Extensions to the multivariable Nyquist array (MNA) method are used to design a feedback control system for the quiet clean shorthaul experimental engine. The results of this design are compared with those obtained from the deployment of an alternate control system design on a full scale nonlinear, real time digital simulation. The results clearly demonstrate the utility of the MNA synthesis procedures for highly nonlinear sophisticated design applications

Leininger, G. G.

English

NASA Technical Reports Server

MULTIVARIABLE NYQUEST ARRAY METHOD WITH APPLICATION 
TO TURBOFAN ENGINE CONTROL 
Gary G. L e i n i n g e r  
Purdue  Un ive r s i ty  
School  of  Mechanical  Engineer ing 
West L a f a y e t t e ,  I n d i a n a  
SUMMARY 
R e c e n t  e x t e n s i o n s  t o  t h e  m u l t i v a r i a b l e  N y q u i s t  a r r a y  (MNA) method are 
u s e d  t o  d e s i g n  a feedback  cont ro l  sys tem for  the  Genera l  Elec t r ic -NASA Quie t  
Clean  Shorthaul   Experimental   Engine (QCSEE). The r e s u l t s  o f  t h i s  d e s i g n  
are compared w i t h  t h o s e  o b t a i n e d  f r o m  t h e  d e p l o y m e n t  o f  t h e  G e n e r a l  Electric 
con t ro l  sys t em des ign  on  a f u l l  scale n o n - l i n e a r ,  real-time d i g i t a l  s i m u l a -  
t i o n .  The r e s u l t s  o f  t h i s  r e s e a r c h  p r o g r a m  c l e a r l y  d e m o n s t r a t e  t h e  u t i l i t y  
o f  t h e  MNA s y n t h e s i s  p r o c e d u r e s  f o r  h i g h l y  n o n - l i n e a r  s o p h i s t i c a t e d  d e s i g n  
a p p l i c a t i o n s .  
The QCSEE t u r b o f a n  e n g i n e  w a s  developed by the  Genera l  Electr ic  Corpora- 
t i o n  u n d e r  c o n t r a c t  t o  t h e  NASA L e w i s  Resea rch  Cen te r  du r ing  the  pe r iod  
1974-1978.  The d e s i g n   i n c o r p o r a t e s   p e r f o r m a n c e   a n d   s t r u c t u r a l   c h a r a c t e r i s t i c s  
u n l i k e  t h o s e  i n  a n y  e n g i n e  i n  p r o d u c t i o n  t o d a y  a n d  i n c l u d e s  
1. An ex t remely   h igh   by-pass   ra t io   and  a h i g h  t h r o a t  
Mach number i n l e t  f o r  n o i s e  s u p p r e s s i o n  
2 .  R e v e r s i b l e   p i t c h   f a n   b l a d e s   f o r   r a p i d   t h r u s t   r e s p o n s e  
(0 .8  seconds  f rom approach  to  fu l l  power )  
3 .  Geared   t u rb ine l f an   combina t ions   fo r   l ow  f an   speeds  
w i t h  a h i g h  t h r u s t  r a t i n g  
4 .  D i g i t a l   e l e c t r o n i c   e n g i n e   c o n t o l s  
5. Ex tens ive   u se   o f   compos i t e s   fo r   d rag   r educ t ion  
and  we igh t  cons ide ra t ions  
To i n c o r p o r a t e  a l l  f i v e  c h a r a c t e r i s t i c s  i n t o  a s i n g l e  p r o p u l s i o n  s y s t e m  
r e p r e s e n t s  a s i g n i f i c a n t   b r e a k t h r o u g h   i n   t u r b o f a n   e n g i n e   t e c h n o l o g y .   D u r i n g  
1978-1979, t h e  QCSEE e n g i n e  w a s  s u c c e s s f u l l y  t e s t e d  a t  the NASA L e w i s  test 
f a c i l i t y .  
