Table Of Content/,,'IS
207289 AIAA Paper No. 97-3498
A Theory for the Roll-Ratchet Phenomenon in
High Performance Aircraft
Ronald A. Hess _
Dept. of Mechanical and Aeronautical Engineering
University of California
Davis, CA 95616
Abstract
Roll-ratchet refers to a high frequency roll ratchet phenomenon, e.g. Refs. 1-6. Perhaps one
oscillation which can occur in pilot-in-the-loop control of the first explanations of the phenomenon was offered
of roll attitude in high performance aircraft. The in Ref. 2, and discussed in some detail in Ref. 1. The
frequencies of oscillation are typically well beyond authors of Ref. 2 were the first to suggest the
those associated with the more familiar pilot-induced importance of acceleration cues in catalyzing roll
oscillation. A structural model of the human pilot ratchet:
which has been employed to provide a unified theory "Suppose the pilot reverts to an
for aircraft handling qualities and pilot-induced abrupt input technique to demand the
oscillations is employed here to provide a theory for the desired response more rapidly,
existence of roll-ratchet. It is hypothesized and creates high angular accelerations
demonstrated using the structural model that the pilot's and then switches his closure to
inappropriate use of vestibular acceleration feedback can angular acceleration error, instead of
cause this phenomenon, a possibility which has been bank angle error. Then with
discussed previously by other researchers. The possible sufficient pilot gain, aratcheting type
influence of biodynamic feedback on roll ratchet is also oscillation of = 16 rad/s results."
discussed.
While recognizing the importance of
Introduction acceleration cues, other researchers have maintained
Figure I, taken from Ref. 1 shows two time that the interaction of the pilot's neuromuscular system
histories involving the Air ForcelCALSPAN NT-33A and the cockpit control inceptor are the important
variable-stability aircraft and the prototype YF-16 factors in understanding ro_l-ratcbet, e.g. Refs. 3 and
vehicle. As the figure indicates, high frequency roll 5. Consider Fig. 2 from Ref. 3. This figure shows the
oscillations (12.17-12.5 rad/s) occurred under piloted Bode plots of a series of measured pilot-vehicle transfer
control. Oscillations such as these have been termed functions from a fixed-base simulation of a roll tracking
roll-ratchet by pilots and flight control engineers. The task when a force-sensing cockpit inceptor was being
term finds its origin in pilot descriptions of the event, used, i.e. the force which the pilot applied was sensed
i.e. the pilots often describe what they perceive to be a and used as a command to the vehicle and/or flight
ratcheting-like motion. The ratcheting sensation may be control system. The amplitude peaking evident just
attributable to a threshold nonlinearity in the human beyond 10 rad/s should be noted. To induce an
inner ear where acceleration is sensed. While not a oscillatory response, the phase lag at the frequency
dangerous condition, per se, roll ratchet often precludes where this amplitude peak crosses the 0dB line has to
acceptable performance in air-to-air tracking tasks, and be reduced to -180 deg. The authors hypothesize that
almost invariably leads to a significant degradation in the pilot's use of motion cues provides this phase lag
handling qualities ratings. reduction. In Fig. 2, the 0.1 _ x 57.3 is the phase lead
which the authors state can be provided by "inner-loop"
There has been a considerable amount of roll-rate feedback. The authors conclude that avoiding
research devoted to seeking the mechanism behind the the use of force-sensing cockpit inceptors can minimize
*Professor, Associate Fellow AIAA
the occurrence of roll ratchet, a conclusion also reached roll acceleration sensed through the vestibular system.
in Ref. 5.
The Revised Structural Model
More recent flight test results have Figure 3 shows what will be referred to here
demonstrated that merely avoiding force command as the "revised structural model" of the human pilot.
inceptors is not sufficient to prevent the occurrence of The model has its genesis in a previously described
roll ratchet. In Refs. 4 and 6, flight test data from the structural model, e.g., Ref. 8, and in a later
Air Force/CALSPAN NT-33A variable-stability aircraft modification of that model, s As shown in Fig. 3, the
demonstrated that roll ratchet can occur with either model is describing compensatory pilot behavior, i.e.,
position or force-sensing inceptors. The data from behavior involving closed-loop tracking in vdaich the
these references is particularly interesting in that pilot- visual input is system error. The elements within the
vehicle transfer functions, like that shown in Fig. 2 dashed box represent the dynamics of the human pilot.
