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NASA / CR-2000-209863
Motion Cueing Algorithm Development:
Initial Investigation and Redesign of the
Algorithms
Robert J. Telban, Weimin Wu, and Frank M. Cardullo
Department of MechanicaI Engineering
State University of New York, Binghamton, New York
March 2000
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NASA / CR-2000-209863
Motion Cueing Algorithm Development:
Initial Investigation and Redesign of the
Algorithms
Robert J. Telban, Weimin Wu, and Frank M. Cardullo
Department of Mechanical Engineering
State University of New York, Binghamton, New York
National Aeronautics and
Space Administration
Langley Research CenterHampton, Virginia 23681-2199
Prepared for Langley Research Centerunder Contract NAS1-20454
March 2000
Available from:
NASA Center for AeroSpace Information (CASI)7121 Standard Drive
Hanover, MD 21076-1320
(301 ) 621-0390
National Technical Information Service (NTIS)
5285 Port Royal Road
Springfield, VA 22161-2171(703) 605-6000
Table of Contents
Symbols ..................................................................................................................... 3
Abstract ..................................................................................................................... 9
.
2.
.
4.
°
.
.
Introduction ................................................................................................... 11
Background Information ............................................................................... 13
2.1,
2.2.
2.3.
2.4.
2.5.
Effect of Simulator Motion and Human Perception Motion ............. 13Reference Frames .............................................................................. 15
Coordinate Transformation ............................................................... 18
Actuator Extensions .......................................................................... 21
Input Scaling and Limiting ................................................................ 22
Structure of Simulation Software .................................................................. 25
Descriptions of the Four Washout Algorithms ............................................. 29
4.1.
4.2.
4.3.
4.4.
Classical Algorithm ........................................................................... 30
NASA Coordinated Adaptive Washout Algorithm ........................... 35
UTIAS Coordinated Adaptive Washout Algorithm .......................... 40
MIT/UTIAS Optimal Washout Algorithm ........................................ 45
Changes Made in Project to Original Algorithms ......................................... 57
5.1.
5.2.Instability in the UTIAS Adaptive Algorithm ................................... 59
Spikes in the Outputs of NASA and UTIAS Adaptive Algorithms.. 63
Phase 1 Results .............................................................................................. 69
6°1.
6.2.
6.3.
Translational Input Case .................................................................... 69
Rotational Input Case ........................................................................ 73Conclusions and Recommendations .................................................. 75
Changes Made in Project for Phase 2 ............................................................ 77
7.1.
7.2.
7.3.
7.4.
7.5.
New Vestibular and Semicircular Models ........................................ 78
Redefinition of Center of Rotation .................................................... 79
Revised Development of Optimal Algorithm ................................... 82
Nonlinear Gain Algorithm ................................................................ 93
Actuator Extension Limiting ............................................................. 95
8. Phase2 Results..............................................................................................99
8.1, Pitch/SurgeModeandRoll/SwayMode...........................................998.2. HeaveMode ......................................................................................1018.3. PitchMode andRoll Mode...............................................................1018.4. Yaw Mode........................... 1028.5. BrakingAlgorithm ............................................................................102
9. Conclusions...................................................................................................103
References.................................................................................................................105
AppendixA: HumanSemicircularCanalSensationModel....................................107
AppendixB Phase 1 Rotational Output Figures ................................................... 122
Appendix C: Phase 2 Test Run Output Figures ..................................................... 151
Symbols (unless otherwise noted in report)
a(t)
_jS
_jl
A, B, C, D
f
CO, Cl, C2, C3
d, e, y, _., 8, rl
E{ }
El, E2, E3, E4
g
F or F(0
Fr
f
Go
Gc
g
H
acceleration of a point
a function of time which increases from 0 tolt / 2 gradually
the coordinates of the upper bearing block of the j-th
actuator in Frs components
the coordinates of the lower bearing block of the j-th
actuator in Fn components
matrices which define the state-space model of a control
system
a matrix in the state-space model of the standard form optimal
control system
coefficients of the nonlinear gain polynomial
NASA adaptive algorithm washout parameters
mathematical mean of a statistical variable
actuator extensions
pilot's sensation error
a matrix which relates the states of the optimal control
system with the input to the controlled plant
reference frame
specific force = a- g
sensed specific force
a constant in the UTIAS otolith sensation model
UTIAS adaptive algorithm steepest descent parameters
acceleration due to gravity
a matrix related to the white noise input in the state-space
model of a control system
I
Jsub
K
ksub, psub
Ls_
p(t)
p
q
r
Rl, R2, R3, R
P, Pt,Q, Rd
R
s
So, s1
t
Ts
To, TI, 1"2, T3
TF
U,V,W
identity matrix
system cost function
a constant in the UTIAS otolith sensation model
NASA adaptive algorithm steepest descent parameters
UTIAS adaptive algorithm washout parameters
displacement of the i-th hydraulic actuator
transformation matrix from frame Ers into frame F_._
solution of the algebraic Riccati equation
roll rate component of o_
pitch rate component of co
yaw rate component of
weighing matrices in a cost function
weighing matrices in a cost function
radius vector
simulator centroid displacement
Laplace variable
slopes of the nonlinear gain polynomial
time
transformation matrix from angular velocity to Euler angle rates
coefficients in the semicircular canal sensation model
transfer function
x-, y-, and z-components of velocity V
4
u
U'
w
V
W(s)
x,X
w
0
u/
p
t_
co
(Ob
ton
input to a control system
input to a standard form optimal control system
filtered white noise
white noise
velocity V = [u v wIT
optimal control open-loop transfer function matrix
system state vector
output of a control system
output of the pilot's vestibular system
rotation angle of the simulator platform
Euler angles _ = [ _b0 tO ]T
Euler pitch angle component of
Euler roll angle component of _.
Euler yaw angle component of
scalar weight in optimal cost criterion
cost criterion for optimal algorithm
time constants in the semicircular and otolith sensation models
angular velocity about the body frame co = [ p q r ]T
first-order high-pass filter break frequency
second-order system undamped natural frequency
sensed angular velocity
second-order system damping ratio
Subscripts (main symbol)s.bs_
In most cases, subscripts indicate to what the main symbol is related.
()A
()_
()CA
()CO
( )O
( )O_
( )_
()_
( )L
()n
()o,o
( )pA
(_S
( )S
()SR
( )_
( )ST
( )V
()_y_
relates to aircraft
relates to aricrait rotation
relates to aircraft point corresponding to simulator centroid
relates to center of gravity of aircraft
relates to simulator states included in the cost function
relates to filtered white noise disturbance model
relates to desired output
relates to inertial reference frame
relates to low pass filtering
relates to white noise input states
relates to otolith model
relates to pilot in aircraft
relates to pilot in the simulator
relates to reference model
relates to simulator
relates to simulator rotation
relates to semicircular canals sensation model
relates to simulator tilt coordination
relates to pilot's vestibular model
x,y, or z components
6
Su_rscripts (main symbol) su_m_ipt
In most cases, superscripts indicate which frame the main symbol is in
( )A
( )_
( )s
inaircraft frame FrA
in inertial frame Frl
in simulator frame Frs
This Page Intentionally Left Bl_tk.
8
Abstract
This project was conducted in two phases. In Phase I, four algorithms including
the classical algorithm, the NASA adaptive algorithm, the UTIAS adaptive algorithm,
and the optimal algorithm were investigated. The classical algorithm generated results
with more distortion, more delay and lower magnitude than the results generated by the
other three algorithms. The classical algorithm is the fastest one. This is of little
importance since today's computers are fast and none of the four algorithms will run
beyond the required time. Therefore, the classical algorithm has no advantage and was
not considered in Phase 2.
The two adaptive algorithms are basically similar. The NASA algorithm is well
tuned with satisfactory performance. The UTIAS adaptive algorithm strives for more
flexibility, but results show that it does not behave better than the NASA algorithm while
having more undesirable properties. Some changes were made to the adaptive algorithms
such as reducing the magnitude of undesirable spikes.
The optimal algorithm was found to have the potential to behave much better than
it did in Phase 1. In Phase 2, the optimal algorithm was redesigned. The center of
simulator rotation was redefined. More terms were involved in the optimal algorithm
cost function to yield more flexibility in tuning the algorithm. A new design approach
featuring a Fortran/Matlab/Simulink interactive design was used. Each set of selected
parameters could be tested in only 30 seconds while the old design approach could
require as much as 15 minutes. This makes it possible to try hundreds of sets of
parameters. As a result, the optimal algorithm was well tuned in Phase 2 that also
incorporated a revised vestibular sensation model.
Theeffect of motion wasalsodiscussed.Thetopic coverswhat typeof motion is
desirableand what type is undesirable. A new semicircular canal sensation model was
constructed and justified. The discussion and the new sensation model helped to develop
the optimal algorithm and to evaluate the motion-base driving algorithms.
