Process Control

Experiment 13: Process Control 1 (Armfeld PCT 9 & 10)  James Forst! Forst! "001#$$% 'rop $ Perormed: 1*t! Fe+rar #01% ,+mitted: 1*t! -arc! #01% ,per.isor: Proessor ' -ar/x

1

Contents ,nopsisPae 3

2ntrodctionPae 2ntrodctionP ae 3

 T!eorPae 3

Experimental Tec!ni4ePae 5

6esltsPae 6esltsP ae 

7iscssionPae 1#

ConclsionPae 13

6eerencesPae 6eerencesPae 13

AppendicesPae 13

Synopsis #

 T!e prpose o t!is experiment 8as to in.estiate dierent control sstems 2t in.ol.ed loo/in at +ot! ono and linear control sstems and 8it!in t!at Proportional and Proportional2nteral T!e reslts 8e ained 8ere .alid and accrate and a.e a od indication o all t!e dierent sstems loo/ed at and 8!at occasions t!e are most appropriate and t!e optimm settin or sin t!em

Introduction  T!e aim o t!is experiment 8as to compare t!e perormance o a nm+er o dierent control sstems T!e experiment in.ol.ed comparin an ono  controller aainst a linear eed+ac/ controller ;e t!en loo/ed at comparin dierent tpes o linear control sstems< a proportional controller and a proportionalinteral controller ;e also determined t!e optimm .ale or t!e controller ain< = c< and in.estiated !o8 t!e response o a proportional control sstem depends on t!e .ale o = c

Theory 2n t!is in.estiation 8e loo/ed at t8o dierent tpes o control sstems< ono control and linear eed+ac/ control >no is t!e simpler o t!e t8o as t!e sstem ?st literall trns its sel on and o constantl in order to ac!ie.e a relati.el sta+le .ale called t!e set point T!is sstem !o8e.er !as its alts in t!at o rarel et t!e exact .ale t!at o desire< t!e sstem ?st @ctates +et8een limits and t!e controller is constantl +ein trned on and o For or experiment a tan/ o 8ater 8it! a set !ei!t 8as sed and t!e @o8 o 8ater in 8as constantl trned on and o in order to maintain t!e same li4id le.el >no sstems are sed so commonl +ecase o t!eir simplicit and are c!eaper  T!e ot!er control sstem 8e loo/ed at 8as linear eed+ac/ control A linear control sstem 8or/s + recei.in a measrement rom t!e sensortransmitter and comparin it 8it! a pre alined set point T!e dierence or error (e(t)) +et8een t!e t8o is t!en calclated and t!e controller otpt is calclated rom t!is error T!ere are dierent 8as o doin t!is dependin 8!at set p on t!e sstem is sed T!e t8o main controller sed are proportional (P) and proportional interal (P2) controllers T!e e4ation sed or calclatin t!e otpt sinal rom t!e error is t!e ollo8in:

m ( t )=m ´ + K c e ( t )

3

;!ere

( ) is t!e otpt sinal o t!e controller< m´ is t!e +ias or

m t 

controller otpt sinal i t!e error is Bero<  K c  is t!e controller ain and e ( t )  is t!e error K c  is also /no8n as t!e proportional +and 8!ic! ta/es

t!e orm

 PB=

100

 K c

.

 T!e e4ipment 8e sed a.e .ales o 1% o t!e

proportional +and< so t!is !ad to +e con.erted 8!en calclatin

 K c

.ales T!e reason t!at P2 controllers are more commonl sed is t!at t!e P controllers e.en at stead state do not reac! t!e exact set point 8!ic! leads to an oset T!e .ale o t!is oset is dependent on t!e controller ain P2 controllers are sed to et rid o t!is oset and are t!ereore more accrate< !o8e.er t!e e4ation sed to descri+e t!e controller otpt is more complicated: ´ + K c e ( t ) + m ( t )=m