were measured in tracking tasks involving sum-of-
sinusoids roll-command inputs. The interpretation of The model of Fig. 3isdiscussed thoroughly in
this data, however, varies. That is, referring to the Ref. 7, and part of that discussion is repeated here for
work of Refs. 3 and 5, there is some evidence that the sake of completeness. Starting from the left, one
neuromuscular mode peaking is occurring with roll sees the system error e(0 following one of two possible
ratchet, but it is not always present in the transfer paths. One path is intended to model the human's
functions where ratchet is occurring. This, of course, visual rate-sensing dynamics, here modeled by a
can be explained by the fact that ratcheting is a sporadic differentiator (s), an injected noise signal, and a gain
event, and describing functions are time-averaged
K_. The remaining path describes normal error sensing
linearizations of the entire tracking sequence. Thus,
and gain compensation K,, including the possibility of
those periods when ratchet did not occur were averaged
with those where it did, and the result shows evidence the human's accomplishing low-frequency trim (or
of peaking, but no ratchet. integral) compensation via e/s. In this study, ¢ - 0.
The switch labeled $1 allows switching between error
A Model-Based Theory for Roll Ratchet and error-rate tracking. This switching has been
Introduction
hypothesized to play a critical role in the initiation and
The explanations for roll-ratchet briefly
sustenance of pilot-induced oscillations. _ S_tches S_
described in the preceding paragraph, while plausible,
suffer from the fact that they require some rather and $2 are assumed to operate in unison, i.e., whenS 1
special conditions to be met for their validity. For is in the "up" position, so is $2. For this study,
example, the theory forwarded in Refs. 1and 2 requires however, it is assumed switches $1 and $2 remain in
the pilot to visually sense the second derivative of the the "down" position and normal error sensing and
system error, not an easy task based upon what is
compensation isused. Acentral processing time delay x0
known of human pilot visual sensing capabilities. The
is also included. An inner, proprioceptive feedback
work reported in Ref. 3 indicates that conditions can
loop is encountered next. In the forward portion of this
occur in which the amplitude of the neuromuscular
loop, the elements YtoJ and Yrs are inteaded to
mode peak is near or at unity (0 dB), at the frequency
where the phase lag is near or at -180 deg. These represent, respectively, the open-loop dynamics of the
conditions are those which would imply a high- neuromuscular system driving the cockpit inceptor, and
the dynamics of the inceptor force-feel system, itself.
frequency, closed-loop oscillation.
The feedback portion of this loop contains the element
The explanation to be proposed herein, draws Yrr, which receives as its input the proprioeeptively
upon both of the previous hypotheses to some extent. sensed inceptor output 6,,(t). The element Yn, and its
However, it is based upon a simple model of the human position in the model iscentral to the philosophy of the
pilot which has been used to provide a unified theory structural model, i.e., that the primary equalization
for aircraft handling qualities and pilot-induced capabilities of the human pilot are assumed to occur
oscillations. 7 As will be seen, with this model the
through operation upon a proprioceptively sensed, as
phenomenon of roll-ratchet can be explained by the
opposed to a visually sensed, variable. The switch$ 3
pilot's use of an inappropriately large feedback gain on
allows either position-sensing orforce-sensing inceptors
tobemodeled.
8M = OCe-' for =
r,rcqo) = --fqo).vcqo)
Timederivativeosfthevehicloeutpurte(t) are jo
assumed to be individually sensed as indicated in Fig.
(4)
3. Switch S,_allows either rate or acceleration cues or
neither to be used in vehicular control. It should be
noted that feeding back output rate is predicated on that i.e., YpYc(jo) follows the dictates of the crossover
signal creating an acceleration which can be sensed by model of the human pilot. 9 The gain K appearing in
Eq. 2 is chosen so that, with all other loops open, the
the middle ear. In this study, K_ = 0. A visual
minimum damping ratio of any quadratic closed-loop
feedback of vehicle output completes the model.
