Pressure Instrument Trainer

8/16/2019 Pressure Instrument Trainer

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Pressure Instrument Trainer 1

ForewordForewordForewordForeword

Welcome to value-conscious company. We are proud of the advanced engineering andquality construction of each equipment we manufacture.

This manual explains the working of equipment. Please read it thoroughly and have allthe occupants follow the instructions carefully. Doing so will help you enjoy many yearsof safe and trouble free operation.

When it comes to service remember that K.C. Engineers knows your equipment bestand is interested in your complete satisfaction. We will provide the quality maintenanceand any other assistance you may require.

All the information and specifications in this manual are current at the time of printing.However, Because of K.C. Engineers policy of continual product improvement wereserve the right to make changes at any time without notice.

Please note that this manual explains all about the equipment including options.

Therefore you may find some explanations for options not installed on your equipment.

You must follow the instructions and maintenance instructions given in the manualcarefully to avoid possible injury or damage. Proper maintenance will help ensuremaximum performance, greater reliability and longer life for the product.

K.C. Engineers


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PRESSURE INSTRUMENT TRAINER

INTRODUCTION:

Currently, the PID algorithm is the most common control algorithm used in industry.

Often, people use PID control processes that include heating and cooling systems, fluid flow

monitoring, flow control and temperature control. In PID control, you must specify a process

variable and a set point. The process variable is the system parameter you want to control

such as temperature, pressure and flow rate and the set point is the desired value for the

parameter you are controlling. A PID controller determines a controller output value, such as

the heater power or valve position. The controller applies the controller output value to thesystem, which in turn drives the process variable towards the set point value.

CONTROL SYSTEM:

The control system is that means by which any quantity of interest in a machine,

mechanism or equipment is maintained or altered in accordance with a desired manner.

Control system is of two types: -

1. OPEN LOOP CONTROL SYSTEM:

It is shown in figure1. Any physical system, which doesn’t automatically correct forvariation in its output, is called open loop system. In these systems, the output remains

constant for a constant input signal provided the external; conditions remain unaltered. The

output may be changed to any desired value by appropriately changing the input signal but

variations in external or internal parameters of the system may cause the output to vary from

the desired value in an uncontrolled fashion. The open loop control is, therefore, satisfactory

only if such fluctuations can be tolerated or system components are designed and constructed

so as to limit parameter variations and environmental conditions as well controlled.

It is important to note that the fundamental difference between an open and closed

loop control system is that of a feedback action. Consider, for example, traffic control system

for regulating the flow of traffic at the crossing of two roads. The system will be termed open

loop if red and green lights are put on by a timer mechanism set for predetermined fixed

Controller PlantInput Output

Fig. 1: Open Loop


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intervals of time. It is obvious that such an arrangement takes no account of varying rates of

traffic flowing to the road crossing from the two directions. If on the other hand a scheme is

introduced in which the rate of traffic flow along both directions are measured and are

compared and the difference is used to control the timings of the red and green lights, a

closed-loop system results. Thus, the concept of feedback can be usefully employed to traffic

control.

Unfortunately, the feedback, which is the underlying principle of most control

systems, introduces the possibility of undesirable system oscillations.

2. CLOSED LOOP CONTROL SYSTEM:

A closed loop control system consists of a process and a controller that automatically

adjusts one of the inputs to the process in response to a signal feedback from the process

output. The performance of the system can be judged by the transient response of the output

to specific changes in the input. The change in the input may be a change in set point or a

change in any one of the several load variables. If the purpose of the control system is to

make the process follow changes in set point as closely as possible, the operation is called

“servo-operation”. The term “regulator operation” is used when the main problem is to keep

the output almost constant in spite of changes in load. The designer must be aware of the

purpose of the control system, since the system that gives optimum servo-operation will

generally not be the best for regulator operation.

DEFINITIONS:

(Referred from Modern control Engineering By Katsuhiko Ogata, 4th

edition, page no.

2 and Control system engineering By I.J Nagrath and M.Gopal, 3rd

edition, page no. 195)

CONTROLLED VARIABLE & MANIPULATED VARIABLE:

The controlled variable is the quantity or condition that is measured and controlled.

The-manipulated variable is the quantity or condition that is varied by the controller so as to

affect the value of the controlled variable. Normally, the controlled variable is the output of

the system. Control means measuring the value of the controlled variable of the system and

applying the manipulated variable to the system to correct or limit deviation of the measured

value from a desired value.


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PLANTS:

A plant may be a piece of equipment, perhaps just a set of machine parts functioning

together, the purpose of which is to perform a particular operation.

PROCESSES:

A process may be defined as natural, progressively continuing operation or

development marked by a series of gradual changes that succeed one another in relatively

fixed way and leads toward a particular result or end; or an artificial or voluntary,

progressively continuing operation that consists of a series of controlled actions or

movements systematically directed towards a particular result.

SYSTEMS:

A system is a combination of components that act together and perform a certain

objective. A system is not limited to physical ones. The concept of system can be applied to

abstract, dynamic phenomena such as those encountered in economics. The word system

should therefore, be interpreted to imply physical, biological, economic and the like systems.

DISTURBANCES:

A disturbance is a signal that tends to adversely affect the value of the output of a

system. If a disturbance is generated within the system, it is called internal, while the external

disturbance is generated outside the system and is an input.

FEEDBACK CONTROL:

Feedback control refers to an operation that, in the presence of disturbance tends to

reduce the difference between the output of a system and some reference input and does so on

the basis of this difference. Here only the unpredictable or known disturbances can always be

compensated for within the system.

DELAY TIME:

It is the time required for the response to reach 50% of the final value in first attempt.

It is represented by td. It is shown in figure 2.


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R ISE TIME:

It is the time required for the response to rise from 10% to 90% of the final value for

over damped systems and 0 to 100% of the final value for under damped systems. It is shown

in figure 2.

PEAK TIME:

It is the time required for the response to reach the peak of time response or the peak

overshoot. It is represented by ts. It is shown in figure 2.

PEAK OVERSHOOT MP:

It indicates the normalized difference between the time response peak and the steady

output and is defined as:

Peak percent overshoot = [Ctp – C∞/C∞ ] x 100%

The M p is represented in figure 2.

SETTING TIME:

It is the time required for the response to reach and stay within a specified tolerance

band (Usually 2% to 5%) of its final value. It is represented by ts in figure 2

Figure : 2

0.5

1.0

Mp

Ttd

Ttp

Tt

Tc(t)

Ttr

A l l o w a b l e T o l e

r a n c e


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INTRODUCTION TO PID CONTROL EQUATIONS:

This section will show you the characteristics of the each of proportional (P), the

integral (I), and the derivative (D) controls, and how to use them to obtain a desired response.In this section, we will consider the following feedback system:

PLANT:

System to be controlled.

