Wind tunnel and flight tests indicate that fuel savings of 2 percent can be achieved by center of gravity (C.G.) management for an L-1011 with the current wing configuration. The normal c.b. location is at 25 percent mean aerodynamic center (MAC). The maximum fuel saving occurs for a C.G. location of 35 percent MAC. However, flight at 35 percent requires that the C.G. range be extended aft of the 35-percent point. Flight at C.G. locations aft or 35 percent requires a pitch active control system (PACS) so that handling qualities are not significantly degraded. The development of this PACS is discussed

Henke, K. R.

Rising, J. J.

English

NASA Technical Reports Server

L-1011 TESTING WITH 
RELAXED STATIC STABILITY 
J. J. Rising and K. R. Henke 
Lockheed California Company 
Burbank, California 
First Annual NASA Aircraft Controls Workshop 
NASA Langley Research Center 
Hampton, Virginia 
October 25-27, 1983 
443 
https://ntrs.nasa.gov/search.jsp?R=19840012523 2020-03-22T08:19:05+00:00Z
Wind tunnel and flight tests indicate that fuel savings of 2 percent can be 
achieved by c.g. management for an L-1011 with the current wing configuration. The 
normal c.g. location is at 25 percent MAC as shown in figure 1. The maximum fuel 
saving occurs for a c.g. location of 35 percent MAC. However, flight at 35 percent 
requires that the c.g. range be extended aft of the 35-percent point. Flight at c.g; 
locations aft of 35 percent requires a pitch active control system (PACS) so that 
handling qualities are not significantly degraded. Figure 1 shows that the near- 
term PACS was flight tested with the c.g. at 39 percent MAC. 
DRAG 
BENEFIT = .lM (L/D) 
‘I NEAR-TERM - TEST 
RANGE 
/ 23% AC.G. 
CUYRENT RANGE - 
I 
PITCH AUGMENTATION REQUIRED 
I 
CURRENT WING 
-S/N 1001 
(39) (41) (% C.G.) 
5 
i 
+ 
2 NEUTRAL 
POINT 
STATIC STABILITY (%I 
Figure 1 
444 
The near-term pitch stability augmentation system consists of a lagged pitch 
rate damper with washed-out column feed-forward loop. The damper serves to provide 
the necessary short-perfod frequency and damping characteristics while also suppress- 
ing turbulence effects, and the feed forward .was designed to "quicken" the pitch rate 
response and reduce stick force gradients without affecting system stability. A 
block diagram of the system is shown in figure 2. 
r -------------0-----------me- 1 
, DIGITAL (80-HZ ITERATION RATE) GAIN IA0 I 
I I I 
Ka 
I 
7hg!s+1 I 
_ I 
E%m?) 
PREFILTER 
1 
.03s+1 
I r ----------------------w--B 
I I 
I SERVO 
I 
POWER 
LIMIT J CURVE SERVO 
I 
+1.2 
I ’ -A==-( 
1.25 AIRFRAME -+ 
I 
4.8 
ca> (&gL) 
(%a 
I I 
i 
L,------em 7 FEED-FORWARD 
GAIN 
’ r”;;l( ;“N::E:) 
I LOOP 
; 
‘, 
I 
I I 
(A%$ 
I 
,WASHOUT,+ LAG ) PREFILTER 
I 
I 
.nh .4 
. 6 COL 
NOTES: ‘ANALYZED WITH AND WITHOUT WASHOUT. 
/ \ 
L 
I “ANALYTICAL APPROXIMATION FOR SAMPLE AND HOLD 
------------A AND TRANSCRIPT DELAYS IN DIGITAL COMPUTER. 
Figure 2 
445 
The schedules of pitch rate feedback gain and lag time constant were chosen so 
that the augmented stability L-1011 has good short-period frequency and damping 
characteristics for the complete center-of-gravity range (25 to 39 percent iZ) investi- 
gated in flight test. The gain and lag schedules are defined as a function of cali- 
brated airspeed. Characteristics with and without augmentation are shown in 
figure 3. 