poles of °U(s) is _=ia = 0.15. Finally. Kc is selected
Model Parameterization e,,
The reader is referred to Ref. 7 for a
so that the desired crossover frequency of 2.0 rad/s is
discussion of model parameterization, which will only obtained. As will be demonstrated, the inclusion of a
be summarized here. Elements Ysu and Yrr are given nonzero K,_ (with switch S, in the "up" position) can
by alter the high-frequency characteristics of the open-loop
2
transfer function M(s) and produce oscillatory behavior
Y_u = 2
s2÷2£_,_sus+o_ very similar to that seen in roll ratchet. The inclusion
of anonzero K_, after selection of K, in the modeling
procedure described inthe preceding ispossible since K,_
K(s ÷a) or, has only a small effect upon the crossover frequency.
g
Yep -- I K or, (2)
Analysis of Roll Ratchet
Kl(s+a)
Data Base
The data to be used is taken from that
with the particular equalization of Eq. 2dependent upon presented in Ref. 4 and discussed in Ref. 6. Itinvolves
the form of the vehicle dynamics around the crossover a series of roll-tracking tasks conduced on the Air
frequency. The crossover frequency is chosen as 2.0 Force/CALSPAN NT-33A variable stability aircraft.
rad/s. Attention will be focused upon eleven configurations
which have been identified in Ref. 6 as either not
Nominal values for "f'Lxed" model parameters experiencing or experiencing roll-ratchet in flight test.
can be given as Figure 4 describes the short-hand notation used to
identify the configurations. The eleven configurations
analyzed are shown in Table 1.
xo = 0.2 s
(3)
It is useful to provide some validation of the
o_u = I0 radls
structural model and parameter selection procedure
(_u = 0.7 described in the preceding. To this end, a comparison
can be made between a pilot-vehicle transfer function
obtained from flight test and one generated by the
structural model. Configuration 221P(I8) was selected
The relatively simple relations of Eqs. 1-3, the for comparison. Figure 5 shows the flight test and
model results. In terms of the variables in Fig. 3, Fig.
crossover relation _c = 2.0 radls and the selection of
one of the three forms on the right hand side of Eq. 2
5 is a Bode plot of Mqco). The shaded circles
allow implementation of the model of Fig. 3. The
appropriate form in Eq. 2 is chosen so that the resulting represent magnitude and phase measurements from
open loop transfer function flight test at the frequencies of the command input
sinusoids comprising c(t) while the solid and dashed
curves represent the model results. The model was ,go
obtained using the pilot-vehicle analysis technique poles of the transfer function c(s), for four values of
outlined in the preceding with one exception: the
the "visual" gain _. These correspond to factors of 1,
crossover frequency for the model pilot-vehicle system
2, 5, and 10times the nominal value which yielded the
was reduced from 2.0 rad/s to 1.5 rad/s to provide an
2.0 rad/s crossover frequency with K_ -- 0. Note the
acceptable match to the amplitude data and allow an
very small change in the position of the oscillatory
easier comparison with this data. As the figure
"roll-ratchet" roots. Taking the model at face value,
indicates, with the one exception of the crossover
this result means that the pilot cannot stop a roll-ratchet
frequency the comparison isquite good. The crossover
frequency discrepancy was not deemed serious, and will by varying his/her outer-loop, "visual" gain, K. The
be ignored in what follows. ratchet can only be stopped by a reduction in K_. It is
interesting to compare this result with that implied by
Acceleration Feedback Fig. 2 and Ref. 3. There, the existence of a roll-
The simple hypothesis offered here isthat the ratchet is predicated upon an appropriate outer-loop
roll-ratchet phenomenon can be induced by the pilot gain which forces the magnitude of the open-loop
adopting an inappropriately large gain K,_. It isfurther transfer function tobe unity (0 riB) at the frequency at
hypothesized that this large gain is induced by roiling which the phase angle is-180 deg. A similar statement
accelerations created by the aircraft and flight control can be made about the model proposed in Ref. 1.
system which the pilot deems excessive for the task at
hand. This latter hypothesis is identical tothat offered Figure 8shows a the output m(t) and the force
in Refs. 1and 2. The difference, however, isthat the input 8v(t) to a unit step input for configuration
acceleration sensing occurs ina feedback loop, through 143P(I8). This pair of time histories are interesting in
the vestibular system and is not occurring through that they are qualitatively similar to recorded roll-
visual means inthe forward-loop. Theinterplay of the ratchet time histories. That is, only a small amplitude
neuromuscular system and the nature of the force-fcel oscillation is evident in roll-attitude, while a large
system is obvious from the structure of the amplitude oscillation isevident incontrol input. Figure
proprioceptive feedback loop in Fig. 3. Thus, this 8 shows the pilot control force input during flight-test
hypothesis has many of elements in common with that roll-ratchet encounter with configuration 143P(18).
offered in Ref. 3. However, as will be demonstrated, The frequency of oscillation is I0.4 rad/s, while that
only a single gain variation need beemployed to induce obtained with the model is 9.8 rad/s.
a closed-loop oscillation very similar to a roll-ratchet.