CONTROLLER:

Provides the excitation for the plant; Designed to control the overall system behavior.

THE THREE-TERM CONTROLLER

The transfer function of the PID controller looks like the following:

s

Ti KcsTdsTds

s

Ti Kc

++=++

2

K c = Proportional gain

Ti = Integral gain

Td = Derivative gain

First, let's take a look at how the PID controller works in a closed-loop system using

the schematic shown above. The variable (e) represents the tracking error, the difference

between the desired input value (R) and the actual output (Y). This error signal (e) will be

sent to the PID controller, and the controller computes both the derivative and the integral of

this error signal. The signal (u) just past the controller is now equal to the proportional gain

(Kc) times the magnitude of the error plus the integral gain (Ti) times the integral of the error

plus the derivative gain (Td) times the derivative of the error.

dt

deTd edt Tie Kcu +∫+×=

This signal (u) will be sent to the plant, and the new output (Y) will be obtained. This

new output (Y) will be sent back to the sensor again to find the new error signal (e). The

controller takes this new error signal and computes its derivative and its integral again. This

process goes on until the error becomes equal to zero.

R e u YController Plant

+ _


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THE CHARACTERISTICS OF P, I, AND D CONTROLLERS:

A proportional controller (Kc) will have the effect of reducing the rise time and will

reduce, but never eliminate, the steady state. An integral control (K i) will have the effect of

eliminating the steady-state error, but it may make the transient response worse. A derivativecontrol (K d) will have the effect of increasing the stability of the system, reducing the

overshoot, and improving the transient response. Effects of each of controllers Kc, Ti, and Td

on a closed-loop system are summarized in the table shown below.

Controller Response Rise Time Overshoot Settling Time Steady-State Error

K c Decrease Increase Small Change Decrease

Ti Decrease Increase Increase Eliminate

Td Small Change Decrease Decrease Small Change

Note that these correlations may not be exactly accurate, because Kc, Ti, and Td are

dependent of each other. In fact, changing one of these variables can change the effect of the

other two. For this reason, the table should only be used as a reference when you are

determining the values for K c, Ti and Td.

GENERAL TIPS FOR DESIGNING A PID CONTROLLER:

When you are designing a PID controller for a given system, follow

the steps shown below to obtain a desired response.

1. Obtain an open-loop response and determine what needs to be improved.2. Add a proportional control to improve the rise time.

3. Add an integral control to eliminate the steady-state error.

4. Add a derivative control to improve the overshoot.

5. Adjust each of Kc, Ti, and Td until you obtain a desired overall response.

Lastly, please keep in mind that you do not need to implement all three controllers

(proportional, derivative, and integral) into a single system, if not necessary. For example, if

a PI controller gives a good enough response, then you don't need to implement derivative

controller to the system. Keep the controller as simple as possible to obtain the system with

no overshoot, fast rise time, and no steady-state error.


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VARIOUS TYPES OF CONTROLS:

(Referred from Process control By Peter Harriott, page no. 6)

1. PROPORTIONAL CONTROL:

The cycling inherent with the on-off control would be objectionable for most

processes. To get steady operation when the disturbances are absent, the controlled variable

must be a continuous function of error. With proportional control, the most widely used type;

the controller output is a linear function of the error signal. The controller gain is the

fractional change in output divided by the fractional change in input.

P = Kc* e -------------------------(1)

Where:P = fractional change in controller output,

e = fractional change in the error.

Kc = controller gain.

The control action can also be expressed by the proportional bandwidth B. The

bandwidth is the error needed to cause a 100% change in the controller output, and it is

usually expressed as a percentage of the chart width. A bandwidth of 50% means that

controller output would go from 0 to 1 for an error equal to 50% of the chart width or from,

say, 0.5 to 0.6 for an error of 5%.

B = 1/Kc * 100 ------------------(2)

Some pneumatic controllers are calibrated in sensitivity units, or pounds per square

inch per inch of the pen travel. For a standard controller with a 3 to 15 psi range and a 4-inch

chart, the gain and sensitivity are related by equation:

S = 3Kc psi/inch ------------------------(3)

2. PROPORTIONAL + INTEGRAL CONTROL:

This mode of control is described by the relationship:

)4(−−−−−−−−−−−+∫+×= Psedt Ti

Kce Kc P

Where:

Kc = gain

Ti = integral time, seconds

Ps = constant


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P = output

In this case, we have added to the proportional action term, Kc * e, another term that

is proportional to the integral of the error.

There is no offset with the integral control, since the output keeps changing as long as

any error persists. However, the initial response to an error is slow and proportional control is

ordinarily used with integral control. The integral action corrects for the offset that usually

occurs with proportional control only, and the effect is similar to manual adjustment or

resetting of the set point after each load change. The terms “ reset action” and “reset time” are

widely used to characterize the integral action of a proportional – integral controller.

)5()1

( −−−−−−−−−−−−−−∫+= dt Ti

e Kc P

Where:

Ti = reset time

Kc = gain

P = output

3. PROPORTIONAL + DERIVATIVE (PD) CONTROL:

This mode of control may be represented by:

)6(−−−−−−−−−−−−+×=dt

de KcTd e Kc P

Where: Kc = gain

Td = derivative time, seconds

P = output

In this case, we have added to the proportional term another term, KcTd (de/dt) that is

proportional to the derivative of the error. Other terms that are used to describe the derivative

action are rate control and anticipatory control.

Derivative action is often added to proportional control to improve the response of

slow systems. By increasing the output when the error is changing rapidly, derivative action

anticipates the effect of large load changes and reduces the maximum error.


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DESCRIPTION:

FOR PRESSURE CONTROL TRAINER:

The basic objective of this flow controller is to control the pressure in the process tank.

This set up consists of the following components:

SETUP ASSEMBLY:

This assembly is used for supporting the various components on the front panel of the

equipment i.e. pressure gauges which is used to measure the pressure, Current to pressure

converter having a range in between 3 to 15 psi i.e. 3 psi for a current of 4mA and 15 psi for

current of 20mA which is given to the I/P converter by DIGITAL INDICATING

CONTROLLER. The setup also contains a pneumatic actuator.

SHEMATIC DIAGRAM OF PRESSURE CONTROL TRAINER

PRESSURE TRANSMITTER:

The pressure in the process tank is sensed by the pressure transmitter with the help of

pressure sensor fitted in the line and after that is transmitted by the transmitter to the

computer through interfacing unit which shows the value of the process variable. This

transmitter converts that accordingly into 4-20mA i.e. 4mA for 0% pressure and 20mA for

100 % pressure.

