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8/15/2019 Advance PC Report

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1.0 ABSTRACT

A proportional-integral-derivative controller (PID controller) is a control loop feedback

mechanism (controller) commonly used in industrial control systems. A PID controller

continuously calculates an error value as the difference between a desired set point and ameasured process variable. his type of controller re!uired optimum combination of P" I and

D value in order to achieve steady and constant product !uality and maintained the process at

steady state. he ob#ectives of performing this water level and flow process control is to

determine the optimum P and I value that capable to drive the process towards steady state

and maintained the process variable at set point value. Its start with open loop test to obtain

the process characteristics which are $$" d and c that will be used for P and I calculation

via selected tuning rules. P and I calculated were input into close loop test and fine tuning is

done.

2.0 INTRODUCTION

%ost of the manufacturing and chemical process industries have been using PID

controllers in their automatic control system at late of &'s. *rom then" it has evolved from

a pneumatic mechanical to a digital electronic device. oday+s PID controllers have

incorporated new control strategies such as model based control" dead time compensation

and variable gain ad#ustment to cater for non-linear and longer dead time processes. he

governed by a mathematical e,pression or known as the control algorithm is by using current

digital PID. he PID algorithm is the most popular feedback controller used within the

process industries and successfully used for over years. herefore" it can provide e,cellent

control performance despite the varied dynamic of characteristics of the process plant.

he process stability of a PID control loop depends on the proportional (P)" integral (I)"

and derivative (D) constants that need to be used. y using the tangent method and the

proper tuning rule" the optimum P" I and D can be estimated. his value of optimum P"I and D

will set into the controller" an optimum response is normally achieved. he PID algorithm

consist of three basic modes" the proportional mode" the integral mode and derivative mode.


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/hen utili0ing this algorithm" it is necessary to decide which modes are to be used and then

specify the parameters and settings for each mode used.

he PID controller functions is to correct the error between a measured process variable

(P1) and desired set point (2P) by calculating and then the output will give value for acorrective action that can ad#ust the process accordingly. PID controller algorithm which

consist of P" I and D " have its own function which are" the proportional value determines the

reaction to the current error" the integral term determines the reaction based on the sum of

recent errors and derivatives value determines the reaction to the rate at which the error has

been changing. he weighted sum of these three constants is used to ad#ust the process via a

control element such as the position of a control valve.

/hen tuning these three type of constants in the PID controller algorithm" the controller

can provide control action designed for specific process re!uirements. he response of the

controller can be described in terms of the response of the controller to an error" the degree to

which the controller overshoots to the set point and the degree of system oscillation in the

graf. PID algorithm for control does not guarantee optimal control of the system or system

stability.

3.0 OBJECTIVES

3b#ectives of operating the D42-*o,boro are as follows 5

&. o perform open loop test.

6. o determine the process characteristics $$" d and c of the process by using selected

method.

7. o determine optimum P and I value that will optimally drive the process towards set

point by using selected various tuning rules.

. o perform closed loop test" set point test and fine tuning on inserted P and I.

4.0 THEORY

here are three controller parameters in process control" which are Proportional (P)" Integral (I)"

and Derivative (D) and for the modes of control are P modes" PI modes and PID modes. 2ome

application may re!uire using only one or two parameters to provide the appropriate system


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control. It can be achieved by setting of any undesired parameter control to 0ero. A PI control

modes is very general thing" since its derivative action is very sensitive to measurement noise"

and the absence of an integral value may prevent the system from reaching its target value.