The inappropriately large gain K,_ may be
Figure 6 shows the structural model pilot-
attributed to the following: In maneuvering, the
vehicle transfer function for configuration 143P(18)
panieular flight configurations which are prone to roll
with two values of K_, zero and avalue yielding a very ratchet, create a rolling acceleration which the pilot
lightly-damped high-frequency mode. Itshould benoted finds excessive for the task at hand. This may occur
that such a gain increase may only be transient, i.e. it even if the task itself involves relatively modest
may not occur over a long enough period of time to be accelerations in an absolute sense. If a physiological
accurately captured by a single transfer function sensor is available to measure this acceleration (which
measurement such as that shown in Fig. 5. Also note itobviously is), the natural tendency on the pan of the
in Fig. 6, that there is only a modest change in pilot may be to feedback this variable and attempt to
crossover frequency with the non-zero K,_. Finally, the reduce it through control activity. However, because
closure of the outer, visual loop in Fig. 3 has little of the structure of the pilot's feedback system, this
effect upon the relative stability ofthe oseiUatory mode. action merely leads to a very lightly damped mode and
This is shown in the root locus diagram of Fig. 7. a roll ratchet.
Here, the open-loop transfer function M(s) includes the Vehicle Characteristics
If initial acceleration response is involved in
acceleration loop closed with the non-zero K,i. The
the initiation of roll ratchet, it may be possible to
small squares indicate closed-loop root locations, i.e.,
distinguish some differences in open-loop acceleration
response to applied force inputs, at least for the eleven
configurations of Table 1. To this end, the transfer hypothesis that initial acceleration responses to force
inputs that exhibit large lags or large amplitudes in the
function was plotted for each set of
frequency domain may induce the pilot to employ an
inappropriately large acceleration feedback gain in an
configurations in Table l, i.e., those with no ratchet attempt to control the resulting response. As an
and those with ratchet. Note that this transfer function
example of such responses in the time domain, Fig. 12
will contain just vehicle, actuator and force-feel system
compares the time-domain roll acceleration responses to
dynamics when a position-sensing inceptor is being step applied forces for configurations 301P(18) (no
used, and vehicle and actuator dynamics, alone, when
ratchet) and 143P(18) (ratchet). Figures 10and 11also
a force-sensing actuators is being used. Note that no
show a pair of phase-amplitude boundaries which can
pilot dynamics are included. Figures 10 and 11 be used to delineate the roll-ratchet proneness of these
summarize the results. Since it is the initial
configurations. That is, if a the magnitude or phase of
acceleration response which is of interest (t < < 1),
attention should be focused on the characteristics of
/,_2 "_---- (S'/ violates either of these bounds, the
L VF _
/s2"M(s) / for values of j_ which are large but do configuration experienced roll-ratchet in flight test. Of
L _r js.jw course, it is presumed that some minimum magnitude
not exceed the upper limit of the frequency range of
oer ,11 a,
i,nte0rest fo r omanuwal con,trol, i.e., _ -- 10 radls. Figure 10 rad/s would be required to
y _ t _ ls-l_
induce roll ratchet. The relatively small data set of
t _p .t, Table 1 does not permit an estimate of this lower
did not exhibit roll ratchet, while Fig. 11 shows the bound.
function for those that did. Even for this small data
set, some basic differences appear. The no-ratchet Biodynamlc Feedback
cases all had phase lags at 10 rad/s which were less A discussion of the roll-ratchet would not be
than -75 deg i.e., less negative. In contrast, all but one complete without considering the possible role which
of the ratchet cases had phase lags greater than -75 deg biodynamic feedback may play in the phenomenon.
i.e., more negative. The configuration in Fig. 11 The terms biodynamic or biomechanical feedback are
which did not have a phase lag at I0 rad/s exceeding used here to imply the effects which vehicle roll
75 deg did, however, have a relatively large magnitude acceleration might have on the pilot's arm and cockpit
at this frequency. The magnitude and phase for this inceptor, and how these effects may serve to catalyze
configuration (201P(18)+55) are denoted by arrows in roll ratchet.
