Industrial Process Control Course

7/28/2019 Industrial Process Control Course

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Helwan University

Faculty of Engineering

Helwan

Prepared by

Dr. Mohiy Bahgat

2012


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Industrial Process Control

Dr. M. Bahgat Page 2

Course Contents

Chapter1:Components and characteristics of industrialprocesses

1.1. What is a process?

1.2. What does a control system do?

1.3. Why is control necessary?

1.4. Why is control possible?

1.5. How it can be done?

1.6. Where it can be implemented?

1.7. What are the control engineers interests?

1.8. How can the process control be documented?

1.9. Control strategies.

1.10. Components of industrial processes.

1.11. Exercises.Chapter 2: Mathematical modeling of industrial

processes

2.1. Modeling Procedure.

2.2. Linearization.

2.3. Numerical Solution of ODE.

2.4. Model Analysis of Processes.

2.5. Exercises.

Chapter 3: Measurement of control system parameters

3.1. Temperature Sensors.

3.2. Position sensors.

3.3. Speed Sensors.


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3.4. Pressure Sensors.

3.5. Force Sensors (strain gauges).

3.6. Fluid Sensors.

3.7. Flow Measurements.

3.8. Exercises

Chapter 4: Industrial controllers

4.1. On-off

4.2. P, I, D, PI, PD, PID

4.3. Temperature control

4.4. Pressure control

4.5. Flow rate control

4.6. Level control

Chapter 5: Forward control, Sequential control &

Multi-circuit

5.1. Feedback Control.

5.2. Multivariable Control.

5.3. Feed Forward Control.

5.4. Feed Forward plus Feedback Control.

5.5. Cascade Control.

5.6. Batch Control.

5.7. Ratio Control.

5.8. Selective Control.

5.9. Fuzzy Control.

Chapter 6: Introduction to process automation

6.1. Introduction.

6.2. PLC Operation Scan.


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6.3. PLC Addressing.

6.4. Relay Ladder Logics (RLL).

6.5. Exercises.

Chapter 7: Application to process automation using

PLCs

7.1. Signal Lamp Simple Process.

7.2. Machine Safety Process.

7.3. Central Heating Process.

7.4. Automatic Mixing Process.

7.5. Automatic Packing Process.

References


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Chapter (1)

Components and

Characteristics of

Industrial Processes


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Chapter (1)

Components and Characteristics

of Industrial Processes

Process control is an engineering discipline that deals with architectures,

mechanisms, and algorithms for controlling the output of a specific

process. This can be simple as making the temperature in a room kept

constant or as complex as manufacturing an integrated circuit.

For example, heating up the temperature in a room is a process that has

the specific, desired outcome to reach and maintain a defined temperature

kept constant over time. Here, the temperature is the controlled variable,

at the same time, it is the input variable since it is measured by a

thermometer and used to decide whether to heat or not. The desired

temperature is called the set-point. The state of the heater, for example,

the setting of the valve allowing hot water to flow through it; is called

the manipulated variable since it is subject to control actions.

A commonly used control device called a programmable logic controller,

or a PLC is used to read a set of digital and analog inputs, apply a set of

logic statements, and generate a set of analog and digital outputs. Using

the previous heating example, the room temperature would be an input to

the PLC. The logical statements would compare the set-point to the input

temperature and determine whether more or less heating was necessary to

keep the temperature constant. A PLC output would then either open or

close the hot water valve, an incremental amount, depending on whether

more or less hot water was needed.

Larger more complex systems can be controlled by a Distributed Control

System (DCS) or SCADA system.


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To make a good introduction to the process control, we should answer

some questions such as :

1. What is a process?2. What does a control system do?3. Why is control necessary?4. Why is control possible?5. How it can be done?6. Where it can be implemented?7. What are the control engineers interests?8. How can the process control be documented?9. What are control strategies?

1.1.What is a process control?Process control is an engineering discipline that deals with

architectures, mechanisms, and algorithms for controlling the output of

a specific process. This can be as simple as making the temperature ina room kept constant or as complex as manufacturing an integrated

circuit.

In practice, the industrial processes are different in behavior,

architecture and characteristics. So, they can be characterized as one or

more of the following forms :

1. Discrete processes.2. Batch processes.3. Continuous processes.4. Hybrid processes.


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Discrete process : it can be found in many manufacturing,motion and packaging applications. Robotic assembly, such as that

found in automotive production, can be characterized as discrete

process control. Most discrete manufacturing involves the

production of discrete pieces of product, such as metal stamping.

Fig (1.1)Robot arm control in a discrete process.

Batch process : where some applications require that specificquantities of raw materials be combined in specific ways for

particular durations to produce an intermediate or end result. One

example is the production of adhesives and glues, which normally

require the mixing of raw materials in a heated vessel for a period

of time to form a quantity of end product. Other important

examples are the production of food, beverages and medicine.

Batch processes are generally used to produce a relatively low to

intermediate quantity of product per year (a few pounds to millions

of pounds).


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Fig (1.2)Batching processes.

Continuous process : often, a physical system is representedthough variables those are smooth and uninterrupted in time. The

control of the water temperature in a heating jacket, for example, is

a form of continuous process control. Some important continuous

processes are the production of fuels, chemicals and plastics.

Continuous processes, in manufacturing, are used to produce very

large quantities of product per year, millions to billions of pounds.

Fig (1.3)Continuous reject process.


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Hybrid processes : Applications having elements of discrete,batch and continuous process control are often called hybrid

applications.

Fig (1.4)Product line processes as a hybrid process.

1.2.What does a control system do?A control system normally performs three main steps :

1.Measurement process for the variable to be controlled, orcollecting data from the controlled plant. This is done by sensors

or data acquisition cards.

2.Comparison between the measured variable and a referencevalue, doing some calculations to get the change in the variable,

or data processing for the collected data. This is done by

comparators, or through running of an algorithm or program.

3.Making a final decision in order to maintain the sensed variablewithin a desired range, or sending some control signals to the

controlled plant. This is done via the system actuators or final

control elements.


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The following sample of examples illustrates the process manual control

steps and the corresponding automatic process control scheme.

Level process control :

Fig (1.5)Manual level process control steps.

Fig (1).6Automatic level process control system.


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Heating process control :

Fig (1.7)Manual heating process control steps.

Fig (1.8)Automatic heating control system

So, the final goal of the control is to maintain or adapt desired conditions

in a physical system or an industrial process by adjusting selected

variables in that system. This can be done by making a use of an output

signal of the system to influence an input signal of the same system,

which called feedback control.


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1.3.Why is control necessary?The control and dynamic operation is an important factor in an

industrial process design. In other words, the industrial processes need

some degree of control for two main reasons :

1.The first one is to maintain the controlled conditions orvariables in a physical system or an industrial process at the

desired values when small or large disturbances occur.

2.The second reason is to respond to changes in the desiredvalues by adjusting the selected variables in the process. The

response is based on the analysis of the process operation and

objectives.

Finally, the process control will assure the following issues :

a. Safety.b.

Environmental protection.

c. Equipment protection.d. Smooth plant operation.e. Product quality.f. Profit optimization.g. Monitoring and diagnosis.

These issues are usually translated into values of the system or process

variables such as temperature, pressure, flow rate, liquid level, speed of

a motor or conveyor, displacement and so forth which are to be

controlled.


