CH 4_Process Control J5800

8/3/2019 CH 4_Process Control J5800

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This topic shall elaborate on types of control actionwhich are proportional control (P), integral control (I),

derivative control (D) and combination of control

system.


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INTRODUCTION Process controllers are control system components

which basically have an input of the error signal, i.e.the difference between the required value signal andthe feedback signal, and an output of a signal tomodify the system output.

The ways in which such controllers react to error

changes are termed the control laws, or often, thecontrol modes.


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The simplest form of controller is an on-offdevicewhich switches on some correcting device when thereis an error and switches it off when the error ceases(berhenti).

However, such a method of control has limitations andoften more sophisticated controllers are used.

The 3 basic control modes areproportional (P),integral (I), and derivative (D); the 3 term controller isa combination of all 3 modes.


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ON-OFF CONTROL The controller is essentially a switch which is activated

by error signal and supplies just an on-off correctingsignal.

The controller output just have two possible value; onor off

Sometimes called two-step controller.

A simple and inexpensive and is often used wherecycling can be reduced to an acceptable level.


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Example: bimetallic thermostat; used with a simple

temperature control system.


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PROPORTIONAL CONTROL (P)With P the size of the controller output is proportional

to the size of the controller error, i.e. the controllerinput.

The correction element of the control system will havean input of a signal which is proportional to the size ofthe correction required.

Controller Output = KP X Controller InputKP = A constant called the gain


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Proportional control


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Application:

The float method of controlling the level of water in acistern (tangki air) is an example of the use of aproportional controller. The control mode isdetermined by the lever.


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Application:

An amplifier; for the control of temperature of theoutflow of liquid from a tank, the use of a differentialamplifier as a comparison element and anotheramplifier as supplying the proportional control mode.


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Proportional band Note that it is customary to express the output of a

controller as a percentage of the full range of outputthat it is capable of passing on the correction element.

Thus, with a valve as a correction element, as in thefloat operated control of level, we might required it tobe completely closed when the output from thecontroller is 0% and fully open when it is 100%.


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percentages

Water level control system


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Terminology Range

Two extreme values between which the system operates.A common controller output range : 4 20 mA

Span

The difference between the two extreme values withinwhich system operates, e.g. a temperature controlsystem might operate between 0C and 30C and so havea span of 30C.


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Absolute deviation

The set point is compared to the measured value to givethe error signal; deviation. Absolute deviation is used

when the deviation is just quoted as the differencebetween the measured value and the set value, e.g. atemperature control system might operate between 0Cand 30C and have absolute deviation of 3C.


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Fractional deviation

This being the absolute deviation as a fractional orpercentage of the span. Thus, temperature controlsystem operating between 0C and 30C with an error of3C has a percentage deviation of (3/30) x 100 = 10%


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Generally with process controllers, the proportionalgain is described in terms of itsproportional band(PB). The PB is the fractional or percentage deviationthat will produce a 100% change in controller output


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The 100% controller output might be a signal that fullyopens a valve, the 0% being when it fully closes it. A50% PB means that a 50% error will produce a 100%change in controller output; 100% PB means that a100% error will produce a 100% change in controlleroutput.


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Since the percentage deviation is the error e as a

percentage of the span and the percentage change inthe controller output is the controller outputy as apercentage of the output span of the controller:

Since the controller gain Kp is y/e


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ExampleWhat is the controller gain of a temperature controller

with a 60% PB if its input range is 0C to 50C and itsoutput is 4 mA to 20 mA?


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ExampleA proportional controller has a gain of 4. what will be

the percentage steady state error signal required tomaintain an output from the controller of 20% whenthe normal set value is 0%?

% controller output = gain x % error

20 = 4 x % errorhence the percentage error is 5%


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exampleFor the water level control system described in figure,

the level is at the required height when the linearcontrol valve has a flow rate of 5 m3/h and the outflowis 5 m3/h. the controller output is then 50% andoperates as a proportional controller with a gain of 10.what will be the controller output and the offset whenthe outflow changes to 6 m3/h?


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answerSince a controller output of 50% corresponds to 5 m 3/h

from the linear control valve, then 6 m 3/h means thatthe controller output will need to be 60%. To give a

change in output of 60

50 = 10% with a controllerhaving a gain of 10 means that the error signal into thecontroller must be 1%. There is thus an offset of 1%.


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INTEGRAL CONTROL (I) I is the control mode where the controller output is

proportional to the integral of the error with respect totime, i.e.:

And so we can write:

Where KI is the constant of proportionality and, whenthe controller output is expressed as a percentage andthe error as a percentage, has units of s-1 .


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To illustrate what is

meant by the integral ofthe error with the errorwith respect to time,consider a situation

where the error varieswith time in the wayshown in figure. Thevalue of the integral at

some time t is the areaunder the graph betweent = 0 and t.


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Thus as t increase, the area increase and so thecontroller output increase. Since, in this example, thearea is proportional to t then the controller output is

proportional to t and so increases at a constant rate.Note that this gives an alternative way of describingintegral control as:

A constant error gives a constant rate of change ofcontroller output.


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ExampleAn integral controller has a value of KI of 10 s

-1 . Whatwill be the output after of (a) 1 s, (b) 2 s, if there is asudden change to a constant error of 20%, as

illustrated in figure?