Fig. 11. The one configuration in Fig. 10which comes
close to exceeding -75 deg (342P(I8)) also exhibits the A very simple model of biodynamic feedback
smallest magnitude in the high frequency range. This can be obtained by considering the pilot's hand/arm and
pair is also denoted by arrows in Fig. 10. It is the inceptor grip as consisting of an effective point
interesting that of the two piloted evaluations of mass ra a distance r above the instantaneous roll axis
configuration (342P(18)) reported in Ref. 4, one of the of the aircraft, s Consider the situation in which both
pilots reported no roll ratchet and gave the
the control stick pivot point and the location of the
configuration a Cooper-Harper rating of 2. The second effective point mass are above the instantaneous roll-
pilot, however, did report some oscillation problems axis of the aircraft. When the aircraft is undergoing a
that he found objectionable, but said that there were no
rolling maneuver with roll acceleration _, the force
PIO problems. He gave the configuration a Cooper-
which the pilot must apply to keep the inceptor from
Harper rating of 5 because of these oscillations. It is
not known for certain whether these oscillations were moving relative to the cockpit is simply -rm,_. To
roll ratchet, however, one might expect that they were account for dynamics obviously neglected in this simple
since the pilot explicitly exonerated the vehicle from model, one can consider the biodynamic element to be
PIO tendencies (which are typically categorized by
rm,s2e ''', where the time delay x accounts, in a
pilots as being of lower frequency than roll-ratchet).
rudimentary way, for the phase effects of neglected
Thus, the "close-call" for configuration 342P(18) in
higher frequency dynamics in the biodynamic model.
Fig. 10 may be reasonable. These results support an
Figure 13shows how the structural model of Fig. 3 can intended to demonstrate that atheory could be proposed
be modified to incorporate this rudimentary model of to explain the origins of the roll-ratchet phenomenon
biodynamic feedback. that was consistent with previous observations and
could be part of a larger theory which has attempted to
Figure 14 shows the root locus diagrams for unify aircraft handling qualities and the lower frequency
phenomena typically identified as pilot-induced
the closed-loop poles of the --M-M(st)ransfer function
oscillations. 7 It is not proposed that the boundaries
shown in Figs. 10and 11be considered as a metric for
from Figs. 3 or 13, with "_=0.025, 0.05, andO.1 s
assessing the roll-ratchet proneness of anyvehicle. One
with vehicle dynamics and model parameters (YrF) for obvious reason for this is that different vehicles will
Config. 143P(18). The closed-loop poles in Fig. 14 induce different accelerations to identical control force
correspond to those values of rm, chosen to produce inputs due merely to different pilot station locations.
oscillatory roots. For the case when x = 0.I s the The fact that the eleven configurations of Table 1were
frequency ofthe oscillatory mode is11.4 rad/s, close to created on the same test vehicle made the comparisons
roll-ratchet frequency of 10.4 rad/s obtained in flight of Figs. 10 and 11possible. As stated in the previous
test for Config. 143P(18). An open-loop transfer section, these figures merely support the idea that the
function very similar to that indicated by the solid characteristics of initial acceleration response may be a
curves in Fig. 6, was obtained for the case with key factor in initiating roll ratchet. Finally, the
biodynamic feedback and x = 0.1 s, a result which is possibility that biodynamic feedback may act as a
not too surprising seeing that the same variable isbeing catalyst for roll-ratchet iscertainly plausible, but is felt
fedback in both cases, albeit into different locations in tobe a less-likely explanation than the theory proposed.
the pilot model.