In Phase 2 comparisons were made between the NASA adaptive algorithm and
the redesigned optimal algorithm. Results showed that the optimal algorithm has some
advantages over theNASA adaptive algorithm and might be the best among the four
algorithms involved in this study. At the same time the NASA adaptive algorithm was
observed to be a very well developed algorithm.
There were some general problems left unresolved in Phase I that required
solutions. The first problem was that when inputs had large magnitudes, all the
algorithms tended to drive the simulator beyond its motion limit. A new nonlinear gain
algorithm was designed in Phase 2, the effect of which was that the simulator would not
reach its motion limit in most input cases, while the gain in low magnitude input cases
remained high. The second problem was that when the simulator reached its limit, an
algorithm was needed to brake the simulator to a full stop and then release the brake at
some proper time to allow the simulator to follow the output of the washout algorithm
again. This braking algorithm was developed in Phase 2.
10
1. Introduction
With continuing improvement in hardware and soi_are, flight simulation plays
an expanding role in the training of aircral_ crews, design of new aircraft, and
entertainment. This study evaluates a motion-base driving algorithm for a modem six-
post synergistic aircraft simulator. Three types of algorithms, classical, adaptive, and
optimal, axe evaluated within the scope of this study. Some implemented cueing
algorithms were first investigated, with some efforts then spent to improve or even re-
design them.
The purpose of a motion simulation is to provide task-critical motion and force
information (i.e., cues) and any required components of the stressor-induced workload
increment that would be present in flight. Since a ground-based flight simulator system
cannot duplicate the motions of an actual aircraft, it becomes necessary to determine the
best way to utilize its limited capabilities to provide the most necessary and beneficial
motion cues. It is also critical for the cueing algorithm to avoid any improper motion
cues since it is commonly known that improper motion cues in some flight conditions
have great negative effects on the simulation. It is reported that some motion systems
experienced being turned off to avoid improper motion cues. A principle component of a
motion simulator design is the determination of the motion information that is relevant to
the task, can impact human performance, and can be provided within technical and
economic constraints. This requires some knowledge regarding the human's motion
perception that is therefore also an important portion of this study.
The motion system usually works in conjunction with a visual system to
accomplish effective simulation. Although some of the aspects of the visual system are
11
taken into consideration in this study, a detailed study of the visual system or the co-
operation of the two systems is beyond the scope of this research.
This project was conducted in two phases. In Phase 1, four motion cueing
algorithms, the classical algorithm, the NASA adaptive algorithm, the UTIAS adaptive
algorithm, and the optimal algorithm were investigated. The results of these algorithms
were compared with modifications made to correct problems observed with both the
NASA adaptive algorithm and the UTIAS adaptive algorithm. In Phase 2, the NASA
adaptive algorithm and a redesigned optimal algorithm were further investigated, with the
optimal algorithm incorporating a revised model of the human vestibular system.
General problems common to all algorithms not resolved in Phase 1 were also addressed
in Phase 2.
The motion cueing algorithms are intended to drive the MCFADDEN 676B-B046
simulator at the NASA Langley Research Center. The simulator is a hydraulic six-post
synergistic full motion simulator.
12
2. Background Information
2.1. Effect of Simulator Motion and Human Motion Perception
The goal of the motion system, along with the visual system, is to provide a
virtual environment to the pilot so that in a simulator the pilot can perform the controls
and maneuvers which are consistent with how they are to he performed in a real aircraft.
The simulation can be employed to help in the design of new aircraft, the gaining of
pilots, and research. What is critical to understand is whether motion helps the
simulation and what kind of motion is really desirable. Although early studies showed
some controversy on the effect of motion on aircraft simulation, results of further studies
converged to some consistent conclusions.
2.1.1. Effect of Motion Cue
Gundry [1] reported that Douvilier, et al., Matheny, et al., Perry and Naish, and
Tremblay, et al. found that although motion did not always help to reduce pilot
performance error in some simulation tests, there were always differences in the pilot
control activity power spectra. When motion was provided, there was an increase in the
occurrence of high-frequency/low amplitude control movements. These changes served
to make the control activity in the moving simulator appear more like that observed
during flight than that recorded in a fixed base simulator. The presence of motion was
found to reduce phase lag, increase the mid-frequency gain and crossover frequency, and
reduce the size of the remnant.
Gundry [1] also reported that Sadoff, et al., and Meiry found that when the
simulator dynamics were stable, the presence of maneuver motion did little to improve
control. But as the vehicle became unstable, maneuver motion became more important;
13
its presence allowed the operator to exercise control even in regions where control by
visual cues alone would be impossible.
The visual system alone could provide motion illusions in many simulation tests.
It was found that as long as there was some proper simulator motion at the beginning of
each maneuver, the motion illusions introduced by the visual system could be established
more easily and faster. In some simulation cases the motion illusions could exist all the
time after its establishment without continuing involvement of simulation motion. This
implies that the simulation motion onset requires high attention.
Improper simulator motion could be very harmful for it might conflict with the
visual cue and then break the motion illusions introduced by the visual system. The
motion cue that conflicts with the visual cue is called a negative motion cue in the
literature. Negative motion cues should always be avoided whenever possible.
Clark, et al. [2] found that a pilot's vestibular system could process low level,
constant acceleration in the presence of vibratory acceleration as efficiently as it could
without the vibratory noise. In other words, vibratory acceleration had little or no
masking effect on the detection of constant acceleration over a wide range of intensity
levels of constant acceleration. This implies that it is not practical to employ vibrations
to mask some motion sensation such as the rotational sensation when the simulator tilts to
simulate sustained linear acceleration.
2.1.2. Human Motion Perception
As pointed out in the UTIAS report [3], [4], deriving the human's motion
sensation models is important for the evaluation of motion-base drive algorithms and the
formulation of the optimal control algorithm. The human vestibular system located in the
14
head is found to be dominant in human motion sensation. The vestibular system consists
of two important parts. One part is the semicircular canals that sense rotational motion
and the other are the otoliths that sense linear motion. The UTIAS report [3], [4]
provided models for both the semicircular canaIs and the otoliths.
The semicircular canal sensation model is given as:
(0 "CL'Cas2-- = (2-1-1)
(ZLS+I)(ZsS+I)(Z aS+I)
where 0) is the angular velocity input and _ is the sensed angular velocity. ZL, XS, and za
are time constants. The model represents a second order torsion pendulum with an
adaptation term. ZL has a unique value for each rotational degree of freedom: 6.1 sec (roll
input p), 5.3 sec (pitch input q), and 10.2 sec (yaw input r). Xs = 0.1 sec and "ca= 30 sec
for all three degrees of freedom.
The otolith sensation model is given as:
f" K(%s + 1)-= (2-1-2)_f (%s+l)('css+l)
where £ is the input specific force and _ is the sensed specific force. %, "rs, and "caare
time constants and K is also a constant. "cL----5.33 sec, "rs = 0.6 sec. "ca= 13.2 sec, K = 0.4.
2.2.Reference Frames
In describing the development of motion cueing algorithms it is convenient to
employ several reference frames. These reference frames are defined below and are
shown in Figure 2.1.
15
2.2.1. Frame Frs
The simulator reference frame Frs has its origin at the centroid of the simulator
payload platform, i.e. the centroid of the simulator's upper bearing attachment points. It
is fixed with respect to the simulator payload platform. Xs points forward and Zs
downward with respect to the simulator cockpit. Ys points toward the pilot's right hand
side. The x-y plane is parallel to the floor of the cockpit.
2.2.2. Frame Fr^
The aircraft reference frame FrA has its origin at the same relative cockpit location
as the simulator reference frame Frs. FrA has the same orientation for XA, YA, and ZA
with respect to the cockpit as the simulator frame Frs.
2.2.3. Frame FrcG
The aircraft center of gravity reference frame FrcG has its origin at the center of
gravity of the aircraft. Frame FrcG has an orientation for Xc_, YcG, and Zc_ that is
parallel to reference frames Frs and FrA.
2.2.4. Frame Fr_
This is a frame attached to the simulator pilot's head with its origin located at a
point midway between his left and right vestibular systems. Frame Frps has an
orientation for X_, Y_, and Z_ which is parallel to FrA and Frs.
2.2.5. Frame FrpA
This is a frame attached to the aircraft pilot's head with its origin located at a point
midway between his left and right vestibular systems. Frame FrpA has the same
orientation for Xp^, YPA, and ZpA as Fr_.
16
2.2.6. Frame Frl
The inertial reference frame Fr_ is earth-fLxed with Z1 aligned with the gravity
vector g. Its origin is located at the center of the fixed platform motion base. X_ points
forward and Y_ points to the right hand side with respect to the simulator pilot.