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1.4.Why is control possible?If the plant or the industrial process equipment is not properly

designed, the control system will perform poorly, inadequately or

might be impossible. Therefore, when designing an industrial process

or a plant, several considerations must be accounted such as :

a. Providing adequate equipment : which means includingadequate rapidly responded sensors for the process variable

and appropriate final control elements so that the control

actions can be taken in real time? Moreover, such sensors and

final control elements should be shielded and protected

against the surrounding effects due to the process operation.

b. Expected changes in the plant variables : which concernsabout the anticipation of the expected changes in the process

disturbances or the desired values of the controlling variables

and providing or adding adequate equipment during the plant

design? So, the adequate design calculations must be based on

the expected changes.

c. Adding a percentage extra capacity for the equipmentsizing : this is to allow the plant equipment to respond to all

expected disturbances or system variables by merely adding a

percentage extra capacity in accordance to the anticipated

changes.

If the previous considerations are not correct, or the plant design is not

accurate, the control may not be possible and the plant operation

through manipulating the final control elements may not be achieved.


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1.5.How can control be done?1.In simple process control, it can be done using the human

feedback.

2.In complex processes the feedback actions are automated bysensing, calculating, manipulating the controlled variables by

communicated parts of the control system. Currently, most

automatic control is implemented using electronic equipment at

some levels of current or voltage to represent the values to be

communicated.

3.So, one can say that, the process control is done automaticallyusing instrumentation and computation that perform all the

features of feedback control without requiring or allowing the

human intervention.

1.6. Where can control be implemented?

In order to operate an industrial process on a minute-to-minute basis, a

lot of information from much of the process has to be available at a

central location which known as the control room or control center.

Such control scheme is generally known as SCADA system where :

Sensors and control elements are located in the process.Signals which are mostly electronic or communications with the

control center to be viewed to the operator.

Distances between the process and the control center rangesfrom few hundred feet to a mile or more.

In some processes, small control panels are used nearby theequipment to allow access to them.


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Fig (1.9)Local and centralized control equipment

1.7. What are the control engineers interests?

The main interests of the process control engineers are :

a. Process design : where the process must be designed suchthat being with rapid response and minimal disturbances.

b. Measurements : where the sensors has to be selected withrapid response and high accuracy.

c. Final elements : where the final control elements must beprovided and handled so that the manipulated variables can be

adjusted by the control calculation.

d. Control structure : where the basic issues in designing thecontroller must be considered such as which control element

should be manipulated to control which measurement.

e. Control calculations : where equations are used to handle themeasurements and the desired values in calculating the

manipulated variables.


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1.8. How can the process control be documented?

The process control can be documented in many forms :

a. Equipment specifications and sizing.b. Operating manuals.c. Technical experiments and control equations.d. Engineering drawings.e. ROMs for storing the control algorithms.f. Additional EPROMs.

Fig (1.10)Stirred-tank with composite control

Fig (1.11)Flow controller


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The process drawings include some symbols such as :

A analyzer.

F flow rate.

L level of liquid or solids in a vessel. P pressure. T temperature.

and so on

1.9. What are the control strategies?

The following diagram displays a sample of the most commonly used

control strategies. Of course, the control strategy is different from one

process to another in accordance to its topology, complexity and

objectives.

Classical

ControlModern

Control

Industrial

Controllers

+

PLCs

Adaptive

Control

Optimal

Control

Robust

Control

A.I

Control

Computer Control

Control Strategies


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1.10. Components of industrial process

The industrial processes comprise several types of components :

1. Process : which in general can consist of a complexassembly related to some manufacturing sequence. The

process involves some variables needed to be controlled in

order to accomplish the desired goal of it. So, one can say that

the process may be single variable process or multivariable

process according to the number of variables to be controlled.

2. Measuring elements (sensors) : which representsthe devise that transforms or converts the measured variables

into some forms required by the other elements in the process

control operation. Signal conditioning may be required to

complete the measurement function in some cases.

3.Error detectors (comparators) : which is a physical

part of the controlling circuit that determines the difference

between the actual variable and the set-point value before

taking any control action.

4. Controllers (industrial or computer) : whichperforms the action should be taken in accordance to the

determined error and regulates or compensates the controlled

variable to bring it to the desired set-point or reference value.

5. Final control elements (actuators) : which is thedevice that exerts a direct influence on the process or provides

the required changes in the controlled variable to bring it to

the set-point.


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1.11. Exercises :


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Chapter (2)

Mathematical

Modeling of



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Chapter (2)

Mathematical Modeling of


2.1.Modeling Procedure :The general steps for building a mathematical model of a process can

be summarized as follows :

1. Define goals :a. Specific design decisions, which means that the goal should be

specific and clear.

b. Numerical values, where the goal is sometimes beingrepresented by numerical values.

c. Functional relationship, where in some cases the systemsbehavior is the goal.

d. Required accuracy, the model accuracy should also beincluded in the goal definition.

2. Prepare information :The information needed to be prepared are :

a. Sketch process and identify the system : identifying theprocess, the key variables and the system boundaries.

b. Identify variables of interest : the data regarding the physicalprocess components and the external inputs to the process.

c. State assumptions and data : the assumptions on which themodel will be built on.


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3. Formulate the model:When formulating a model of an industrial process, the first step is to

select the variables whose behavior is predicted and then deriving the

equations based on the conservation balance in mass and energy in

addition to the accumulation as follows :

a. Formulate the conservation balances (Energy balance Eqns.)b. Formulate the constitutive equations.c. Combine equations and collect terms.d. Check degrees of freedom.e. Convert to the dimensionless form.

Material Balance :

Accumulation of mass = (Mass)in(Mass)out

Energy Balance :

Accumulation of energy = (H + PE +KE)in

(H + PE + KE)out + QWs

where :

H : enthalpy = E + pv

PE : potential energy

KE : kinetic energy

Ws : work done by the process on the surroundings

Q : heat transferred to the process from the surroundings.Q = h . A . T

E : internal energy

pv : flow work


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Fig (2.1)Energy balance in a process.

4. Determine the solution :Determining the process model solution is very important. This can

be made either analytically or numerically. The analytical solutionunder some approximations is usually sought first. If such solution

results in unacceptable errors, numerical solutions are then sought.

Despite they are not exact but errors can be made less. The

analytical solution steps are :

Calculate the required specific numerical values. Determine the important functional relationships among the

process model, variables and system behavior.

Make a sensitivity study of the results associated with datachanges.


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5. Analyze the results :a.The first step of result analysis is to evaluate whether the

solution is correct or not, this can be done by ensuring the

following :

The results satisfy initial and final conditions. Obey the process bounds. Contains negligible errors associated with numerical

solutions.

Obey the process semi-quantitative expectations suchas output change sign.

b.The second step of result analysis is to analyze the processbehavior, this can be done by :

Determining the numerical results quantitavelly to helpin making decisions regarding the equipment operation

and sizing.

Plotting the results. Observing the process characteristic behavior like

oscillations in case of max or min oscillations.

Evaluate sensitivity, which means studying the processbehavior associated with change in data or important

variables.

Relate results to data and assumptions. Answer what if questions.


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6. Validate the model :The model validation involves determining whether the results

obtained in the previous steps are truly representing the physical

process.

This can be done by comparing the obtained results with some

experimental results taken from the process at different operating

points to assure the model validity in representing the process. In

other words, the steps of model validity are :

a. Select key values for validation.b. Compare with experimental results.c. Compare with results from more complex model.

The previous procedure can be divided into two main sections :

a.Model development steps (steps 1 to 3).b.Model solution and simulation (steps 4 to 6).

Example (1) :For the mixing tank shown in figure :

Fig (2.2)Mixing process configuration.


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1. The goal is to determine the dynamic response due to a stepchange in the inlet concentration. In other words, determining the

time needed for the outlet reaches 90% of change in concentration

after the step change in the inlet.

2. The information :a. The process is the tank with its fluid in it, its design and shape

and the speed of making the fluid uniform.

b. Assumptions : well-mixed vessel, density is the same for A andsolvent S in addition the flow in is constant.

c. Data : F0 = 0.085 m3/min , CAinit = 0.925 mole/m3 , CA0 =0.925 mole/m

3and CA0 = 1.85 mole/m

3after the step. The

system is initially at steady state.