Air ReleaseValve

ProcessTank

SurgeTank

ControlValve

PressureRegulator

MoistureSeparator

Air Supply

PressureTransmitter

SafetyValve

SafetyValve

PressureGauge

PressureGauge

Digital IndicatingPID Controller I/P Convertor


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CONTROL VALVE:

A control valve basically performs the function of controlling the input of air pressure in the

process tank. It is a diaphragm type pneumatic actuator, which varies the flow of the air

according to the movement of the stem at a pressure range of 3 to 15 psi, which is receivedfrom I/P converter.

INTERFACING UNIT:

The interfacing unit is basically a medium for communicating with the equipment from the

computer. In case of pressure controller, the pressure of the air in process tank is sensed by

the pressure sensor in the pipe line, which is further transmitted into 4-20 mA which means

that the current is 4mA for 0% pressure and 20mA for 100% pressure and are displayed on

the interfacing unit in terms of 0 to 100%. These signals are further transmitted to the

computer through this interfacing unit by using a RS-232C where the signals are displayed on

the computer screen. The output of the interfacing unit is then transmitted to the I/P

converter, which converts it into 3 to 15 psi that means 3 psi for 4mA and 15 psi for 20mA.

CURRENT TO PRESSURE CONVERTER (I/P CONVERTER ):

This converter is basically used to convert the current to pressure having a range of 3 to 15

psi, which shows 3 psi at 4 mA and maximum 15 psi at 20 mA. This I/P converter receives

the continuous input pressure of more than 15 psi and then converts this pressure into 3 to 15

psi according to the 4 to 20 mA current received by it from the digital indicating controller.

INSTALLATION R EQUIREMENTS: -

This section gives the necessary details regarding the installation of the equipment and the

software used for interfacing with the equipment.

For the installation of the equipment, following components are required: -

1) Table for support.

2) Water supply.

3) Electricity 220V, single phase, 50Hz, 5 Amps socket.

For the installation of the software, following components are required: -


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COMPUTER:

A computer, which is the basic requirement for installing the software for interfacing with

the equipment. But the computer must fulfill the following requirements:-

1. The Processor must be at least celeron 286 MHZ, Pentium III is recommended.

2. It must have at least 16 MB RAM.

3. It must have 30 MB hard disk space.

4. It must have at least Windows 95 OS or higher version of operating system.

5. There must be an A4 size printer, which is used to get a hard copy of the stored data

required.

SOFTWARE

INSTALLATION:

1) Close all the programs running before inserting the Cd into CD drive.

2) Insert the provided CD for the software in the CD drive of computer.

3) It is an AUTORUN CD. Follow the instructions appeared on the computer

screen and install the software in desired directory.

4) After completion of installation, reboot your computer.

5) Then, Open the software directory and double click the exe file of the

software to run the program.

6) Follow the steps according the experimentation.

MENUS & BASIC FUNCTIONS: -

This section gives us the detailed information regarding the menus and the basic function of

the control software, which is used to control the equipment. It is shown in figure 3.

LOGIN:

This menu enables you to start the experiment. In this option, we are given with the User

Name i.e. name of the institute and the Password, which is “k.c.engineers”. Here we have

also the option of the entering the “Professors Name” under whose supervision test is going

to be performed, “Student’s name” and the “Roll Number” of the student who is

performing the experiment, which can be used during the report generation. It is compulsory

to select this option first and to fill the correct user name and password to continue the


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experiment. Without enabling this option and trying to continue the process or to select any

other option in the front panel shows the display box indicating that the user must login first

for selecting any other option. In this option, password is compulsory for running the

software. In case of wrong password the software will not run and a dialogue box will appear

with the software. All other options can be skipped off if not desired.

VIEW DIAGRAM: -

After LOGIN, we have to select VIEW DIAGRAM. This option, which shows us the

complete block diagram of the equipment and tells us how the equipment functions and also

helps in preparing the equipment connection. After that we have to choose the BACK option

and then decide to choose either the SIMULATION to access data from the simulation logic

in order to start the experiment or INTERFACE to access with the real time data.

SIMULATION:

Selecting this option accesses data from the PID simulation logic. This option doesn’t use any

real time data. In this case, the process values and set point are to be entered by the user and

then observes the change in the controller output. In this we have the option to put some

value of disturbance. Now as the value of the load or the disturbance increases in a process,

then the corresponding error between the SP and PV increases. Hence as a result, the output

response also increases and vice-versa. Also in case of manual mode in the Simulation, when

the controller output is made equal to zero, then the value of PV decreases and finally reaches

to zero.

SIMULATION MODE:


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INTERFACE:

Selecting this option, accesses real time data from using interfacing unit. In order to make the

system stable, we have to change the values of P, I, D.

START:

By enabling this option, the equipment will be ready to perform the experiment.

LOG:

On clicking the LOG button ON or selecting this option enables the data to be logged in

some particular file, which can be used later for continuing the experiment. In order to view

this saved data-logging file, click VIEW DATA FILE.

OFF:

Selecting this option disables the data logging.

FUNCTION GENERATOR:

The function generator is basically used to apply the dynamic waveform of some particular

period and amplitude to the process. The waveform is applied to the set point in case of the

close loop operation and is applied to the output in case of the open loop function.

ON:

This option enables the function generator selection and also enables the waveform to be

applied to the process.

OFF:

Selecting this option disables the function generator so that it stops functioning.


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FUNCTION GENERATOR PARAMETERS:

SIGNAL TYPE:

This function enables you to select one waveform out of the sine, triangular, square

and saw tooth waveform to be applied to the process.

R EFERENCE POINT:

This function is used to set the reference point equal to set point which helps in

making PV equal to the set point.

PERIOD:

This function is basically used to provide some time period to a waveform so that the

waveform completes its one complete cycle in some particular interval of time.

AMPLITUDE:

This function is used to set the amplitude of the waveform, which is selected to be

applied to the process.

PROCESS: -

This function is responsible for either increasing or decreasing the value of PV in the

SIMULATION mode.

LAG (MIN): -

It is also known as delay time and is measured in minutes. It is the amount of time

required for the response to reach 50% of the final value in first attempt. As the value of the

lag time increases, the change in the value of PV also increases.

DISTURBANCE (%):

A disturbance is a signal that tends to adversely affect the value of the output of a

system. If a disturbance is generated with in the system, it is called internal, while an external

disturbance is generated outside the system and is an input.