2.2.7. Reference Frame Locations
In Figure 2.1 are four vectors which def'me the relative location of the reference
frames. R, defines the location of Frs with respect to Fr_. Ks defines the location of FrPs
with respect to Frs. Similarly, KA defines the location of FrpA with respect to FrA. ]?_cc
defines the location of FrA with respect to Frco.
XpA
Fr^ XA
Aircraft Xs
Simulator
/zs
Figure 2.1. Reference Frame Locations.
Frl Xl
Zi
17
2.3. Coordinate Transformation
Consider a body having both translational and rotational motion with respect to
Fn. In Figure 2.2, the inertial translational acceleration of a point b on the body located
at a distance 8_ = 8_ + 8y] + 8_fc from the origin of any body reference frame FrB can be
expressed by:
_a'b =_a_ +_ +2co_ ×&_ +_ xS__ +co_ x(o__ xS__) (2-3-1)
where
ia B is the acceleration of the origin of FrB with respect to Fn.
_ is the angular rate of FrB with respect to Fn.
p,q,r are the three components of _, i.e., _ = p _ + q ] -_r 1_.
Assuming point b is fixed with respect to FrB, then _ = 8__ = 0.
i., (G×82)a_ = a B+Co BxSb x _
I= a_B + [--8_(q 2 + r2)+Sy(lXl-i)+8,(pr+d.)]
+ [ 8_(pq+i) -Sy(p 2 +r2)+8,(qr -15)]]
+[
Frl
Figure 2.2.
8,(pr-_l) +Sy(qr+ 15)-8.(p 2 +q2)] 1_
XB
ZB
Coordinate System for Inertial Acceleration.
(2-3-2)
18
2.3.1. Euler Angles
The orientation between two reference flames Fri and FrB can be specified by
three Euler angles: _ = [_ 0 W]T which define a sequence of rotations which will carry
Fr_into FrB. A vector V expressed in the two frames can be related by the transformation
matrix Lm ( Frl --) FrB ) or Lm ( FrB ---*Frl ):
vB=LIBV I and VI=LBI VB
where
Lm = ]L,_ = L_I
LBI =
cos Ocos
cos 0 sin gf
- sin0
sin t_sin 0 cos _ - cos t_sin
sin t_sin 0 sin _ + cos t_cos
sin _ cos 0
(2-3-3)
cos _ sin Ocos V + sin _ sin V-
cos _ sin Osin _- sin _ cos
cos_cos0
The angular velocity of FrB with respect to Fri can be related to the Euler angle
rates _ by the following.
frame FrB, then
where
and
where
Let _ represent the components of this angular velocity in
TB = cos_ -sin_ / (2-3-4)sin_ sec0 cos_sec0J
I!°T;' = cos, -sin_
- sin0
sin _ cos 0
cos _,cos O
19
PAYLOAD
PLATFORM
Al
1
FIXEDPLATFORM
Figure 2.3. Illustration of a Six Post Synergistic Motion Base Geometry.
20
2.4. Actuator Extensions
The geometry of a six degree-of-freedom synergistic motion base is given in
Figure 2.3. The relevant vectors relating the locations of the upper and lower bearings of
the j-th actuator are shown in Figure 2.4:
R,
O
Os Aj_-----___.___.
_Bj
Figure 2.4. Vectors for the j-th actuator.
In Figure 2.40s and Oi are the centers of the payload platform and fixed platform
respectively. Os and Oi are respectively the origins for Frs and Frl.
It can be seen that the relation among those vectors is:
_R,+A_j= Rj = B'j+_ej (2-4-1)
Then the actuator length vector can be found from:
=_A]÷_R,-_B'j (2-4-2)
Expression of -_i in Frl is desired:
(2-4-3)
21
Where A_ are the coordinates of the upper bearing attachment point of the j-th actuator
in Frs and _B_BI are the coordinates of the lower bearing attachment point of the j-th actuator
in Fn.
The actuator extensions can then be found from
Ataj(t) = ti(t ) - _j(0)
= (Ls,(t)-Ls,(0))A _ +(S'(t)- S'(0))
Usually Ls_(0 ) = I and S_(0) = 0, where I is the identity matrix. Therefore.
A_tI -- + AS_'
Using small angle approximation tO.,s_ can be expressed as:
0
ALsl = W s
-0 s
-_s 0s
0 -%
Cs 0
(2-44)
(24-5)
(2-4-6)
Employing Equations (2-4-5) and (2-4-6) the actuator extensions can then be calculated.
It is observed that a smaller AIj will result in smaller actuator extensions for a given
simulator rotation angle. This information might be useful for simulator hardware
design.
2.5. Input Scaling and Limiting
Scaling and limiting are applied to both aircraft translational input signals a_ and
rotational input signals ^__^. Scaling and limiting modify the amplitude of input
uniformly across all frequencies. Limiting is a nonlinear process that clips the signal so
22
that it is limitedto belessthanapreselected magnitude. Scaling and limiting can be used
to reduce the motion response of a flight simulator. Two input scaling and limiting
algorithms were used in the current simulation software. They were suggested and used
in [3], [4], and [5].
2.5.1. Linear Input Scaling in Combination with an Input Limiting
The first algorithm is characterized by a linear input scaling in combination with
an input limiting. Each component of _a_ and ___
scaled and limited separately but in the same manner.
x component of _a,_is given as an example, where S,, is the slope from -Xl to X1:
Sxah _a x = SxX_
- S_X 1
in different degrees of freedom is
The scaling and limiting of am, the
[a_,ol-< Xl
a_ >_X_
a_ <-X_
(2-5-1)
OUTPUT
* INPUT
Figure 2.5.1. Linear Input Scaling.
2.5.2. Nonlinear Input Scaling
The second algorithm is characterized by a nonlinear input scaling. Input limiting
is not used. Each component of a_ and o__ in different degrees of freedom is scaled
23
A
separately but in the same manner. The sealing of aAx, which is the x component of a^,
is used as an example:
Sxax °a x = Sxaxo - 0.7S x(axo - X t )
S_a_ ° 0.7S_(ax ° +X 1)
la_ol_<X_
axo > X_
axo <-X 1
(2-5-2)
s x,
OUTPUT SLOPE = 0.3 S_/
/
./
x_ INPUT
-Sx_
Figure 2.5.2. Nonlinear Input Scaling.
24
3. Structure of Simulation Software
The execution of the software begins with input of a set of simulation commands.
The simulation commands contain selection of input degree of freedom, input type, input
magnitude and duration, duration of simulation, and type of cueing algorithm. Each of
the input channels for six degrees of freedom can be selected. Maximum duration of
simulation is set to be 40 seconds. There are six aircraft input options: step, pulse, pulse
doublet, sinusoidal, half sine pulse, and ramp to step. Aircraft translational acceleration
at the point corresponding to the centroid of the simulator payload platform ac_ and
aircraft angular acceleration "^to^ are used as input vectors.
From the aircraft inputs the aircraft response and the simulator response are both
calculated. Next the aircraft pilot's sensation and the simulator pilot's sensation are
calculated and compared. Actuator extensions are generated based on the simulator
responses output by the cueing algorithm.
The aircraft response is assumed to follow the input command without error.
Then the acceleration at the pilot's head aA^ can be calculated from ac^^ and _A'^ By
subtracting the gravity vector g the specific force on the pilot's head f_ can next be
calculated. By passing _,_ and f_ through the vestibular model the aircra__ pilot's
sensation will be generated.
The simulator response is calculated by passing the aircraft commands through
the selected cueing algorithm and the platform dynamics filter. The cueing algorithms
are the kernels of this software. They are responsible for maximizing the motion cueing
effects while restricting the physical motion to be within the displacement, velocity and
acceleration capacity of the motion system hardware. The cueing algorithm outputs the
25
desired translational and rotational platform positions S__ and [3s_ which are used to
compose the desired actuator commands g_ that will drive the simulator platform.
In a real simulation, the platform dynamics will cause some error between the
platform motion and the motion commands. Passing the motion commands through a
filter that is a model of the platform dynamics can simulate this. Then the filter outputs
[3s and S l are assumed to be the real platform positions. Based on _-s and _SI both the
simulator translational acceleration _ and angular rate _ss may be obtained. The
specific force on the simulator pilot's head fs is also available. By passing _ and fs
through the vestibular model both the sensed angular rate and sensed specific force are
obtained. The flowchart of the simulation sol,are is shown in Figure 3.1.
26
USER CHOOSES TYPE OF FILTER; DURATION OF
SIMULATION; INPUT DOF; INPUT TYPE,MAGNITUDE AND DURATION OF INPUT.