3.The model formulation :Since the problem involves concentration, hence using the material

balance equation we can get :

Accumulation of mass = Mass inMass out

(V)(t+t) (V)(t) = Fo .t F1 .t

Dividing by t and taking the limit as t 0

Assuming that the level in the tank is almost constant, which means

that the flows in and out are equal, i.e : Fo = F1 = F

or : dV/dt = Fo F1 = 0 , i.e : V = constant (1)

Applying the same material balance for component A :

Accumulation of comp A = Comp AinComp Aout

10 F-FdtdV

dt)V(d


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(M WA V CA)(t+t)(M WA V CA)(t) = ( M WA F CAo

M WA F CA )t

Dividing by t and taking the limit as t 0

(2)

Applying the same material balance for component S :

Accordingly :

The process variables are :CA and F1

The external variables are :F0 and CA0

The process model is represented by equations (1) & (2) .4.Determine the solution :

As it can been seen from eqn.(2) the process model is a linear 1st

order

ordinary differential equation that can be transformed to the separable

form using an integral factor as follows :

, with V/F = = time constant

Use the integrating factor I.F =e( (1/)dt

= et/

)C-(CFWMdt

dCVWM AA0A

AA

)C-(CFWMdt

dCVWM ss0s

ss

)C-(CFWMdt

dCVWM AA0A

AA

)C-(CF

dt

dCV AA0

A

A0AA C

1C

1

dt

dC

t/A0AAt/ eC

)C1

dt

dC(e

t/A0At/t/

A

At/

e

C

dt

)Ce(d

dt

ed

Cdt

dC

e


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Using the initial conditions, we get : K = CAinitCA0

Substituting with the given numerical values :

(3)

Two aspects of the process dynamic response have to be considered :

The speed of response which is characterized by the timeconstant .

The steady state gain which is :

1. Result analysis :The solution of the process model described in eqn. (3) is an

exponential curve as displayed in the Fig (2.3). The process response

from the change beginning to the end is affected by the time constant

(), where the large time constant the slow process response and vice

versa. According to the goal, it is needed to know the time taken to get

90% of the change in outlet concentration. This time can be calculated

from eqn. (3).

dteC

dteC

)eCd( t/A0t/

A0t/A

KeC

eC t/A0t/A

-t/A0A eKCC

)e-(1])(C-[CC-C

e.)C-(CCC

t/-initA0A0AinitA

-t/A0AinitA0A

)e-(1].9250-[C0.925-C -t/24.7A0A

1C

C

input

outputK

A0

Ap


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Fig (2.3) - Dynamic response of the process.

6.Validation :By performing an experiment on a stirred tank as described in the

controlled process and taking samples of the outlet material,

analyzing the obtained samples and drawing the data points, one can

get the shown Fig (2.4). By visual evaluation, one can say the model

is valid in representing the process.

Fig (2.4)Model validation of the process.


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Example (2) : for the On-Off room heating processshown in figure :

Fig (2.5)On-Off room heating process configuration.

1. The goal : is to determine the dynamic response of the roomtemperature. Also, ensure that the furnace does not switch on or off

more than once per 3 minutes.

2. The information :a. The process is the air inside the room. The important variables

are the room temperature and the furnace on-off status.

b. Assumptions : the air in the room is well mixed, no transfer ofmaterial to or from the room, the heat transferred depends only

on the temperature difference between the room and the outside

environment, no heat is transferred from the floor to the ceiling

and effects of kinetic and potential energies are negligible.

c. Data : the heat capacity of the air CV = 0.17 cal/g C, the overallheat transfer coefficient UA = 45 x 10

3

cal/C hr, the size of the


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room is 5 m by 5 m by 3 m high, the furnace heating capacity Qh

is 0 (of) or 1.5 x 103 cal/hr (on), the furnace switches inst. At 17

C (on) and at 23 C (off), the initial room temp. is 20 C, and the

outside temp. is 10 C.

3.The model formulation :Since the process is defined as the air inside the room, hence using the

energy balance equation one can get :

dE/dt = KE + PE + QWs

KE = PE = Ws = 0 from assumptions

dE/dt = Q .. (1)

but dE/dt = V CV dT/dt

and Q = - UA (TTa) + Qh

and Qh is represented by :

0 when T > 23 C

Qh = 1.5 x 106 when T < 17 C

unchanged when T < 23 C

Finally, the process model is :

.. (2)

Accordingly :

The process variables are :T and Qh

The external variables are :Ta

The process parameters are :UA , CV , V and

haV Q)T-T(UA-dt

dTCV


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4.Determine the solution :Rearranging eqn. (2) gives the process model which is a linear 1 st

order ordinary differential equation that can be transformed to the

separable form using an integral factor as follows :


= et/

Using the initial conditions, we get :

.. (3)

where : t = time from step in Qh

= time constant = 0.34 hr

Tfinal = final value of T as t = Ta + Qh / UA

= 10 C when Qh = 0

= 43.3 C when Qh = 1.5 x 106

Tinit = the value of T when a step in Qh occurs.

UA

CVwith,

CV

QUA TT

1

dt

dT v

v

ha

v

hat/t/

CV

QUA T.e)T

1

dt

dT(e

v

hat/t/t/

t/

CV

QUA T.e

dt

)T.d(e

dt

deT.

dt

dT.e

dtCV QUA T.e)T.d(e v hat/t/ dteCV QUA T)T.d(e t/v hat/

KeCV

QUA T.T.e t/

v

hat/

t/-

v

ha e.KCV

QUA T.T

)e-1()T-T(T-T -t/initfinalinit


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Fig (2.6) - Dynamic response of the process.

5.Result analysis :From the previous figure (2.6), it can noticed that the room

temperature decreases until it reaches 17 C, the furnace will start

heating and the temperature increases until it reaches 23 C. This

process will be repeated with the heater On and Off periodically.

2.2.LinearizationIf the developed process model is linear, analytical solutions can be

obtained easily. Most of the physical system models are nonlinear. The

analytical solutions of the nonlinear models are not available, thus the

numerical simulations are sought. Instead of obtaining non-

understandable solutions for the nonlinear models by numerical

simulations, approximate linearized solutions can be used for

representing realistic processes.


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A model is to be linear if it satisfies the properties of additivity,proportionality and superposition which mean that when it is

subjected to a sum of inputs, a sum of outputs will result. For

example, if there is a system with an input of :

x3(t) = x1(t) + x2(t)

it should result in an output of :

y3(t) = y1(t) + y2(t)

A system satisfies the property of superposition, if a sum of scaledinputs results in a sum of scaled outputs. i.e :

f(Ax + By) = f(Ax) + f(By) = A . f(x) + B . f(y)

If the system has the following performance equation :f(x) = k . X

f(Ax1 + Bx2) = k . (Ax1 + Bx2)

k . (Ax1) + k . (Bx2)

Thus the above system in not linear, it is nonlinear system, and so on.

To illustrate the dynamic behavior of a process, consider the following

example stirred tank heat exchanger when being subjected to a change in

the feed temperature and cooling fluid flow rate.

Fig (2.7) - Stirred tank heat exchanger


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Fig (2.8) - Process response due Fig (2.9) - Process response due to

to a change in feed temperature a change in cooling fluid flow rate

Fig (2.10) - The total process response due to a change in both feed

temperature and cooling fluid flow rate

According to the dynamic behavior of the process, one can say that thisprocess is linear because it obeys the superposition principle. In general a

nonlinear process model can be linearized and approximated by a linear

model using Taylor series expansion. For example, a process nonlinear

model with one variable can be linearized around its S.S point as :

R)xx(

dx

dF

2

1)xx(

dx

dF)F(x)x(F 2s

x

s

x

s

ss


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A process nonlinear model with two variables can be linearized around its

S.S point as follows :

Fig (2.11) - Comparison between linear and exact nonlinear models.

