An autopilot can be used to provide precise control to meet the demanding requirements of flight research maneuvers with high-performance aircraft. This paper presents the development of control laws for a flight test maneuver autopilot for an F-15 aircraft. A linear quadratic regulator approach is used to develop the control laws within the context of flight test maneuver requirements by treating the maneuver as a finite time tracking problem with regulation of state rates. Results are presented to show the effectiveness of the controller in insuring acceptable aircraft performance during a maneuver

Alag, G. S.

Duke, E. L.

English

NASA Technical Reports Server

NASA Technical Memorandum 86799 
NASA-TM-86799 19860004805 
-- Development of a Flight Test 
Maneuver Autopilot for an F·15 
Aircraft 
Gurbux s. Alag and Eugene L. Duke 
December 1985 
NI\S/\ 
National Aeronautics and 
Space Administration 
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DEC 1 6 1985 
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https://ntrs.nasa.gov/search.jsp?R=19860004805 2020-03-20T16:32:37+00:00Z
NASA Technical Memorandum 86799 
Development of a Flight Test 
Maneuver Autopilot for an F·15 
Aircraft 
Gurbux S Alag 
Western Michigan University, Kalamazoo, Michigan 
Eugene L Duke 
Ames Research Center, Dryden Flight Research FacIlity, Edwards, California 
1985 
NI\S/\ 
National Aeronautics and 
Space Administration 
Ames Research Center 
Dryden Flight Research FacIlity 
Edwards, California 93523 
DEVELOPMENT OF A FLIGHT TEST MANEUVER AUTOPILOT FOR AN F-15 AIRCRAFT* 
Gurbux S. Alag 
Western M1ch1gan Un1vers1ty 
Kalamazoo, M1ch1gan 
and 
Eugene L. Duke 
NASA Ames Research Center 
Dryden Fl1ght Research Fac1l1ty 
Edwards, Cal1forn1a 
An autop1lot can be used to prov1de prec1se 
control to meet the demand1ng requ1rements of fl1ght 
research maneuvers w1th h1gh-performance a1rcraft. 
Th1S paper presents the development of control laws 
for a fl1ght test maneuver autopllot for an F-15 
a1rcraft. A llnear quadrat1c regulator approach 1S 
used to develop the control laws w1th1n the context 
of fl1ght test maneuver requ1rements by treat1ng the 
maneuver as a f1n1te t1me track1ng problem w1th regu-
lat10n of state rates. Results are presented to show 
the effect1veness of the controller 1n 1nsur1ng accept-
able a1rcraft performance dur1ng a maneuver. 
Introduct1on 
Convent1onal p1lot1ng techn1ques are often 1nade-
quate to meet the demand1ng requ1rements of fl1ght 
research maneuvers w1th h1gh-performance a1rcraft. 
These maneuvers frequently requ1re prec1se control of 
onset rates 1n extreme fl1ght cond1t1ons. Thus, the 
p1lot may be trY1ng to control an a1rcraft at h1gh 
angles of attack and h1gh g's wh1le attempt1ng to 
1ncrease normal accelerat10n at a prescr1bed rate 
through a maneuver spec1f1ed to the very llm1ts of the 
accuracy of the COCkP1t 1nstruments. 
A new fl1ght test techn1que to a1d the p1lot 
dur1ng these maneuvers was developed at the Dryden 
Fl1ght Research Fac1l1ty of the NASA Ames Research 
Center (Ames-Dryden).1 The essence of th1S tech-
n1que 1S the appl1cat1on of an autop1lot to prov1de 
prec1se control dur1ng the requ1red fl1ght test 
maneuvers. The fl1ght test maneuver autop1lot (FTMAP) 
1S deS1gned to prov1de prec1se, repeatable control of 
a h1gh-performance a1rcraft dur1ng certa1n prescr1bed 
maneuvers so that a large quant1ty of data can be 
obta1ned 1n a m1n1mum of fl1ght t1me. 
The FTr1AP can be used for varlOUS maneuvers, such 
as stra1ght-and-level fl1ght, level accelerat10ns and 
decelerat10ns, pushover pullups, excess-thrust w1ndup 
turns, and thrust-l1m1ted turns. Each of these maneu-
vers compr1se track1ng certa1n states of the a1rcraft, 
hold1ng certa1n states w1th1n prescr1bed values, and 
ma1nta1n1ng constra1nts on the der1vat1ves of the 
states. For example, an excess-thrust windup turn is 
performed at constant alt1tude and Mach number w1th 
the angle of attack 1ncreas1ng at a spec1f1ed rate to 
the f1nal angle of attack. 
