An analytic technique capable of predicting the landing characteristics of proposed aircraft configurations in the early stages of design was developed. In this analysis, a linear pilot-aircraft closed loop model was evaluated using experimental data generated with the NT-33 variable stability in-flight simulator. The pilot dynamics are modeled as inner and outer servo loop closures around aircraft pitch attitude, and altitude rate-of-change respectively. The landing flare maneuver is of particular interest as recent experience with military and other highly augmented vehicles shows this task to be relatively demanding, and potentially a critical design point. A unique feature of the pilot model is the incorporation of an internal model of the pilot's desired flight path for the flare maneuver

George, F. L.

English

NASA Technical Reports Server

COMPARISON OF CLOSED LOOP MODEL WITH
FLIGHT TEST RESULTS
Frank L. George
Air Force Wright Aeronautical Laboratories
f
Introduction
The analysis presented here is part of a larger effort to develop an
analytic technique capable of predicting the landing characteristics of pro-
posed aircraft configurations in the early stages of design. In this first
analysis, a linear pilot-alrcraft c]osed loop model is evaluated using exper-
imental data generated with the NT-33 variable stability in-flight simulator.
The pilot dynamics are modeled as inner and outer servo loop closures around
aircraft pitch attitude, and altitude rate-of-change respectively. The
landing flare maneuver is of particular interest as recent experience with
military and other highly augmented vehicles has shown this task to be rela-
tively demanding, and potentially a critical design point. A unique feature
of the pilot model used here is the incorporation of an internal model of
the pilot's desired flight path for the flare maneuver.
Model Development
Data from Ref. I suggests the landing flare maneuver can be modeled as
a closed-loop tracking task, as pictured in the following sketch.
V,-
I
Everything inside the dotted box in this model pertains to the pilot.
The pilot model is partitioned into two parts. The left hand part represents
the pilot's internal model of the flare maneuver, and provides the basic
error signal for tracking. This part of the model will be discussed more in
following paragraphs. The right hand part of the model includes all the
pilot dynamics which, as will be discussed below, consist of two gains and a
time delay, plus possible first order lead or lag compensation.
,r
As can be seen from the sketch, this model only considers pitch axis
dynamics and assumes linearized small perturbation equations. The following
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variables are pertinent to the discussion.
O - rad. Aircraft Pitch Attitude
- m/sec. Altitude rate of change, or vertical velocity
of aircraft
" HTD - m/sec. The pilot's desired vertical velocity at
touch-down
He - m/sec. Error in desired vertical velocity as per-
celved by pilot
I/T F - i/sec. Flare model inverse time constant
- rad sec/m Pilot's internal gain to convert he toKp_ an
attitude command
Oc - rad Pilot's internal estimate of attitude re-
quired to correct he
0e - tad Error between desired and actual aircraft
attitude; as perceived by pilot
Kpe - m/tad. Pilot's internal gain to convert O to an
elevator (pitch) control motion e
T - sec. Pilot's delay time; approximates internal
p_oce_sing plus neuromuscular delays
TL -sec. Pilot's optional lead compensation time
T1 - sec. Pilot's optional lag compensation time
Fes - N Pilot's pitch control force
As suggested in Ref. I, the pilot's internal flare model, mentioned
above, can be represented as a first order exponential. In other words, as
a linear relationship between H and H, depicted in the following phase plane
sketch,
!
Touchdovn • I
\ " I Flare
Point, iI_ _dl.li lnlilstll_
Nr ............ CONSTA.'_T II
G, IDL_LOPI l'l.teif i IIC
define the pilot's desired sink rate along the flare trajectory as Hc, where
Hc= Z/ZriI+ HTO
and I/TF, the inverse tim constant of the corresponding exponential dsc_y
is :
I/TF = _ ,, .......
AH 0 - HF
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Data from Ref. 2 will be used to test the model descrlbed above. For the
experiment described in Ref. 2, characteristics representative of modern
fighter aircraft with augmented dynamics were modeled in the variable stabil-
ity NT-33. A series of ILS approaches was flown using a nondnal glldeslope
of .044 tad (2.5 degrees); each approach was concluded with a visual flare
and landing task. l_e flare maneuver was initiated at a nomlna] altitude
of 15.24m (50 feet) above ground. A sink rate of .762 m/see. (2.5 ft/sec.)
at touchdown is considered acceptable. The configuration designated as 2-7
in Ref. 2 will be used as a specific example for further discussion here.
For the visual flare, it is assumed the pilot has selected a desired touch-
down point on the runway so the important speed is equivalent ground speed,
which for this example was 61.73 m/see. (120 knots or 202 ft/sec.) at flare
initiation. Using the definitions above, these values give the ideal flare
model as,
= -.II(H + 6.92) m/see.
with the exponential solution,
H = 22.16(_'iit-.31) m
The airplane, actuator, augmentation and feel system dynamics for configura-
tion 2-7 of Ref. 2 were examined and it was determined that a reduced order
model using only the short period and command augmentation dynamics plus
feel syster, gain would be adequate in the frequency range of .i < J_ < 20.
tad/see.
The inal closed loop model was generated by first closing an inner loop
for atti :ude control, and then an outer loop for altitude rate. Ref. 3 sug-
gests bandwidth and phase angle criteria for attitude control during landing
of
_B = 1.2 rad/sec, _nl_B = 7/2
