1Enhanced Single-Loop Control Strategies1. Cascade control2. Time-delay compensation3. Inferential control4. Selective and override control5. Nonlinear control6. Adaptive controlChapter 162Example: Cascade ControlChapter 163Chapter 164Chapter 165Cascade Control

Distinguishing features:1. T!o "# controllers $%t only a sin&le control valve 'or ot(er final control element).2.*%tp%t si&nal of t(e +master+ controller is t(e set-point for ,slave+ controller.3. T!o "# control loops are +nested+ !it( t(e +slave+ 'or +secondary+) control loop inside t(e +master+ 'or +primary+) control loop.

Terminology: slave vs. mastersecondary vs. primary inner vs. o%terChapter 166Chapter 16-121212= hot oil temperature= fuel gas pressure= cold oil temperature (or cold oil flow rate= supply pressure of gas fuel= measured !alue of hot oil temperature= measured !alue of fuel gas temmmYYDDYY1 122perature= set point for = set point for spspY YY Y%Chapter 161 212 2 2 2 1 2 2 1 1'16 5)1P dc v p m c c v p p mG GD G G G G G G G G G GY= + +.Chapter 16Example "#$"Consider t(e $loc/ dia&ram in "i&. 16.4 !it( t(e follo!in& transfer f%nctions0( ) ( )1 21 2 2 15 411 4 1 2 111 1.15 1.23 1v p pm m d dG G Gs s sG G G Gs= = =+ + += = = =+2Chapter 1611Chapter 16Example "#$%Compare t(e set-point responses for a second-order process !it( a time delay 'min) and !it(o%t t(e delay.T(e transfer f%nction isAss%me and time constants in min%tes. 3se t(e follo!in& 4I controllers."or min5 !(ile for min t(e controller &ain m%st $e red%ced to meet sta$ility re6%irements( ) ( )( ) 16 1. ' )5 1 3 1speG ss s =+ +1m vG G = =15 =13.12 6.5cK and = =2 =( )11.235 -.1min .cK = =11Chapter 16( )( )1 1 216 12spE E Y Y Y Y Y = = % % %'If the process model is perfect and the disturbance is zero, then 2Y Y =%and( )116 21spE' Y Y = %For this ideal case the controller responds to the error signal that would occur if not timewere present.Assuming there is not model errorthe inner loop has the effective transfer function( )5 G G =%( )( )16 211 7 1cscG PGEG G e = =+ '12&or no model error:#y contrast5 for conventional feed$ac/ control=* - sG= G G e%( )1 11 1 =+ = = + +cc* sc* sc c* s *spc cGGG G eG G e G G YYG G e G GChapter 16( )716 231 7scsspcG G e YYG G e= +13Chapter 1614Chapter 1615Chapter 16'nferential Control

4ro$lem0 Controlled varia$le cannot $e meas%red or (as lar&e samplin& period.

4ossi$le sol%tions01. Control a related varia$le 'e.&.5 temperat%re instead of composition).2. Inferential control0 Control is $ased on an estimate of t(e controlled varia$le.

T(e estimate is $ased on availa$le meas%rements.8Examples0 empirical relation5 9alman filter

:odern term0 soft sensor16'nferential Control with &ast and Slow (easured )aria*lesChapter 161-Selecti!e Control Systems + ,!errides

"or every controlled varia$le5 it is very desira$le t(at t(ere $e at least one manip%lated varia$le.

#%t for some applications5 NC> NM !(ere0NC ;n%m$er of controlled varia$lesNM;n%m$er of manip%lated varia$lesChapter 16

Solution:3se a selective control system or an override.1.

Low selector:

-igh selector:Chapter 16

(edian selector:

The output. /. is the median of an odd num*er of inputs12

m%ltiple meas%rements

one controller

one final control elementChapter 16Example:-igh Selector Control System 21% measurements. % controllers. " final control elementChapter 1621,!errides

An override is a special case of a selective control system

*ne of t(e inp%ts is a n%merical val%e5 a limit.

3sed !(en it is desira$le to limit t(e val%e of a si&nal 'e.&.5 a controller o%tp%t).