Th1S paper presents the development of the FTMAP 
control laws w1th1n the context of fl1ght test maneu-
ver requ1rements. The FTMAP des1gn represents a well-
def1ned and completely spec1f1ed problem aga1nst Wh1Ch 
*The work presented here was supported 1n part by a 
Nat10nal Research Counc1l Fellowsh1p. 
var10us des1gn methodolog1es can be tested. Not only 
does th1S problem represent a real-world sltuat1on, 
but the FTMAP control law des1gn problem also forces 
cons1derat1on of a slgn1f1cant des1gn 1ssue 1n a1r-
craft controls - controll1ng a plant that changes as 
veh1cle att1tude or fl1ght cond1t10ns change. 
Problem Formulat10n 
The funct10nal capab1l1ty of the FTMAP 1S der1ved 
from 1tS ab1l1ty to generate control laws requ1red 
to execute a maneuver. The FTMAP control laws are 
developed uS1ng the Ames-Dryden deta1led nonl1near 
aerodynam1c model of the F-15 a1rcraft. The model 
1S llnear1zed by tr1mm1ng the a1rcraft at the des1red 
fl1ght cond1t10n and der1v1ng llnear models by numer1-
cal perturbat1on. The llnear model may be represented 
1n the standard state equation form as 
. 
x Ax + Bu 
Y Hx 
(1 ) 
(2) 
where the states x and 1nputs u represent perturbat10n 
around nom1nal tr1m values x and u, respectively. 
Also, y is the output and A, B, and H are matrices of 
appropr1ate d1mens1ons. 
In order to perform a certain maneuver, a control 
algor1thm 1S developed to take the a1rcraft from a 
certa1n spec1f1ed 1n1t1al tr1m state to another spec-
1f1ed state. The FTMAP control law des1gn can be 
formulated as an opt1mal track1ng problem, 1n Wh1Ch 
1t 1S des1red to track a constant f1nal state 1n 
f1n1te t1me. It 1S also necessary to regulate the 
state rate 1n certa1n maneuvers. 
Mult1variable llnear quadrat1c control theory 1S 
a powerful tool for the development of the fl1ght test 
controller. The control des1gn problem selects 1nputs 
u to dr1ve the perturbat10n states x to the des1red 
f1nal state by opt1m1z1ng a quadrat1c performance 
index. Because control of the der1vat1ves of states 
1S also des1red, add1t1onal terms are added to the 
performance 1ndex and the resultant control laws are 
computed d1rectly from the performance index. 
Control Law Synthesis 
An opt1mal tracking problem may be formulated as 
follows. Re1terat1ng Eqs. 1 and 2, the system 1S 
given as 
. 
x = Ax + Bu 
y = Hx 
It lS deslred to mlnlmlze a performance lndex of the 
form 
where e(t) lS equal to z(t) - y(t), z(t) lS the deslred 
state to be tracked and lS a known functlon, and Q and 
Rare welghtlng matrlces. 
To track a constant flnal state z and also to be 
able to regulate the derlvatlves of the states, an 
addltlonal term lS added to the performance lndex to 
be mlnlmlzed. The performance lndex may be wrltten as 
T 
J = 1/2 fa [e(t)TQe(t) + u(t)TRU(t) 
• T· 
+ (Ex - Eo) S(Ex - Eo)] dt 
Here, 
p = z - y(t) 
Q ) 0 
R > 0 
S ) 0 
Also, z lS the deslred constant flna1 state, and 
Eo lS the deslred state rate. 