with a pure time delay of 0.3 sec. For this analysis a pilot time delay of
O. 33 sec was used since this value gave a convenient first order Pade° ap-
proximate expression for linear frequency domain analysis. The pilot's time
delay and any compensation introduced were lumped in the attitude loop
closure. Parameters were selected for the inner loop to approach the cri-
teria mentioned above as closely as possible, while maintaining reasonable
closed loop damping, for example, _CL = 0.5. For the configuration selected,
this rationale resulted in a fairly low-_ain system, but it was felt this
would be consistent with the pilot's desire to not overcontrol so close to
the ground. Figure 1 summarizes the characteristics of the attitude closed
loop with no pilot compensation considered. Continuing with the o ter loop
closure, and accounting for initial conditions as suggested in Re_ C, the
final closed loop flare model was,
• VT --
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!
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where the lower case letters are used to indicate pertuzbatlon values. The
final closed loop transfer function was,
-38.61 (S - 6) '
-- mR •
HF (S + 1.164)(S + 6.O05)[S + .771_+ J 1.431][S + 8.356_+ J 8.611]
The forcing function for this model, using the conditions defined above, was
a step scaled to represent the altitude rate at flare Initlati_on.
Model Evaluation
Figure 2 summrizes the response characteristics of the final closed
loop system, and Figure 3 compares the landing trajectories of the piloted
closed loop model with an ideal exponential curve. The trajectories in
Figure 3 representing the piloted system with lead and lag were generated
from models developed by the same procedure as described above. The pilot
lead and lag were introduced as cascade compensation within the pitch atti-
tude loop. Figure 3 shows the pure gain and lead compensated mode]_ both
result in early flares and overshoot the ideal exponential touchdown time,
leading to long gliding landings which pilots might describe as "floaters".
The lag compensated model, on the other hand, generally follows the expo-
nential, but with some low frequency oscillation. An example flare traJec- i
tory from the inflight experiment is also shown on Figure 3. As the figure :_
shows, the real flight trajectory does not follow the exponential or the
analytic model path very closely except in the last 4 seconds before _ouch-
down, where the flight trajectory is somewhat similar to the exponential.
Figure 4 presents a second comparison of the flight path characteristics,
using the H vs H phase plane. This presentation clearly shows the oscilla-
tory nature of the lag compensated closed loop model. The figure also
clearly shows the difference between the actual flight trajectory and the
ideal exponential.
L
Planned Work ._
Further analysis of the Inflight data is planned to investigate differ-
ences between the experimental and predicted flare trajectories. It is felt
the closed loop model is a valid approach for the landing flare analysis be-
cause of pilot comments and the nature of observed pilot control inputs
during the flare. Figure 5 shows some examples of the pilot's longitudinal
control activity during flare. The experlme_ al data will be examined to
determine if significant time-varying or nonlinear characteristics are pre-
sent which would account for the discrepancies with the linear, constant co-
efficient model.
Reference 4 investigated STOL aircraft approach and landing using the
optimal control pilot model. The flare maneuver was treated as a time optt-
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1982005792-299
T
A
real problem in that study, resulting in time varying control. An example
flare trajectory from the Reference 4 results is plotted in Figure 4. Al-
though the trajectory is rotated because of the steeper approach angle used
in the STOL study, the shape generally resembles the NT-33 actual landing
trajectory. This observation lends credence to the plan to extend the pre-
sent investigation to consider tlme-varylng closed loop models.
References
i. Hoh, Roger, Craig, S.J. and Ashkenas, I.L., "Identification of Minimum
Acceptable Characteristics for Manual STOL Flight Path Control, Volume Ill
Detailed Analyses and Tested Vehicle Characteristics", US DOT Report
No. FAA-RD-75, 123, Ill, June 1976, DTIC: ADA029250.
2. Smith, Rogers E., "Effects of Control System Dyna_fcs on Fighter Approach
and Landing Longitudinal Flying Qualities, Volume I", Air Force Flight Dy-
namics Lab Report, AFFDL-TR-78-122, March 1978, DTIC: ADA067550.
3. Chalk, C.R., et al, "Revisions to MIL-F-8785B(ASG) Proposed by Cornell
Aeronautical Laboratory Under Contract F33615-71-C-1254", Air Force Flight
Dynamics Lab Report, AFFDL-TR-72-41, April 1973, DTIC: AD778489.
4. Klelnman, D.L. and Killlngsworth, W.R., "A Predictive Pilot Model for
STOL Aircraft Landing", NASA Langley Research Center Report, NASA CR-2374,
March 1974.
I
1
FIGURE1. Clemed Loop Attitude I_mpo_e with Pure Gain Pilot
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--;.,_r CLOS[_LOOP,Ze-.|, Z_.o.I;. T*Uo.33. _ CG.'.P I --; ;_.S_h:_. :h r_[, TAt,..]], _ ¢Gr._. Ze.IX..S
_* .., _'_.s, - _
, . Io. | O I ,I 6 | le
fi(_"4 b,_V * IC,*IPI,I J • -IIVL - $111!. (_10 FLail i41"ISTII_]
FIGURE 2. Closed Loop Flare Response with Pure Gain Pilot
\
_, ". _ AIlIII_ I - |l. (|.2111'1)
...... P_l qldllN PI_.OT _i
_S_ • _" °S mLkCTW_ L.LIRG*OI4
' _IITII. wll_ M.A
• !
-'_, -IS _*_'_ P' ""
'n+'++-,.. (_;_ :::t,_) FIGURE 4. Flare Trajectory
Phase Plots
FIGURE 3. Closed Loop Flare Trajectories
; NT-33A FLIGHT • 1898 RECORO • 13
_e TOUCH DOWN
i. BEGIN FLARE
FIGURE 5. Pilot Control Inputs in Flare
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Comparison of closed loop model with flight test results

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