M = 0.83, h = 33,000 ft, W = 360,000 lb 
AILERONS 
----AILERONS 
ACTIVE 3 
INACTIVE 
AUGMENTED 
2 
C.G. =,,%E+ 1’ 
UNAUGMENTED 
&j-SEC-’ 
ho,, - SEC -’ 
Figure 3 
446 
In cruise, the near-term augmentation system without feed-forward compensation 
provides slightly higher maneuver stability column force gradients at the relaxed 
static stability aft limit than the basic airplane has at mid c.g. without augmenta- 
tion. The effect of feed-forward compensation is to reduce the column force gradi- 
ents to levels comparable to the basic unaugmented airplane at typical c.g. locations. 
The initial force.gradients comply with MIL-F-8785C (ref. 1) requirements; however, 
there is a deviation from linearity which results in a short-term negative gradient 
in the 1.6- to 2.0-g range which is unacceptable in terms of MIL-F-8785C requirements. 
These characteristics are shown in figure 4. While these negative gradient character- 
istics may not be desirable, they are not uncommon to Class III transport configura- 
tions which cruise at Mach numbers above 0.8. It is suggested that some narrow 
region of negative gradient may be acceptable as long as a substantial force level is 
maintained and there is adequate buffet onset or otherwarning prior to limit load 
factor. 
M= 0.83, h = 33,00 ft, W = 360,000 lb 
70 
60 
MAXIMUM 
ACTIVE AILERONS \/ BUFFET 
PITCH 
. DAMPER 
OFF 
OFF 
ON 
ON 
FEED 
FWD 
OFF 
OFF 
OFF 
ON 
LOAD FACTOR-g’s 
Figure 4 
447 
The near-term pitch active control system was ultimately evaluated in an actual 
flight test program utilizing the Lockheed in-house research airplane, L-1011 S/N 1001. 
The near-term PACS flight test aircraft is fully instrumented for performance 
of flight test programs. This aircraft has been equipped with extended wing tips 
and an aileron active control system. The increase in wing aspect ratio increases 
the aerodynamic efficfency of the aircraft, and the aileron active control system 
provides wing load alleviation which results in lower structure weight. This 
increased aerodynamic efficiency and lower structural weight provide approximately a 
3-percent fuel savings. A unique feature of the basic L-1011 longitudinal control 
system is the flying stabilizer with a geared elevator. Modifications made to the 
L-1011 for the near-term PACS program are shown in figure 5. 
Three pilots participated in the evaluation, which concentrated on two cruise 
altitude conditions and an overspeed condition (VMC) at high dynamic pressure. The 
test program covered 47 hours of flying, 14 for flutter clearance, and 33 for flying 
qualities evaluation. Flying qualities were evaluated at c.g.'s from 25 to 39 per- 
cent E, where the airplane with active ailerons is close to being neutrally stable 
(1 to 2 percent static margin) at high-altitude trim conditions. 
EXTENDED WING 
TIPS 
TRANSFERABLE WATER 
BALLAST SYSTEM 
ACTIVE CONTROL 
AILERONS 
STABILIZER 
Figure 5 
448 
The pitch active control system utilizes a series servo which connects to the 
pitch control system in such a manner that the PACS commands are fed into the 
stabilizer power actuators without reflecting these commands into the pilot input 
control column. This is shown in figure 6. 
PILOT 
INPUT 
)PILOT 
SERVO 
SERIES 
SERVO SERIES --_-- 
Figure 6 
449 
Flight test evaluation of the L-1011 with the near-term PACS operative shows 
a significant improvement in pilot ratings resulting in acceptable ratings to the 
flight test limit of 39 percent MAC which was 1 percent from the neutral stability 
point. The variations of pilot ratings with center-of-gravity locations with and 
without augmentation are shown in figure 7. 
8 
7 
PILOT W 
A,lLERONS ACTIVE 
SMOOTH AIR 
UNACCEPTABLE 
43 
--------_-------___----_---- LL- 
UNSATISFACTORY 
SATISFACTORY 
2 
l- 
24 26 28 30 32 34 36 38 40 42 44 
CENTER OF GRAVITY - ‘K-c 
Figure 7 
450 
The fuel saving benefits to be gained by c.g. management are highly dependent 
on the aircraft wing configuration. Figure 8 shows that for advanced wing concepts 
aft movement of the c.g. location may result in fuel savings up to 4 percent. This 
4 percent is based on increased aerodynamic efficiency determined by analyses and 
wind tunnel tests. The maximum benefits occur when the c.g. location is at approxi- 
mately a -lo-percent static stability margin. An advanced PACS that has a reliabil- 
ity of 10-q is required for flight at this negative stability margin. 
