A performance logic algorithm (PSL) was developed to optimize the performance of propulsion systems for component and sensor degradations by monitoring the performance of the engine system and minimizing thrust specific fuel consumption (TSFC) while retaining a constant engine net thrust. Engine constraints such as surge margin, speed, pressure, and temperature are observed. The PSL algorithm was applied to the quiet, clean, short haul experimental engine. Engine control set points were modified for component degradations in order to restore the nominal net thrust. Results show convergence to the optimum value can be obtained within 60 to 90 seconds, which makes the program acceptable to on line operation with present state of the art minicomputers. Tests indicate that in most cases the PSL algorithm offers some improvement in thrust specific fuel consumption over the manual throttle

Seldner, K.

English

NASA Technical Reports Server

PERFORMANCE-SEEKING CONTROLS 
Kurt Seldner 
National Aeronautics and Space Administration 
L e w i s  Research Center 
Cleveland,  Ohio 
INTRODUCTION 
C o n s t a n t l y  i n c r e a s i n g  f u e l  c o s t s  j u s t i f y  t h e  i n v e s t i g a t i o n  of c o n t r o l  
methods to  opt imize  the  per formance  of  a i rc raf t  p ropuls ion  sys tems.  The t a s k  
r e q u i r e s  a method t o  trim e n g i n e  c o n t r o l  v a r i a b l e s  t o  a n  optimum cond i t ion .  
Engine control  schedules  are usua l ly  deve loped  du r ing  the  des ign  and  t e s t ing  
s t a g e s .  However, s ince  pe r fec t  eng ine  con t ro l  ma tch ing  is time consuming  and 
c o s t l y ,  c o n t r o l  s c h e d u l e s  are u s u a l l y  less t h a n  p e r f e c t .  More important  i s  t h e  
fac t  tha t  engine- to-engine  component v a r i a t i o n s  are n o r m a l l y  s u f f i c i e n t  t o  
cause  the  eng ine  to  ope ra t e  a t  a nonoptimum c o n d i t i o n .  A l s o ,  d u r i n g  t h e  l i f e  
of the  engine ,  component  and s e n s o r  d e g r a d a t i o n  c a n  r e s u l t  i n  a h i g h e r  f u e l  
consumption to  ma in ta in  a p a r t i c u l a r  e n g i n e  t h r u s t .  
This  paper  descr ibes  a performance-seeking logic  a lgori thm (PSL) t h a t  op- 
t imizes  the  pe r fo rmance  o f  p ropu l s ion  sys t ems  fo r  component  and sensor  degra-  
d a t   i o n s .  
PERFORMANCE-SEEKING LOGIC 
The objec t ives  of  the  per formance-seeking  log ic  (PSL) a lgo r i thm are t o  
monitor the performance of the  engine  sys tem and  to  minimize  thrus t  spec i f ic  
fuel  consumption (TSFC) w h i l e  r e t a i n i n g  a cons t an t  eng ine  ne t  t h rus t .  Eng ine  
cons t r a in t s  such  as surge margin,  speed,  pressure,  and temperature  must  be ob- 
served. The PSL a lgo r i thm w a s  a p p l i e d  t o  t h e  q u i e t ,  c l e a n ,  s h o r t - h a u l  e x p e r i -  
mental   engine (QCSEE) ( r e f s .  1 and 2 ) .  This  NASA-funded research  program was 
under taken  to  deve lop  fu ture  STOL engine  technology. The QCSEE propuls ion  sys-  
tem f e a t u r e s  a high-Mach-number i n l e t ,  a va r i ab le -p i t ch  f an ,  and  a v a r i a b l e  ex- 
h a u s t  n o z z l e  ( f i g .  1). A d i g i t a l  e l e c t r o n i c  c o n t r o l l e r  and a hydromechanical 
fue l  sys t em are used to  implement  required control  funct ions.  The fou r  QCSEE 
v a r i a b l e s  t o  b e  c o n t r o l l e d  are e n g i n e  p r e s s u r e  r a t i o  (EPR), i n l e t - d u c t  Mach 
number, fan   speed ,   and   compressor   s ta tor   angle .  The funct ion  of   the  hydro-  
mechan ica l  fue l  con t ro l  i s  t o  c o n t r o l  EPR; f an  speed  con t ro l  i s  achieved by 
v a r y i n g  t h e  p i t c h  f a n  a n g l e .  A c o n s t a n t  i n l e t - d u c t  Mach number i s  maintained 
by vary ing  the  exhaus t  nozz le  area i n  o r d e r  t o  r e d u c e  a i r c r a f t  n o i s e  p r o b l e m s .  