INITIAL:

This is the value of the PV when we continue the process without allowing the

process variable to reach its initial state i.e. equal to zero or its ambient temperature.


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AMBIENT TEMPERATURE: -

This is the initial value of PV, or due to the room temperature of the place where the

experiment is to be performed.

OUTPUT R ANGE: -

This corresponds to the maximum and the minimum range of the controller output,

which is to be set by the user.

OUTPUT HIGH

It corresponds to the maximum limit of the controller output means that the output of

the controller never exceeds this limit. This value is set by the user in order to obtain the

accurate result.

OUTPUT LOW:

It corresponds to the lowest limit of the controller output means that the output of the

controller can never be less than this value.

PID GAINS:

This corresponds to the various values of the Kc, Ti and Td, which are to be selected

by the user in order to make the system stable. In other words, these values are selected in

order to make PV equal to SP.

MODE STATUS: -

This option tells you that in which mode the system is operating i.e. whether the

system is operating in P, PI or PID.

P:

This option tells you that the system is operating in proportional controller mode. P

represents the proportional gain. In order to get the steady operation when the disturbances

are absent, the controlled variable must be a continuous function of error. With proportional

control, the controller output is a linear function of the error signal.

PD:

This option indicates that the system is operating in Proportional + Derivative

controller mode.


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PID:

This option indicates that the system is operating in proportional + Integral +

Derivative controller

BIAS:

Bias is the value of the normal output of the controller at zero error. This is added to the

proportional controller.

Thus, when a process is under P only control and the SP equals the measurement (when error

equals zero), some bias value of the controller output must exist or the measured PV will drift

from the set point. This bias value of the controller output is determined from the design flow

of operation of the process to be controlled. Specifically, bias is the value of the controller

output, which in open loop causes the measured PV to maintain steady state at the design

flow of the operation when the process disturbances are at their design.

ACTION:

There are mainly two actions for controlling the process variable and controller output.

These actions are:

1) INC-INC

2) INC-DEC

Using INC-INC action will cause increase in output with the corresponding increase in

process variable. Using INC-DEC action will cause decrease in controller output with

increase in process variable. This action should be observed by the user, which will further

depend on the final control element functioning.

For example: Consider a case of pneumatic actuator, which is open for air and otherwise

closed which means that the actuator valve is open for 15 psi pressure and close for 3 psi pressure. So, the final control element sets INC-INC action or INC-DEC action.

SWITCHING BETWEEN AUTO AND MANUAL:

Auto and Manual:

There’re two different modes option in this software i.e. Auto and Manual. In case of auto

mode, the software automatically controls the output of the process. In this case, user doesn’t


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do anything to control the output of the process. So, if the output is increasing with increase

in the value of the Kc, the controller automatically decreases its output in order to make it

stable. But in case of manual control, the user controls the output of the process. Click AUTO

to select the AUTO mode and Click again to change the system to manual mode.

EXIT:

This option enables you to logout of the simulation or interfacing mode.

VIEW DATA FILE:

This option accesses data from the data stored in the stored file using LOG button.

Results and data of the experiment conducted are observed .The user can see the data stored

in the file in the form of tables as well as graphs. After enabling this option, user enters into a

window where user has to open the file in which he has stored his/her data while performing

the experiment using the LOG button and this shows the data in the form of table which

indicates date and time i.e. which indicates when the experiment was performed and at what

time, PV, set point, output, upper and lower range and the limit of the upper and lower

hysteresis. This window also indicates the User i.e. the name of the institute which is

performing the experiment and also the Professor name i.e. under whose supervision the

experiment is going to be performed, Student Name and Roll Number i.e. name and roll

number of the student who is performing the experiment.

STOP:

This option enables you to logout out of this window.

R UN/PAUSE:

This option enables the graph to run or pause to show the waveform according to the

data shown the table in that window.

PRINT GRAPH:

Use print graph option for printing graphs according to the data that is saved in the

data log file.

Enabling this option enables you to enter into the print window, which shows the

User i.e. the name of the institute, Professor’s Name i.e. under whose supervision test is to

be performed, Student’s Name and Roll number i.e. the name and the roll number of the

student who is performing the experiment and the File path i.e. the path of the file which was


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saved using the LOG button. In this window the user has two options at the top of the

window i.e. one option of Print Window, which is used to take out the printout of the

window, and the second option is of Stop, which enables the user to come out of the window.

PRINT

TABLE:

Use print table option to print table from data file that are saved in the data log file.

This option opens all the data stored using the log button in the excel file where the user has

an option to set the left, right margins of the page.

BODE PLOT:

To view this, switch off the start button so as to return back to the front panel and

click bode plot.

COMPARE DATA:

This option enables you to compare the data between to two experiments having

different values of P, I, D. This option also enables you to compare data between the

SIMULATION mode and INTERFACING mode.

EXIT:

Selecting this option allows you to return back to the desktop or logout you from the

software.

VARIOUS PID CONTROL METHODS:

1. COHEN AND COON R ULES (C-C):

(Referred from Process systems Analysis and Control By Donald R.Coughanowr, 2nd

edition,

page no.288)


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The open loop method of tuning in which the control action is removed from the

controller by placing it in manual mode and an open loop transient is induced by a step

change in the signal. This method was proposed by COHEN and COON in 1953 and is often

used as an alternative to the Z-N method. Fig shows a typical control loop in which the

control action is removed and the loop opened for the purpose of introducing a step change

(M/S). The step response is recorded at the output of the measuring element. The step change

to the valve is conveniently provided by the output from the controller, which is in manualmode. The response of the system is called the process reaction curve; a typical process

reaction curve exhibits an s-shape as shown in the fig. 5

It is represented by equation:

1)(

+

×=

−

Ts

e Kc sGp

Tds

------------------(7)

The C-C method is summarized in the following steps: -

Typical process Reaction Curve showing graphical construction to determine first order with Transport lag Model

Figure : 5

Block Diagram of a Control loop for measurement of the Process reaction Curve

COHEN-COON METHOD

To Recorder

Loop Opened

H

B

CGc

M/S

Gv GpR=0

Uu=0

+

-

+

+

Tangent Line;Slope S = Bu/T

Time

Td0

Tt

M

0


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1) After the process reaches steady state at the normal temperature of operation, switch

the controller to manual. In modern controller, the controller output will remain at the

same value after switching as it had before switching.

2) With the controller in manual, introduce a small step change in the controller output

and record the transient, which is the process reaction curve.