• A A t_A _ aCA
TO PILOTS [
A HEAD [m__A
L
i_-----_ g
TRA_iFORMTO EULERANGULAR
RATE
V]:_STIBULJ_.R [
IMODEL
J_A L
(ANGULAR RATE ANDSPECIFIC FORCE SENSED
BY AIRCRAFT PILOT )
aAA = avA FOR OPT. ALG. PHASE 1
a_ ac_ FOR OTHER ALGs. & OPT. P2
CUEING
ALGORITHM
-_s,_ S_ |EXTENSION -_
>[ALGORITHM
PLATFORM [
DYNAMICS [
ACTUATOR I _
£4
VESTIBULARMODEL
i ,L(ANGULAR RATE ANDSPECIFIC FORCE SENSED
BY SIMULATOR PILOT )
i TRANSFORM TOiSIMULATOR FRAME
ANGULAR RATE
Figure 3.1. Overall Structure of the Software
27
This Page Intentionally Left Blank.
28
4. Descriptionsof the Four Washout Algorithms
Four algorithms are used in this study. The first is known as the classical
algorithm. This type of algorithm is generally denoted in the literature as a linear cueing
algorithm [3], [4]. The second algorithm evaluated in this study is the NASA Langley
Research Center developed "Coordinated Adaptive Washout Algorithm" [5]. The next
cueing algorithm reviewed in the study is a variation of the Coordinated Adaptive
Washout Algorithm. This was developed by L. Reid and M. Nahon at the University of
Toronto [3], [4]. The Optimal algorithm, the fourth algorithm employed in this study is
that developed at MIT by Sivan, et al. [6] and implemented as described in [3] and [4].
The basic task of the washout algorithms is to create a specific force vector and an
angular velocity vector at the pilot's location in the simulator approximating those that the
pilot would experience in an actual aircraft. The translational and rotational motion
effects on the simulator pilot are expected to approximate the motion effects on the
aircraft pilot:
A_f__-_f_^,_ - __p^
The relation between the specific force acting on the simulator (aircraft) pilot and the
specific force at the origin of the simulator (aircraft) frame can be found from Equation
(2-3-2):
fs = aS_gSw
_-__s+o__×_Rs+o__×(o__×g_)- gS=f_+_ss×_R_+___,,(__s,,R__)
_f_,=__,,_-g"=_ +o__,,_,, +o__×(_ ×R_,,)-g^
29
Usually R^ = Rs, ¢0_ = cos , cot = coP_" Thus the washout algorithms attempt to
achieve:
_f__ft --.t-gA
co__co_
_ft,o__Iorat, cot areu_edasw_houtalgorithminputs.
4.1. Classical Algorithm
This algorithm employs aircraft body axes acceleration a t and angular velocity
co_ as the aircraft state vector elements that provide the input to the cueing algorithm. A
linear scaling in combination with a limiting as described in Section 2.5 is applied within
the algorithm to modify the input. The architecture of the classical approach is such that
there are separate filters for the translational degrees of freedom and the rotational
degrees of freedom with a crossover path to provide the steady state or gravity align cues.
This algorithm behaves like open-loop control. The details of this algorithm are
presented below.
4.1.1. Translational Degrees of Freedom
The aircraft acceleration vector a t is first scaled and limited. This scaling can be
either linear or nonlinear. It should be noted at this point that it is not the scaling that
makes the cueing algorithm either linear or nonlinear, but rather it is the formulation of
the washout filters that is responsible for that characteristic. For the classical algorithm a
scaling and limiting scheme as described in Section 2.5.1 is used. ARer scaling and
limiting, the aircraft specific force _ is computed and then transformed from the
3o
simulator frame Frs into the inertial frame Frl, whereupon the inertial frame vector
subtracts the gravity vector, with the difference f_2 filtered by a high pass filter (transfer
function) of the form
S3
TF = (s 2 +2qo°s+o20)(s+o_ ) (4-1-1)
Where On is a second order system undamped natural frequency and CObis a first order
system break frequency, q is a second order damping ratio. The output is then
integrated twice to provide the simulator translational position S_.
4.1.2. Rotational Degrees of Freedom
The rotational rate vector is first scaled and limited by the same scheme for the
translational channel. The resulting vector is transformed to the Euler angular rate. The
Euler angular rate is then filtered through a high-pass filter (transfer function) of the form
S 2
TF= (s+ob) 2 (4-1-2)
The output is then integrated to provide the desired simulator Euler angular position
corresponding to the aircraft rotational input.
4.1.3. Tilt Coordination
Sustained translational acceleration is sensed by the pilot as a long term change in
the magnitude and direction of the specific force in the absence of rotational motion.
This cannot in general be simulated by translatio_2J motion due to motion-base travel
limits. It is possible to alter the direction of the steady-state specific force experienced by
the pilot in the simulator by tilting the cab. It has become common practice in flight
simulators to employ cab tilt to simulate the effect of sustained translational inertial
31
acceleration. Because this tilt coordination process cannot alter the long term magnitude
of the specific force vector, it is an approximation to the desired effect. [3], [4]
The formulation of the tilt coordination Euler angles _--STstarts with aLA as shown
in Figure 4-1-1. a_ is formed by filtering a_ through a low pass filter of the form:
20) n
TF = s2 + 2qto ns + co_ (4-1-3)
fLA Can be considered to be the specific force components that are to be simulated
through simulator cab tilt. In the absence of other cab rotational displacement and
translational motion, fLA in FrA is shown in Figure 4.1.1 (a). By tilting the simulator cab
can be rotated with respect to Frs _igure 4.1.1 (b)). It is found that this change in
the direction of the sensed sustained specific force by the simulator pilot is quite useful in
the simulation of low frequency aircraft acceleration components. When the desired tilt
angle a, -- a0, _f_= k _f_, wherek --g/If_l, _f_is successfiflly aligned. It is easy to
see that the desired tilt angles a _ are:
=tan (-f_y / g) _, -f_y / g)SL -I A
0SL = tan-'(f& / g) _ f_x / g
32
_gl
FrA=Frx
(a)
czl _f_ =-gl Frs
1
b)
Figure 4.1.1. Simulator Cab Tilt
_-sx is usually restricted under the threshold of pilot perception for avoiding undesired
cue.
4.1.4. Summation of Two Rotational Channels
The summation of __sTand _-sR will yield [3s, the angular position of the
simulator. Lsl and Ts can be formed by Equations (2-3-3) and (2-3-4). Then the
simulator translational position S__ and the angular position [3s can be transformed from
degree-of-freedom space to actuator space. These are the actuator lengths required to
achieve the desired platform translation.
The block diagram for the classical algorithm is shown in Figure (4-1-2).
33
_ -
_-.'7
÷! i
l.-_ IN_ ,
r_
-t-
E_
roar
T81
m
'N
m
_4
7..,
34
4.2. NASA Coordinated Adaptive Washout Algorithm
This algorithm was developed at the NASA Langley Research Center in 1977.
The intent of the algorithm is to adapt the severity of the simulator washout filters
according to the current state of the simulator. In this way it should be possible to make
full use of the simulator motion system at all time. This algorithm also employs
a A and _ as the input to the cueing algorithm. A nonlinear scaling as described in
Section 2.5 is applied to modify the input. The general architecture is similar to the
classical algorithm in the aspect that there are separate filtering channels for the
translational degrees of freedom and the rotational degrees of freedom with a crossover
path to provide the steady state or gravity align cues. The block diagram for this type of
adaptive algorithm is shown in Figure 4-2. The signals -f_land __^ represent the inertial
frame acceleration components and Euler angles which if applied to the simulator frame
Frs will produce specific force and rotational velocity components in Frs identical to the
corresponding FrA components in the aircraft. _^ is passed through the rotational channel
with an adaptive gain ;5to produce a simulator angular rate command. The gravity vector
g is added to f_ to yield a new specific force f1_ that will actually be simulated as
simulator motion, fl2 is passed throu_ a translational channel with an adaptive gain _. to
produce a simulator translational acceleration command and passed through a crossover
tilt channel with a fixed gain _, to generate a simulator angular rate command. These
commands drive the simulator to the desired translational and angular positions.
and_ _ are employed as feedback as shown in Figure 4-2. Adaptive parameters
_. and _5 are continuously adjusted according to the current state of the simulator and
35
aircraft input. The control equations for this cueing algorithm are presented below. The
motion equations are separated and dealt with as four parallel modes: pitch/surge,
roll/sway, yaw, and heave.
4.2.1. Pitch/Surge Mode
Control law:
(4-2-i)
where dx,e x & "/x are fLxed parameters for the pitch/surge mode; k x andfi x are the
pitch/surge adaptive parameters which are continually adjusted in an attempt to minimize
the instantaneous value of the cost function.
Cost function:
1 +__({_^ + +__X2Jx = _-(f_ -X) 2 -0s) 2 -b-_-x 2 (4-2-2)
where Wx, bx, and Cx are constant weights which penalize the difference in response
between the aircraft and simulator, as well as restraining the translational velocity and
displacement in the simulator.