The compresso r  co re  s t a to r  ang le  is scheduled by t h e  d i g i t a l  c o n t r o l l e r ,  w h i c h  
a l so  inco rpora t e s  t he  eng ine  con t ro l  limits. The PSL a lgor i thm only  modi f ies  
t h e  r e f e r e n c e  s e t - p o i n t  s c h e d u l e s  f o r  t h r e e  o f  t h e  f o u r  e n g i n e  v a r i a b l e s .  
These include EPR, f an  speed ,  and  in l e t  Mach number.  The PSL a lgor i thm does  
no t  a t t empt  to  mod i fy  the  compresso r  s t a to r  ang le  schedu les .  The  hard  engine 
limits are no t  v io l a t ed  and  mus t  be  ma in ta ined  fo r  s a fe  eng ine  ope ra t ion .  
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I 
The PSL a lgo r i thm was a p p l i e d   t o  a real-time d i g i t a l   e n g i n e   s i m u l a t i o n .  I 
F igu re  2 p r e s e n t s  a s i m p l i f i e d   b l o c k   d i a g r a m   o f   t h e   c o n t r o l l e r ,   t h e  PSL algo- \ 
rithm, and  the  engine.  The f u n c t i o n  of th i s  d i ag ram is t o  i l l u s t r a t e  t h e  nom- 
ina l  s e t -po in t  s chedu les  r equ i r ed  to  set t h e  c o n t r o l  i n p u t  v a r i a b l e s .  The PSL 
a lgor i thm ( lower  por t ion  of  f ig ,  2) is a s e c o n d a r y  c o n t r o l l e r  t h a t  o p e r a t e s  i n  
con junc t ion  wi th  the  no rma l  eng ine  con t ro l l e r .  Spec i f i c  eng ine  ou tpu t  va r i a -  
b l e s  can  be  connec ted  to  the  PSL b lock  tha t  con ta ins  the  op t imiza t ion  a lgo r f thm 
to  min imize  th rus t  spec i f i c  fue l  consumpt ion  sub jec t  t o  s e l ec t ed  eng ine  con- 
s t r a i n t s .  The output  in format ion  f rom the  PSL a l g o r i t h m  r e p r e s e n t s  a change 
from the  nomina l  va lues  fo r  t he  con t ro l  i npu t  va r i ab le s .  The output  of  the PSL 
a l g o r i t h m  m o d i f i e s  t h e  s e t - p o i n t  s c h e d u l e s  t o  r e s t o r e  t h e  p r o p u l s i o n  s y s t e m  t o  
optimum cond i t ion .  The PSL algori thm performs system opt imizat ion under  
s t e a d y - s t a t e  c o n d i t i o n s .  
PERFORMANCE CRITERION 
The important  considerat ion in  any opt imizat ion problem is  t h e  s e l e c t i o n  
of a per formance  c r i te r ion .  The pe r fo rmance  func t ion  fo r  t he  PSL a lgo r i thm is 
J = Q, ( 1 - m ) 2 + Q 2  TSFCN ( l - zT+Q3 FNNOM (i-&)ZtQ4 NLNOM (l-x)2 NHNOM 
where Q,, Q , Q3, and Q, are we igh t ing   f ac to r s .  The f i r s t  term i d e n t i f i e s  
the  minimizagion  var iab le  TSFC; the remaining terms are t h e  p e n a l t y  f u n c t i o n s .  
These terms p e n a l i z e  t h e  p e r f o r m a n c e  c r i t e r i o n  f o r  d e v i a t i o n s  f r o m  t h e i r  nomi- 
n a l  v a l u e s .  The nominal values are dependent  on the engine operat ing condi t ion.  