Conclusions
Figure 14 suggests that biodynamic feedback A theory for the roll-ratchet phenomenon can
may, itself, produce oscillatory behavior of the kind and be forwarded which is based upon a revised structural
frequency associated with roll ratchet. However, one pilot model. The theory states that roll-ratchet is
must bear in mind that the "gain" on the root locus caused by the pilot's inappropriate use of vestibular
diagrams of Fig. 14 isnot a variable quantity as in the acceleration feedback. The proposed theory contains
elements found inprevious explanations of roll ratchet,
case of K,_, but rather a geometrical/biomechanical
i.e., the importance of acceleration cues and the
constant, whose value is a function of the mass
influence of the pilot's neuromuscular dynamics. Using
distribution of the control inceptor, the mass, position
the structural model, one can create oscillations whose
and tension of the muscle groups subject to motion
frequency closely approximates that found in flight test
under acceleration, and the position of the aircraft's
of roll-ratchet prone aircraft. In addition, the nature of
instantaneous roll axis. While it is certainly possible
the time histories which can be produced by the model
that these quantities may produce oscillatory root
are qualitatively similar to those found in flight test,
locations, itwould appear to the author tobe less likely
i.e., small amplitude oscillations in roll-attitude time
than in the case of acceleration feedback via K,i.
histories, but strong evidence in control input time
Finally, itshould be noted that conditions which would
histories. As opposed to other model-based
increase the likelihood of biodynami."cally-induced roll
explanations for roll ratchet, the structural model
ratchet, e.g. lack of sufficient arm support, and/or lack
implies that the pilot cannot halt a roll ratchet encounter
of a mechanical break-out in acontrol inceptor, are also
by changes in his/her visual gain, but only by reduction
conditions which would adversely affect the operation
in the vestibular acceleration feedback gain. For the
of the hypothesized propriocep.tive loop in Fig. 3.
series of flight tests analyzed, the nature of the initial
This, inturn, could induce the pilot to use acceleration
(open-loop) acceleration response of the vehicle could
feedback in an attempt to ameliorate roll accelerations
be used to categorize the roll-ratchet proneness in the
produced by control stick inputs of less precision than
eleven configurations chosen for study. Biodynamic
desired.
feedback was modeled in rudimentary fashion and
found to be a plausible but, in the author's opinion, a
Discussion
less-likely candidate for catalyzing roll ratchet. At
The previous analysis is obviously not
present, the data base is not sufficient to delineate
exhaustive in terms of configurations analyzed. It was
Acknowledgement 5Hess, R. A., "Analyzing Manipulator and
This research was supported by NASA Langley Feel System Effects in Aircraft Flight Control," IEEE
Research Center under grant No. NAGl-1744. Dr. Transactions on Systems, Man, and Cybernetics, Vol.
Barton Bacon was the contract technical manager. 20, No. 4, 1990, pp. 923-931.
6Mitchell, D. G., Aponso, B. L., and Klyde,
References D. H., "Effects of Cockpit Lateral Stick Characteristics
_Chalk, C. R., "Excessive Roll Damping Can on Handling Qualities and Pilot Dynamics," NASA CR-
Cause Roll Ratchet," Journal of Guidance, Control and 4443, June, 1992.
Dynamics, Vol. 6, No. 3, 1983, pp. 218-219. 7Hess, R. A., "A Unifying Theory for Aircraft
2Smith, R. E., Monagan, S. J., and Bailey, R. Handling Qualities and Adverse Aircraaft-Pilot
E., "An In-flight Investigation of Higher Order Control Coupling," Journal of Guidance, Control, and
System Effects on the Lateral-Directional Flying Dynamics, to appear.
Qualities of Fighter Airplanes," AIAA Paper No. 81- SHess, R. A., "A Model for the Human's Use
1891, 1981. of Motion Cues in Vehicular Control," Journal of
_Johnston, D. E., and Aponso, B. L., "Design Guidance, Control, and Dynamics, Vol. 13, No. 3,
Considerations of Manipulator and Feel System 1990, pp. 476-482.
Characteristics in Roll Tracking," NASA CR-4111, _McRuer, D. T. and Krendel, E. S.,
Feb., 1988. "Mathematical Models of Human Pilot Behavior,
'Bailey, R. E., and Knots, L. H., "Interaction AGARDograph-AG- 188, 1974.
of Fell System and Flight Control System Dynamics on
Lateral Flying Qualities," NASA CR-179445, Dec,
1990.
Table 1 _ Test CoctlllFu'aflom Aemly'_ed from Ref. 4 _,.e,. " [2.t7 rad/s
,._. /
_ _daet
I
1.411=(10) 143P(18)
30IP(18) 201P(18) +55
(a)
3021(18) 22tP(18)
3411=(18) 3011=(18)+110
342P(tS) 302_18)+55 roll-rata J t
342JF(18) t
_,_,o. " 12.J rad/s
S_Ck
force
o 1 2 3 t s
5EC
(b)
Fig. 1 Roll ratchet time histories;
(a) NT-33A, (b) YF-16.