 K c τ  I 

∫ e ( t ) dt 

 T!e interation part o t!is e4ation remo.es t!e oset since t!e error Anot!er controller tpe t!at cold +e sed is a proportional interal deri.ati.e or P27 controller T!is tpe o controller is sed i t!ere is a need to predict t!e error and t!ereore do somet!in to pre.ent it T!is tpes can onl +e sed in specifc cases t!o!< or example i t!e sstem ma/es a lot o noise t!is 8ill aect t!e @ctations o t!e error dierence o.er t!e time dierence

Experimental Technique  T!e e4ipment sed or t!is experiment 8as called an Armeild Process -odle or le.el and @o8 control and 8as set p in t!e ollo8in manner:

5

Figure 1: Sketch of the PCT9 Process Module for ow and level control 

As .isi+le orm t!e diaram t!e sstem consists o # tan/s< T1 and T# T!e 8ater le.el in T# is 8!at 8old +e controlled or t!e frst part o t!e experiment T# contained a 8ater le.el sensor and an o.er@o8 T!e nit consisted o % manall controlled .al.es and 3 solenoid .al.es A rotameter controlled t!e @o8rate o 8ater 8!ic! flled T# al.es 3< 5< ,>D# and ,>D3 all controlled t!e @o8rate o 8ater comin ot T#  T!e control modle sed or t!is experiment 8as called T!e Armfeld PCT10 T!e diaram +elo8 s!o8s t!e ront o t!e modle: 7iital Process Controller

oltmeter

Ammeter

Po8er ,ppl

5#0 mA -anal >tpt Positioner ,8itc!ed >tpt or >n>-otor control ,inal Conditionin C!annels  (C"1) (C"#) %

Figure 2: The front of PCT10

 T!e pmp 8as connected to t!e #50 connection on t!e side o PCT10 and t!e sstem tested to ensre t!at T# flled 8!en t!e pmp 8as on T!e rotameter 8as tested to ensre it 8as nctionin correctl + ad?stin .al.e # ,>D1 8as closed + connectin it to t!e #5 otlet in t!e section mar/ed motor positioner on PCT10 T!e motor positioner and manal otpt 8ere connected T!is stopped t!e @o8 into t!e tan/ ,>D# and 3 8ere also tested in t!is manner T!e .al.es opened 8!en t!e manal otpt /no+ is t8isted to open 8!ic! applied t!e po8er >n> Control:  T!e frst part o t!e experiment in.ol.ed loo/in at ono control T# 8as emptied and ,>D< 3 and 5 8ere all closed T!e ono controller s8itc! 8as placed in t!e tan/ T!e le.el s8itc! 8as connected to connections A and C in t!e >n> control section on PCT10 T!e pmp 8as s8itc! on and # 8as ll opened to allo8 t!e tan/ to fll p T!e le.el s8itc! 8as set to a !ei!t o $0mm 8!ic! is t!e !ei!t t!at 8e 8ant t!e sstem to maintain >nce t!e 8ater reac!ed t!is le.el ,>1 started trnin on and o  continosl in order to /eep t!e 8ater at t!is le.el T!is 8as t!en repeated openin ,>D# and t!e time inter.als +et8een t!e @o8 trnin o and on recorded T!is 8as t!en repeated aain 8it! ,>D3 open and ,>D# closed and t!en aain openin +ot! ,>D# and 3 T!e time +et8een ,>D1 s8itc!in on and o 8as recorded eac! time