Thus schedul ing of these nominal  values  must  be considered to  make t h e  PSL al- 
go r i thm e f fec t ive  ove r  t he  f l i gh t  enve lope .  The p e n a l t y  terms were s e l e c t e d  t o  
cause  the  spec i f ic  engine  var iab les  of  the  degraded  engine  sys tem to  re turn  to  
nea r  t he  des ign  va lues .  By a l lowing  the  engine  speeds  to  vary ,  i t  could  be 
p o s s i b l e  t o  g e n e r a t e  a n  i m p r o v e d  v a l u e  f o r  TSFC for  the degraded engine condi-  
t i o n .  A t h r u s t  measurement   must   be  avai lable   for   the PSL algori thm.  For   the 
a c t u a l  e n g i n e  t h e  e n g i n e  p r e s s u r e  r a t i o  o r  e n g i n e  f a n  s p e e d  c a n  b e  u s e d  t o  gen- 
erate a n  e q u i v a l e n t  t h r u s t  v a l u e .  A Kalman es t imator  could  also be  used  for  
t h i s   a p p l i c a t i o n .  The Q f a c t o r s   p r o v i d e  a w e i g h t i n g   c a p a b i l i t y   t o   i n c r e a s e  
t h e  e f f e c t  of a se lec ted  parameter .  For  example ,  the  weight ing  for  ne t  th rus t  
was i n c r e a s e d  i n  r e l a t i o n  t o  o t h e r  w e i g h t i n g  f a c t o r s  t o  a s s u r e  a n e a r l y  c o n s t a n t  
n e t  t h r u s t .  
OPTIMIZATION TECHNIQUES 
S e v e r a l  o p t i m i z a t i o n  a l g o r i t h m s  ( r e f s .  3 t o  8) were cons ide red  to  de t e r -  
mine a method t h a t  was b e s t  s u i t e d  f o r  t h e  PSL algori thm. The requirement w a s  
t h a t  t h e  r o u t i n e  b e  e f f i c i e n t ,  a c c u r a t e ,  and i n s e n s i t i v e  t o  i n i t i a l  c o n d i t i o n s .  
The t e s t e d  methods are as fol lows:  
(1) Fletcher-Reeves - problems encountered  due  to  cons t ra in ts  
( 2 )  Hooke-Jeeves - d i d  n o t  y i e l d  minimum v a l u e  f o r  a l l  cases 
(3) Powell - e f f i c i e n t  method; no problems encountered 
( 4 )  Zangwill-Powell - e f f i c i e n t  method; no problems encountered 
The var ious  methods  de te rmine  the  uncons t ra ined  minimum of  mul t ivar iab le  func-  
t i o n s .  The  methods r e q u i r e  a unimodal  type  of  func t ion ;  o therwise  severa l  in i -  
12 
t i a l  s t a r t i n g  values mus t  be  cons ide red  to  a s su re  a t r u e  minimum p o i n t .  The 
well-known Fletcher-Reeves method is  a conjugate  grad ien t  method tha t  requi res  
c a l c u l a t i o n  of g r a d i e n t s .  Some d i f f i c u l t i e s  w i t h  t h i s  method were encountered 
because of  the hard engine constraints .  The rout ing  has  a tendency  to  become 
los t  du r ing  the  sea rch  p rocess .  The Hooke-Jeeves,  Powell,  and  Zangwill-Powell 
optimization methods are s e a r c h  r o u t i n e s  t h a t  do n o t  r e q u i r e  c a l c u l a t i o n  o f  t h e  
g r a d i e n t s .  The Hooke-Jeeves w a s  disregarded s ince convergence and the minimum 
va lue  were n o t  a c h i e v e d  f o r  a l l  test cases. 