Function examples :

1. F(x) = x xs + xs- (xxs)2. F(x) =

R)xx)(xx(

xx

F

2

1)xx(

x

F

2

1

)xx(x

F

2

1)xx(

x

F

)xx(

x

F)x,xF()x,x(F

s22s11

x,x21

22

s22

x,x

2

2

2s11

x,x

2

2

s22

x,x2

s11

x,x1

s2s121

s2s1s2s12

s2s11s2s1

s2s1

xa1

x

)xx()xa1(21

xa1

x s2

ss

s


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Example (3) : for the tank draining process shown infigure :

Fig (2.12)Tank drainingprocess configuration.

1.The goal : is to determine the model of this tank process. Also,evaluate the accuracies of the linearized model at small (10 m3/hr) and

large (60 m3/hr) step changes in the inlet flow rate.

2. The information :a.The process is the liquid in the tank. The important variables are

the level and the flow out.

b.Assumptions : the density is constant, the cross sectional area ofthe tank A does not change with height, the system is at quasi-

steady state because the pipe dynamics is fast with respect to that

of the tank level, the pressure is constant at inlet and outlet,

c.Data : the initial steady state conditions are : Flows F0 = F1 =100 m3/hr, Level L = 7 m, the cross sectional area A = 7 m2 .


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3.The model formulation :Since the process is defined as the liquid in the tank and the level

depends on the total amount of liquid, thus using the material balance

equation one can get ::

. (1)

Another equation is required, one can relate the outlet flow to the head

as follows :

. (2)

Finally, combining the two eqns., the process model will be :

. (3)

This model has a nonlinear term which can be linearized as :

... (4)

Replacing the nonlinear term in Eqn.(3) and Subtracting the S.S

conditions and putting the input as a constant step : Fo= Fo , one can

get the final process model as :

.. (5)

Accordingly :

The process variables are :L

The external variables are :Fo

The process parameters are :A and kF1

F-Fdt

dLA 1o

Lk)P-L-(PkF0.5

F1

0.5

aaF11 0.5

Fo Lk-Fdt

dLA

1

)L-(LL0.5LL s-0.50.50.5ss

L')L(0.5k-F=dt

dL'A 5.0Fo s1

-


40/149



5.Determine the solution :Rearranging eqn. (5) gives the process model which is a linear order

ordinary differential equation that can be transformed to the separable

form using an integral factor as follows :


= et/

Using the initial conditions, we get :

where : t = time from step in Fo

= time constant = 0.98 hr

kp = 0.14 hr/m2

0.5-sF1

oLk5.0

Awith,F

A

1L'

1

dt

'dL

ot/t/ F

A

1.e)L'

1

dt

'dL(e

ot/

t/t/t/ F

A

1e

dt

)'Ld(e

dt

deL'

dt

'dLe

dtFA1e)'Ld(e ot/t/ dteAF)'Ld(e t/ot/

KeA

F'Le t/ot/

t/-o e.KA

F'L

A

FK o

)e-1(

A

F'L t/-o

5.0s1F

pt/-

poLk5.0

1

AKithw)e-1(KF'L


41/149



Fig (2.13) - Process response to a small change in inlet flow rate.

Fig (2.14) - Process response to a large change in inlet flow rate.


42/149



6.Result analysis :From the previous figures (2.13) and (2.14), it can be noticed that the

solution of the linearized model is quite accurate with the small

change in the inlet flow rate.

On the other hand, it is inaccurate with the large change in the inlet

flow rate and it gives impossible negative level at S.S.

The general trend is the linearized model is more accurate with small

changes than with the large ones.

2.3.Numerical Solutions of O.D.EAs seen before, most of the practical modeling of process and process

control would result in nonlinear models. The nonlinear algebraic and

differential models cannot be solved analytically. Such models are

solved using different methods of numerical solutions.

The numerical solutions do not give expressions as before, but they

give points close to the exact solutions of the process models. The

concept of the numerical methods is to use initial values and an

approximation of the derivatives over a step of integration, and hence

calculate the variables after that step. Most of the numerical methods

for solving differential equations consider the Taylor series expansion

and make approximations by choosing specified terms of the series.

The most commonly used methods are :

1.Eulers method : which considers the first two terms of theTaylor series :

yi+1 = yi + f(yi, t).t


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2.Heuns method : which considers the first three terms of theTaylor series :

k1 = f(yi, t).tyi+1 = yi + f(yi+k1/2 , t+t/2).t

3.Runge-Kutta fourth order method : which considers thefirst four terms of the Taylor series?

yi+1

= yi+t/6 (k

1+2k

2+2k

3+k

4)

where :

k1 =

k2 =

k3 =

k4 =

The selection of the step size t is very important in reaching theapproximate solution of the process model using the numerical

solutions.

In Eulers method the error is proportional to the step size t,however, in Runge-Kutta method the error is proportional to

(t)4.

In most engineering applications, the appropriate step size ist = 0.01 sec.

)t,y(f ii

)2

tt,

2

k.ty(f i

1i

)

2

tt,

2

k.ty(f i

2i

)

2tt,

2k.ty(f i

3i


44/149



2.4.Model Analysis of ProcessesThe process model which comprises a linear differential equation can

be solved by analytical solution. On the other hand, the process model

which comprises a set of linear differential equations with constant

coefficients can be solved by Laplace transform method.

A control system involves several simultaneous processes and control

calculations can be modeled using input and output variables with the

aid of block diagrams and transfer functions. The process behavior to

sine inputs can be carried out easily using the frequency response

method to illustrate the influence of input frequency.

When a process is subjected to a step disturbance, it is required to

determine whether its behavior is stable or not.

2.4.1.Laplace transformThe Laplace transform is a very powerful method for engineers to

analyze the process control and control systems. It converts the constant

coefficient differential equations to algebraic equations which can be

solved easily. It replaces the time domain by a frequency domain or

complex domain. The Laplace transform is defined as :

The Laplace transform is linear operator, i.e :L[a.f1(t) + b.f2(t)] = a.L[f1(t)] + b.L[f2(t)]

Inverse Laplace can be achieves as :L-1[F(s)] = f(t) for t 0

Laplace transform for a constant :L(C) =

0

st- dtf(t).eF(s)))t(f(L

s

C

es

C

-dteC

st-

0

st-


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Laplace transform for an exponential :L(eat) =

Laplace transform for a step function :

The Laplace Transform properties can be summarized as follows :ExampleProperty

L[a.f (t) + b.g(t)] = a.F(s) + b.G(s)Linearity

Time Change

L( f (t T )) = esT F(s)Time axis displacement

L(eatf (t)) = F(s a)S axis displacement

Initial Value Theorem

Final Value Theorem

a-s

1e

s-a

1dtee a)t-(s-

0

st-at

0t0

0t;A)t(x

s

Ae

s

A-)s(X

dtA.edtx(t).eX(s)

0

st-

0

st-

0

st-

)a

s(F

a

1)]at(f[L

)s(FsLim)t(fLim s0t )s(FsLim)t(fLim 0st


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Tables of Laplace transform and its inverse transform are availablefor most commonly used functions as follows :

Laplace F(s)Function f(t)

1 unit impulse

1 / sU(t) unit step or constant

A / s

A / s2

n! / sn+1tn

1 / (s-a)eat

1 / (s+1)

/ (s2 + 2)sin (t)

s / (s2 + 2)cos (t)

s F(s)

sn F(s)

F(s) / s

0t0

0t;A)t(u

0t0

0t;At)t(r

at0

at)at(f)t(f

/te

1

F(s)e as

dt

)t(df

n

n

dt

)t(fd

dt)t(ft

0


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2.4.2. Partial FractionsIn order to get the time response for any plant or process, the dynamical

model of such plant should be solved. When the model in derived in

Laplace domain, the inverse Laplace can be utilized as follows :

Taking the inverse Laplace for both sides, one can get :

where Ci are constants and Hi(s) are the factors of the characteristic

polynomial D(s) = 0.