(4) 
If the performance lndex lS mlnlmlzed by uSlng 
Lagrange mu1tlp11er, the optlma1 control u* that wl11 
derlve the alrcraft to the deSlred termlna1 condltlon 
lS 
where 
u* = -(R + BTETSEB)-l[BTp(t) 
+ BTETSEAx - BTETSEo] 
R1 (R + BTETSEB) 
P(t) = K(t)x(t) - g(t) 
and K and 9 are obtalned from the Solutlon of the 
fo110wlng equatlons uSlng approprlate termlnal con-
dltlons. 2 Hence, 
where 
A = A - BR1-1BTETSEA 
E = BR1-1BT 
6 = HTQH + ATETSEA - ATETSEBRI-1BTETSEA 
L = _ATETS + ATETSEBR1-1BTETS + KTBTR1-1BTETS 
(6) 
However, the optlma1 control u* need not be 
derlved by a flnlte tlme formulatlon but may be ob-
2 
tal ned by emp10Ylng steady-state control laws. ThlS 
lS equlva1ent to assumlng that the z(T) perslsts as a 
constant value for a long perlod. Wlth the foregolng 
assumptlon, K lS a constant matrlx that satisfles the 
algebralc Rlccatl equatlon and g(t) = O. Thus, the 
slmp11fled control law becomes 
where 
C1 = R1-1BTK + R1-1BTETSEA 
C2 _R1-1BTL1-1HTQ 
C3 R1-1(BTL1-1L + BTETSE) 
L1 (A - EK)T 
~lcatlon of Control Laws 
The 11nearlzed equatlons of motlon of an F-15 
alrcraft are glven by Eq. 1 
where 
x = Ax + Bu 
v = ve10clty, ft/sec 
a = angle of attack, deg 
q = pltch rate, deg/sec 
e = pltch angle, deg 
x = h = a1tltude, ft 
u = 
e = sldes11p angle, deg 
p = roll rate, deg/sec 
r = yaw rate, deg/sec 
~ = roll angle, deg ["J . """0 d,fl,,"'o 0e = elevator def1ectlon 
or = rudder def1ectlon 
aT = throttle dlsplacement 
(8) 
For a f11ght condltlon correspondlng to an a1tl-
tude of 20,000 ft and Mach 0.8, the matrlces A and B 
are as follows. For matrlx A, columns 1 to 9 are 
-0.0108 24.1966 0.0000 -32.1129 
-0.0001 -1.0942 1.0000 0.0001 
-0.0001 -3.2862 -2.1922 0.0009 
0.0000 0.0000 1.0000 0.0000 
0.0000 -829.5390 0.0000 829.5390 
0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 0.0000 
0.0000 -0.2337 0.0358 -0.9994 0.0387 
0.0000 -40.0103 -2.1420 1.2406 0.0000 
0.0000 9.0098 -0.0340 -0.6040 0.0000 
0.0000 0.0000 1.0000 0.0358 0.0000 
Matrlx B lS glven by 
0.0000 -1.0734 0.0000 0.3792 
0.0000 -0.1504 0.0000 0.0000 
0.0000 -16.1223 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 0.0000 
-0.0022 0.0000 -0.0388 0.0000 
13.5934 0.0000 -1.4674 0.0000 
0.1488 0.0000 -4.5577 0.0000 
0.0000 0.0000 0.0000 0.0000 
Three sets of traJector1es show the results of the 
appl1cat10n of developed control laws to the a1rcraft. 
In the f1rst case, 1t 1S necessary to hold the a1rcraft 
at tr1m cond1t10ns of the spec1f1ed fl1ght cond1t10n. 
The fl1ght cond1t10n corresponds to an alt1tude of 
20,000 ft and a Mach number of 0.8. The a1rcraft 1S 
1n stra1ght-and-level fl1ght. The control law des1gn 
1S 1ntended to ma1nta1n the a1rcraft at the spec1f1ed 
alt1tude and veloc1ty. 
For th1S f1rst case, f1gures 1 and 2 show the 
var1at10n 1n veloc1ty and alt1tude, respect1vely, when 
the a1rcraft 1S requ1red to be flown stra1ght and 
level at a glven alt1tude and Mach number. F1gures 3 
and 4 show the correspond1ng var1at10ns 1n the eleva-
tor deflect10n and throttle d1splacement, respect1vely. 
The a1rcraft 1S held to the tr1m values by the con-
troller des1gned. 
In the second case, the fl1ght cond1t10n corre-
sponds to an alt1tude of 20,000 ft and the 1n1t1al 
Mach number 1S 0.5. The a1rcraft 1S to be accelerated 
to Mach 0.8 wh1le 1t 1S held at the spec1f1ed alt1-
tude. Because of the var1at10n of the parameters 
wh1le the plane accelerates, the feedback ga1ns were 
updated m1dway through the maneuver. ~lgures 5 and 6 
show the var1at10ns of veloc1ty and alt1tude as the 
a1rcraft undergoes the maneuver. The response was not 
cons1dered sat1sfactory because of sp1kes observed at 
the t1me of update of ga1ns. F1gures 7 and 8 show the 
var1at10ns of the veloc1ty and alt1tude for the same 
maneuver when the a1rcraft 1S 1n1t1al1zed to the 
fl1ght cond1t10n correspond1ng to Mach 0.8. 