The Powell and Zangwill-Powell methods are e s s e n t i a l l y  similar and genera- 
t e d  t h e  minimum v a l u e s  f o r  t h e  v a r i o u s  test condi tons.  The methods  converged 
rap id ly  and  were i n s e n s i t i v e  t o  i n i t i a l  c o n d i t i o n s .  The Zangwill-Powell  method 
w a s  s e l e c t e d  s i n c e  i t  r e f l e c t s  a departure  f rom the or iginal  Powell  method i n  
t h a t  i t  tests fo r  l i nea r  dependence  o f  t he  con juga te  d i r ec t ion  vec to r .  Th i s  
test a s s u r e s  t h a t  a t r u e  minimum v a l u e  w i l l  be achieved. 
APPLICATION 
The e f f e c t i v e n e s s  of t h e  PSL a lgo r i thm w a s  evaluated as shown i n  f i g u r e  3. 
A s  m e n t i o n e d  p r e v i o u s l y  t h e  d i g i t a l  s i m u l a t i o n  of t h e  QCSEE engine w a s  u sed  to  
perform the evaluat ion phase.  An engine component w a s  degraded  from i ts  nomi- 
n a l  c o n d i t i o n  w i t h  a r e s u l t a n t  l o s s  i n  t h r u s t .  F o r  example, t h e  e f f i c i e n c y  o f  
t h e  low-power turbine  could  be  reduced by seve ra l  pe rcen tage  po in t s .  Thrus t  
w a s  t h e n  r e s t o r e d  by  two d i f fe ren t  methods .  A bas is  for  compar ison  ( re ference)  
w a s  t hen  e s t ab l i shed  by a manual method i n  which t h e  t h r o t t l e  was v a r i e d  u n t i l  
t h e  n e t  t h r u s t  w a s  fu l ly  r e s to red  to  the  nomina l  va lue  o f  t he  nondegraded  en- 
g ine .  The fan and compressor speeds were scheduled  by  the  thro t t le  and  were 
not  cons t ra ined .  Fur thermore  the  engine  cont ro l  limits were e f f e c t i v e  f o r  t h i s  
process.  The t h r u s t   s p e c i f i c   f u e l   c o n s u m p t i o n  (TSFC) w a s  computed. To evalu- 
a te  t h e  PSL a lgor i thm,  the  s imula t ion  w a s  re turned  to  nominal  and  the  PSL al-  
gorithm w a s  a c t i v a t e d .  The component degradat ion w a s  i n se r t ed ,  and  the  PSL al- 
gori thm reopt imized the TSFC a n d  r e s t o r e d  t h r u s t  t o  i t s  nominal  value.   For 
t h i s  case the engine speeds were cons t r a ined  to  the i r  nomina l  va lues  a t  t h e  
s t e a d y - s t a t e  c o n d i t i o n .  The  two va lues  of TSFC were compared. 
The r e s u l t s  f o r  s e v e r a l  e n g i n e  component degradat ions are shown i n  t a b l e  I. 
Typ ica l  deg rada t ions  inc lude  lo s s  o f  e f f i c i ency  and  power r equ i r emen t s  fo r  t he  
engine  components.  With  the  manual  procedure  used as t h e  r e f e r e n c e ,  cases B ,  
C, E,  and H d i d   n o t   e x h i b i t   a n  improvement f o r   t h e  PSL algorithm.  The  nota- 
t i o n s  11 and P d e s i g n a t e  a change i n   e f f i c i e n c y  and  power requirement.   For 
t h e s e  m a l f u n c t i o n s  t h e  p i l o t  c a n  r e s t o r e  t h e  l o s s  of t h r u s t  a n d  o b t a i n  compar- 
ab le  va lues  o f  TSFC. For real eng ine  ope ra t ion  the  change  in  component e f f i -  
c i enc ie s  and  power requirements is a g radua l ,  l ong- t e rm e f fec t  t ha t  w i l l  b e  
c o n t i n u a l l y  c o r r e c t e d  by t h e  PSL algori thm. The l a r g e  p e r t u r b a t i o n s  were 
chosen  to  accentua te  the  process  and  so t h a t  w e  cou ld  obse rve  the  e f f ec t iveness  
of t h e  "smart" log ic .  Fo r  excess ive ly  l a rge  va r i a t ions  the  a lgo r i thm migh t  no t  
c o r r e c t  f o r  t h e  d e f i c i e n c i e s  u n l e s s  c e r t a i n  c o n s t r a i n t s  c a n  b e  r e l a x e d .  