If H(s) is a 1st order term, then :

If H(s) is a 2nd order term, then :If there are repeated factors :

Example (4) :For the stirred-tank mixing model in deviationvariables is :

using Laplace transform :

V s CA(s) = F [ CAO(s)CA(s) ]

s CA(s) + CA(s) = CAO(s)

.....)s(H

C

)s(H

C

)s(D

)s(NY(s)

2

2

1

1

....])s(H

1[LC]

)s(H

1[LCY(t)

2

1-2

1

1-1

.....)s(H

B

)s(H

A

)s(D

)s(NY(s)

21

.....)s(H

C)s(HBsA

)s(D)s(NY(s)

21

1n1n

221

n )as(

C.....

)as(

C

)as(

C

)as(

M(s)Y(s)

)C-(CFdt

dCV 'A

'A0

'

A


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CA(s) ( s + 1) = CAO(s)

Considering a step change in the inlet concentration, i.e :

CA0(s) = CA0/s

Using the inverse Laplace, one can get :

Example (5) :Consider an industrial process having a modelin deviation variables as:

Using Laplace transform :

Take the input x(t) as a step function, then its Laplace transform will

be : and the output final equation is :

By then, we have four conditions described as follows :

1. if > o the process characteristic equation will have two realdistinct roots as :

1)s(s

1C(s)C A0

'A

)1ss

1(C(s)C A0

'A

)e-(1C(t)C-t/

A0

'

A

G.x(t)y(t)(t)y'2(t)y"1

20

20

G.x(s)Y(s)sY(s)2Y(s)s1

20

2

20

x(s).

s2s

.GY(s)

20

2

20

s

AX(s)

]s2s.[s

.GAY(s)

20

2

20

222,1 --r


49/149



Finally, the process output y(t) will be :

This condition is called the over damping condition where the

output response does not have any oscillations as shown :

Fig (2.15) - Output response of an over

damped controlled process.

2.if = o the process characteristic equation will have two realequal roots as :


This condition is called the critically damped where the output

also does not have oscillations as shown :

)r(s

k

)r(s

k

s

GA

)rs()r(ss

.GAY(s)

2

2

1

1

21

20

tr

2

tr

121 ekekG.A)t(y

-rr 2,1

221

2

20

)r(s

k

)r(s

k

s

GA

)r(ss.GAY(s)

t21 e)k(kG.A)t(y


50/149



Fig (2.16) - Output response of an critically


3.if < o the process characteristic equation will have twocomplex conjugate roots as :


This condition is called the under damped where the output has

decayed oscillations as shown :

Fig (2.17) - Output response of an under


j-r 222,1

)r(s

k

)r(s

k

s

GA

)rs()r(ss

.GAY(s)

2

2

1

1

21

20

)tsin(ekG.A)t(y dt


51/149



4.if = 0 the process characteristic equation will have twocomplex conjugate roots as :


This condition is called the oscillatory condition where the output

will have continuous oscillations as shown :

Fig (2.18) - Output response of an oscillatory process.

2.4.3.Transfer FunctionThe process transfer function is defined as the Laplace transform of the

output Y(s) divided by the Laplace transform of the input X(s).

Transfer Function = T.F = G(s) =

jrr 2,1

)j(s

k

)j(s

k

s

GA

)j(s)j(ss

.GA

Y(s)

21

20

t)(scokG.A)t(y 0

)s(X

)s(Y


52/149



Basic definitions :

Order : the system order is the highest power of s in thedenominator of the T.F.

Pole : it is a root of the denominator of the T.F or a root of thesystem characteristic equation.

Zero : it is a root of the numerator of the T.F.Steady state gain : it is the ratio Y/X at steady state or

yss/xin and usually denoted by K.

Example : For a system or a process whose T.F is :

The system is 2nd order The poles are : s = - 8.95 j 5.92 The zero is : s = 7.64 The S.S gain is : K = 45.83/35.8 = 1.28

2.4.4.Block diagramThe block diagram method is a powerful graphical representation for

the system or process individual components based on their T.F. It has

some advantages :

1.It retains individual systems and allows model simplificationand changes.

2.It provides a visual representation of the relationshipsbetween the system components.

3.It gives insight into the effect of components on the overallsystem performance.

8.35s789.1s

45.83-s6

)s(X

)s(Y2


53/149



Fig (2.19) - Block diagram for a general control system.

Fig (2.20) - Physical process control.


54/149



Fig (2.21) - Block diagram of the process control.

Fig (2.22) - OnOff control of a heating or cooling process.


55/149



Fig (2.23) - Analog control of the heating process.

Fig (2.24) - Digital control of the heating process.


56/149



Fig (2.25) - PLC control of the heating process.

Fig (2.26)Multi-loop industrial process control system.

315 psi

L

Flow

valve

Flow

valve

Flow

valve

315 psi

315 psi

420 mA

420 mA

420 mA

Flow

sensor

Temp.

sensor

Level

sensor

Steam


57/149



Block diagram Notations :

There are some standard symbols to be used in developing the block

diagram of any system plant or process. The following is a sample of

such symbols :

X3(s) = x

1(s) + x

2(s) X

3(s) = x

1(s) = x

2(s)

G(s) = Y(s) / X(s)

Fig (2.27)Block diagram notations.

Block diagram Algebra :

1. Series or Cascaded Blocks :

Y1(s) = G1(s) . X1(s)

Y1(s) = X2(s)

Y2(s) = G2(s) . X2(s) = G2(s) . Y1(s)


58/149



= G2(s) . G1(s) . X1(s)

= G(s) . X1(s)

G(s) = G1(s) . G2(s)

2. Parallel Blocks :

Y1(s) = G1(s) . X(s)

Y2(s) = G2(s) . X(s)

Yt(s) = Y1(s) + Y2(s) = G1(s) . X(s) + G2(s) . X(s)

Yt(s) = ( G2(s) + G1(s) ) . X(s)

= G(s) . X(s)

G(s) = G1(s) + G2(s)


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3. Feedback System Blocks :

Example(6):

Apply the block diagram reduction rules to obtain the overall transfer

function Y(s) / X(s).

H(s)G(s)1

G(s)

R(s)

C(s))s(Gt

(s)RC(s).H(s)G(s)C(s) (s)R)

G(s)

G(s)H(s)

G(s)

1(C(s)

(s)R)G(s)

G(s)H(s)1(C(s)

(s)RB(s)E(s)


60/149




61/149



Fig (2.28)Block diagram reduction example.

2.4.5.Frequency response :The frequency response is very important when studying the systemdynamic behavior associated with sinusoidal input at different

frequencies. A stable linear system subjected to a sinusoidal input X(t)

will, at steady state, have a sinusoidal output Y(t) of the same

frequencyas the input. But the amplitude and phase of output will be

different from those of the input. The relationship between input and

output can be characterized by :

))Re(G(j

))(G(jIm

tan=

)G(j==Pahseangle

))(G(jIm+))Re(G(j=

)G(j=)t('X

)t('Y=

magnitudeInput

magnitudeOutput=atioAmplituder

1-

22

max

max


62/149



Example (7) : For the mixing process shown in Fig (2.29) :

Fig (2.29)The mixing process.