3) Draw a straight line tangent to the curve at the point of inflection, as shown in fig .the

intersection of the tangent line with the time axis is the apparent transport lag (Td);

the apparent first order time constant (T) is obtained from the

T=Bu/S ------------------------------(8)

Where Bu is the ultimate value of B at large t and S is the slope of the tangent line.

The steady state gain that relates B to M in fig is given by

K p=Bu/M -----------------------------(9)

4) Using the values of K p, T and Td from step 3, he controller settings are found from the

relations as given below:

TYPE OF CONTROL PARAMETER SETTING

Proportional (P) )3

1(T

Td

KpTd

T Kc +=

Proportional – Integral (PI) )1210

9(

T

Td

KpTd

T Kc +=

)

209

330(

T

Td T Td

Td Ti

+

+=

Proportional- Derivative (PD) )64

5(

1

T

Td

KpTd Kc +=

)

322

26

(

T

Td T

Td

Td td

+

−=

Proportional – integral-derivative (PID) )43

4(

T

Td

TdKp

T Kc +=

)

813

632

(

T

Td T

Td

Td Ti

+

+=


22/45


)

211

4(

T

Td Td td

+

=

2. ZIEGLER’S NICHOL’S METHOD:

(Referred from Modern Control Engineering By Katsuhiko Ogata)

According to Zeigler – Nichol, PID controllers can be classified into two categories: -

1) A controller in which the dynamic model of the plant is not known.

2) A controller in which the dynamic model of the plant is known.

FIRST METHOD:

In this method, we obtain experimentally the response of the plant to a unit step input.

If the plant involves neither integrator nor dominant complex conjugate poles, then such a

S Shaped Response Curve

Figure : 6

Tangent Line atInflection point

TimeL T

0

K

C(t)

Unit Step Response of a Plant

Zigler-Nichol’s Method

PLANT

C(t)Uu(t)

1


23/45


unit step response curve may look S-shaped. This method applies if the response to a step

input exhibits an S-shaped curve. Such step response curves may be generated experimentally

or from a dynamic simulation of the plant.

The S-shaped curve may be characterized by two constants, delay time L and time

constant T, which is shown in fig. 6 constant are determined by drawing a tangent line at the

inflection point of the S-shaped curve and determining the intersections of the tangent line

with the time axis and line C (t)=K, as shown in the figure.

The transfer function C(s)/U(s) may then be approximated by first order system with a

transport lag as follows: -

1)(

)(

+

×=

−

Ts

e K

sU

sC Ls

----------------------(10)

Zeigler and Nichols suggested setting the values of Kp, Ti and Td according to theformula shown in below table.

Type of controller K c Ti Td

P T/L ∞ 0

PI 0.9T/L L/0.3 0

PID 1.2T/L 2L 0.5L

Notice that the PID controller tuned by the first order method of Zeigler- Nichols

rules gives: )5.02

11(2.1

11()( Ls

Ls L

T Tds

Tis KcS Gc ++=++=

Thus the PID controller has the pole at the origin and double zeros at S=-1/L.

SECOND METHOD:

It is shown in fig. 7. In the second method, we first set Ti=infinity and Td=0. Using

the proportional control action only, increase Kc from 0 to critical value Kcr at which the

output first exhibits sustained oscillations, (If the output doesn’t exhibit sustained oscillations

for whatever value Kp may take, then this method doesn’t apply). Thus, the critical gain Kcr

and the corresponding period Pcr are experimentally determined. Zeigler and Nichols

suggested that we set the values of the parameters Kc, Ti and Td according to the formula

shown in the table

Notice that the PID controller tuned by the second method of Zeigler-Nichols rules

gives:


24/45


s Pcr s KcrPcr

Pcrs Pcrs

Kcr

TdsTis

Kc sGc

2

)/4(075.0

)125.05.0

11(6.0

)1

1()(

+=

++=

++=

Thus the PID controller has the pole at the origin and double zeros at S=-4/Pcr.

Type of controller K c Ti Td

P 0.5K cr ∞ 0

PI 0.45K cr Pcr /1.2 0

PID 0.6K cr 0.5Pcr 1.25Pcr

Note that if the system has a known mathematical model (such as transfer function),

then we can use the root locus method to find the critical gain Kcr and the frequency of the

sustained oscillations Wcr, where 2*pi/Wcr=Pcr. These values can be found from the

crossing points of the root locus branches with the jw axis. (Obviously, if the root locus

branches do not cross the jW axis, this method doesn’t apply).

COMMENTS:

Zeigler-Nichols tuning rules (other tuning rules presented in the literature) have been

widely used to tune PID controllers in process control system where the plant dynamics are

not precisely known. Over many tears, such tuning rules proved to be very useful. Zeigler-

Shaped Response Curve

Figure : 7


TimeL T

0

K

C(t)


25/45


Nichols tuning rules can, of course, be applied to plants whose dynamics are known. (If the

plant dynamics are known, many analytical and graphical approaches to the design of the PID

controllers are available, in addition to the Zeigler-Nichols tuning rules).

3.

QUARTER

DECAY

R ATIO

METHOD:

The following controller tuning procedures are based on the work of Zeigler and

Nichols, the developers of the Quarter Decay ratio-tuning techniques derived derived from a

combination of theory and empirical observations.

CLOSED LOOP (ULTIMATE TUNING) TUNING PROCEDURE:

Although the closed loop tuning procedure is very accurate, you must put your

process in steady state oscillation and observe the PV on a strip chart. Complete the following

steps to perform the closed loop tuning procedure.

1) Set both the derivative time and integral time on your PID controller to zero.

2) With the controller in automatic mode, carefully increase the proportional gain (Kc)

in small increments. Make a small change in SP to disturb the loop after each

increment. As you increase Kc, the value of the PV should begin to oscillate. Keep

making changes until the oscillation is sustained, neither growing nor decaying

overtime.

3) Record the controller proportional band (PBu) as a percent, where PBu=100/Kc.

4) Record the period of oscillation (Tu) in minutes.

5) Multiply the measured values by the factors shown in the below table and enter the

new tuning parameters into your controller. This table provides the proper values for a

quarter decay ratio.

If you want less overshoot, increase the gain Kc.

Controller PB (%) Reset (min.) Rate (min.)

P 2PBu --------- --------

PI 2.22PBu 0.83Tu -------

PID 1.67PBu 0.50TTu 0.125Tu


26/45


OPEN LOOP (STEP TESTING) TUNING PROCEDURE:

The open loop tuning procedure assumes that you can model any process as a first

order lag and a pure dead time. This method requires more analysis than the closed loop

tuning procedure, but your process doesn’t need to reach sustained oscillation. Therefore, the

open loop tuning procedure might be quicker and the PV on a strip chart that shows time on

the X-axis. Complete the following steps to perform the open loop tuning procedure.