Effects of Controer !"#n$ %c

he proportional term or gain makes a change to the output that is proportional to the

current error value. he proportional response can be ad#usted by multiplying the error by a

constant 8p" the proportional response. he proportional term is given by5

/here"

p (t )=~ p+ K pe ( t )

p(t) 9 4ontroller output

9 integral time or reset time

8p 9 Proportional gain" the tuning parameter

e 9 2et Point (2P) : Process 1ariables (P1)

~ p 9 bias (steady state value)"

t 9 ime or Instantaneous time

~ P is controller output when the error is 0ero. he proportional is given by the controller gain"

8c. he controller gain which is 8c determines how much the amount of output from the

controller changes for a given change in error. /hen large change in the output for a givenchange in the error is result from the high proportional gain. If the proportional gain is too high"

the system can become unstable. /hen a small gain results" it will give small output of

response " and the less responsive will give less sensitive controller. If the proportional gain is

too low" the control action will be too small when responding to system disturbances. ;ven with

the absence of disturbances" the process control will not get the target value" but will retain a


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p(t) 9 4ontroller output

9 integral time or reset time

e 9 2et Point (2P) : Process 1ariables (P1)

~ p 9 bias (steady state value)"

t 9 ime or Instantaneous time

Integral control action mostly used because it provides elimination of offset . In order for the

controlled process to be at steady state" the controller output p(t) need to be constant so that the

manipulated variable will be constant. It will continuously changing for p(t) " unless the error is

0ero. /hen integral action is used" p automatically changes until it reach the value re!uired to

make the steady-state error 0ero. his desirable situation always occurs unless the the final

control element saturates and thus is unable to bring the controlled variable back to the set point.

*inal control element saturation occurs whenever the disturbance or set-point change is so large

that it is out of the range of the manipulated variable. Although elimination of offset is really

important to control but the integral controller is rarely used by itself" because a little control

action takes place until the error signal has been persisted . In contrast" proportional control will

take the action immediately as corrective action of the error is detected. 4onse!uently" integral

control action is normally used in con#unction with proportional control as the proportional-

integral (PI) controller. 2o for" the contribution from the integral time is proportional to both

magnitude of the error and the duration of the error. 2umming the instantaneous error over time

by integrating the error gives the accumulated offset that should be corrected


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he magnitude of the contribution of the integral time to the overall control is determined by

value of inserted. As it mention before" the integral control action is normally used in

con#unction with proportional control. Integral times will accelerate the movement of the process

toward set point and eliminates the residual steady state error that caused by P-only controller.


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=ote that a proportional controller only reacts to a deviation in process variable" making no

distinction as to the time period over which the deviation develops. Integral control action is also

ineffective for a sudden deviation in P1" because the corrective action depends on the duration of

the deviation. hus" derivative control is needed. ack to the e!uation" τ

d the derivative time"

has units of time. =ote that the controller output is e!ual to the nominal value p as long as the

error is constant (that is" as long as de>dt 9 ). hen" derivative action is never used alone? it is

always used in con#unction with proportional or proportional-integral control. y providing

control action" the derivative mode tends to be stabili0e the controlled process. hus" it is often

used to counteract the destabili0ing tendency of the integral mode. Derivative control action also

can to improve the dynamic response of the controlled variable by the settling the time and the

time it takes reduce to reach steady state. ut if the process measurement is noisy" that is" if it

contains high-fre!uency" random fluctuations" then the derivative of the measured variable will

change wildly" and derivative action will amplify the noise unless the measurement is filtered.

Derivative action is seldom used for flow control" because flow control loops respond !uickly

and flow measurements tend to be noisy.

T)n#n& of *$ I "n+ D

Automatic control is performed by a set controller algorithm which consist of

proportional (P)" integral (I)" derivative (D)" set point (2P)" and process variable (P1) that are

re!uired for the computation of controller action (%1). A controller action with &@ may

represent a full opening of control valve which indicates to reach ma,imum. here are thousands

of combinations of P" I and D values" but there is only one combination that will drive the

process toward to the set point. Poor combination of P" I and D values D give the process towards

undesirable results" which are deviation and oscillation. *or the optimum P" I and D values"

several techni!ues have been introduced. 3ne of them is open loop method that offers short test

time.


