagram window.

A ‘property editor’ window will appear. Select ‘units’

option and then change AR from (db) to (abs). Then

find the value of AR at from the new curve.

2. Use the formula: Reading in db = 20 log AR

𝑲𝒖 =𝟏

𝑨𝑹

Results and discussion

Control Strategy with Digital Control:





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Figure 3: Control strategy of the Fluidized Bed Dryer with Digital Control

Control of the Air Temperature (Loop 1):

Conversion to z-transform:

For P-controller, the closed loop transfer function in

Laplace domain is:

G(s) =7.874𝑠 + 39.37

0.1s3 + 1.52s2 + 5.3s + 40.37

The closed loop transfer function in z-domain is:

𝐺(𝑧) =0.2859𝑧2 + 0.03319𝑧 + 0.1253

𝑧3 − 1.834𝑧2 + 1.251𝑧 − 0.2187


From the overall transfer function:

𝐺(𝑧) =0.2859𝑧2 + 0.03319𝑧 + 0.1253

𝑧3 − 1.834𝑧2 + 1.251𝑧 − 0.2187





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Figure 4: Stability and transient response using MATLAB

From the above figure:

𝜔𝑛 = 0.17 𝜋/𝑇, where T is the sampling time.

For 𝑇 =1

10 𝑠𝑒𝑐, 𝜔𝑛 = 5.341 𝑟𝑎𝑑/𝑠𝑒𝑐

And 𝜉 = 0.15

Step response in digital control system:

The overall transfer function for P-controller:

𝐺(𝑧) =0.2859𝑧2 + 0.03319𝑧 + 0.1253

𝑧3 − 1.834𝑧2 + 1.251𝑧 − 0.2187





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Figure 5: Step response in the set point of the digital control system

Tuning:

Discrete Root Locus:

𝐺(𝑧) =0.2859𝑧2 + 0.03319𝑧 + 0.1253

𝑧3 − 1.834𝑧2 + 1.251𝑧 − 0.2187





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Figure 6: Root locus for the discrete system

From the plot, the system is stable because all poles are

located inside the unit circle, and Ku = 0.373

Bode plot:

𝐺(𝑧) =0.2859𝑧2 + 0.03319𝑧 + 0.1253

𝑧3 − 1.834𝑧2 + 1.251𝑧 − 0.2187

Figure 7: Bode plot for the discrete system

𝐴𝑅 = 2.8, 𝐾𝑢 =1

𝐴𝑅=

1

2.8= 0.360





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Table 1: Comparison between the methods of tuning used for the discrete system

The method Ku

Root Locus 0.373

Bode 0.360

Average 0.367

The two methods are in agreement.

Effect of sampling time on overall T.F in z-domain and on system response:

The overall T.F for the system at different sampling time were determined as following:

Table 2: Overall T.F's and (OV) at different sampling time

Sampling Time Overall T.F's G(z) Overshoot(%)

0.01 0.003806 z^2 + 5.846e-005 z - 0.0035

------------------------------------

z^3 - 2.854 z^2 + 2.713 z - 0.859

88.2

0.1 0.2859 z^2 + 0.03319 z - 0.1253

----------------------------------

z^3 - 1.834 z^2 + 1.251 z - 0.2187

88

1 0.4894 z^2 + 0.1811 z - 0.04745

----------------------------------------

z^3 - 0.5419 z^2 + 0.1808 z - 2.505e-007

6.81

1.5 1.184 z^2 + 0.02086 z - 0.02017

-----------------------------------------

z^3 + 0.1377 z^2 + 0.07687 z - 1.253e-010

21.4

2 0.9357 z^2 + 0.1462 z - 0.008577

------------------------------------------

z^3 + 0.06793 z^2 + 0.03268 z - 6.273e-014

4.42

2.5 0.9332 z^2 - 0.07602 z - 0.003647

----------------------------------------

z^3 - 0.1387 z^2 + 0.0139 z - 3.127e-017

1.17

By changing the values of Ts from 0.01 to 0.1, 1 , 1.5 , 2 and 2.5, the response plots are:





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Figure 8: system response at Ts = 0.01 sec






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Figure 10: System response at Ts = 1 sec






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Figure 12: system response at Ts = 2 sec

Figure 13: System response at Ts = 2.5 sec

The values of overshoot decreases as Ts increases.