3 
In the th1rd case, the maneuver that was per-
formed was the same as 1n the second case, except 
that a constra1nt was placed on the state rate. It 
1S des1red to ma1nta1n the Mach rate at 0.005 Mach 
per sec. Figures 9 and 10 show the var1at1ons 1n the 
veloc1ty and altitude as the a1rcraft goes through the 
maneuver. The response obta1ned 1n th1S th1rd case 
was cons1dered sat1sfactory. 
Conclud1ng Remarks 
Th1S paper presents a synthes1s techn1que that 
1S appl1cable for control of an a1rcraft undergo1ng a 
specif1ed maneuver. It assumes that a glven maneuver 
can be modeled as a state traJectory to be tracked. 
The techn1que that 1S descr1bed uses the opt1mal 
regulator approach to the traJectory control problem. 
Results are presented for traJectory track1ng for the 
a1rcraft undergo1ng alt1tude-hold level accelerat10n. 
For more complex maneuvers, 1t 1S necessary to 
generate a set of state and control h1stor1es to 
serve as commands for the fl1ght test maneuver 
autop1lot (FTMAP), uS1ng a data base that cons1sts 
of tr1m cond1t10ns. The maneuver model can be 
d1v1ded 1nto a smaller set of state traJector1es 
for sU1table updat1ng of a1rcraft parameters and 
ga1n schedul1ng. The development has the potent1al 
of slmultaneously controll1ng mult1ple parameters 
to demand1ng tolerances. 
References 
IDuke, E.L., Jones, F.P., and Roncol1, R.B., "Develop-
ment of a Fl1ght Test Maneuver AutOP1lot for a H1ghly 
Maneuverable A1rcraft," AIAA 21st Aerospace SC1ences 
Meet1ng, Reno, Nev., Jan. 1983. 
2Alag, G.S., and Duke, E.L., "Development of Control 
Laws for a Fl1ght Test Maneuver AutoP110t for an F-15 
A1rcraft," Amer1can Control Conference Proc., Boston, 
Mass., June 1985, pp. 1209-1210. 
8300 F 
Velocity, 82951'"--______ --------
It/sec 
8290L--L--L--L--L--L--L--L-~ 
o 2 4 6 8 10 12 14 16 
Time, sec 
Fig. 1 Va~ations in velocity with time for 
straight-and-level flight oondition of Mach 0.8 
and 20.000-ft altitude 
deflection, 
deg -,--"--"---'1r--r-
Elevator ---.3~8: Vb 
_40L-_L-__ L-__ L-_L-__ L-__ L-_L-~ 
024 6 8 10 12 14 16 
Time, sec 
F~g. 3 Va~ations in elevator deflection with 
time for straight-and-level flight condition of 
Mach 0.8 and 20.000-ft altitude 
850 
800 
750 
700 
Velocity, 
It/sec 
650 
600 
550 
500 L--_L--__ L-__ L-_.l.-_..l.-_....L_--L_---I 
o 10 20 30 40 50 60 70 80 
Time, sec 
Fig. 5 Variations in velocity with time for 
flight cond~t~on of 20.000-ft altitude with ini-
tial Mach 0.5 accelerated to Mach 0.8 (gains 
updated midway through maneuver) 
4 
Altitude, 20,002 
20'004~ 
It 20,000 
19,998 L-_L----l_---l_---L_--L_--L_---L_---I 
o 2 4 6 8 10 12 14 16 
Time, sec 
Fig. 2 Variations in altitude with time for 
straight-and-level fl~ght condition of Mach 0.8 
and 20.000-ft altitude 
displacement, 10 30 
Throttle 1040 ~ 
percent 1020 _L----lL----lL-_L-__ L-_L-__ L-_L--.I 
o 2 4 6 8 10 12 14 16 
Time, sec 
Fig. 4 Variations in throttle d~splacement with 
time for stra~ght-and-level fl~ght cond~tton of 
Mach 0.8 and 20.000-ft altitude 
Altitude, 
It 
20,010 
20,000 
19,995 0~-:':---:'-----l-----l40L--.J50---.J60-----170-----180 
Time, sec 
F~g. 6 variations in altitude with time for 
flight cond~tion of 20.000-ft with initial 
Mach 0.5 accelerated to Mach 0.8 (gains up-
dated mid~y through maneuver) 
850 
BOO 
750 
Velocity, 700 
It/sec S50 
SOO 
550 
500L-__ L-__ L-__ L-__ L-__ L-~L-~L-~ 
o 20 40 SO 80 100 120 140 1S0 
Time, sec 
F~g.? Variat~ons in velocity ~th time ~th 
aircraft parameters initial~3ed to Mach 0.8 at 
20.00o-ft altitude 
B50 
800 
750 
700 
Velocity, 
ftlsec 
S50 
sao 
550 
500 
0 20 40 SO 80 100 120 140 
Time, sec 
1S0 
Fig. 9 Var~ations in veloc~ty ~th time for 
fl~ght cond~tion of 20.000-ft altitude and Mach 
number increased from 0.5 to 0.8 at attempted 
state rate of 0.005 Mach per sec 
5 
Altitude, 20 000 
20'020~ 
It ' ~ 
19,980 L----.JL---1 __ -l._--L_-l-_-'-_~____:_'. 