Steepest descent for the adaptive parameters:
c_Jx
i., = -K,.. +K,,..(X,o-
(4-2-3)
OJ_
.g,, = -K_ "_7 + K_, (8,,o - 8,, )
where K_,,K_.,Ks, and Kis" are constants. The first right hand side term of each
equation in (4-2-3) defines that the change of the adaptive parameter (kx or _) is toward
a minimum cost function _had also defines the rate of change together with the second
36
fight hand side term. The second fight hand side term also restrains the deviation of
either _,x or G from their original values.
4.2.2. Roll/Sway Mode
The control law, cost function and steepest descent for the adaptive parameters
are in the same form as for the pitch/surge case. Therefore by a substitution of y for x
and 6 for 0 the roll/sway motion equations may be obtained. Note that the adaptive
parameters, cost function weights and steepest descent constants are unique for the
roll/sway mode with a subscript y replacing the subscript x.
4.2.3. Yaw Mode
Control law:
where e_ is a fixed parameter while rl_, is an adaptive parameter.
Cost function:
1 b_,
-ks)2 +T s 2
where b v is a constant weight in the cost function.
(4-2-4)
(4-2-5)
37
Steepestdescent:
aJ_/1_, = -K,h, _ + Ki, 1 (ri,_o - rl_,)
C3rl_, v
where Kn, and Kin , are constants.
4.2.4. Heave Mode
Control law:
where rl, is a fixed parameter while dz and ez are adaptive parameters.
Cost function:
1 f I + ___ Z 2 22Jz = _( z - z) _ +-_
where bz and Cz are constant weights in the cost function.
Steepest descent:
aJzfi, = -Kn. _ + Ki_ (rl, 0 - rIz )
0rl,
where Kn. and K,_. are constants.
(4-2-6)
(4-2-7)
(4-2-8)
(4-2-9)
38
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m _
j-
T+ 1 41"1
E]
E
B]81
8_
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39
4.3. UTIAS Coordinated Adaptive Algorithm
This algorithm was developed at the University of Toronto in 1985. The general
philosophy and structure of this algorithm are the same as those of the NASA adaptive
algorithm. The UTIAS adaptive algorithm adapts the severity of the simulator washout
filters according to the current state of the simulator. _a_ and (o A are the input to the
cueing algorithm. A linear scaling in combination with a limiting as described in Section
2.5 is applied to modify the input. The block diagram is shown in Figure 4-3. The
signals fl and _A represent the inertial frame acceleration components and Euler angle
rate which if applied to the simulator frame Frs will produce specific force and rotational
velocity components in Frs identical to the corresponding FrA components in the aircraft.
_^ is passed through the rotational channel with adaptive gain p,a to produce a simulator
angular rate command, f_2 is passed through a translational channel with an adaptive
gain Pxl to produce a simulator translational acceleration command and passed through a
crossover tilt channel with an adaptive gain p_2 to generate a simulator angular rate
command. These commands drive the simulator to the desired translational and angular
positions. _i and SI_ _ are used as feedback as shown in Figure 4-3. Adaptive parameters
P,,I, Px2 and p_ are continuously adjusted according to the current state of the simulator
and aircraft input. The difference between the UTIAS and the NASA adaptive
algorithms is that the UTIAS algorithm made more pa, arneters adjustable and employed
more terms in the cost function in an attempt to improve the effect of the adaptive
washout filter. The parameter in the crossover tilt channel is adjustable in the UTIAS
algorithm and remains fixed in the NASA algorithm. The absolute values of [3 and f3
4o
alongwith thedeviationof the adaptive parameters from their initial values are employed
in the cost function. The control equations for this cueing algorithm are presented below.
The motion equations are separated and dealt with as four parallel modes: pitch/surge,
roll/sway, yaw, and heave.
4.3.1. Pitch/Surge Mode
Control law:
SI x = Pxlflx -kxlSIx - kx2glx (4-3-1)
Os = lim(px2 f_x) + Px3 ().
where kx_ and kx2 are fixed parameters and parameters pxl, px2, and p_ are adaptive
parameters which are continually adjusted in an attempt to minimize the instantaneous
value of the cost function.
Cost function:
Jx = 0.5 [ Tx (f_x- Stx)2 + Wxl(Ox - ()s)2
+ px(w,_s'x2 +w,_s'_2+ Wx,6_+wx5o_)+ Wx6 (Pxl - PxlO) 2 + Wx7 (Px2 - Px20) 2 + Wx8 (Px3 - Px30) 2 ]
(4-3-2)
where l'x, px, and Wxi are constant weights. In (4-3-2) the first group of terms in the
cost function penalizes the difference between the aircraft and simulator responses. The
second group restrains the translational velocity and displacement of the simulator. The
third group restrains the deviation of the adaptive parameters from their original values.
41
4.3.2. Roll/Sway Mode
The control law and cost function are in the same form as for the pitch/surge case.
Therefore by substituting y for x and dpfor 0 the roll/sway equations may be obtained.
4.3.3. Yaw Mode
Control law:
_s= P, _^- kv] _s dt'k_2_s (4-3-3)
where k_,_ and k_2 are fixed parameters and p, is an adaptive parameter.
Cost function:
J,_ = 0.5 [(_/A- _/S) 2 +P_, (W,, _/S2 + Wv2 _gs2) + Wv3(p_ - pro):]
where Pv and W_,i are constant penalty weights.
4.3.4. Heave Mode
Control law:
_i = p_ flz _ k_, ISi_dt o k., Siz - k_ si.
where kzi are fixed parameters and pz is an adaptive parameter.
Cost function:
_ "'i2 "12 S_z,)_Jz = 0.5 [(f_z s_) + o_(w_]s_ + w., + w_ (pz- p_0)2]
where pz and Wzi are constant penalty weights.
(4-3-4)
(4-3 -5)
(4-3 -6)
42
4.3.5. Steepest Descent for the Adaptive Parameters
For all four channels the steepest descent has the same form:
0 J...._.._c (4-3-7)lb,.j= - G,.j c3Pcj
With the subscript c corresponding to x, y, and z, for _ the subscript j corresponds to 1,
2, and 3, and Gc are constants.
43
81
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44
4.4. MIT/UTIAS OptimalWashoutAlgorithm
4.4.1. OptimalControlTheory
A linear optimal control theory can be applied to the aircraft simulation problem.
The defmitions and solutions of linear optimal control problems have some simple
standard forms, which make it convenient to apply the optimal control theory and fmd the
solution to a specific optimal control problem.
I. Deterministic Linear Optimal Regulator Problem
The problem can be illustrated by Figure 4.4.1. The problem is to determine
some constant matrix F that relates the control system input u to the system states x and
minimizes the optimal criterion J.
u XJ System I ._
"l Dynamics I
-F __
Figure 4-4-1.
System equations:
'_x_= A_x + Buy = Cx with x = x(O) at t = O.
Criterion: J= fi[xTR_ _x + uTR2 u]dt + xT(t_)P_ _x(t_)
which
Deterministic Linear Optimal Regulator.
The problem, of determining an input u for
deterministic linear optimal regulator problem.
J is minimized
(4-4-I)
(4-4-2)
is called the
45
II. Stochastic Linear Optimal Regulator and Tracking Problems
(a) Regulator Problems with Disturbances: the Stochastic Regulator Problem
The problem can be illustrated by Figure 4.4.2. Disturbance input v is a filtered
white noise with limited bandwidth. The problem is to determine a constant matrix F that
determines u by relating it to the system states x and the disturbance input v so that the
optimal criterion J is minimized.
System equations:
w1Noise Filter
V
- _tem
-T -,° I, Ve-1
x
F1, F2 are partitionsof F.
FfIF1 F21
Figure 4.4.2. Stochastic Linear Optimal Regulator.
__= Ax_+Bu+ v
y= Cx
i'_x,_= A,l_ x_di_+ w
__v= Cdt, Xdi_
w is white noise. (4-4-3)
Define _ = , thenS
46
I c ,l FBI Fol
A .J LoJ-L_ J
Optimal criterion:
where Rl = C x R3 C,
defined as the mathematical mean of a statistical variable.
(4-4-4)
(4-4-5)
, Ri, R2, Ra, and P1 are constant matrices, and E is
Co) Stochastic tracking problems.
This problem can be illustrated by Figure 4-4-3. _ is the state of a reference
system which has a white noise input, x is the state of the control system which strives
for following the reference system. The problem is to determine a constant matrix F
which determines u by relating it to the state of the reference system _ and the state of
the control system _xso that the optimal criterion J is minimized.
w [ Reference I Xr-_ System "_
m
m u(t) _[
System I x(t)
Dynamics [ i -_
F1, F2 are partitions
of F.