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answerWe can use the equation:

(a) The area under the graph between a time of 0 and 1 sis 20%s. thus, the controller output is 0.10 x 20 = 2%.

(b) The area under the graph between a time of 0 and 2 s

is 40%s. thus, the controller output is 0.10 x 40 = 4%.


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DERIVATIVE CONTROL (D) With D the change in controller output from the set point

value is proportional to the rate of change with time of theerror signal, i.e. controller output rate of change of error.

Thus we can write:

It is usual to express these controller outputs as apercentage of the full range of output and the error as apercentage of full range.

KD is the constant of proportionality and is commonlyreferred to as the derivative time since it has units of time.


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Figure illustrates the

type of response thatoccurs when there is asteadily increasing errorsignal.

Because the rate ofchange of the error withtime is constant, the Dcontroller gives a

constant controlleroutput signal to thecorrective element.


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With derivative control, as soon as the error signalbegins to change there can be quite a large controlleroutput since it is proportional to the rate of change of

the error signal and not its value.

Thus with this form of control there can be rapidcorrective responses to error signals that occur.


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exampleA derivative controller has a derivative constant KD of0.4 s. what will be the controller output when the error(a) changes at 2%/s, (b) is constant at 4%?

(a) Using the equation given above, i.e.

Controller output = 0.4 x 2 = 0.8%

(b)With a constant error there is no change of error withtime and thus the controller output is zero.


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PD CONTROL D controllers give responses to changing error signals

but do not, however, respond to constant error signals,since with a constant error the rate of change of error

with time is 0.

Because of this, D is combined with proportionalcontrol. Then:


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Figure shows how, with

P+D control, thecontroller output canvary when there is aconstantly changingerror.

There is an initial quickchange in controlleroutput because of the D

action followed by thegradual change due to Paction.


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This form of control can thus deal with fast processchanges better than just P control alone. It still, like Pcontrol alone, needs a steady state error in order to

cope with a constant change in input conditions or achange in the set value.


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The above equation for PD control is sometimeswritten as:

KD/KP is called the derivative action time TD and so:


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PD control can deal with fast process changes betterthan just P control alone. It still needs a steady stateerror in order to cope (menampung) with a constant

change in input conditions or a change in the set value.


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exampleWhat will the controller output be for a P+D controller

(a) initially and (b) 2 s after the error begins to changefro, the 0 error at the rate of 2%/s. the controller has

KP = 4 and TD= 0.4 s.


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(a) Initially the error is 0 and so there is no

controller output due to P action. There will,however, be an output due to D action since theerror is changing at 2%/s. since the output of thecontroller, even when giving a response due to D

action alone, is multiplied by the proportionalgain, we have:

controller output = TD x rate of change of error= 4 x 0.4 x 2%

= 3.2%


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(b) Because the rate of change is constant, after 2 s the error

will have become 4%. Hence, then the controller outputdue to the P mode will be given by:

controller output = KP x error

= 4 x 4% = 16%

The error is still changing and so there will still be an outputdue to the D mode. This will be given by:

Controller output = KP TD x rate of change of error

= 4 x 0.4 x 2% = 3.2 %

Hence the total controller output due to both modes is thesum of these two outputs and 16% + 3.2% = 19.2%


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PI CONTROL The I mode control is not usually used alone but

generally in conjunction (hubungan) with the P mode.

When I action is added to a P control system thecontroller output is given by:

Where KP is the P control constant and KI the I controlconstant.


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Figure shows how asystem with PI control

reacts when there is anabrupt (tiba-tiba)change to a constanterror. The error gives rise

to a P controller outputwhich remains constantsince the error does notchange. There is then

superimposed on this asteadily increasingcontroller output due tothe I action.


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The combination of I modewith P mode has one great

advantage over theproportional mode alone:the steady state error can beeliminated. This is becausethe I part of the control can

provide a controller outputeven when the error is 0. thecontroller output is the sumof the area all the way backto time t = 0 and thus even

when the error has become0, the controller will give anoutput due to previouserrors and can be used tomaintain that condition.

Figure illustrate this.


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The above equation for PI controller output is oftenwritten as:

KP/KI is called the integral action time TIand so:


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PID control Combining all 3 modes of control enables a controller

to be produced which has no steady state error andreduced the tendency (kecenderungan) for oscillations

(goyangan). Such a controller is known as a 3 mode controller or

PID controller.


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The equation describing its action is:

The above equation can be written as:


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A PID controller can be considered to be aproportional which has integral control to eliminatethe offset error and derivative control to reduce time

lags (ketinggalan)


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ExampleDetermine the controller output of three-mode

controller having KP as 4, TI as 0.2s, TD as 0.5s attime :a) t = 0

b) t = 2s

c) t = 3s

When there is an error input which starts at 0 attime t = 0 and increase at 2%/s as shown in figure.


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Answeri. t = 0P = KP [Error + (1/TI) x integral of error + TD x rate of change

of error]

= 4 [0 + 0 + 0.5x2]= 4%

ii. t = 2s

P = KP [Error + (1/TI) x integral of error + TD x rate of changeof error]

= 4 [4 + (1/0.2) x 2 + 0.5 x 2]

= 60%


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iii. t = 3s

P = KP [Error + (1/TI) x integral of error + TD x rate ofchange of error]

= 4 [6 + (1/0.2) x 2 + 0.5 x 2]

= 68%

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CH 4_Process Control J5800