Dinear Feed+ac/ Control:  T!e le.el sensor frst !ad to +e cali+rated T!e sensor in T# 8as aain connected to PCT10 and t!e rest o t!e sstem 8as set p as +eore T!e tan/ 8as flled to 130mm and t!en # 8as closed so t!ere 8as no @o8 ot or in t!e tan/< it 8as set at 130mm T!e readin on t!e .oltmeter 8as ad?sted sin a small scre8dri.er to read exactl 1 T!e tan/ 8as t!en emptied to 30mm at 8!ic! point t!e .oltmeter 8as aain ad?sted to read exactl 0 T!e tan/ 8as t!en flled to 130mm aain and t!en emptied in 10mm inter.als 8it! a .oltmeter readin +ein ta/en at eac! inter.al ext t!e @o8 sensor 8as cali+rated T!e sensor 8as connected to PCT10 and 8as connected to t!e .oltmeter ;it! t!e motoriBed .al.e ll open< # 8as ad?sted to i.e a @o8 o 3000cm3min At t!is @o8rate t!e .oltmeter 8as ad?sted sin a small scre8dri.er to i.e a readin o 1 # 8as t!en closed to i.e a @o8rate o 0 and t!e .oltmeter ad?sted to read 0 T!e @o8 8as t!en trned +ac/ on and set to 3000cm3min T!e @o8 8as ad?sted sin # and .oltae readin 8ere ta/en at %00 cm3min inter.als do8n to 0

*

 T!e sstem 8as t!en set p or linear eed+ac/ control All .al.es 8ere closed apart rom # and 5 8as opened to a 30o anle T!e motoriBed .al.e 8as ll opened to i.e a @o8rate o 3000cm3min T!e le.el sensor 8as aain connected to PCT10 so +ot! sensors 8ere connected  T!e ta+le +elo8 s!o8s t!e controller settins or le.el control 8it! a proportionalinteral controller: Parameter Proportional Gand

Cod e Prop

,ettin  10

2nteral Time 7eri.ati.e Time Ccle Time >tpt Dimit ,et Point Dimit Dinear 6ane

nits 1#0t!s o Controlled aria+le ,panH ie actal proportional +and I %xProp -intes ,econds ,econds L L For 5#0mA I 0100L

2nt 0# dEr 0 CKt #0 PrD 100 ,PD 100 C, 0%$ 1 7irect 6e.erse Action C, r 6e.erse Actin Controller # MM 7enotes M7onNt care .ales

 T!e sstem 8as connected to t!e compter to record t!e data  T!e set point 8as set to #0L and t!e data loin sstem 8as started  T!e set point 8as t!en c!aned consecti.el to 50L< *0L< $0L and 100L 8!ilst continall recordin T!e dataloin 8as stopped ater it reac!ed 100L ext t!e a+ilit o a proportional controller to deal 8it! a distr+ance 8as in.estiated T!e set point 8as set to %0L and 5 8as opened to 30o T!e controller 8as set p in t!e ollo8in manner: Parameter Proportional Gand

Cod e Prop

,ettin  #0

2nteral Time 2nt 0 7eri.ati.e Time dEr 0 Ccle Time CKt #0 M >tpt Dimit PrD 100  ,et Point Dimit ,PD 100 M Dinear 6ane C,1  0 % $ 7irect 6e.erse Action C,#  r   7enotes M7onNt care .ales

nits 1#0t!s o Controlled aria+le ,panH ie actal proportional +and I %xProp -intes ,econds ,econds L L For 5#0mA I 0100L 6e.erse Actin Controller

 T!e settins sed made t!e controller operate in manal mode so t!ere 8as no control ,>D# 8as opened to create a distr+ance and t!e 

dataloin 8as trned on and at!ered inormation ntil t!e sstem reac!ed a stead state  T!is exact procedre 8as repeated repeated 8it! t!e controller s8itc!ed to normal mode T!is 8as t!en repeated aain a rt!er * times< eac! time alterin t!e Proportional Gand to 10< 5< #< 1< 0% and 0 respecti.el  T!e dataloer 8as reset and recorded t!e data indi.idall or eac! Prop .ale  T!e exact procedre 8as t!en repeated aain to test t!e a+ilit o a proportionalinteral controller to deal 8it! t!e same distr+ance T!e set p 8as identical !o8e.er and 2nteral time .ale o 0# 8as set< as opposed to 0 or proportional T!e same .ales o PG 8ere sed: #0< 10< 5< #< 1< 0% and 0