The model of the stirred tank was written before as :

Since the inlet will be used as a sinusoidal input, i.e : CA0 = A sin(t) ,

one can rewrite the system model as :

Using = V/F and taking the Laplace transform, the system model

becomes as :

Using the partial fraction method, the system model becomes as :

)C-(CFdt

dCV AA0

A

AA C.F-t)sin(AF.

dtdCV

)s(C-s

.A(s)Cs A22A

s

.As)(1(s)C22A

)js(

k

)js(

k

)1

(s

k

)s()1

(s

/.A(s)C

321

22A


63/149



where :

Finally, the system model becomes as :

which can be rewritten in the form :

Note that the input was : CA0(t) = A sin(t)

)js(

k

)js(

k

)1

(s

k(s)C 321A

221 1

Ak

)(tan

e1

1

j2

Ak

e1

1

j2

Ak

1

j

223

j

222

)t-j(3

)tj(2

-t/1A ekekek(t)C

)tsin(1

Ae

1

A(t)C

22

t/-

22A


64/149



2.5.Exercises :


65/149



Chapter (3)

Measurement of

Control System

Parameters


66/149



Chapter (3)

Measurement of Control

System ParametersIndustry and industrial processes use a variety of sensors to control its

operations; the most familiar devices include thermocouples, pressure

gauges, encoders and others , which measure a single variable at a single

point in the process. As manufacturing processes have become more

complex, additional types of information and measurements are required.

Some of industrial processes now need measurements of film thickness,

particle size, solids concentration, and contamination detection. Most of

the used sensors operate on relatively simple principles that are based on

the interaction between matter and sound, light, or electric fields. These

devices or sensors are used in process control to measure some parameters

and the resulting data is used to control the process. In addition, such

measurements enable better process understanding, which often drives

process improvement such as improving the productivity or achieving the

uniformity of a product. Figure (3.1) displays that the process

measurements are very important and representing the basic step leading to

several aspects which finally maximize the process profit and process

improvement. There is often more than one type of sensors that will

function adequately in a given application. For instance:

1. Temperature Sensors.2. Position Sensors.3. Pressure Sensors.4. Force Sensors.5. Fluid (Flow rate) Sensors.


67/149



Fig (3.1) - Process measurement as a crucial step to plantoperation and profitability.

The choice of a sensor always depends on the specific details of the

application, so it is imperative to understand the operation and limitations

of each measuring or sensing device. Clearly, other factors such as cost or

vendor issues have to be considered, but from a purely technical point of

view the best choice of sensor for a given application ultimately depends

on the details of the measurement process.

The performance of any process sensor, new or old, can be summarized as

follows :

The sensor must be completely reliable under continuous operationand ideally require no preventive maintenance.

The sensor should be installed in such a way that it can be replacedquickly in case it does eventually malfunction.

The sensor is easy to use and does not require a complicatedcalibration sequence.

The data it provides should be directly related to the physicalproperties of interest. For example, a sensor that purports to measure

viscosity but in reality is also sensitive to changes in pressure is of


68/149



limited usefulness.

The data it provides should be easily interpreted. For example,sensors that measure scalar quantities such as temperature or flow

rate generally output a signal that is proportional to these quantities.

If the sensor interface is digital, the readout should be provided in the

correct units.

The sensor should be compatible with other sensors and with theexisting distributed control system.

The sensor must provide an immediate pay-off relative to its cost ofpurchase and installation, which is usually many times more than the

purchase price.

3.1. Temperature sensors :

Temperature is a basic measurement used throughout many processes. It

is a measure of the thermal energy in a body, which is the relative

hotness or coldness of a medium and normally measured in degrees

using one of the following scales; traditional Fahrenheit scale (F),

Celsius which is originally called centigrade scale (C) or the absolute

Kelvin scale (K) as standard units of measurement. Temperature

sensors are used in the process control that concerns with temperature

regulation. It depends on the electrical methods of measuring

temperature. The basic types of temperature sensors are :

1. Bimetallic temperature sensor.2. ResistanceTemperature Detectors (RTD) sensors.3. Thermistors or semiconductor usage in measuring temperature.4. Thermocouples.


69/149



3.1.1. Bimetallic temperature sensors :The bimetallic temperature sensors have some advantages of simplicity

and low cost, on the other hand, its main disadvantages are the

existence of hysteresis, inaccuracy and the slow time response. Such

sensors are used in numerous applications, particularly where an

ON/OFF cyclic operation is needed rather than smooth or continuous

control.

The sensor basic operation is built on the thermal linear expansion

which is the change in dimensions of a material due to temperature

changes. The change in dimensions of a material is due to its

coefficient of thermal expansion that is expressed as the change in

linear dimension () per degree temperature change.

L = Lo ( 1 + . t )

where : L = the final length.Lo = the initial length.

t = T To = temperature difference.

= the linear thermal expansion coefficient.

The bimetallic sensor consists of two materials with grossly different

thermal expansion coefficients bounded together. When the sensor is

being subjected to heating, the different expansion rates of the two

materials will cause the sensor assembly to be curved as shown in

Fig(3.2). This effect can be used to close switch contacts or to actuate

an ON/OFF mechanism when the temperature increases to some

appropriate set-point.


70/149



Fig (3.2)Bimetallic strip sensor.

3.1.2. Resistance temperature sensors :One of the most important methods for electrical measurement of

temperature is based on the electrical resistance change of a conducting

material. So, the principle of measuring or sensing temperature is to

place a conducting material with sensitive change of resistance with

respect to temperature in contact with the environment whose

temperature is to be measured or sensed. By then the device will take

the temperature of the environment. Thus a measure of the conducting

material resistance will indicate the temperature of the sensor and the

environment. The resistance of a conductor varies according to the

following factors :

The resistance is directly proportional to the conductor length :Rl

The resistance is inverse proportional to the conductor crosssection area :R1/a

The resistance depends on the type of the conductor material :R= .l / a

The resistance is affected by the surrounding resistance such that :

1

2 < 1

at To


71/149



RT = RTo ( 1 + . t )

where : RT = the conductor resistance at a temperature T.

RTo = the conductor resistance at a temperature To.

t = TTo = temperature difference.

= the linear change coefficient in resistance with

respect to temperature.

The resistance-temperature detector (RTD) is a temperature sensor

whose operation is based on the resistance variation of a metal

conductor with temperature. Metal used in such a sensor vary from

platinum which is quit sensitive and expensive to nickel which is more

sensitive and less expensive.

The sensitivity of the RTD sensor depends on the value of the linear

change coefficient in resistance with respect to temperature ().

Typical values of such coefficient for different materials are :

= 0.004 /C for platinum.

= 0.005 /C for nickel.

In general the RTD has a time response ranges between 0.5 to 5

seconds or more. This slow response is due to the slow thermal

conductivity in bringing the sensor into thermal equilibrium with the

surrounding environment.

The RTD sensor construction is basically in the form of a wire wound

as a coil to achieve small size, improved thermal conductivity and

decreased time response. This coil is protected by a sheath or a tube.

The resistance of the coil will be monitored as a function of

temperature. Fig (3.3) shows the internal construction of an RTD.


72/149



Fig (3.3)Internal construction of a typical RTD.

This design has a platinum element surrounded by a porcelain

insulator. The insulator prevents a short circuit between the wire and

the metal sheath. A nickel-iron-chromium alloy is normally used inmanufacturing the RTD sheath. When placed in a liquid or gas

medium, the sheath quickly reaches the temperature of the medium and

the change in temperature will cause the platinum wire to heat or cool,

resulting in a proportional change in resistance. This device is normally

used in a bridge circuit. Fig (3.4) shows an RTD protective well and

terminal head, which can be used for temperatures up to 1100C.

Fig (3.4)RTD protection and terminal head.