1. Put the controller in manual mode, set the output to a nominal operating value and

allow the PV to settle completely. Record the PV and output values.

2. Make a step change in the output. Record the new output values.3. Wait for the PV to settle. From the chart, determine the values as derived from the

sample displayed in the given figure.

4. Multiply the measured values by the factors shown in fig (a) and enter the new tuning

parameters into your controller. The table provides the proper values for a quarter

decay ratio. If you want less overshoot, reduce the gain, Kc.

Controller PB (%) Reset (min) Rate (%)

P 100KTd/T --------- ----------

PI 110KTd/T 3.33Td ----------

PID 80KTd/T 2Td 0.50Td

Output & PV Step Change

Figure :

TimeTd

T

Output

Max.

Min.

63.2%(Max.Min)PV


27/45


VARIOUS STABILITY METHODS:

1. BODE PLOT:

(Referred from Process Control By Peter Harriot, Page no. 91)

A convenient method of presenting the response data at various frequencies is to use a

log –log plot for the amplitude ratios, accompanied by a semi log plot for the phase angles.

Such plots are called “ Bode diagrams”, after H.W Bode, who did basic work on the theory of

feedback amplifiers. By using wT as a parameter, a general plot for first order system is

obtained. Since the amplitude ratio approaches 1.0 at low frequencies and 1/wT at high

frequencies, the straight line portion of the response if extended would intersect at wT = 1.0.

The frequency corresponding to the wT = 1 is called the “corner frequency” and the amplitude

ratio is 0.707 at this point. The phase lag is 45 degree at the corner frequency and the phase

curve is symmetrical about this point.

The system shown in fig. 6 has a gain of 1, which means that the output equals the

input as the frequency approaches zero. If the system gain K is greater than 1, the output

amplitude is greater than the input amplitude at low frequencies and a more comprehensive

definition of amplitude ratio is needed. The amplitude ratio is defined as the ratio of output

amplitude to input amplitude at a given frequency, divided by the ratio of the amplitudes at

zero frequency. This is equivalent to dividing the measured ratio by B/A by the gain K, which

makes the amplitude ratio dimensionless and makes equation and curves applicable to the first

order process.

Sometimes, the amplitude ratio is defined just as B/A, or output over input, which

leads to amplitude ratios, which may not be dimensionless. There is nothing unsound about

this procedure but the use of different units for each process element makes it somewhat

harder to plot the overall response of the system.

Whenever a sinusoidal input is applied to a linear system, the output has steady state

and transient terms. After a few cycles, the transient dies out and the output is a sine wave of

the same frequency. This eventual response can be characterized by the amplitude ratio and

the phase angle. Typical curves for a first order process are shown below. At low frequency,

the output is almost equal to the input, and there is only a slight phase lag. At high frequency,

the fluctuations in the input are severely damped because of the capacity in the system and

the output lags the input by almost 90 degree.


28/45


A.R =

2

1

22 )1(

1

T w+

The phase angle is always negative for a first order system and the negative angle iscalled “ phase lag”. The phase lag is 360(dt/p) in fig. And approaches a limit of 90 degree at

high frequencies.

2. R OUTH‘S ALGORITHM METHOD:

(Referred from Problems and Systems of control systems By A.K. Jairath, 3rd

edition, page

no. 6.1)

The Routh test is a purely algebraic method for determining how many roots of the

characteristics equation have positive real parts; from this it can also be determined whether

the system is stable, for if there are no roots with positive real parts, the system is stable. The

test is limited to the systems that have polynomial characteristic equations.

As per Routh’s stability criterion the necessary conditions for a system to be stable are:

1) None of the co-efficient of the characteristics equations should be missing or zero.

2) All co-efficient should be real and should have same sign.

The sufficient condition for a system to be stable is that each and each term of the first

column of Routh’s array should be positive and should have same sign.

Routh’s array for the characteristic equation

A0 s*n + A1 s*n-1 +A2 s*n-2 + ------------------An-1s + An = 0 -------------(11)

Where n=7 is formed as given below

A0 A2 A4 A6

A1 A3 A5 A7

B1 B3 B5

C1 C3

D1 D3

E1

F1


29/45


Where

A1A2 – A0A3

B1 = ------------------

A1

A1A4 – A0A5

B3 = -----------------

A1

A1A6 – A4A7

B5 = ---------------

A1

B1A3 – A1B3

C1 = ------------------

B1

B1A5 – A1B5

C3 = ------------------

B1

C1B3 – B1C3

D1 = -----------------

C1

C1B5 – B1 0

D3 = -----------------

C1

If we study the array successive rows have one term fewer than the preceding row,

and hence the array is triangular. The following are the limitations of the routh’s stability

criterion:

It is valid only if the characteristic equation is algebraic.

1) If any co-efficient of the characteristic equation is complex or contain power of ‘e’,

this criterion can’t be applied.2) It gives us information as to how many roots are lying in the right hand side of the s-

plane. Values of the roots are not available. Also, it cannot distinguish between real

and complex roots.


30/45


CONDUCTING EXPERIMENT:

DESCRIPTION:

This section gives the functional details of the product, which is used to conduct the

experiment. Functional details and control loop description enables us to understand the

working principle of the product.

PRESSURE CONTROL TRAINER (TYPE SCADA):

The SCADA is basically an interfacing unit and is a medium for communicating with the

equipment from the computer. In case of pressure controller, the pressure of air in process

tank is sensed by the sensor, which is further transmitted into 4-20 mA which means that the

current is 4mA for 0% pressure and 20mA for 100% pressure and are displayed on the

interfacing unit in terms of 0 to 100%. These signals are further transmitted to the computer

through this interfacing unit by using a RS-232C where the signals are displayed on the

computer screen and the error signals, which are produced by the controller, are displayed on

the interfacing unit. The output of the interfacing unit is then transmitted to the I/P converter,

which converts it into 3 to 15 psi that means 3 psi for 4mA and 15 psi for 20mA.

START UP:

1. All the drains should be closed.

2. Switch on the main supply.

3. Check whether all the valves are properly working or not.

4. Switch on computer and the interfacing unit.

5. Select the Auto mode to perform the experiment automatically and in Manual mode to

change the values manually.

6. Connect the equipment with compressed air supply.

SHUT DOWN:

1. Exit from the software.

2. Switch off the interfacing unit.


31/45


Following experiments can be conducted with the product.

Experiment No. 1. To study the open loop or manual control.

Experiment No. 2. To study the Proportional control.