105 
https://ntrs.nasa.gov/search.jsp?R=19810003591 2020-03-21T16:24:01+00:00Z
During  th i s  per iod  of  deve lopment  and  tes t ing  of  the  QCSEE engine,  
NASA developed a h igh ly  non- l inea r  accu ra t e  real-time d i g i t a l  s i m u l a t i o n  o f  
t h e  e n g i n e  a t  sea-level s t a t i c  condi t ions.  This  non-l inear  model  w a s  used 
i n  e x t e n s i v e  tests a t  t h e  NASA Ames i n - f l i g h t  s i m u l a t o r  f a c i l i t y  f o r  t es t  
p i lo t  eva lua t ions  o f  i n t eg ra t ed  eng ine  a i r f r ame  combina t ions  [l]. 
Using  the  non- l inear  s imula t ion ,  a set o f  t r a n s f e r  f u n c t i o n  matrices 
were genera ted  for  each  of  f ive  power l eve r  s e t t i ngs  cove r ing  the  r ange  f rom 
approach power t o  f u l l  power, i .e . ,  62.5% t o  100%. The  method  used t o  o b t a i n  
t h e  l i n e a r  m o d e l s  i s  i d e n t i c a l  t o  t h a t  u s e d  i n  t h e  F/100 s tudy.  S t e p  response 
compar ison  of  the  l inear  models  wi th  the  non- l inear  QCSEE s imula t ion  va l ida t ed  
the models a t  each  ope ra t ing  po in t .  
For  the  QCSEE e n g i n e ,  t h e r e  are th ree  man ipu la t ed  va r i ab le s  ( inpu t s ) :  
f u e l  f l o w ,  n o z z l e  area, and  f an  b l ade  p i t ch  ang le .  The measurable   outputs  
f o r  t r a n s f e r  f u n c t i o n  e v a l u a t i o n  were s e l e c t e d  t o  b e :  f a n  s p e e d ,  i n l e t  d u c t  
p re s su re  (P12), and  combustor exi t  p re s su re  ( P 4 ) .  I n l e t   d u c t   p r e s s u r e   c o n t r o l  
p r o v i d e s  a n  i n d i r e c t  c o n t r o l  o v e r  i n l e t  Mach number fo r  no i se  suppres s ion  
wh i l e  combus to r  ex i t  p re s su re  con t ro l  p rov ides  a con t ro l  o f  eng ine  th rus t  
response.  
With the  inpu t s  and  man ipu la t ed  ou tpu t s  i den t i f i ed  above ,  an  ex tens ive  
cont ro l  synthes is  program was executed  us ing  the  mul t ivar iab le  Nyquis t  a r ray  
(MNA) method [ 2 , 3 , 4 ]  a n d  t h e  r e c e n t  e x t e n s i o n s  t o  m u l t i v a r i a b l e  Bode diagrams 
(MBD) and   Nichols   char t s  (MNC) [ 5 , 6 , 7 ] .  The QCSEE des ign  was i n i t i a l l y  pe r -  
formed holding nozzle area f u l l  open  wi th  f ixed  f an  b l ade  p i t ch  ang le  a t  a 
power s e t t i n g  o f  62.5% of f u l l  power.  The con t ro l  des ign  was then  eva lua ted  
a t  o t h e r  power s e t t i n g s  a n d  t e s t e d  i n  t h e  n o n - l i n e a r  s i m u l a t i o n  t o  e v a l u a t e  
engine performance during a power slam from 62.5% t o   f u l l  power (100%). 
Non- l inea r  s imula t ion  t r ans i en t s  were then  compared w i t h  t h e  f u l l  scale 
G e n e r a l  E l e c t r i c  c o n t r o l  time response.  
The G e n e r a l  E l e c t r i c  c o n t r o l  d e s i g n  is based upon a series o f  s i n g l e  
inpu t ,  s ing le  ou tpu t  des ign  eva lua t ions  wi th  loop  in t e rac t ions  accoun ted  fo r  
q u a l i t a t i v e l y   r a t h e r   t h a n   q u a n t i t a t i v e l y  [ 8 ] .  In   t he   ac tua l   imp lemen ta t ion  
of t h i s  con t ro l ,  t he  man ipu la t ed  inpu t  va r i ab le s  a re  schedu led  acco rd ing  to  
engine operat ing environment .  In  a power slam mode f u e l  f l o w  i s  t h e  o n l y  
v a r i a b l e  i n p u t  o v e r  t h e  62 .5% t o  80% power range. A t  80% power, f a n  p i t c h  
ang le  is ac t iva t ed  and  a two i n p u t  s i t u a t i o n  i s  i n  o p e r a t i o n .  A t  t h e  power 
l e v e l  of 90% e x i t  n o z z l e  area is ac t iva t ed  and  a t h r e e  i n p u t  s i t u a t i o n  arises 
u n t i l  f u l l  power i s  achieved.  A l l  MNA des ign  s imula t ions  were compared wi th  
time r e s p o n s e s  r e s u l t i n g  f r o m  t h i s  GE c o n t r o l .  