CIJRRFNT I PITCH -AUGMENTATION REQUIRED ADVANCED 
E 
--....I.-. 
C.G. RANGE 
DRAG* 
3ENEFIT t 
CURRENT 
(%) ‘5” WING 
I I NEUTRAL I 
*AM (L/D) POINT I I I I V I I 
20 10 0 -10 
STATIC STABILITY(%) 
Figure 8 
451 
Figure 9 shows the control model used in an eigenstructure placement control 
law synthesis technique. 
With the feedback matrix [F] closed, the state-space equation becomes 
{ii> =[ A + BFC] lx} + {Z) 
In the synthesis process, 
of [A + BFC] at any c.g. 
[F] is computed such that the eigenvalues and eigenvectors 
condition are nearly the same as those for [A] with the 
c.g. at 25 percent is. 
M = rJ$ KU sz Ki, 3 
This set of gains operates on the four feedback signals: incremental pitch attitude, 
incremental speed, normal acceleration, and pitch rate. 
I I 
{;l=[A+BFC](x/+{z} 
Figure 9 
452 
Plots of the feedback gains indicated that gain scheduling could be expressed 
as polynomial functions of dynamic pressure q and of horizontal stabilizer trim 
position 6hT. Comparisons of least-mean-square (LMS) values determined the order 
of polynomials to be used for each set of curves. The second-order polynomial 
format 
K = a + bq + cq2 + dsHT + esHT2 
was found to provide satisfactory curve fits for all gains. Pseudo-inverse matrix 
operations efficiently determined the coefficients to yield the least-squares fit for 
each set of gain values. Scheduled feedback curves of the pitch rate input are 
shown in figure 10. 
. 
K8 
- SEC. 
-0.08 
-0.32 
-0.80 
CASES 
0 3 254 
A 4 461 
l 5 461 
0 6 203 
0 7 218 
Q 8 234 
v 9 258 
0 10 255 
0 11 285 
DYNAMIC 
PRESS 
1.60 -2.80 -2.00 -1.20 -0.40 
‘HT- DEG 
Figure 10 
453 
Figure 11 shows conglomerate short-period poles on the S-plane for all flaps-up 
flight conditions. Nearly all closed-loop poles fall within the objective 
boundaries: 
l Short Period Mode 
0.W 5 an 5 2w, 
0.5 5 5 5 0.8 
where w. is the short-period frequency of the corresponding open-loop configuration 
at 25 percent E. A few of the short-period damping ratios are higher than 0.8 but 
are considered to be acceptable. 
-!- YY 
V 
1.60 
1.2; 
jWdh 0.80 
SEC-’ 
0.40 
0.00 
* 
/\ 
I- 
I I tr 
-1.60 -1.20 -0.80 -0.40 
bN” SEC-’ 
0.00 0.40 
Figure 11 
454 
Control of the phugoid mode requires a velocity component, Ku u, in the 
feedback signal. Because of frequent velocity changes associated with changing 
trim conditions, however, use of a velocity sensor is undesirable. Knowledge of 
the transfer functions implicit in the equation 
{xl = [IS-Al-l [B] cu) 
provides the transfer function relating u and 8, as shown in the figure. The com- 
posite signal B can be closely approximated by passing 0 throeh a lag-lead network 
as shown in figure 12 resulting in the following: 
B K3 (y+l) -= 
9 b2s+l) 
I 1 
e KIGl U 
b b 
K2G2 
K” 
P 
b Ke b 
Figure 12 
455 
Figure 13 shows conglomerate phugoid poles on the S-plane for all flaps-up 
flight conditions. 