Results >n> control: ,>D# >pen and ,>D3 closed  A.erae time on I 0%3 seconds I 0009 min A.erae time o I 1%3 seconds I 00#* min Flo8rate ,>D# I

3 3 t on  cm  cm =772 3000  × min t off − t on min

,>D3 >pen and ,>D# closed  A.erae time on I 1** seconds I 00#$ min A.erae time o I 100* seconds I 001 min 3

Flo8rate ,>D3 I

 cm 1868 min

Got! >pen  A.erae time on I 501% seconds I 0**9 min A.erae time o I 0*% seconds I 0011 min 3

Flo8rate ,>D3 I

cm 2952 min

 T!e @o8rate 8!en +ot! 8ere open is almost exactl e4al to t!at o t!e @o8rate in

$

Dinear Feed+ac/ Controller: Table 1 Calibrating Level Sensor "ei!t (mm) 130 1#0 110 100 90 $0 0 *0 %0 50 30

oltae () 1003 0$$ 09 0*$ 0%* 05% 03* 0# 019 00$# 0

Figure 1

oltae .s "ei!t 150 1#0

6O I 1

100 $0

"ei!t (mm)

*0 50 #0 0 0

0#

05

0*

oltae ()

9

0$

1

1#

 T!is fre s!o8s !o8 t!e controller 8as sccessll cali+rated +et8een 130mm and 30mm

Table  Calibrating Flo! Sensor Flo8rate (cm3min)

oltae ()

%00

001

1000

0#5

1%00

0395

#000

0%93

#%00

0

%$3000

1

Figure 

10

Florate .s oltae 1# 1 6O I 1 0$

oltae () 0* 05 0# 0 0

%00

1000

1%00

#000

#%00

3000

3%00

Flo8rate (cm3min)

Fire # s!o8s t!e @o8 sensor 8as cali+rated correctl T!ere is a .er small readin at %00 cm3min since at sc! a lo8 @o8rate t!e sensor strles to pic/ ant!in p< !ence t!e tin increase rom 0%00< rom %00 p8ard it increases rapidl in a linear as!ion

11

C!anin T!e ,etpoint 1#0 100 $0

LT  LC

*0 50 #0 0 0

%0

100

1%0

#00

#%0

300

3%0

500

5%0

 Time (sec)

C!ani n t!e ,etpoint: Figure "

;!ere ,eries 1 I Di4id "ei!t ,eries # I >tpt oltae ,eries 3 I >tpt Flo8rate Fire 3 s!o8s !o8 8!en t!e set point is c!aned t!e otpt .oltae and otpt @o8rate almost c!ane at t!e same rate in order to reac! t!e ne8 set point< 8it! t!e otpt @o8rate sli!tl slo8er as s!o8n + t!e cr.ed line p ntil 100L rat!er t!an t!e distincti.e @at almost 90o anle s!o8n + t!e otpt .oltae Eect o a 7istr+ance on Proportional Controller 8it!ot control: Figure #

Proportional Controller  ;it!ot Control *0 %0 50

L "ei!t 30 #0 10 0 0

#0

50

*0

$0

 Time

1#

100

1#0

150

;!ere ,eries 1 I Di4id "ei!t ,eries # I >tpt oltae ,eries 3 I >tpt Flo8rate Fire 5 s!o8s !o8 8!en t!e distr+ance occrred 8it! t!e sstem on manal t!e controller does not respond and t!ereore t!e tan/ 8ill ?st /eep on emptin T!is is clearl .isi+le + t!e li4id le.el droppin rapidl and no c!ane at all in t!e otpt .oltae or otpt @o8rate Proportional Controller: Fires %11< 8!ic! can +e ond in t!e appendices< s!o8 t!e rap!s or !o8 a Proportional Controller 8it! dierent Proportional Gands o #0< 10< 5< #< 1< 0% and 0 cope 8it! a distr+ance For eac! fre: Series 1 $ Liquid %eight Series  $ &utput 'oltage Series " $ &utput Flo!rate From t!ese rap!s it is clear t!at a PG o # is t!e most accrate as it ets closest to t!e set .ale< !as t!e 4ic/est response and !as a lot less @ctations t!at 1< 0% and 0 T!ese reslts 8ill +e analsed in more detail in t!e discssion Proportional2nteral Controller: Fires 1#1< 8!ic! can +e ond in t!e appendices< s!o8 t!e rap!s or !o8 a Proportional2nteral Controller 8it! dierent Proportional Gands o 10< 5< #< 1< 0% and 0 can cope 8it! a distr+ance For eac! fre: Series 1 $ Liquid %eight Series  $ &utput 'oltage Series " $ &utput Flo!rate  T!e oscillations at lo8er .ales o =c or t!e @o8rate 8ere less 8!en sin a P2 controller

