Chapter 2 -- Discrete-State Control Part I

7/26/2019 Chapter 2 -- Discrete-State Control Part I

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Chapter 2

Discrete-State ControlPart I


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Content

2Prepared by Wong CheeWoon

UEEA2413 Process Control andInstrumentation

Defnition o Discrete-State ProcessControl

Characteristic o the System

ObjectivesTo understand the nature o discrete-

state process-control system.

Describe a discrete-state process interms o the objectives and hardware.


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any industrial processes are controlled in se!uence.

" discrete statee#presses that each event in the

se!uence can be described by specifyingthecondition o all operatin$ units o the process.

For example:% valveAis open % valve Bis closed&

% conveyer Cis on % limit switch 1is closed" techni!ue or desi$nin$ and describin$ the se!uence

o process events& call ladder diagram,whichevolved rom the early use o electromechanical relaysto control the se!uence in such process.

The most common control system or discrete controlis implemented by aprogrammable logic controller(PLC).

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Introduction


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The f$ure shows a manuacturin$ process and thecontroller. (nput variables )1& 2& 3* and outputvariables )C1& C2& C3* can only be in two value.

+Prepared by Wong CheeWoon


Discrete State Process Control


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, or e#ample valves are open / closed& motors are on / o0&temperature is hi$h / low& limit switches are closed / open.

, ( there are ' input variables and ' output variables& thepossible states are 1+ since each variable can tae on two

values )2 2 2 2 2 2*.

, "n eventin the system is defned by aparticular stateo the system& as lon$ as the input variables remain in thesame state and the output variables are let in theassi$ned state.




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(ndustrial processes involve many operations

and steps4 some steps occur in series&

4 some steps occur inparallel&

4 some events involve regulation ofcontinuous variableover the duration oevent )e$. 5ater level- up and down*.

The discrete-state process control systemunctions as the master control systemorthe entire plant operation.



Characteristics of the Sstem


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!efri"erator#Free$er




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The discrete-state input variablesare4 door open/closed&4 cooler temperature hi$h/low&4 ree7er temperature hi$h/low&4 rost eliminator timer time-out/not time-out&4 power switch on/o0&

4 rost detector on/o0.The discrete-state output variablesare

4 li$ht on/o0&4 compressor on/o0&

4 rost eliminator timer started/not started&4 rost eliminator heater and an on/o0&4 cooler ba8e open/closed.

There is a total o 99 two-state variables $ivin$211= 204possible events.

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Frost Free !efri"erator#Free$er


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%he event se&uences are

'a( ( the door is opened& the li$ht is turned on.

'b( ( the cooler temperature is hi$h and the rost eliminator iso0& the compressor is turned onand the ba8e is openeduntilthe cooler temperature is low.

'c( ( the ree7er temperature is hi$h and the rost eliminatoris o0& the compressor is turned onuntil the temperature is low.

'd( ( the rost detector is on& the timer is started& thecompressor is turned o0& and the rost eliminator heater/anare turned onuntil the timer times out.

;vents o )a* can occur in parallel with any o the others.

The event o )b* and )c* can occur in parallel.

;vent )d* can only be serial with )b* and )c*.

owchart.

The narrative statements arereormatted into >owchart

symbols.

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Flo*charts of the vent Se&uence


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'9Prepared by Wong CheeWoon


1i S ) i bl D i i


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1inar-State )ariable Description

Jsed to describe the se!uence oevents in terms o the se!uence odiscrete states o the system.

;ach o the state& includin$ both inputand output variables be specifed.

The input variables cause the state othe system to chan$e becauseoperations within the system cause achan$e o one o the state variables.

The output variables are chan$ed inthe system state that are caused bythe control system itsel.



Construct a state variable description of


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1. Fill tan$ to LA 'sing valve A.

2. Fill tan$ to L( 'sing valve (

3. Start & stir S and heater ".

. ! min. stop S and ".!. )pen % empty tan$ to L4.

#. Reset & repeat.

Input:

+LA& L(& L4& 5-

Output:

+A& (& %& & S& "-

Construct a state variable description ofthe process as sho*n/ %he timer output'%( is initiall lo* *hen its input '%3( islo*/ 4hen %3 is ta5en hi"h the outputstas lo* for 6 minutes and then "oes

hi"h/ It resets to lo* *hen %3 is ta5enlo*/ 7ll level sensors become true *henthe level is reached/ %he processse&uence is:

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xample2/2

S l ti


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Solution

Eecause each variable is a two-state variable& we

use a binary representation true K 9 and alse K=.

Thus& or input& i level " has not been reached&then " K =& and vice versa.

et us tae the binary LwordM describin$ the state

o the system to be defned by bits in the order

"&E&;&TJ&F"&FE&FC&T&S&G

'+Prepared by Wong CheeWoon


9 ill " i l


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9. ill tan to " usin$ valveF".

2. ill tan to E usin$ valveFE

'. Start T& S and G.+. 3 min. stop S and G.3. @pen FC empty tan to ;.1. Neset T& repeat.

Input Output Description

+LA-+L(-+L4-+5- +A-+(-+%-+-+S-+"-

6666 7 166666 Starting state& open valve A

6616 7 166666 Reaches level 4& contin'e with A fill

1616 7 616666 Reaches level A& close valve A& open valve (

1116 7 666111 Reaches level (& close valve (& start timer& heater& stir

1111 7 661166 ime 'p& stop stir and heater& open valve % to empty

1611 7 661166 Reaches level (& contin'e with empty

6611 7 661166 Reaches level A& contin'e with empty

6661 7 666666 an$ empty& t'rn off timer& go to first state



8 i t


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8o"ic "ates



1 l l b


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1oolean al"ebraFariable 7)e.$. temperature*&

i the temperature is hi$h 7K 9& i it is low 7;!uality ( 7K 1& and 7K 9& then 1K 9.

Complement ( 7K 9& then K =.

"AD& ( 7K 9 and 1K 9& and CK 7 1&

@N& O ( CK 7O 1& CK 9 i 7or 1or both

Deor$an

A

BABA

BABA

=+

+=




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Example

Simplify the expression

)( CBACBAD ++=

':Prepared by Wong CheeWoon


CCCBABA .++=

0++= CBABA

BA =

)1( CBA +=

1 l ti


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5e may use Eoolean al$ebratechni!ues to represent the process>ow since the variables are binary.

The e!uation will then determine whenthat variable is taen to its true state.

The e!uation may depend not only on

the set o input variables& but on someo the output variables.

'

Chapter 2 -- Discrete-State Control Part I

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