o 20 40 SO 80 100 120 140 1S0 
Time, sec 
Fig. 8 Variations in altitude ~th time ~th 
aircraft parameters initialized to Mach 0.8 at 
20.000-ft altitude 
Altitude, 20 000 
20'020~ 
It' _ 
19,980 0 20 40 siD 80 100 120 140 1S0 
Time, sec 
Fig. 10 Variat~ons ~n altitude ~th t~me for 
flight condition of 20.o00-ft att~tude and Mach 
number increased from 0.5 to 0.8 at attempted 
state rate of 0.005 Mach per sec 
1 Report No I 2 Government Accession No 3 Recipient's Catalog No 
NASA TM-86799 
4 Title and Subtitle 5 Report Date 
Decpmber 1985 
DEVELOPMENT OF A FLIGHT TEST MANEUVER AUTOPILOT 
FOR AN F-15 AIRCRAFT 6 Performing Organization Code 
7 Author(s) 8 Performing Organization Report No 
Gurbux S. Alag and Eugene L. Duke H-1328 
10 Work Unit No 
9 Performmg Organization Name and Address RTOP 533-02-21 
NASA Ames Research Center 
Dryden Fllght Research Faclllty 11 Contract or Grant No 
P.O. Box 273 
Edwards, CA 93523-5000 13 Type of Report and Period Covered 
12 Sponsoring Agency Name and Address Technlcal Memorandum 
Nat10nal Aeronaut1cs and Space Adm1n1strat10n 14 Sponsoring Agency Code 
Wash1ngton, D.C. 20546 
15 Su pplementary Notes 
Prepared as IEEE paper presented at the 24th IEEE Conference on Decls10n and Control on 
December 11, 1985. Work presented 1n thlS document was supported 1n part by Nat10nal Research 
Counc1l Fellowsh1p. 
16 Abstract 
An autop1lot can be used to prov1de prec1se control to 
meet the demand1ng requ1rements of fl1ght research maneuvers 
w1th h1gh-performance a1rcraft. Th1S paper presents the 
development of control laws for a fllght test maneuver auto-
pllot for an F-15 a1rcraft. A llnear quadrat1c regulator 
approach 1S used to develop the control laws w1th1n the con-
text of fl1ght test maneuver requ1rements by treatlng the 
maneuver as a f1n1te tlme track1ng problem w1th regulat10n 
of state rates. Results are presented to show the effec-
t1veness of the controller 1n 1nsurlng acceptable a1rcraft 
performance durlng a maneuver. 
17 Key Words (Suggested by Author(s)) 18 Distribution Statement 
A1rcraft control systems Unclass1f1ed - Unl1mlted 
Multlvar1able control systems 
Opt 1 mal control systems 
Optlmal track1ng 
STAR category 08 
19 Security Classlf (of thiS report) 
/20 
Secunty Classlf (of thiS page) 21 No of Pages 22 Price" 
Unclass1f1ed Unclass1f1ed 6 A02 
*Pop sale by the Nat~onal Technical InfoPmation service, SpPingfield, Vipginia 22161. 
End of Document 


Development of a flight test maneuver autopilot for an F-15 aircraft

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