13

(iscussion  T!e frst part o t!e experiment in.ol.ed sin an ono control sstem  T!e @o8rates o t!e 8ater @o8in t!ro! ,>D# and 3 8ere calclated + timin t!e lent! o time t!e @o8 8as trned on and o T!e @o8 trned +ot! on and o rapidl 8!en ,>D3 8as closed and ,>D# 8as let open 8it! it +ein on or 0%3 seconds and 1%3 o T!is reslted in a @o8rate o # cm3min @o8in ot o ,>D3 ext ,>D# 8as closed and ,>D3 opened T!is reslted in +ot! +ein in and o or ro!l t!e same time< a+ot 1 second eac! T!is reslted in a !i!er @o8rate o 1$*$ cm3min ;!en +ot! 8ere open it 8as on or 50 seconds and o or ?st 0*% T!is reslts in lare @ctations or t!e actal li4id le.el 8!ic! is a disad.antae o ono control  T!e next part o t!e experiment 8as to c!ane to a linear controller T!e le.el and @o8 sensors 8ere sccessll cali+rated 8it! a .er sli!t error cased + onl doin t!e cali+ration once T!is 8old +e a possi+le impro.ement to accrac s!old t!e experiment +e repeated  T!e c!anin o t!e set point 8as t!en loo/ed at + settin t!e initial le.el to #0L o t!e !ei!t< %0mm< and startin t!e dataloer T!e set point 8as c!aned p to inter.als o 50< *0< $0< and 100L T!e reslts can +e seen rom fre 3< 8!en t!e set point 8as c!aned o can clearl see t!e s!arp increase orm t!e .oltae otpt 8!ic! 8as 4ic/l ollo8ed + t!e otpt @o8rate< 8!ic! cases t!e le.el to increase to t!e ne8 set point Fire 5 s!o8s !o8 i t!e control sstem is ?st set to manal t!en 8!en a distr+ance is created t!e sstem 8ill not do ant!in to ad?st T!ere is no sinal otpt and t!ereore no @o8 so t!e tan/ 8ill ?st slo8l drain till it reac!es a stead state mc! lo8er t!an t!e set point Fires %11 s!o8 t!e rap!s or !o8 a Proportional Controller 8it! dierent Proportional Gands o #0< 10< 5< #< 1< 0% and 0 cope 8it! a distr+ance T!ese .ales or PG can +e con.erted to =c sin t!e  PB=

100

 K c

e4ation< i.in 1< #< %< 10< #0 and 50< (eac! PG .ale 8as

mltiplied + %) As t!ese .ales o =c increased t!e li4id !ei!t ot closer to t!e set point ater t!e distr+ance and 8as 4ic/er p ntil a .ale o =c I 10 Ater t!is point t!e .oltae otpt and t!ereore otpt @o8rate @ctated massi.el resltin in t!e li4id !ei!t @ctatin more also ,o a PG .ale o # 8!ic! e4als a =c .ale o 10 8as t!e optimm one to se 8!en sin a Proportional Controller Fires 1#1 s!o8 t!e rap!s or !o8 a Proportional2nteral Controller 8it! dierent Proportional Gands o 10< 5< #< 1< 0% and 0 can cope 8it! a distr+ance T!ese reslts 8ere .er similar to t!e proportional controller 15

ones T!e onl dierence +ein a sli!tl smaller osetQ 8!ic! means or more accrate reslts T!is can +e seen + comparin t!e rap!s o t!e same PG< 8!ic! s!o8 t!at t!ereQs a smaller dipQ ater t!e distr+ance