The next  phase of t h e  MNA design program used fuel  f low and fan pi tch 
a n g l e  as inpu t s  w i th  f an  speed  and combustor ex i t  p re s su re  as the measured 
outputs .   Nozzle  area was a g a i n  h e l d  t o  a f ixed   open   pos i t ion .   Us ing   the  MNA 
method w i t h  t h e  Bode and  Nichols  op t ions ,  cont ro l  sys tems were synthes ized  
f o r  t h e  two inpu t ,  two output  models.  It was e s t a b l i s h e d  t h a t  a f i x e d  c o n t r o l  
conf igura t ion  could  be  used  over  the  power l eve r  r ange  p rev ious ly  ind ica t ed .  
T h i s  c o n t r o l  u n i t  w a s  t h e n  a p p l i e d  t o  t h e  n o n - l i n e a r  s i m u l a t i o n  and  compared 
w i t h  t h e  GE con t ro l  r e sponses .  The s i g n i f i c a n t  r e s u l t  e s t a b l i s h e d  a t  t h i s  
p o i n t  was t h a t  f a n  p i t c h  a n g l e  (and fue l  f l ow)  can  be  used  e f f ec t ive ly  a t  low 
106 
power s e t t i n g s  w i t h o u t  v i o l a t i n g  t h e  p h y s i c a l  c o n s t r a i n t s .  It p rov ides -  fo r  
a r ap id  th rus t  r e sponse  wi th  a s ign i f i can t  l ower  expend i tu re  o f  t o t a l  fue l  
consump t ion .  
The r e s u l t s  of t h e  two inpu t ,  two output  case above were e x t e n d e d  t o  t h e  
three  input - three  output  sys tem w i t h  nozz le  area as t h e  t h i r d  i n p u t .  T h i s  
i n p u t  v a r i a b l e  is used t o  p r o v i d e  a d d i t i o n a l  c o n t r o l  o v e r  i n l e t  Mach number 
w i t h  i n l e t  d u c t  p r e s s u r e  as t h e  t h i r d  o u t p u t  v a r i a b l e .  System  dominance w a s  
ea s i ly  ob ta ined  a t  each power set t ing with closed loop system performance 
des igned  us ing  the  mul t iva r i ab le  Bode diagrams.  Non-linear  simulation 
r e s u l t s  of t h e  MNA c o n t r o l  are compared with those obtained from the GE con- 
t r o l .  A representat ive comparison i s  p rov ided  in  the  accompanying f i g u r e s .  
The dashed  curve  in  each  of  the  f igures  represents  the  t i m e  response of 
the  non- l inear  s imula t ion  to  the  Genera l  Elec t r ic  cont ro l  under  a s t e p  power 
demand from  62.5%  of f u l l  power t o  100% f u l l  power. The so l id  cu rves  r ep re -  
s en t  t he  co r re spond ing  r e su l t s  u s ing  the  con t ro l  des ign  ob ta ined  from t h e  
mult ivar iable  Nyquist  array method.  
The MNA design w a s  ob ta ined  through the  fo l lowing  procedure :  
S t e p  1. 
Step 2 .  
Step 3 .  
S t e p  4 .  
Step 5. 
Determine l inear  s t a t e  space models and system transfer 
func t ions  about  the  s teady  s t a t e  ope ra t ing  po in t s  of 
the non-l inear  s imulat ion with the GE c o n t r o l  and 
r e l a t ed  con t ro l  cons t r a in t s  d i sengaged .  
Using  [7]  obtain  diagonal  dominance. 
(Nominally 2 CPU minutes on a PDP 11/70) 
Evaluate  performance in  each control  loop using [6] .  