The r e s u l t s   o b t a i n e d   f o r   c o n d i t i o n s  A, D, F,  and G i n d i c a t e   t h a t   t h e  
PSL a lgo r i thm w a s  ab le  to  opt imize  and  genera te  an  improved  TSFC o v e r  t h a t  gen- 
e r a t e d  by t h e  manual  method.  For  example, a lower low-pressure-turbine'effi- 
13 
c i e n c y  r e s u l t e d  i n  
quirement caused a 
a 1 .8-percent  h igher  va lue  for  TSFC; a h i g h e r  f a n  power re- 
1.6-percent  higher  value  of TSFC. S i m i l a r l y  a combination 
of d e f i c i e n c i e s  (i. e., A-B , A-D) provided a h ighe r  va lue  o f  TSFC f o r   t h e  manual 
t h r o t t l e  change.  These lat ter cases imply  tha t  t he  schedu l ing  o f  t he  con t ro l  
i n p u t  v a r i a b l e s  f o r  t h e  r e g i o n  m i g h t  n o t  b e  optimum and thus that a h i g h e r  f u e l  
f l ow wou ld  be  r equ i r ed  to  r e s to re  the  nomina l  t h rus t .  An i n t e r e s t i n g  test w a s  
case I, w h e r e  t h e  t h r u s t  c o u l d  n o t  b e  f u l l y  r e s t o r e d  t o  t h e  n o m i n a l  v a l u e .  F o r  
t h e  manual  case  thrus t  w a s  r e s t o r e d  t o  w i t h i n  2 . 5  p e r c e n t  of nominal; the PSL 
algori thm w a s  a b l e  t o  r e t u r n  t h e  t h r u s t  t o  w i t h i n  0.8 percent  of  nominal.  These 
r e s u l t s  i n d i c a t e  t h a t  i f  some e n g i n e  c o n s t r a i n t s  were re l axed  and speeds allowed 
t o  s e e k  a new va lue ,  improved r e su l t s  migh t  be  ob ta ined  fo r  t he  PSL algori thm. 
Although a l i m i t e d  number of t es t  c o n d i t i o n s  were demonstrated,  i t  can be 
deduced  tha t  the  PSL a lgor i thm can  do as w e l l  o r  b e t t e r  t h a n  t h e  manual  control .  
S ince  deg rada t ion  e f f ec t s  are minimal,  accruable,  and  long term, i t  i s  ev iden t  
t ha t  t he  added  secondary  con t ro l l e r  serves a use fu l  pu rpose  in  ma in ta in ing  op t i -  
mum sys tem per formance  and  in  re l iev ing  the  p i lo t  o f  an  added  burden .  
CONCLUSIONS 
The o b j e c t i v e  o f  t h e  PSL a lgo r i thm i s  to  opt imize  the  per formance  of  the  
propulsion  system a t  a s t e a d y - s t a t e  c o n d i t i o n .  The  major  function is to  modify 
t h e  e n g i n e  c o n t r o l  s e t - p o i n t  s c h e d u l e s  f o r  component d e g r a d a t i o n s  i n  o r d e r  t o  
r e s t o r e  t h e  n o m i n a l  n e t  t h r u s t .  The r e s u l t s  o f  t h e  s t u d y  i n d i c a t e  t h a t  t h i s  
task  can  be  achieved  wi th  the  PSL a lgor i thm.  Convergence  to  the  optimum v a l u e  
can  be  obta ined  wi th in  60 t o  90 seconds, which makes the program acceptable fo r  
on - l ine  ope ra t ion  wi th  p re sen t  s ta te  of t h e  a r t  minicomputers. 
Several  0pt imizat io .n  procedures  were eva lua ted ;  however , .  d i f f i cu l t i e s  were 
experienced  with  the  Fletcher-Reeves  and  Hooke-Jeeves  methods.   These  problems 
are a t t r i b u t a b l e  t o  t h e  h a r d  e n g i n e  limits. The s e l e c t e d  method w a s  t h e  
Zangwil l -Powell   technique,   which  offered  rapid  and  accurate   convergence.  The 
tests i n d i c a t e  t h a t  i n  most  cases  the PSL a l g o r i t h m  o f f e r s  some improvement i n  
t h r u s t  s p e c i f i c  f u e l  c o n s u m p t i o n  o v e r  t h e  m a n u a l  t h r o t t l e .  