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Control of the fluidized bed pressure (Loop 2):


For P-controller, the closed loop transfer function in

Laplace domain is:

G(s) =8.703𝑠+43.52

0.6s3+5.06s2+10.5s+44.52


𝐺(𝑧) =0.0648𝑧2 + 0.01863𝑧 − 0.03514

𝑧3 − 2.286𝑧2 + 1.765𝑧 − 0.4303


From the overall transfer function:

𝐺(𝑧) =0.0648𝑧2 + 0.01863𝑧 − 0.03514

𝑧3 − 2.286𝑧2 + 1.765𝑧 − 0.4303




For 𝑇 =1


And 𝜉 = 0.17





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𝐺(𝑧) =0.0648𝑧2 + 0.01863𝑧 − 0.03514

𝑧3 − 2.286𝑧2 + 1.765𝑧 − 0.4303

Figure 15: Step response in the set point of the digital control system

Tuning


The method Ku

Root Locus 3.59

Bode 3.50

Average 3.545

The two methods are in agreement.





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Sampling Time Overall T.F's G(z) Overshoot (%)

0.01 0.000717 z^2 + 2.682e-005 z - 0.0006743

--------------------------------------- z^3 - 2.917 z^2 + 2.837 z - 0.9191

66.3

0.1 0.0648 z^2 + 0.01863 z - 0.03514

---------------------------------- z^3 - 2.286 z^2 + 1.765 z - 0.4303

65.5

1 1.617 z^2 + 0.9244 z - 0.0305

-------------------------------------- z^3 + 1.206 z^2 + 0.3632 z - 0.0002175

65.4

1.5 0.9816 z^2 + 0.2567 z - 0.01804

----------------------------------------- z^3 + 0.02879 z^2 + 0.2195 z - 3.208e-006

23.8

2 0.5919 z^2 - 0.1849 z - 0.01088

--------------------------------------- z^3 - 0.7272 z^2 + 0.1324 z - 4.73e-008

0

2.5 0.9689 z^2 + 0.06496 z - 0.006565

------------------------------------------ z^3 - 0.02895 z^2 + 0.07988 z - 6.976e-010

8.63

Control of the outlet air humidity (Loop 3):


For P-controller, the closed loop transfer function in Laplace domain is:

G(s) =1.198𝑠+11.98

0.1s3+1.2s2+2.1s+12.98


𝐺(𝑧) =0.05596𝑧2 + 0.03194𝑧 − 0.01934

𝑧3 − 2.137𝑧2 + 1.512𝑧 − 0.3012


The overall transfer function:

𝐺(𝑧) =0.05596𝑧2 + 0.03194𝑧 − 0.01934

𝑧3 − 2.137𝑧2 + 1.512𝑧 − 0.3012





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For 𝑇 =1


And 𝜉 = 0.12



𝐺(𝑧) =0.05596𝑧2 + 0.03194𝑧 − 0.01934

𝑧3 − 2.137𝑧2 + 1.512𝑧 − 0.3012





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Tuning:


The method Ku

Root Locus 1.88

Bode 1.87

Average 1.875

The two methods are in agreement




Sampling

Time(sec)

Overall T.F's G(z) Overshoot(%)

0.01 0.000595 z^2 + 5.267e-005 z - 0.0005348

--------------------------------------- z^3 - 2.885 z^2 + 2.772 z - 0.8869

68.5

0.1 0.05596 z^2 + 0.03194 z - 0.01934

---------------------------------- z^3 - 2.137 z^2 + 1.512 z - 0.3012

68.4

1 1.531 z^2 + 0.9722 z - 0.004256

--------------------------------------- z^3 + 1.276 z^2 + 0.4319 z - 6.144e-006

65.9

1.5 0.7874 z^2 + 0.05001 z - 0.002788 23.1





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---------------------------------------- z^3 - 0.3796 z^2 + 0.2838 z - 1.523e-008

2 0.5499 z^2 - 0.158 z - 0.001832

--------------------------------------- z^3 - 0.764 z^2 + 0.1865 z - 3.775e-011

1.06

2.5 1.085 z^2 + 0.3207 z - 0.001204

---------------------------------------- z^3 + 0.3994 z^2 + 0.1226 z - 9.357e-014

17.6

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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