Experiment No. 3. To study the Two mode (P+I) control.

Experiment No. 4. To study the Two mode (P+D) control.

Experiment No. 5. To study the Three mode (PID) control.

Experiment No. 6. To study the tuning of controller (Open loop method) using

Zeigler-Nichols method.

Experiment No. 7. To study the stability of the system using the BODE PLOT.


32/45


EXPERIMENT NO. 1: OPEN LOOP (MANUAL) CONTROL.

OBJECTIVE:

To study the open loop or manual control.

THEORY:

In these systems, the output remains constant for a constant input signal provided the

external; conditions remain unaltered. The output may be changed to any desired value by

appropriately changing the input signal but variations in external or internal parameters of the

system may cause the output to vary from the desired value in an uncontrolled fashion. The

open loop control is, therefore, satisfactory only if such fluctuations can be tolerated or

system components are designed and constructed so as to limit parameter variations and

environmental conditions as well as controlled, whereas in case of closed loop system, the

controlled variable is measured and compared with reference input and the difference is used

to control the elements.

EXPERIMENTAL PROCEDURE:

1. Start up the setup as mentioned in the starting.

2. Select the manual mode.

3. Set the controller output to 100%.

4. Apply a step change of 10% to the controller output and wait for the PV to reach the

steady state.

5. Repeat the above steps i.e. 2 and 3 until the output of the controller reaches to 0%

temperature

6. Shut down the apparatus as mentioned in the starting..


33/45


34/45


EXPERIMENT NO. 2: PROPORTIONAL CONTROL

OBJECTIVE:

To study the proportional control (P control).

THEORY:

In order to get steady operation when the disturbances are absent, the controlled

variable must be a continuous function of error. With proportional control, the most widely

used type; the controller output is a linear function of the error signal. The controller gain is

the fractional change in output divided by the fractional change in input.

P = Kc* e -------------------------(1)

Where,

P = fractional change in controller output,

E = SP-PV = fractional change in the error.

K c = controller gain.

Whereas the equation of the proportional controller output is given by

P = Kc (SP – PV) + P0 -----------------------(13)

Where P0 = bias i.e. the value of the controller output at zero error.

In this experiment, the measured process value (PV) and set point (SP) is compared

And the output of the controller is proportional to the resulting error signals.


1. Start up the set up as mentioned previously.

2. Select the controller in AUTO mode.

3. Set the value of Kc as high as possible.

4. Observe the process and the output response.

5. If output response doesn’t shows cycling, adjust the value of Kc to half of its previous

value.

6. Repeat steps 4 and 5 until cycling is observed.

7. Then, increase the value of Kc to twice its value and observe the Output response.

8. Repeat step 7 until cycling is observed.


35/45


9. Record the value of Kc at which you observe the oscillations and record the

overshoot.

10. Now increase the value of Kc in steps and observe the corresponding overshoots.

11. Compare the relative overshoot with the value of Kc.

OBSERVATIONS & CALCULATIONS:

1. Observe that as the value of Kc increases, then the error or the difference between the

SP and PV increases. In other words, as the error decreases, the proportional band

decreases.

2. In case of proportional controller, the control system is able to arrest the rise of the

controlled variable and ultimately bring it to rest at a new steady state value. The

difference between this new steady state value and the original value is called

OFFSET. There is always some offset present in case of proportional controller.

T

PV

Kc=1

T

PV

Kc=10

T

PV

Kc=15

T

PV

Kc=20


36/45


EXPERIMENT NO. 3: TWO MODE (P+I) CONTROL

OBJECTIVE:

To study the steady state and transient response to a proportional + Integral control.

THEORY:

This mode of control is described by the relationship:

)14(−−−−−−−−−−−−+∫+×= Psedt Ti

Kce Kc P

Where:

Kc = gain

e = error = (SP-PV)

Ti = integral time, seconds

Ps = constant

P = output

In this case, we have added to the proportional action term, Kc * e, another term that

is proportional to the integral of the error.

There is no offset with the integral control, since the output keeps changing as long as

any error persists. However, the initial response to an error is slow and proportional control is

ordinarily used with integral control. The integral action corrects for the offset that usually

occurs with proportional control only, and the effect is similar to manual adjustment or

resetting of the set point after each load change. The terms “ reset action” and “reset time” are

widely used to characterize the integral action of a proportional – integral controller.

)15()1

( −−−−−−−−−−−−−−−−−∫+= edt Ti

e Kc P

Where:

Ti = reset time.

Kc = gain

e = error = (SP-PV)

A small reset time corresponds to an increase in the integral action. With P action the

measured value will not necessarily become equal to the set point and a deviation will usually

be present. The control algorithm that applies changes in output as long as deviation exits, so


37/45


as to bring the deviation to zero is called integral action. With integral action the parameters

that determines how fast the output will change in corresponding to some amount.


1. Start up the setup as mentioned previously.

2. Select auto mode option for control.

3. Select a set point.

4. Select some value of Kc as described in proportional controller and Ti as high as

possible.

5. Observe the response of the system. If over damped oscillations are occurring, then

increase or decrease the corresponding values of Kc or Ti so as to make PV equal to

SP.

6. Then, observe the output response curve. If on decreasing the value of either Ti or Kc

makes the PV equal to SP, then continue decreasing the value until PV becomes

nearly equal to SP.

7. After experimentation, switch off the apparatus as mentioned previously.


1. The addition of integral action nearly eliminates the offset and the controlled variable

Ultimately returns to the original value.

2. It is shown the fig., that the addition of integral action introduces an oscillatory

motion in the system and with the increase in the value of the integral time, the

difference between the SP and PV decreases.

Tt

PV

Kc=10

Ti=10

Tt

PV

Kc=10

Ti=5

Tt

PV

Kc=10

Ti=1


38/45


EXPERIMENT NO. 4: TWO MODE (P+D) CONTROL

OBJECTIVE:

To study steady state and transient response to a proportional + derivative control.

THEORY:

This mode of control may be represented by:

P = Kc* e + Kc Td de/dt --------------(16)

Where Kc = gain

Td = derivative time, seconds

In this case, we have added to the proportional term another term, KcTd (de/dt) that is

proportional to the derivative of the error. Other terms that are used to describe the derivative

action are rate control and anticipatory control .

Derivative action is often added to proportional control to improve the response of

slow systems. By increasing the output when the error is changing rapidly, derivative action

anticipates the effect of large load changes and reduces the maximum error.

Larger the derivative time larger is the action. Smaller is the proportional band the larger is

the derivative action.