REFERENCES 
1. Mihaloew, J. R.; and Hart, C .  E. :  Real Time Dig i ta l   Propuls ion   Sys tem Simu- 
l a t i o n  f o r  Manned F l igh t   S imula to r s .  NASA TM-78958, 1978. 
2.  Quiet  Clean  Shoit-Haul  Experimental  Engine (QCSEE) Under-the-Wing (UTW) Sim- 
u la t ion   Repor t .  NASA CR-134914, 1977. 
3. P i e r r e ,  D. A.: Optimization  Theory  with  Applications.   John  Wiley & Sons, 
Inc.  , 1969. 
4 .  Kuester,  J .  L.; and  Mize, J. H.:  Opt imizat ion  Techniques  with FORTRAN, 
McGraw-Hill Book Co., I n c . ,  1973. 
5. S e i d e l ,  R. D.:  Transfer-Function-Parameter Estimation  from  Frequency Re- 
sponse Data - A FORTRAN Program. NASA TM X-3286, 1975. 
14 
6. F l e t c h e r  R.; and Reeves, C. M . :  Function  Minimization by Conjugate 
Gradients.   Computer  Journal  7,   pp.  149-154,  1964. 
7. Powell, M. J. D. :  An E f f i c i e n t  Methad f o r  F i n d i n g  t h e  Minimum of S e v e r a l  
Var iab les   Wi thout   Calcu la t ing  Derivatives. Computer Journal  7,   pp.  155- 
164,  1964. 
8. Zangwill, W. I.: Minimizing a Funct ion  Without   Calculat ing Derivatives. 
Computer Journal  10,   pp.  293-296,  1967. 
TABLE I. - RESULTS OF ENGINE COMPONENT DEGRADATION 
[Thro t t l e  was a d j u s t e d  f o r  c o n s t a n t  t h r u s t  a t  
s teady-s ta te  condi t ion . ]  
:ase E f f e c t  
A 
Cases A, B, C, and E: H 
Cases A and D G 
Cases A and B F 
Accessory  equipment, AP * 100 percen t  E 
Fan  power, AP = 10 pe rcen t  D 
Compressor  power, AP = 10 percen t  C 
High-pressure  turb ine ,  Aq = -10 pe rcen t  B 
Low-pressure  turbine,  An = -10 pe rcen t  
A and B, L!q = -5 p e r c e n t  
C ,  AP = 5 pe rcen t  
E, AP = 100 percen t  
A and B,  An = -10 pe rcen t  
C,  AP = 5 pe rcen t  
E, AP = 100 percen t  
I Cases A, B,  C ,  and E: 
%ominal  values  of  thrust  could not  be achievec i .  
~~ 
Fuel flow - TSFC 
(PSL improvement 
o v e r  t h r o t t l e ) ,  
pe rcen t  
~~ 
1.8 
No change 
No change 
1 . 6  
No change 
. 6  
4.1 
No change 
( a )  
15 
r CMF'OSIlE F R A M  
I 
rVARlABLE FURE 
'LCoMPOSIlE FAN BLADES 
Figure 1. - QCSEE UTW engine. 
NOMINAL 
SET-POINT CONTROL OUTPUT 
POWER 
"SCHEDULES 
SET-POINT DEMAND 
SCHEDULE VARlABLES 
CONTROLLER SIMULATION 
"" . . 
CHANGE IN 
SET-POINT 
SCHEDULES " ~ - " 
I "-7 I 
Figure 2 - Block  diagram  of  performance-seeking  logic  algorithm  applied to QCSEE. 
16 
. . __-__ 
1 STATE CONDKION I RESTORE STEADY- 
REFERENCE 
COMPARE 
RESULTS 
Figure 3. - Evaluation procedure. 
17 
I " 


Performance seeking controls

Abstract

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