73/149



Since the variation of the RTD resistance is relatively small, the RTD

is usually used a branch of a bridge as shown in Fig (3.5) :

Fig (3.5)RTD sensor with signal conditioning.

The effective range of RTD sensors basically depends on the type of

the effective element wire. For example :

Platinum RTD has the range of : - 100 to 650 C

Nickel RTD has the range of : - 180 to 300 C

3.1.3. Thermistor sensors :The thermistor represents another class of temperature sensor that

measures temperature through changes of material resistance. The

characteristics of such devices are very different from those of the

RTDs and depend on the behavior of semiconductor resistance with

temperature.

So, one can say that the word thermistor comes from a contraction of

thermal resistor. The resistance of a thermistor is a function of the

ambient temperature.


74/149



The change in resistance R of the thermistor is proportional to the

change in temperature T when using a first-order approximation over

limited temperature ranges where () is the characteristic temperature

coefficient of the thermistor.

The thermistor construction may take several forms including discs,

beads and rods varying in size from a bead 1 mm in diameter to a disc

of several cm in diameter and thick. This can provide a wide range of

resistance values at any particular temperature.

The effective range of thermistor sensors depends on thesemiconductor material used in constructing the thermistor. The

thermistor practical range is : - 80 to 300 C.

3.1.4. Thermocouple sensors :The thermocouple is a device that converts thermal energy into

electrical energy. A thermocouple is constructed of two dissimilar

metal wires joined at one end. The most important factor to be

considered when selecting a pair of materials is the thermoelectric

difference between the two materials. A significant difference between

the two materials will result in better thermocouple performance.

Figure (3.6) displays the constructions of a typical thermocouple. The

leads of the thermocouple are encased in a rigid metal sheath. The

measuring junction is normally formed at the bottom of the

thermocouple housing. Magnesium oxide surrounds the thermocouple

wires to prevent vibration that could damage the fine wires and to

enhance heat transfer between the measuring junction and the medium

surrounding the thermocouple.


75/149



Fig (3.6) - Internal construction of a typical thermocouple.

Other materials may be used in addition to those shown in figure, for

example: Chromel-Constantan is excellent for temperatures up to 2000

F and Tungsten-Rhenium is used for temperatures up to 5000 F.

When a thermocouple is subjected to changes in temperature, it will

cause an electric current to flow in the attached circuit. The amount of

produced current depends on the temperature difference between the

measurement and reference junction; the characteristics of the two

metals used; and the characteristics of the attached circuit. Fig (3.7)

illustrates a simple thermocouple circuit.

Fig (3.7) - Simple thermocouple circuit.


76/149



Fig (3.8) - Thermocouple circuit with temperature

control and signal conditioning.

Heating the measuring junction of the thermocouple produces a voltage

which is greater than the voltage across the reference junction. The

difference between the two voltages is proportional to the difference in

temperature and can be measured on the voltmeter (in milli-volts) or

amplified and then sent to operate a control circuit.

3.2. Position sensors :The measurement of displacement, position, or location is important in

the process industries. The requirements of measuring such variables

and the used sensors are varied in the industries. For examples :

Location and position on conveyor systems.Orientation of steel plates in a rolling mill.Liquid or solid level monitoring, etc

The most commonly used sensors for displacement, position or

location are :

3.2.1. Potentiometers :The simplest type of displacement sensor involves the action of

moving the wiper of a potentiometer. This device converts the linear or


77/149



angular motion into a changing in resistance that may converted

directly into a voltage and/or current signals as shown in Fig (3.9).

Fig (3.9)Linear potentiometer displacement sensor.

The output voltage of the sensor can be calculated from the following

formula :

3.2.2. Capacitive sensor :The basic operation of a capacitive sensor can be derived from the

capacitance equation of the parallel plate capacitor :

where :

o

is the air permittivity = 8.85 pF/m

r is the dielectric constant.

A is the plate common area.

d is the plate separation.

The capacitance of the capacitor can be changed by varying the

distance between the plates (d), or by varying the shared area of the

plates (A) as shown in Fig (3.10).

Motion

Wiper

R

r

VinVout

inout V.R

rV

d

AC ro


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Fig (3.10)Variation of capacitance with the distance

or the area between the plates

An A.C bridge or other active electronic circuit is employed to convert

the capacity change to a current or voltage signal.

3.2.3. Inductive sensor :The inductance type transducer consists of three parts : a coil, a

movable magnetic core, and a position sensing element. The element is

attached to the core, and, as position varies, the element causes the core

to move inside the coil. An A.C voltage is applied to the coil, and, as

the core moves, the inductance of the coil changes. The current through

the coil will increase as the inductance decreases.

3.2.4. Linear variable differential transformer (LVDT) :The LVDT is an important displacement sensor in industrial

environment with an operation depending on the inductive sensor

principle and utilizing single core and two coils wound on a single tube

as illustrated in Fig (3.11). The primary coil is wound around the

center of the tube. The secondary coil is divided with one half wound

around each end of the tube.

d

Capacity C

Capacity C

A


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Each end is wound in the opposite direction, which causes the voltages

induced to oppose one another. A core, positioned by a displacement

element, is movable within the tube. When the core is in the lower

position, the lower half of the secondary coil provides the output.

When the core is in the upper position, the upper half of the secondary

coil provides the output. The magnitude and direction of the output

depends on the amount the core is displaced from its center position.

When the core is in the mid-position, there is no secondary output.

Fig (3.10)Construction of the LVDT sensor.


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Fig (3.11)Using the LVDT sensor to produce a bipolar D.C

voltage that varies with core displacement.

3.3. Speed sensors :

The linear speed or position of a translational moving mechanism such

as a conveyor system can be measured or monitored for the purpose of

control by means of a linear optical encoder.

On the other hand, the angular speed or the angular position of a

rotational mechanism such as a motor can be measured or monitored

for the purpose of control by means of either a tachometer or a digital

encoder.

3.3.1. Tachometer as a speed sensor :The tachometer is a permanent magnet D.C generator, when driven

mechanically; it generates an output voltage that is proportional to

shaft speed.

Since : E . N

For permanent magnet machine : = constant


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Hence : E N

Therefore, the tachometer will generate an output voltage proportional

to shaft speed as displayed in Fig (3.12).

The other main requirements for a tachometer are :

1. The output voltage should be smooth over the operating range.2. The output should be stabilized against temperature variations.

Fig (3.12)Tachometer output characteristics.

Small permanent magnet D.C tachometers are frequently used in servosystems as speed sensing devices. These systems usually incorporate

thermistor temperature compensation and make use of a silver

commutator and silver loaded brushes to improve commutation

reliability at low speeds and at the low currents, which are typical of

this application. The tachometer is mounted on the motor shaft and

enclosed within the motor housing as illustrated in Fig (3.13).

Fig (3.13) - Motor with integrated tachometer.


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3.3.2. Optical Encoder sensor :In servo control systems, where mechanical position is required to be

controlled, some form of position sensing device is needed. For

accurate position control, the most commonly used device is the optical

encoder. Optical encoders are devices that convert a mechanical

position or speed into a representative electrical signal by means of a

patterned disk or scale, a light source and photosensitive elements.

Their principle of operation is achieved by moving disk between the

light source and the photosensitive element. The light source may be a

light emitting diode or an incandescent lamp, and the detector is

usually a phototransistor or more commonly a photo-voltaic diode.

When light passes through the transparent areas or the holes of the disk

an output is seen from the detector. There are two forms of the

encoders namely :

Absolute encoders.Incremental encoders.

An incremental encoder : which generates a pulse for a given

increment of the shaft rotation in case of rotary encoder, or a pulse for

a given linear distance travelled in case of linear encoder. Furthermore,

the total distance travelled or shaft angular rotation is determined by

counting the encoder output pulses or with proper interface electronics,

position and speed information can be derived. Rotary encoders are

available as housed units with shaft and ball-bearings or as modular

encoders which are usually mounted on a host shaft at the end of a

motor. The disk count is defined as the number of dark/light line-pairs

that occur per revolution in terms of cycles/revolution or c/r.