Conclusion  T!e frst aim o t!is experiment 8as to loo/ at an ono control sstem  T!e reslts 8e ot s!o8ed !o8 alt!o! itQs a simple sstem it !as its disad.antaes since t!e li4id le.el @ctated arond t!e set point constantl  T!e second aim o t!e experiment 8as to compare Proportional Control aainst Proportional2nteral Control and loo/ at t!e eect o .arin =c .ales T!is 8as done sccessll and it can +e clearl see t!at or proportional control a .ale o PG o # or =c .ale o 10 8as t!e optimm one or le.el control in t!is sstem since it a.e t!e least oset rom t!e %0L set point< !ad t!e least @ctations compared to t!e lo8er PG .ales and !ad t!e 4ic/est response time compared to t!e !i!er PG .ales Comparin Proportional to Proportional 2nteral in terms o =c .ales +ot! 8ere prett similar as seen + t!e rap!s

Re)erences Process Control 8it! t!e Armeild PCT9 and 10: Da+orator otes

*ppendices Figure +

Proportional Controller  PG o #0 0 *0 %0 50

L "ei!t

30 #0 10 0 0

#0

50

*0

$0

 Time (sec)

1%

100

1#0

Figure ,

Proportional Controller  PG o 10 0 *0 %0 50

L "ei!t

30 #0 10 0 0

10

#0

30

50

%0

*0

0

$0

90

 Time (sec)

Figure -

Proportional Controller  PG o 5 0 *0 %0 50

L "ei!t

30 #0 10 0 0

10

#0

30

50

%0

*0

 Time (sec)

Figure . 1*

0

$0

90

Proportional Controller  PG o # 0 *0 %0 50

L "ei!t

30 #0 10 0

0

#0

50

*0

$0

100

1#0

150

 Time (sec)

Figure /

Proportional Controller  PG o 1 $0 0 *0 %0

L "ei!t

50 30 #0 10 0 0

#0

50

*0

$0

 Time (sec)

1

100

1#0

Figure 10

Proportional Controller  PG o 0% 1#0 100 $0

L "ei!t

*0 50 #0 0

0

10

#0

30

50

%0

*0

 Time (sec)

Proportional Controller  PG o 0 1#0 100 $0

L "ei!t

*0 50 #0 0 0

10

#0

30

50

%0

*0

0

 Time (sec)

Figure 11

1$

Figure 1

P2 Controller  PG o 10 $0 0 *0 %0

L "ei!t

50 30 #0 10 0 0

10

#0

30

50

%0

*0

 Time (sec)

Figure 1"

19

0

$0

90

P2 Controller  PG o 5 0 *0 %0 50

L "ei!t

30 #0 10 0 0

10

#0

30

50

%0

*0

0

$0

Axis Title

P2 Controller  PG o # 0 *0 %0 50

L "ei!t

30 #0 10 0

0

10

#0

30

50

%0

*0

0

$0

 Time (sec)

Figure 1#

P2 Controller  P2 o 1 100 $0 *0

L "ei!t

50 #0 0 0

10

#0

30

50

%0

*0

0

$0

 Time (sec)

Figure 1+

#0

Figure 1,

P2 Controller  PG o 0% 1#0 100 $0

L "ei!t

*0 50 #0 0

0

10

#0

30

50

%0

*0

 Time (sec)

P2 Controller  PG o 0 1#0 100 $0

L "ei!t

*0 50 #0 0 0

%

10

1%

#0

#%

30

3%

50

5%

%0

 Time (sec)

Figure 1-

#1