F=IFI F2]
Figure 4.4.3. Stochastic Tracking Problem
47
System equations:
f __=Ax+B_u
y=C_x
i_ = A_Xr + w
y_ = C,x,
w is white noise.
Define Exl= , then
Xr
0 B
IAAroIu+E°IYmY--Yr _--[C -Cr]X
(4-4-7)
Optimal criterion:
J=E { ._[(_y- y,)TR3(Y-y_)+ uTR2u] dt }
(4-4-8)
where R1 = [C -Cr]TR3 [C -Cr]
Equations (4-4-6) and (4-4-8) can be generalized in a common standard form:
System equation: __= A_x + Bu + Hwy = C_x(4-4-9)
Optimal criterion: (4-4-10)
where Rm and RE are constant matrices and E is defined as the mathematical mean of a
statistical variable.
48
III. Solution to the Optimal Control Problems
There is a common linear optimal solution for the deterministic regulator
problem, the stochastic regulator problem and the stochastic tracking problem. The
solution has a standard form:
u = - F x (4.4-11)
where
F = R_ 1B T P(t) (4-4-12)
and P(t) is the solution to the algebraic Riccati equation:
-#=R_-PBR 2B rP + PA + ATP (4-4-13)
with boundary conditions x = x(0) at t = 0 and P(tl) = Pl.
When t_ approaches infinity, it is proven that P has a steady-state solution which satisfies
the equation:
0=RI-PBRxB _P + PA + A'rp (4-4-14)
4.4.2. Aircraft Simulation Problem Definition
The problem is to detem_e a linear filter matrix W(s) which relates the simulator
motion states its to the aircraft motion states 11A SO that some cost function or criterion
which constrains the pilot's sensation error e and the simulator motion simultaneously
will be minimized. The structure of the problem is illustrated in Figure 4.4.4.
49
Aircraft States u_
w
Simulator motion
command
r
Simulator
States lls
_[ Aircraft pilot's
"[ vestibular system
Simulator pilot's
vestibular system
SensationA
Sensations
Figure 4.4.4. Aircraft Simulation Problem Structure
Since the control strives for tracking the output of the aircraft pilot's vestibular
system, the problem is most likely to be treated as a tracking problem. The aircraft
motion can be quite variable. Therefore, it is reasonable to use a filtered white noise that
contains sufficient frequency components to represent the aircraft motion states.
Therefore, the problem is a stochastic tracking problem.
4.4.3. MIT/UTIAS Development of Washout Filter Coefficients
The optimal algorithm documented in this section was developed at the
University of Toronto in 1985. The optimal washout filter design problem is formulated
as follows. The actual aircraft and simulator sensation systems SensationA and
Sensations are given along with the input signal IIA that drives SensationA. A properly
constrained operator W(s) can then be found that generates the simulator input lk to
Sensations on the basis of the input to Sensation^, such that the pilot senation error e is as
small as possible. A mathematical model of the vestibular organ is used. The
optimization criterion that is selected is the mean-square difference between the
physiological outputs of the vestibular organs for the pilot in the aircra_ and for the pilot
50
in the simulator. The structure for the optimal filter is assumed given and the task is to
fmd the optimal values for the parameters of the filter.
The optimal algorithm in this section generates the optimized transfer function
W(s) by an off-line program. W(s) is then applied on-line to generate simulator motion
commands.
W(s) relates the aircraft pilot sensation input to the simulator pilot sensation input
that is assumed to be approximately identical to the simulator motion base input
lls "--W(s) 11A, where IIA consists of aircraft body axes acceleration a_ and angular
displacement 13_. 11s will be used as the command to drive the motion base. A linear
scaling in combination with a limiting as described in Section 2.5 is applied to modify the
input.
W(s) is optimized by minimizing the cost function cr =
J=E {_erQ_e + p (usrRus
e=_ -_
TUs--rL _4"1
0Jdt
+yr_ds Rdy_]}
, where
where _ and Y.aare the pilot's sensations in the aircraft and simulator environments.
For uncoupled system equations, _ r has different meanings for different degrees of
freedom:
For pitch/surge equations:
For roll/sway equations:
For yaw equations:
For heave equations:
r=[ uat 2 u_dt u s]
I_:=[_v_dt 2 _v_dt v s]
r = dt 2 _q/sd t ]_s [H_s
f_:=[ wdt 2 w_dt w s]
51
Q and Ra are positive semi-definite matrices, R is a positive definite matrix and p is a
positive scalar. These parameters determine the weight of each term in the cost function.
The optimal washout is performed in the pilot head flames FrpA and FrPs. It is
claimed in the UTIAS report [3], [4] that this frame selection will avoid sensation cross-
coupling where the sensation cross-coupling may make the calculation of W(s) more
complicated.
The washout filter coefficient W(s) will now be generated. The sensation system
for the pilot in both the aircraft and simulator environments are given as:
__^=A l_x^+B lu A
SensationA: "_y =̂ C I _x^ +D I _u^ (4-4-15)
"_xs = A i Xs +B i Us
Sensations: -Ys = C, _xs + D ! u s (4-4-16)
Where it has been assumed that the same motion sensing system dynamics can be applied
both in the aircraft and in the simulator and all system matrices are taken to be time-
invariant.
Assume I!A consists of filtered white noise:
"_x,=A. x, +B,, w (4-.4-17)u^ = x n
Adjoining all the above systems, the optimal controller equations may be generated:
"_X= AX+Bu s +Hw(4-4-18)
Y=CX+Du_ s
with the cost function o = _ J dt,
where J = E {yTG Y + p U__srRu s } (4-4-19)
52
Fx',
L_ ZEe, °BIIY= y, A= A, 0
-d_ _0 A,
n
C=I-__ , cdC'-__),] D=ID_0,] G=IQ ROd] H=I-00]13.
where p and R are positive scalars.
By matrix substitution and manipulation Equations (4-4-18) and (4-4-19) transform to the
standard form of the stochastic linear optimal regulator problem:
$= A'_x+B u--+H_w
J= E { fl [_xrR'lx+ u__aR2 u'] dt }
whose solution was given in Section 4.4.1"
uS =-F l x,
(4-4-20)
where (4-4-21)
F I = R_tBrP
and P is the solution of the matrix Riccati equation
_0= R; - P B R]IBrP + A'rP + P A' (4-4-22)
53
with definitions of the new notations used in the above equations:
RI =C TG C ;R12=C TG D ; R2=R+D TG D;
R', = R, - RnR]_R_2 ; u" = u s + R]'R__x ;
A'=A-BR]IR_2 ;x=X
Now lls and x can be related:
_us = u_'- R21R_2_x =
where - F = -R] 1 (BTp + RIT)
Partition -F into - [FI F2 F3], then
- R]' (BTP + R_) x= - r x
u s =- [F1 F2F3 ]
Taking the LaPlace transform on (4.4.1) and (4.4.3) yields:
X, = (sI - A)-IB _u^
X s = (sI - A)-IB u s
By the substitution of (4-4-26) into the LaPlace transform of (4.4.25), the relation
between u,(s) and IIA(S) is finally found:
(4-4-23)
(4-4-24)
(4-4-25)
(4-4-26)
as(S) = W(s) u,(s)where
W(s) = 1-I + F2 (sl - A + B F2) -_ B 1 IFI (sl - A) "_B + F31
(4-4-27)
W(s) is the optimized open-loop transfer function linking 11s(s) and lh(s), the optimal
algorithm controller implemented in the UTIAS report. The block diagram for the
optimal algorithm is shown in Figure 4.4.5.
54
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5. Changes Made in Project to Original Algorithms
For evaluation purposes, changes were made to the four algorithms. The NASA
adaptive algorithm and the three washout algorithms implemented by UTIAS (classical,
adaptive, and optimal) are accommodated in one program as described in Section 3.
Some of the subroutines in the NASA soitware have functions overlapping with the
functions of some subroutines in the UTIAS software. These overlapping subroutines are
not included in the current evaluation software.
Limits on angular tilt rates were not included in the optimal and the NASA
adaptive algorithm. In the current software these limits are included. The parameters for
scaling translational and rotational inputs were different for each algorithm. For this
project a scale factor of 1.0 is used in all algorithms for convenience of comparison
between the aircraft motion and the simulator response.
When either the UTIAS adaptive or NASA adaptive algorithm was tun,
convergence to steady state oscillations was observed under rotational input. The
adaptive algorithms were modified in such a manner as to influence the response of the
simulator corresponding to the aircraft rotational input. The modification does not affect
the response of the simulator to the aircraft translational input. The difference is that the
simulator will perform pure rotation to simulate an aircraft pure rotational input. The
original algorithm generated some translational acceleration under aircraft pure rotational
input and this translational acceleration is occasionally unstable. The rotational response
of the simulator to rotational input was not affected. This topic is further discussed in
Section 5.1.