7
American Institute of Aeronautics and
Astronautics
fAddea TransDort _,elQ,i ]
OtO 100 IO00
I t configuration .i_
magnitude 2O
(dB)
_:. _ _nd-fzLred fit
FLIC._"r C_N'PI_CX_ _VST'_,I .rf,_© [
+_+:a,:,++..'='Ib,I
0 (P}: FmCiSMON COk(MANO
(F_: FORCE ¢OMblANO
,_ F:-L c-vs"_.( t3VN,_+C_i
i
PI: [7.2_] I
0 --
_2): [7. '+21
pha_ _ _ haad-faut'd fit (2): {,7:_1
-tO0
t_'IJ
/ L=_,_- :7.N'T=Ct Sv_'r=_,,, .,L.--:_ t
-200 --
LL_ il P.4= | (_): (.7.?_i
__ . Jr573
(2} _:_=.,?.3 (2} _-+30 | (_l: (.7: el
(3) ':,)_=AO O) ")t" .4._ [ (0): NCNE I
i [(1: ('_1
a
_ (a) , s.a
shoa-_._ aoraaon: L[¢.,uj _ _2¢._.s+(+_.
Fig. 2 Measured pilot-vehicle transfer function
characteristics from Ref. 3.
Fig. 4 Configuration identification scheme from Ref.
6.
\
i
, E _-_,,) ,_t ....
C-)_ F-..- --i. ,II
""\ 1....
"4111-1. ii e II& |O|
nl_s
i....................................... ,.,I
Fig. 5 Comparison of pilot-vehicle transfer
Fig. 3 Arevised structuralmodel of the human pilot. functions from flight-test and structural
model; Configuration 221P(18).
I
+rmxnir+ _ _-
i-Ill
-Imll
-Ill
-4"_II
-_1411
-lie
Tlll
-41I i li • il[ ii I
Fig. 6 Structural model pilot-vehicle transfer
function with two values of g,_;Configuration
143P(18).
American Institute of Aeronautics and
Astronautics
m
xu
n
°le \ /'/f_ mvlCtllCtU{_ _u
-amw -tw -_u I iie tmI iv
Fig. 7 Root locus diagram for closed-loop poles of
Fig. 10
2.M(s)] for configurations in Ref.
6r k.j,_
M(s) with open-loop transfer function M(s)
identified as not experiencing roll ratchet.
defined with non-zero K_ of Fig. 6. Closed-
loop roots correspond to varying nonfmalK,
by factors of 1, 2, 5, and 10.
I_ rill _•
v ,.., ,,. 9.m,a,_.t
.... 1%". '.. _ •
-t , • _ ,,_ J = "tl_oi tqlu |•t le I
rod/_
Fig. 8 Closed-loop step response of pilot-vehicle Fig. 11 [Ls_'M6(s,)I L.,.for configurations in aef.
system of Fig. 3, with pilot-vehicle transfer
identified as experiencing roll ratchet.
function of Fig. 6.
5.0
............................. :----'i--'-i""!""i--i-"i-'T-i"i""_
¢/t_l_t == 10.4 r/s I. .---!--i_---!--:_.--i--;_-.._--:_--i--i-:-_: ; " : ..... -i--- i
• 143P(18]
control
force 0
(lb)
_me J
-5.0
-.q 1--- is
/_me $ Fig. 12 Roll acceleration responses to step force inputs
for configurations 301P(18) (no ratchet) and
Fig. 9 Pilot inceptor force inputs from flight test of 143P(I8) (ratchet).
Ref. 4, as reported in Ref. 6, for configuration
143P(18).
9
American Institute of Aeronautics and
Astronautics
biodynamic
#eab,_ck I 2 _,I.
I m 1 q_
m N
_V 005 .r'_
• to 12,7_z ''''''_ 0I0s---''-----'-
6e --q)M
-|•
-t$
-am
.{,
-zl m tm
'PaeaI
-,.,__j..._
Fig. 14 Root locus diagrams for closed-loop poles of
Fig. 13 Modification of Fig. 3 to model biodynamic
feedback. -_u(s) for different = values in biodynamic
feedback model.
10
American Instituteof Aeronautics and
Astronautics