1. Start up the setup as mentioned previously.

2. Select auto mode option for control.

3. Select a set point.

4. Select some value of Kc as described in the proportional controller and the value of

Td to the minimum value.


reduce the value of Td to half of its previous value so as to make PV equal to SP.

6. Then, observe the output response curve and double the value of Td in order to make

PV equal to SP, then continue decreasing the value until PV becomes equal to SP.

7. After experimentation, switch off the apparatus as mentioned previously.


39/45



1. The derivative action is added to improve the response of the slow system.

2. The addition of derivative action to the PI action gives a definite improvement in theresponse. The rise of controlled variable is arrested more quickly and it is returned

rapidly to the original value with little or no oscillations.


40/45


EXPERIMENT NO. 5: THREE MODE (PID) CONTROL

OBJECTIVE:

To study the steady state and transient response to a Proportional + Integral + Derivative.

THEORY:

This mode of control is described by the relationship

)17(−−−−−−−−−−−−−+×+∫+×= Psdt

deeTd Kcedt

Ti

Kce Kc P

Where:

e = error = (SP-PV)

K c = gain

Td is derivative time, Ti is integral time and Kc=proportional gain


1. Start up the setup as mentioned earlier.

2. Select auto mode option for control.3. Select a set point.

4. Select some value of Kc, Ti and Td.


increase or decrease the corresponding values of Kc, Ti and Td so as to make PV

equal to SP.

6. Then, observe the output response curve. If on decreasing the value of either Kc, Ti,

Td makes the PV equal to SP, then continue decreasing the value until PV becomes

equal to SP.

7. After experimentation, switch off the apparatus

8. Using trail and error, select the proportional gain and integral time, which gives a

satisfactory response to step change in set point.

9. Set the derivative time to a non-zero value and carry out the above steps for different

derivative time values.

10. After experimentation shut down the setup as mentioned earlier.


41/45



The addition of derivative action to the PI action gives a definite improvement in the

response. The rise of controlled variable is arrested more quickly and it is returned rapidly to

the original value with little or no oscillations.

T

PV

Kc=10Ti=1Td=10

T

PV

Kc=10Ti=1Td=5

T

PV

Kc=10Ti=1

Td=1


42/45


EXPERIMENT NO.6: TUNING OF CONTROLLER (OPEN LOOP

METHOD)

OBJECTIVE:

To study the tuning of PID controller by open loop method, using Zeigler- Nichols

tuning rules.

THEORY:

This method is basically used to calculate the value of P, I, D using the open loop or

manual control method. The values of P, I, D are selected in such a way that the error or the

difference between the SP and PV should become equal to zero.

Since we are not given with the plant equation. So the process is assumed to be of first

order with steady state gain Kc, integral time Ti and derivative time td. The step response i.e.

process reaction curve, allows to obtain the approximate values of each parameter. With the

feedback loop open, a step response is applied to manipulated variable and the values of P, I

and D are estimated.

The delay time L and time constant T are determined by drawing a tangent line at the

inflection point of a S-shaped curve and determining the intersections of the tangent line with

the time axis and line c (t) = K as shown in the figure obtained by performing the experiment.

S Shaped Response Curve

Figure : 7


TimeL T

0

K

C(t)


43/45


For P, PI and PID controller the parameters are calculated as follows:

Mode Proportional Integral Derivative

P T/L INFINITY 0

P+I 0.9T/L L/0.3 0

P+I+D 1.2T/L 2L 0.5L


1. Start up the set up as mentioned.

2. Select open loop option for control.

3. Select the value of the set point to some desired value.

4. Apply a 20-30% change to controller output. Record the step response. Wait for the

steady state.

5. Start data logging and from the readings draw a step response curve.

6. Calculate the value of Td and L.

7. From this, calculate the values of PID controller settings from the table.

8. After experimentation, shut down the set up.


Tabulate the data from stored file as follows:

Observation No. Time in sec. Process Value (%)

1.

2.

3.

4.

Calculate the value of the P, D and I from the table given in the theory part of this

experiment.


44/45


EXPERIMENT NO. 7: TO STUDY THE STABILITY OF A

SYSTEM

OBJECTIVE:

To study the stability of the system by plotting the bode plots.

THEORY:

A convenient method of presenting the response of the data at various frequencies is

to use a log-log plot for the amplitude ratios, accompanied by the semi log plot for the phase

angles. Such plots are called BODE PLOT. Plotting of BODE plot is relatively easier as

compared to other methods as the loci of (1 + sT) and K/(1 + sT) can be represented by

straight line asymptotes.

In case of Bode plot, multiplication is converted into addition, so if

G(s) = K/(1 + sT)

And putting s = jw,

Then 20 log [G (w)] = 20 log K– 20 log [1 + jwt].

In case of Bode plot, study of relative stability is easier as parameters of analysis of

relative stability are gain and phase margin, which are visibly seen on the sketch.

The transfer function for a first order system is given by

1)(

+=

−

Tds

ke sG

Ls

The amplitude ratio of the above equation can be written as

2

1

22 )1(

1..

T w

R A

+

=

The phase angle is always negative for a first order system and this negative angle is

called “phase lag”.

STABILITY CRITERIA:

1. A system is stable if the phase lag is less than 180 degree at the frequency for which

the gain is unity.


45/45

2. A system is stable if the gain is less than unity at the frequency for which the phase

lag is 180.


1. Rewrite the sinusoidal transfer function in the time constant form.

2. Identify the corner frequencies associated with each factor of the transfer function.

3. Knowing the corner frequency, draw the asymptotic magnitude plot. This plot

consists of a straight line segments with the line slope changing at each corner

frequency by +20 db/decade for a zero and –20 db/decade for a pole For a complex

conjugate zero or pole the slope changes by +/- 40 db/decade.

4. Draw a smooth curve through the corrected point such that it is asymptotic to the

straight-line segments. This gives the actual log-magnitude plot.

5. Draw the phase angle curve for each factor and add them algebraically to get the

phase plot.

6. The ultimate gain value i.e. Wco is that value when the phase angle curve crosses the

180 degree line and the corresponding gain value is called the ultimate gain i.e. Ku.

7. By using these two gains the other parameters that are the values of

P, D and I are calculated from the table given in the theory part of the Zeigler’s closed

loop method.


1. Draw the graphs of Magnitude Vs frequency on log-log scale.

2. Draw the graphs of Phase angle Vs frequency on semi log co-ordinates.

3. Compare the values calculated from Zeigler open loop and this Bode plot.

4. The first order system will be stable only if the phase angle Vs frequency graph has

negative phase lag.

Documents

Pressure Instrument Trainer