57
When either the UTIAS adaptive or NASA adaptive algorithm was run, unwanted
spikes on the specific force of the pilot's head occurred whenever the input contains some
sharp change of translational acceleration. These spikes were in the opposite direction to
the correct response direction. The UTIAS report [3]; [4] mentioned these unexpected
spikes but did not explain the correct reason for their occurrence. No effort was made to
eliminate or decrease the spikes. The cause for the spikes was identified to be angular
acceleration when the simulator is tilting for compensating aircraft translational
acceleration input. This angular acceleration can be so large that it can overpower all
other simulator motions at some points in time and give the pilot a perception in the
opposite direction to which is expected. The angular acceleration is limited in the current
soitware. The spikes were effectively reduced and the overall response of the simulator
did not change significantly. This topic is further discussed in Section 5.2.
A platform dynamics filter was added.
is not currently available. A transfer function
A model of the actual platform dynamics
(l)n 2
is used to approximate
the platform dynamics, where q = 0.707, ¢0o = 10 g rad/s. This filter represents the
specifications for the real platform design. In the output plots in Appendix A, the
notation 'desired simulator displacement' and 'desired simulator angular position' means
the output of a washout filter. This output has not yet passed through the platform
dynamics filter. The notation 'actual simulator displacement' and 'actual simulator
angular position' means the output that has passed through the platform dynamics filter.
58
5.1. Instability in the UTIAS Adaptive Algorithm
In some rotational input cases, the UTIAS adaptive algorithm was unstable. In
the UTIAS report, Volume 2, [4] the instability of the adaptive algorithm was mentioned
but the reason was not discussed. The report suggested restricting the adaptive
parameters to eliminate the instability. But this restriction will make the algorithm lose
some of its adaptive characteristics, i.e., the adaptive algorithm becomes less 'adaptive',
and this restriction may not eliminate the instability completely in some cases. It is
necessary to find the cause of the instability before trying to eliminate it.
As shown in Figure 4.3, the algorithm tries to duplicate f_ in the simulator
frame. The simulator rotates at an angle 0s to simulate an aircraft rotation of 0A. It is
always true that 10 1< un, ssboth zoro.Inmopurerotational input case in
which a_A----0, the aircraft and simulator angular positions are plotted in Figure 5.1 below:
0A
0s
Input: doublet angular acceleration.
Time
Figure 5.1. Aircrait and Simulator Angular Position under Pure Rotational Input
It is observed that with the doublet angular acceleration input, both the aircraft
and the simulator angular positions reach steady state after some time. In these steady
59
states, g imposes a force gA on the pilot's head in the aircraft and a force gS on the
pilot's head in the simulator, where gA ;t gS. For example, in the pitch test case,w w
gA= [ _g, sin 0 A 0 g * COS O A ]T
gS= [_g,sin0 s 0 g'COs0 sITw
withfL=gA-gS= [.g,(sin0 s-sin0 A) 0 g*(COs0 s -COs0^)] T
(5-1)
The UTIAS adaptive algorithm attempted to COmpensate for fi x by passing _1and --_ST
through both the translational and crossover tilt channels. Now look at the" formula for
generating the simulator translational acceleration:
glx =pxl * fi_ kxl * sXx- kx2 * SIx (5-2)
where kxl and kx2 are COnstant scalars and pxl is an adaptive parameter, f_x is not zero in
steady state since [0 s < _A " Since all washout algorithms should attempt to wash out
_SI to zero in steady states, the adaptive algorithms would attempt to bring the simulator
to its neutral position in the steady state. When the simulator reaches its neutral position,
i.e., Six= 0, it holds that Sx"I+k_2* Sx1= P_l * -f2_-I Since f2x_is not equal to zero, _ and
__i cannot both be zero. Then the simulator cannot stay in the neutral position, i.e. it must
continue moving. Because the adaptive algorithms are attempting to return the simulator
to its neutral position in the steady state and the simulator cannot stay in its neutral
position, the simulator oscillates around its neutral position. This is the cause of the
instability under rotational input This analysis is consistent with the results generated by
the original adaptive algorithms before revisions were made.
6o
The difference between gAand gS under rotational input in fact cannot be
eliminated. Itcannot be eliminated by simulator rotation since [0s[ < _3A]. Neither can it
be eliminated by __'because __I cannot be sustained for a long time and fix is a long-
term force. From another point of view, since 0a is simulated by 0s and gA and gS are
just g' rotated by [3A and [3s respectively, it is reasonable to simulate g_A by gS.
The block diagram for the revised algorithm is shown in Figure 5.2. g A is no
longer followed but _gSR is USed as direct input. _g_ is g in an imaginary reference
frame FrsR. If the simulator only responds to angular input, the simulator frame is FrsR.
In the pure rotational case, FrsR = Frs, then gSa = gS.
The original algorithms had an active translational and tilt channel under pure
rotational input. Neither _$T nor _ was zero and it was often unstable under pure
rotational input or a mixture of translational and rotational input. The revised algorithm
generates the same results as the results generated by the original adaptive algorithms
under pure translational input. The difference is that the revised algorithm has a null
translational channel under pure rotational input. Both _---STand S_ are zero. The revised
algorithm is stable under translational, rotational, or a mixture of translational and
rotational inputs.
61
ww "_
q_
li°lC_
k
c_TIt
._._
rL_-_..I
T
J_
_u
c_
E-
°q.i
Z _TIt
_Delm
B2
5.2. Spikes in the Outputs of the NASA and UTIAS Adaptive Algorithms
Some significant spikes occurred when either the NASA Adaptive algorithm or
the UTIAS adaptive algorithm was run as shown in Figure 5.4. Whenever there was a
sharp change in the translational acceleration input, a spike would occur. In the Lrl_S
report [1], [2], the spikes were said to be due to the attenuation of the second pulse of
(simulator acceleration). But after careful examination, the real cause of the spikes is
identified to be the rotational acceleration of the simulator. Since the pilot's head is in a
position some distance away from the centroid of the simulator (the rotational center in
the adaptive algorithms), a simulator rotational acceleration will generate some additional
acceleration at the pilot's head. It is this acceleration that caused the spikes.
The specific force on the pilot's head can be expressed as:
fp= a_s_ gS (5-2-1)
where a s is the acceleration at the pilot's head. a s is then expressed as
$ _ S $ -S Sam- -as + _s + 2 cos x _ + cos xR s + cos x(CO_ x Rs) (5-2-2)
where Rs is the vector from the centroid of the simulator to the pilot's head.
Assuming _s = R---'s= 0, then
s _ s .s s R s) (5-2-3)aps- _as + COs x R s + COsx (coss x
Equation (5-2-3) indicates that both coss and rb_ contribute to _as . The limits for tilting
COs are set to 0.0524 rad/sec. Usually each component of ]Ks_is less than 2 m for most
ssimulators. Therefore each component of o s x (co ss x R s) has a magnitude less than
63
0.05 m/seJ. This term will not contribute much to a s .
to c0___s-s x _Rs , which is expressed as:
SxRs = (i_ _'+/1 ] + f 1_)x (Rs_l + Rsy] + Rsz_:)COs
= (Rszq- Rsyr) _"+ (Rs_f- gszlS) _ + (Rsyl_- g_q) 1_
Major attention will be paid
(5-2-4)
There are two ways to prove that _ss x R s is the cause for those spikes. First, the
magnitude of _ x R s can be estimated by hand calculation. Then the value can be
compared with the magnitude of the spike. The second approach is to set R = (0,0,0),
when the spikes are supposed to be eliminated completely. These two tests were
performed and proved that 6___x R s is the real cause of the spikes.
Since the spikes are generated by 6___x _Rs , there are two ways to decrease the
spikes. The first is to reduce " s_s and the second is to reduce ]_ss. _s is determined by the
position of the pilot's head relative to the position of the center of the simulator rotation.
Only the former can be reduced. In the UTIAS report [3], [4] the center of rotation is
selected to overlap with the centroid of the simulator for minimum extensions of actuator
legs. This selection is quite reasonable and any change will increase the actuator
extensions. Then the only approach left is to reduce _s-"s
The generation of __^was investigated as shown in Figure 5.2. The Pitch/Surge
filter was examined as an example. The Roll/Sway filter has similar characteristics. In
the Pitch/Surge filter,
q = 0 s = px2 * fL + px3 * O. (5-2-5)
64
A rotational acceleration will be generated by:
i . - fl2x(i ) )/dt, (5-2-6)q = 6, = px2 * (f2x(l +1)
where i indicates the current time step and i+1 the next time step. If there is a sudden
change in f_x, an extremely large Os might be generated. Furthermore, the smaller the
step size dt is chosen, the larger Os will be generated. For example, if the longitudinal
acceleration input is a step or a pulse input, and when t = O, O_ = O, then at the first time
step 0_ = px2 * f_x / dt. The UTIAS adaptive algorithm set px2 = 0.12 initially and dt=
0.05 see. Then an input which has an amplitude of 1 m/see 2 would generate 0_ = 0.12 *
1 / 0.05 = 2.4 rad/sec 2 at the first time step. The UTIAS simulator used P. = -0.2 _ - 0.465
- 1.783 1_. Then q = 0s = 2.4 rad/sec 2 would generate:
ch_ xR s = (gszq-Rsyf)l + (Rsx/'-Rszlb)] + (RsylS-Rsxq)fc
= Rszq _" _ Rs_ql_
= -1.783.2.43 + 0.2.2.4f_
- 4.3 _ + 0.48 f_ (m/sec 2)
6_ssx R s contains a component with a magnitude of about 4 m/see 2 in the x direction at
the pilot's head. This acceleration will overpower all other simulator motion effects and
give the pilot a perception in the wrong direction at the beginning of the simulation. This
significantly wrong perception will also happen whenever there is a sudden change in
aircraft translational acceleration.