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his method been applied for controlling flow process. 3nce open loop has been

performed for flow control loop" the initial %1 and final %1 is obtained from the graph. he

result from the open loop test is analy0ed for its response rate ($$)" dead time (d) and time

constant (c) by using either angent method" or reformulated tangent method. . *or this flow

process control" $eformulated angent %ethod is hired. he following formula is used in

determining the re!uired process characteristic" $$" d and c

$$9tanθ

MV

a

b

T d=T d (length )×b

T c(length)×b

$esponse rate ($$)" dead time (d) and time constant (c) which then used in tuning

rules to obtain the P" I and D values combination that will be inserted to the process control to

directs the process towards set point. After that fine tuning is re!uired to ensure both %1 and P1

does not oscillate and maintained. he following are list of tuning rules used5


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T)n#n& R)es ,- Coen/Coon

2ettling criteria 5 uarter amplitude dampening" AD

Performance test 5 Disturbance in load variable

%ode P I D

p 100

1+ μ

3

RRT D

PI 100

1+ μ

11

RRT d

7.77B

1+ μ

11

1+11 μ

5

¿T D

PID 100

1.35 (1+ μ

5) RRd

6.B

1+ μ

5

1+4 μ

5

¿T D

0.37T d

1+ μ

5

T)n#n& R)es ,- T"""s#

2ettling criteria 5 minimum control area

Performance test 5 disturbance in load variable

%ode P I D

P&& $$

T d

P I&& $$

T d 77 T d

P I DCC $$

T d 6.6 T d .

T d


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.0 *ROCEDURE

Oen oo test for fo contro

&. /ater flow and control was selected

6. *I4 7& control loops was activated

7. he process was first stabili0ed in automatic mode until get constant straight line.

. Initial value of manipulated variable" %1(@) was recorded.

. 3nce the process stabili0ed" the process was switched from automatic mode to manual mode

. 2tep change is made to the %1 for about @ from %1i9&E@ to %1f967@.

C. he process was left to stabili0ed back in manual mode until new steady state is reached.

E. he process is paused and data was collected.

Cose+ oo Test 5or 5o Contro

&. *rom 3pen loop test" the process was first stabili0ed in automatic mode.

6. he operation was started with P I mode control for akashi rule. 1alue ofk c and I was

inserted to the computer

7. Process response was observed.

. If there was oscillation occur" thenk c value need divide with with I value times with

until achieved steady state on the graph

. he process is paused and data was collected

C. $epeat the same step for P I D mode control of akashi rule.


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E. he 4ohen coon tuning step was same which was repeated from step & until step for P I and

P I D mode control

6.0 CACUATION

In order to do a set point test" tuning rules by 4ohen-4oon and akahashi from the table of

tuning rules for open loop method are used to find the mode PI and PID.

uning rules by 4ohen-4oon 5

%ode P I D

PI

d T RR ⋅

+&&

&

&))

µ d T

+

+

-

&&&

&&&

77.7 µ

µ

PIDd T RR

⋅

+

-&7-.&

&))

µ d

T

+

+

-

7&

-&-.6

µ

µ

-&

7C.)

µ +

d T

/here"c

d

T

T = µ

uning rules by akahashi 5

%ode P I D

PI

d T RR ⋅⋅&&) d T ⋅7.7


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PIDd

T RR ⋅⋅CCd

T ⋅6.6d

T ⋅(-.)

*rom *I4 6&" the process is an open loop system. It is a self-regulating process where the

process moves to a new steady position after making an open loop test and the final steady state

is observe from the graph obtained. *or *I4 6&" it uses graphical analysis from open loop test

and the calculation is using reformulated tangent method where F is measured from the graph.

he values of a and b are also obtained from the graph.

G 9 CEo

i. a 9 &@ > &Cmm

b 9 &s > &&.mm

H%1 9 @

ii. $$ 9b

a

MV ⋅

∆θ tan

9

⋅

.&&

&

&C

&

CEtan

9 .6 > s


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iii. d 9 d (length) , b

9 & mm , ( &>&&.)

9 &.7 s

iv. c 9 c (length) , b

9 ( 7mm - &mm) , (&>&&.)

9 6.& s

After obtaining the values for $$ and d" the mode PI and PID mode are used because the

process involve flow which is a fast process response and noisy process. he value of $$ and d

are used in the 4ohen-4oon and akahashi tuning rules.