I n s e r t  MNA c o n t r o l  i n t o  n o n - l i n e a r  s i m u l a t i o n  t o  e v a l u a t e  
t i m e  responses.  
Overlay GE and MNA cont ro l  responses .  
I n  a d d i t i o n  t o  t h e  c o n t r o l  d e s i g n  f o r  t h e  QCSEE engine the MNA method 
has  a l so  been  success fu l ly  app l i ed  to  the  F 100 turbofan engine [ 4 ] .  
REFERENCES 
1. Mihaloew, J .  R.  and Hart, C .  E . ,  "Real T i m e  D ig i t a l   P ropu l s ion  System 
Simula t ion  for  Manned Fl ight  S imula tors , "  NASA TM-78958, 1978. 
3 .  Leininger ,  G .  G . ,  "Diagonal Dominance fo r   Mul t iva r i ab le   Nyqu i s t  A r r a y  
Method Using Function Minimization," Automatica, May 1979. 
10 7 
4. Leininger ,  G.   G. ,  "The Mult ivar iable   Nyquist   Array:  The Concept of 
Dominance Sha r ing , "  A l t e rna t ives  fo r  L inea r  Mul t iva r i ab le  Con t ro l ,  
eds.  Sain,  Peczkowski,  and Melsa, NEC Inc.,  1978. 
5. Leininger ,  G.  G . ,  "New Dominance C h a r a c t e r i s t i c s  f o r  t h e  M u l t i v a r i a b l e  
Nyquist  Array Method," International Journal of Control (To appear 1979). 
6 .  Leininger ,  G.   G . ,  'Wul t iva r i ab le  Compensator  Design  using Bode Diagrams 
and Nichols Charts," IFAC-CAD of control Systems Symposium, Zurich,  
August  29-31, 1979, PP. 127-132. 
7. Leininger ,  G .   G . ,  "An I n t e r a c t i v e  D e s i g n  S u i t e  f o r  t h e  M u l t i v a r i a b l e  
Nyquist  Array  Method,"  Ibid,  pp. 305-330. 
8. "Digital  Control  System  Design  Report: QCSEE," General  Electr ic  Corp., 
NASA CR-134920, 1978. 
108 
D i f f e r e n t i a l  
Xflu Fuel Metering 
STEP RESPONSE 
*.XE-I 1 
I ;  
- MNA SIMULATION 
"-. QCSEE SIMULATION 
.- "" """".""""""""""""""""". 
LT"" r"- 1" 7""" 
TIRE It1 SECONDS (XE 0 )  
0.00 1 .ee 2.00 3.08 
INITIAL FLrim 63.5 FXNFIL PLR- i8e.0 POWER CPlD AT 2.89 
STEP RESPONSE 
!%E 2 )  
I ;  
I i  
Different ia l  Ht: Fan Speed 
I / -- QCSEE SIMULATXON I 
1 :  
- MNA SIMULATION 
2*88 7 
0.08 f """ i """""""~""."."".""""""""""""""""~". 
LT"" I"" 7" '7""" 
8.08 1 .ea 2.88 3.88 
INITICIL PUI. 62.5 FIML PM= 1w.o POUER CID at a.00 TIRE I N  SECONDS C X E  8 1 
109 
STEP RESPONSE 
( X €  3) 
D i f f e r e n t i a l  
FN t T h r u s t  
"""""""""""""""" """ ""."" 
LY"" 
IHITIFIL PW- 62.5 F I N ~ L  F L ~ =  109.0 POWER cmo aT 2.00 
r"" 1" 7""- 
TIPlE IN SECONDS <%E 6) 
0 . 0 8  1.80 2.88 3.80 
- MNA SIMULATION 
--. QCSEE SIMULATION 
STEP RESPONSE 
( X €  1 )  
+ D i f f e r e n t i a l  
THETA1 Fan R l a d e  P i t c h  Angze 
I 
I 
I 
- NNCI SIMULATION 
". QCSEE SIMULATION 
I 
I 
I . +"" r"" 1" 7""- 
0.09 1 .e0 2.08 3-80 
1 10 


Multivarable nyquist array method with application to turbofan engine control

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