*verride alternative for t(e sandChapter 1622Chapter 16230onlinear Control Strategies

:ost p(ysical processes are nonlinear to some de&ree. Some are very nonlinear. Examples0 p?5 (i&( p%rity distillation col%mns5 c(emical reactions !it( lar&e (eats of reaction. ?o!ever5 linear control strate&ies 'e.&.5 4I@) can $e effective if01. T(e nonlinearities are rat(er mild. or5 2. A (i&(ly nonlinear process %s%ally operates over a narro! ran&e of conditions. "or very nonlinear strate&ies5 a nonlinear control strate&y can provide si&nificantly $etter control. Two general classes of nonlinear control:1.An(ancements of conventional5linear5 feed$ac/ control 2.:odel-$ased control strate&ieseference0 ?enson B Se$or& 'Ad.)5 122- $oo/.Chapter 1624Enhancements of Con!entional &eed*ac1 Control Ce !ill consider t(ree en(ancements of conventional feed$ac/ control01. Nonlinear modifications of 4I@ control2. Nonlinear transformations of inp%t or o%tp%t varia$les3. Controller parameter sc(ed%lin& s%c( as !ain sc"ed#lin!$ 0onlinear (odifications of 2'D Control:1'1 ' ) ) '16-26)c cK K a % e t % = +Chapter 16

Kc& and a are constants5 and e't) is t(e error si&nal'e = ysp - y). Also called5 error s'#ared controller.

D%estion0 C(y not %se E(ample0 level control in s%r&e vessels. ,ne Example0 nonlinear controller &ain2' )instead of' ) ' ) # e t # % e t % e t ) 250onlinear Transformations of )aria*les

,*3ecti!e: :a/e t(e closed-loop system as linear as possi$le. 'C(y>)

Typical approach: transform an inp%t or an o%tp%t.E(ample* lo&arit(mic transformation of a prod%ct composition in a (i&( p%rity distillation col%mn. 'cf. :cCa$e-T(iele dia&ram)Chapter 16 !(ere (*D denotes t(e transformed distillate composition.

4elated approach: @efine # or y to $e com$inations of several varia$les5 $ased on p(ysical considerations.E(ample*Contin%o%s p? ne%traliEation C+s0p, and li6%id level5 "M+s0acid and $ase flo! rates5 '- and '. Conventional approac"0 sin&le-loop controllers for p, and "$ .etter approac"0 control p? $y adF%stin& t(e ratio5 '- < '.5 and control " $y adF%stin& t(eir s%m. T(%s5 #/ ; '- < '.and #0 ; '- < '.1'16-2-)1* DDDsp(( lo!(=265ain Scheduling

,*3ecti!e: :a/e t(e closed-loop system as linear as possi$le.

6asic 'dea: AdF%st t(e controller &ain $ased on c%rrent meas%rements of a ,sc(ed%lin& varia$leG5 e.&.5#1 y1 or some ot(er varia$le.Chapter 16

Note0 He6%ires /no!led&e a$o%t (o! t(e process &ain c(an&es !it( t(ismeas%red varia$le.2-Chapter 16Examples of 5ain Scheduling

Example "$Titration c%rve for a stron& acid-stron& $ase ne%traliEation.

Example %$ *nce t(ro%&( $oilerT(e open-loop step response are s(o!n in "i&. 16.1. for t!o different feed!ater flo! rates.&ig$ "#$"7 ,pen-loop responses$

2roposed control strategy:Iary controller settin& !it( !5 t(e fraction of f%ll-scale '111J) flo!.'16-31)c c 2 2 D DK 3K 1 4 31 4 31 = = =

Compare !it( t(e I:C controller settin&s for :odel ? in Ta$le 12.1012' ) 5 5 51 2 22sc 2 DcKeG s Ks K += = = + =+ ++(odel -: 2.Chapter 168dapti!e Control A &eneral control strate&y for control pro$lems !(ere t(e process or operatin& conditions can c(an&e si&nificantly and %npredicta$ly. A=ample0 Catalyst decay5 e6%ipment fo%lin& :any different types of adaptive control strate&ies (ave $een proposed. Self-Tuning Control (STC: 8A very !ell-/no!n strate&y and pro$a$ly t(e most !idely %sed adaptive control strate&y.86asic idea: STC is a model-$ased approac(. As process conditions c(an&e5 %pdate t(e model parameters $y %sin& least s6%ares estimation and recent # B y data.0ote: "or predicta$le or meas%ra$le c(an&es5 %se &ain sc(ed%lin& instead of adaptive controlHeason0 Kain sc(ed%lin& is m%c( easier to implement and less tro%$leprone.

22Chapter 166loc1 Diagram for Self-Tuning Control