Coen/Coon7s t)n#n& r)es

%ode PI 5

(''D.)D&.6

7)(.&===

c

d

T

T µ

P 9

d T RR ⋅+&&

&

&))

µ


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9

( ) ( )7)(.&(6(.)

&&

(''D.)&

&))⋅

+

9 6.E' @

I 9

d T

++

-

&&&

&&

&

77.7 µ

µ

9

( ) ( )7)(.&

-

(''D.)&&&

&&

(''D.)&

77.7

+

+

9 6.& s

8 c 9 &> P

9 & > 6.E'

9 &.E'


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Set o#nt test for Coen/Coon7s t)n#n& r)e 8 'o+e *I 9

In *I4 6&" the software in the computer re!uires 8 c and I as input value for the set point test.

In set point test" the controller is set in automatic mode and made a changed in set point of less

than &@ of the process span. he value of 8 c and I is initially &.E' and 6.&s respectively. he

process respond was observed until it stable at set point.


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9

( ) ( )7)(.&

-

(''D.)7&

-

(''D.)&

-.6

+

+

9 6.C' s

D 9-

&

7C.)

µ +

d T

9

( )

-

(''D.)

&

7)(.&7C.)

+

9 .7' s

8 c 9 & > P

9 & > 7C.67

9 6.'


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Set o#nt test for Coen/Coon7s t)n#n& r)e 8 'o+e *ID 9



than &@ of the process span. he value of 8 c and I is initially 6.' and 6.C's respectively. he



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8 c 9 & > P

9 & > .6E

9 &.E&

Set o#nt test for T"""s#7s t)n#n& r)e 8 'o+e *I 9



than &@ of the process span. he value of 8 c and I is initially &.E& and .77s respectively. he



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D 9d

T ⋅(-.)

9

( )7)(.&(-.) ⋅

9 .E

8 c 9 & > P

9 & > 6.C

9 6.7

Set o#nt test for T"""s#7s t)n#n& r)e 8 'o+e *ID 9



than &@ of the process span. he value of 8 c and I is initially 6.7 and 6.EEs respectively. he



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*or open loop test" the value of $$" d and c was calculated by using graphical method (see

4alculation section)" which are .6>s" &.7s" and 6.&s respectively.here are several tuning rules for open loop method in order to determine P" I and D

value which are Jiegler-=ichols tuning rules" 4hien" 9 .C and 6.& , 9

E.s in order for the process stop the oscillation and regain stability. After a few seconds the

process start to stable and the graph is print out as shown in the Appendi, section. *or mode

PID by using same tuning rules (4ohen-4oon)" the initial values for 8c and I calculated are

initially 6.' and 6.C's respectively. oth of these values are used as input value for the set

point test in *I4 6&. he process response was observed until it stable at set point.


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values for 8c and I calculated are initially 6.7 and 6.EEs respectively. oth of these values

are used as input value for the set point test in *I4 6&. he process response was observed

until it stable at set point. 9 .' and 6.EE , 9 &&.Cs

in order for the process stop the oscillation and regain stability. After a few seconds" the

process became stable and the graph is print out as shown in the Appendi, section.

y comparing all the graph obtained" it can be observed that from two types of tuning

rules by using two type of modes (PI and PID modes)" the most stable and reliable method is

akahashi tuning rule for mode PI. his is because" this type of tuning rule give least

oscillation and faster rise time compared to others.

:.0 CONCUSION

In conclusion" comparing the graph of set point test obtained for mode PI and PID of 4ohen-

4oon and akahashi tuning rules" the graph that shows the least oscillation is from the

akahashi+s tuning rules for mode PI. his means that the performances of the value of P and I

calculated for akahashi+s tuning rules can handle changes in the set point of the process.

;.0 RE55ERENCES

a) Ishak A.A Abdullah J. (6&) PID uning *undamental 4oncepts and Applications" Ki%

Press" Kniversiti eknologi %ara" 2hah Alam" 2elangor" %alaysia" page5 & to .

b) Dale e. 2eborg et.al (6&7) 7rd edition Process Dynamic and 4ontrol Lohn /iley 2ons" Inc.

&&& $iver 2treet"

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