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Fig (3.14)Incremental encoders and the resulting signal.

The disadvantage of incremental encoders is the loss of position data at

power-down. This is not a problem if the system can be re-initialized

on power up by searching for the index and re-setting the position

counters.

An absolute encoder : has a number of output channels, suchthat every shaft position may be described by its own unique code. The

higher the resolution the more output channels are required. With this

type of encoders, position information is instantly available as a digital

word on power-up. The disk of an absolute encoder is patterned with a

number of discrete tracks, corresponding to the word-length. Fig (3.15)

illustrates a 3 bit and a 4 bit encoder pattern whose output is reflected


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in binary or Gray code. The advantage of this pattern is that from

position to position only one bit changes its state.

(a)3 bit absolute encoder disk pattern.

(b)4 bit absolute encoder disk pattern.

Fig (3.15)Absolute encoders and the resulting signal patterns.

3.4. Pressure sensors :

The measurement and control of liquid or gas pressure is one of the

most common in most of the industrial processes. The pressure

measurements are very important in order to keep the material under

safe operation.


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The pressure may be either static pressure where the fluid is not

moving or dynamic pressure where the fluid is moving and exerting a

pressure on the surroundings.

Pressure sensors are available in different designs depending on the

pressure to be measured or controlled.

3.4.1. Bellow type sensor :

The metallic bellows pressure sensors are used when it is needed to

sensing low pressures and providing power for activating recording

and indicating mechanisms. Such sensors are most accurate when

measuring pressures from 0.5 to 75 psi. However, when used in

conjunction with a heavy range spring, they can be used to measure

pressures of over 1000 psi. Figure (3.16) shows a basic construction of

the metallic bellows pressure sensing element.

Fig (3.16) - Basic construction of the metallic bellow sensor.

The system pressure is applied to the internal volume of the bellows

where by varying the inlet pressure to the instrument, the bellows will

expand or contract. The moving end of the bellows is connected to a

mechanical linkage assembly.


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As the bellows and linkage assembly moves, either an electrical signal

is generated or a direct pressure indication is provided. The relation

between increments of load and deflection is linear in the range of the

elastic limit of the bellows. This relationship exists only when the

bellows is under compression. So, it is necessary to construct the

bellows such that all of the travel occurs on the compression side of the

point of equilibrium.

3.4.2. Bourdon Tube Pressure sensor :The bourdon tube pressure instrument is one of the oldest pressure

sensing instruments in use today. The bourdon tube consists of a thin-

walled tube that is flattened diametrically on opposite sides to produce

a cross-sectional area elliptical in shape, having two long flat sides and

two short round sides. The tube is bent lengthwise into an arc of a

circle from 270 to 300 degrees.

The pressure is applied to the inside of the tube causing distention of

the flat sections and tends to restore its original round cross-section.

This change in cross-section causes the tube to straighten slightly.

Since the tube is permanently fastened at one end, the tip of the tube

traces a curve that is the result of the change in angular position with

respect to the center. The movement of the tip of the tube can then be

used to position a pointer or to develop an equivalent electrical signalto indicate the value of the applied internal pressure.

Figure (3.17) illustrates the basic construction of bourdon tube pressure

sensor when replacing the pointers by an electronic circuit.


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Fig (3.17) - Basic construction of the bourdon pressure sensor.

3.5. Force sensors (Strain gauge) :

One of the most important force sensors or transducers is the strain

gauge. Figure (3.18) illustrates a simple strain gauge where it is used

for measuring the external force or pressure applied to a fine wire. The

fine wire is usually arranged in the form of a grid or a folded wire.

Fig (3.18) - Basic construction of the strain gauge.


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The pressure change causes a resistance change due to the distortion of

the wire. The value of the pressure can be found by measuring the

change in resistance of the wire grid.

Since : R= .l / awhere :

R = resistance of the wire grid in ohms.

= resistivity constant for the particular type of wire grid.

l = length of wire grid.a = cross sectional area of wire grid.

Therefore, as the wire grid is distorted by elastic deformation, its

length is increased, and its cross-sectional area decreases. These

changes cause an increase in the resistance of the wire of the strain

gauge. This change in resistance is used as the variable resistance in a

bridge circuit that provides an electrical signal for indication of force

or the pressure. Figure (3.19) illustrates a strain gauge pressure

transducer.

Fig (3.19) - The strain gauge as a force sensor.


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Fig (3.20)Using four strain gauges as a bridge force sensor.

Fig (3.21) - The strain gauge as a pressure sensor.

In Fig (3.21), an increase in pressure at the inlet of the bellows causes thebellows to expand and moving a flexible beam to which a strain gauge

has been attached. The movement of the beam causes the resistance of the

strain gauge to change. The temperature compensating gauge

compensates the heat produced by current flowing through the fine wire

of the strain gauge. Strain gauges, which are nothing more than resistors,

are used with bridge circuits as shown in Fig (3.22).


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Fig (3.22) - Strain gauge in a bridge circuit.

Alternating current is provided by an exciter that is used in place of a

battery to eliminate the need for a galvanometer. When a change in

resistance in the strain gauge causes an unbalanced condition, an error

signal enters the amplifier and actuates the balancing motor which moves

the slider along the slide wire, restoring the bridge to the balanced

condition; the sliders position is noted on a scale marked in units of

pressure.

3.6. Fluid sensors :

Liquid level measuring devices are classified into two groups :

a) Direct method. b) Inferred method.

An example of the direct method is the dipstick in the car which

measures the height of the oil in the oil pan. On the other hand, an

example of the inferred method is a pressure gauge at the bottom of a

tank which measures the hydrostatic head pressure from the height of

the liquid.


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The level sensors can be classified as follows :

1. Mechanical sensors Float methods Buoyancy method Vibrating level systems

2. Hydrostatic pressure methods Differential pressure level detectors Bubbler systems

3. Electrical methods Conductivity probes Capacitance probes Optical level switches Ultrasonic level detectors Microwave level systemsNuclear level systems

3.6.1. Floats level sensor :The basic float arm indicator comprises very simply a float connectedto a pivoted arm that drives pointer or a switch. The unit can be made

for either side or top entry. The main disadvantage of such a sensor is

the presence of the moving parts in the liquid which causes corrosion

and seizing to such parts. Methods of providing indication are by using

linkage to a pointer, a potentiometer and magnetic or inductive

switches as displayed in Fig (3.23).


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Fig (3.23)The float level sensor.

3.6.2. Buoyancy level sensor :These devices use Archimedess principle where the mechanical level

indicator consists of the immersion body with calibrated measuring

spring which transmits the change of level to the mechanical or

electrical indicator according to the following equation :

r2 ( h - L ) g = k . L

Fig (3.23)The buoyancy level sensor.


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3.6.3. Ultrasonic level measurement :The measuring equipment consists of the following elements:

A transmitter : which periodically sends an ultrasonic

pulse to the surface of the liquid

A receiver : which receives and amplifies the returningpulse.

A time interval counter : which measures the timeelapsing between the transmission of a pulse and receiption of

the corresponding pulse echo.

The travelling distance can be calculated as :L = c . t / 2

And consequently, the head can be as :

h = LmaxL = Lmaxc . t / 2

where :

c = sonar pulse velocity (m/sec).

t = time in sec.

L = travelling distance (m).


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Fig (3.24)The ultrasonic level sensor.

a) Solid or liquid above b) Liquid material below

surface measurement surface measurement

Fig (3.25)Th

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Industrial Process Control Course