boundaries: 
Nearly all closed-loop poles fall within the objective 
l Phugoid Mode 
wn 5 0.16 (40-second period) 
0.2 I < 5 0.5 
0.16( 
h-q” 
0.080 
SEC-1 
c(4.l - SEC-’ 
Figure 13 
456 
With the feedback and feed-forward loops closed, the system equation is 
(;r) = [A + BFC] {x) + D(w) 
where {w) is the input vector comprising column displacement. Figure 14 shows 
the PACS control model with feed-forward loop closed. 
x0 
I I 
{iii = [A + BFC](x/+ [D] (WI 
Figure 14 
457 
The feedback transfer function KFbGFP(S) is a composite of all four feedback 
signals, as shown in the figure. It should be noted that the total transfer function 
from the input 6, is the same regardless of which signal is designated to be fed 
back. This transfer function is 
J&NNz(S) + KuJ!Ju(S) + F&,(S) + K&(S) 
D(S) 
The frequency variant part of this transfer function can be simplified for the 
purpose of computing GFF(S), because the PACS is not sensitive to this function. 
Simplifying assumptions permitted the approximation: 
GFF = l/(S/wsp + 1) 
A block diagram of this logic is shown in figure 15. 
FEEL FEED-FORWARD 
SPRING TRANSFER 
FUNCTION 
AIRCRAFT 
TRANSFER 
J CURVE FUNCTION 
J’ 
6H 
b KAGA - 
KFB GFB 4 
FEEDBACK 
TRANSFER FUNCTION 
Figure 15 
458 
The secondary gain scheduling is used to compensate for: 
l Pitch-up at high-math/high-g flight conditions 
l Outboard aileron symmetric effects when the aileron active 
control system (AACS) is activated. 
The secondary gain scheduling causes the system "to think" it has an additional 
aft increment by adding an increment to the stabilizer gain-scheduling signal, 
This occurs when the pitch-up phenomena or the AACS mode is sensed in accord- 
ance with the block diagram of the secondary-gain controller. The increment produced 
by the bank angle (Ce6PT2(l - cos 0)) is designed to "straighten" the force gradi- 
ents during high-g turns. The secondary gain controller block diagram logic is 
shown in figure 16. 
2 LL 
6a 
’ 
4 6 
a 
0.25 
Krll 
tL ’ 
0.7 0.8 
MACH 
+ MACH 
AACS; FLA 
0 
&AACS 
ON 
+ 
1 
* ) 6HT 
* 
20s + 1 TO GAIN 
SCHEDULERS 
+ 
+ 
10 
0.33O 
Figure 16 
459 
Figure 17 shows that the advanced pitch active control system with pitch 
excursion compensator completely removes the unstable dip in column dip force gradient 
characteristics. The data show that column maneuver force gradient characteristics 
are satisfactory for all c.g. locations. The initial force gradients are essentially 
the same for all c.g. locations, and they also fall in the middle of MIL-F-8785C 
specified design limits (ref. 1). 
460 
I I I I 
3 1.2 1.4 1.6 1.6 2.0 
“‘s - LOAD FACTOR - g’s 
Figure 17 
With the advanced pitch active control system engaged, the response of the 
airplane to a severe vertical gust (heavy thunderstorm magnitude of 54 fps) is 
shown in figure 18 to be essentially the same for all c.g.'s from 25 percent E 
(15 percent stable) to 50 percent E (10 percent unstable). 
8 
6 
ANGLE OF 
AlTACK - 4 
“FRL - DEG 
2 
0 
M = 0.83 
cL TRIM = 0.54 HIGH (W/a) 
CG = 25%E 
I I I I I 
0 4 8 12 16 
TIME - SEC 
20 24 
Figure 18 
- 
461 
The advanced PACS signals can be grouped into four categories. 
l Feedback signals to provide desired stability 
l The feed-forward signal to provide the desired column-force 
gradient 
l Primary gain scheduling signals to compensate for flight 
condition changes 
l Secondary gain scheduling to provide additional stability 
compensation and force-gradient compensation during special 
flight conditions 
Figure 19 shows these signals as used in the advanced PACS. 
SYMBOL I SIGNAL I TYPE I USE 
FC 
I 
COLUMN FORCE 
I 
FEED-FORWARD 
I 
COLUMN FORCE 
GRADIENT 
Nz NORMAL ACCELERATION SHORT PERIOD 
8 PITCH RATE FEEDBACK MODE 
8 PITCH ATTITUDE PHUGOID MODE 
HORIZONTAL STABILIZER 
FLAP SWITCH 
PRIMARY GAIN COMPENSATION 
SCHEDULING FOR FLIGHT 
CONDITI-ON 
CHANGES 
ANGLE OF ATTACK SECONDARY GAIN COMPENSATION 
* BANK ANGLE SCHEDULING FOR PITCH-UP 
M MACH NUMBER AND AACS 
OUTBOARD AILERON 
OPERATIONS 
Figure 19 
462 
The advanced PACS is shown by the solid lines in figure 20. Inputs to the 
controller are: 
Feedback 
NZ = Normal acceleration 
8 = Pitch attitude 
i, = Pitch rate 
Feed forward 
FC 
= Column force 
Primary gain scheduling 
q = Dynamic pressure 
6 HT = Stabilizer trim angle 
Secondary gain scheduling 
~1 = Angle of attack 
G = Bank angle 
m = Mach number 
The controller output is provided in this planned flight test mechanization to 
two series servos which have position-summed outputs that limit hardover stabilizer 
deflections to +3/4 degree if one series servo fails. The total PACS authority is 
21.5 degrees of stabilizer authority. 
PACS AUTHORITY 
AT - 1 DEG 
TRIM SETTING 
k1.5 DEG 
__---- -- 
Figure 20 
463 
The purpose of the pitch-attitude synchronizer is to remove bias offsets from 
the pitch-attitude signal, and thus to avoid saturating the series servos. The 
integrator provides a reference level which tends to command the airplane as if it 
were in an attitude-hold mode. It has two modes of operation which are pilot 
optional: (1) fixed reference, or (2) controlled ref=rence, selected by the 
switch S2, as shown in the circuit below. With S2 = C, the system is in the fixed 
reference mode and provides a reference attitude 8~ equal to the aircraft trim 
attitude 8T. A block diagram of the pitch synchronizer function is shown in 
figure 21. 
- 
S5 = (F + T) C 
S, = T 
Figure 21 
464 
The advanced pitch active control system was evaluated on the Langley visual 
motion system (VMS) simulator pictured in figure 22. This is a general purpose simu- 
lator consisting of a two-man cockpit mounted on a six-degree-of-freedom synergistic 
motion base. Motion cues are provided by the.relative extension or retraction of 
the six hydraulic cylinders of ,the motion base. Washout techniques are used to 
return the motion base to the neutral- point once the onset motion.cues have been 
commanded. . 
Figure 22 
465 
The handling qualities evaluation at each flight condition covered the c.g. range 
from 25 to 50 percent E, for which the control law was designed; this represents a 
stability range in cruise of 15 percent positive static margin to 10 percent unstable. 
Results of the simulation in figure 23 show that the advanced flight control 
system completely fulfills the function for which it was designed. Pilot ratings 
indicate that handling qualities of the augmented airplane with c.g. at 25 percent ;E 
(10 percent statically unstable) are as good as the basic unaugmented airplane with 
c.g. at 25 percent E (15 percent statically stable). The results are most impressive 
at high-speed conditions where handling qualities of the unaugmented airplane quickly 
degrade to unacceptable levels for c.g.'s aft of 40 percent E. 
Flight condition 10 is an intermediate altitude cruise condition. At this con- 
dition, maneuvering stability about trim is essentially linear. 
CALM AIR 
0 PILOT 1 
A PILOT 2 
M = .83 
C‘ = .392 (w/g = 1.4 X lo6 LB) 
0 PILOT 4 
v PILOT 5 PACS OFF l 
•I PILOT 3* PACS ON 0 
10 
---------- --- ------------------ g 
P 2 0 v ii 
J 
5 
I$ 
---+-;-~~g- ---- 8--A----q z 1 
d 
A B V V E A A 
s 
5 
F 
I I I I I I I I s 
!4 28 32 36 40 44 48 52 56 60 
CG -%C 
Figure 23 
466 
I 
- 
REFERENCE 
1. Military Specification, Flying Qualities df Piloted Airplanes, MIL-F-8785C, 
November 1980. 
467 


L-1011 testing with relaxed static stability

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