A limit on tilting angular acceleration 6 of 0.5 rad/sec 2 has been added in the
current software. Spikes were attenuated significantly at the price of a slower simulator
tilt response as shown in Figure 5.5. In the former example, if the limit of 6_ is set to be
0.2 rad/seJ, then the magnitude of the spikes can then be attenuated by about ten times.
65
At the same time, about 10 *dt is needed to get 0_ to reach the expected value. Then at
about 0.5 seconds, the simulator response is slower than before the new limit is added.
Since it only influences about 0.5 seconds duration, this is more tolerable than the spikes,
which completely reversed the pilot's perception. On the other hand, simulator
translational motion performs a more important role at the beginning of simulating a
translational acceleration change. This makes the slower response more tolerable.
66
!
0.8
_o,6
x 0.4G.<
0.2
0
2
-1
AIrcm_ $peci_c F_ce at Pik,I Heldi j | i
i / / i I I ! I! 2 3 4 5 6 7 8
Sim_ ,Specitlc Foce lit I=',l_ Head (no Imil on anl_UIiVIc_ele_J i t I i J r )
...... L
I / I I 1 I i I I1 2 3 4 5 0 7 8 9
t(_c)
10
I0
t
0.8
_, O.4
0,2
C
3
2
?,o
0
Ai_ 8_m_l _llle Force _ Plot
I 2 3 4 5 8e(see)
i i I7 8 D
i i i i i i
i ] I l i
¢(Nc)
10
lO
Figure 5.4. Specific Forces Generated by the NASA Adaptive Algorithm with No Limit
on Angular Acceleration.
67
1
_" 0.8
O.2
0
.o.2;
3
A2
0
Ain:mtl $ped_ Fome at PilotHeedD i i i
;
l
! ......................................................
I . I I I I I I I l
1 2 3 4 5 6 7 8 9t (,_)
Simu,_lecJ_c Fome at PilotHeadObnitedangulwII,_ekmtlion)i • i i | t l p i
t
lO
I II _ I I I I I I I ;
0 1 2 3 4 5 6 7 8 9 10t (,e¢)
1
o,eo,e0.4
o2/0-
-0.2--0
3
2
1
wO¢o
Aircml Seined Speci_ ForceM Pilot
\\.
X.
1 2 3 4 5 6 7 8 9 10t(uc)
_u. 6ermKI Sp_ Fome it P_ Head(imrled anger accML_'atl_P i _ i i • * I
I I I i' | I I | !
I 2 3 4 5 6 7 8 g 10t (,.¢)
-1
Figure 5.5. Specific Forces Generated by the NASA Adaptive Algorithm With 0.5
rad/sec/sec Limit on Angular Acceleration.
68
6. Phase1Results
6.1. Translational Input Case
Both a pulse input of 1 m/see 2 for a 10 second duration and a sinusoidal input of 1
m/sec 2 with a frequency of 3 rad/sec were used as translational inputs. In each case the
input was applied individually to each translational degree of freedom (surge, sway, and
heave). The pulse contains both high frequency and low frequency components. Figure
6.1 shows the specific force at the pilot's head for the pulse input, and Figure 6.2 shows
the response for the sinusoidal input.
The response onsets, i.e. the start of a response, generated by each algorithm are
significantly different. During the response-sustained period the difference among those
results is not significant. Major attention will be given to the response onsets. For
comparison of the response onsets Figures 6.1 through 6.3 were generated with a shorter
time axis (5 seconds).
As observed in Figure 6.1 the classical algorithm and the UTIAS adaptive
algorithm response onsets have smaller magnitudes and larger phase lag as compared to
the NASA adaptive and optimal algorithm response onsets. If the responses within the
first second are inspected, the classical algorithm generates a response with a magnitude
equal to about one half the magnitude of the aircraft response. The other algorithms
generate responses with higher magnitude. Note that for an easy comparison the input
scaling gain has been set to one for all algorithms. The optimal algorithm had the least
onset lag and the NASA adaptive algorithm had the second least onset lag, with the
classical algorithm and the UTIAS adaptive algorithm having larger lags by about 0.1 to
0.2 seconds. The "sags" following the onsets generated by the classical algorithm and the
69
UTIAS adaptive algorithm were significantly larger than the sags generated by the
optimal and the NASA adaptive algorithm. Large sags usually decrease the fidelity of
motion cues.
The response offsets are similar to the response onsets. It should be noted that the
UTIAS adaptive algorithm has some excessive delay. This delay is due to the tilt
adaptive parameter p2 being driven to a very small value after the input magnitude is
sustained for several seconds. The NASA adaptive algorithm has a fixed tilt channel
parameter k3 so that it avoids the extra delay.
These differences on response onsets and offsets might have significant meaning
in the overall fidelity of those algorithms. For further comparison, in Figure 6.2 the
specific force at the simulator pilot's head corresponding to sinusoidal input was
generated. It is observed that the NASA adaptive algorithm and the optimal algorithm
generated responses with high magnitude. The U_AS adaptive algorithm generated
response with medium magnitude and the classical algorithm generated response with
low magnitude. The optimal algorithm has the highest fidelity in shape. All other
algorithms generated some extra extremum points. The NASA adaptive and UTIAS
adaptive algorithms generated specific forces in a wrong direction during about the
beginning 0.3 seconds. This problem on specific force in a wrong direction was
discussed in Section 5.1.
On the other hand, the optimal algorithm and NASA adaptive algorithm resulted
in significantly larger actuator extension costs than the classical algorithm and the UTIAS
adaptive algorithm.
7O
AIC & Simu. Specific Force atPilotHead1.2 °
0.8
xu. 0.6CO
x 0.4IJ.
x,
115
x,
0"!
- .0 1 2 3 4 5
t (sec)
Line with no marks -- Aircraft response.Line with marks - Simulator response.*- Classical ' o-- NASA Adaptive +-- UTIAS Adaptive x-- Optimal
Input: pulse x-acceleration input, magnitude = 1.0 m/sec 2, duration = 10 seconds.
Figure 6.1. Specific Force at Pilot's Head Corresponding to Pulse Input.
71
AIC & Simu. Specific Force atPilot Head1.5
0.5
-0 -1"50_
2 t (sec) 3 4 5
Sensed Specific Force0.6 ....
_ 0.4
x,
Y, 1-0 6 ' - '
• 0 1 2 3 4 5
t (see)
Line with no marks -- Aircraft response.Line with marks -- Simulator response.*-- Classical o- NASA Adaptive +-- UTIAS Adaptive x--Optimal
Input: sinusoidal x-acceleration input, magnitude = 1.0 m/sec 2, co = 3 rad/sec.
Figure 6.2. Specific Force at Pilot's Head Corresponding to Sinusoidal Input.
72
6.2. Rotational Input Case
A doublet pulse angular acceleration input of 0.05 rad/sec 2 for a 10 second
duration was used. The classical angular rate response has some overshoot when it drops.
This causes the simulator angular position response to have a slight unwanted drop
(Appendix B Figure B.1). The amplitude of the angular position generated by the
optimal algorithm slightly exceeds the aircrat_ angular position (Appendix B Figure B.2).
The UTIAS adaptive algorithm and the NASA adaptive algorithm both have smooth
angular position response. The magnitudes of the simulator angular position responses
are significantly attenuated, especially in the NASA adaptive algorithm (Appendix B
Figures B.3 and B.4). In the UTIAS Report Volume 2 [4], the Bode fi'equency responses
of the classical algorithm and optimal algorithm were presented. These plots show that
the gain of the classical and optimal response fluctuates around one and some small phase
shift would happen in both the classical algorithm and optimal algorithm. These analyses
are consistent with the graphs in Appendix B. For further comparison some sinusoidal
input cases were studied. From Figure 6.3 it can be seen that in some input cases the gain
of the classical and optimal algorithms could exceed one. The phase shifts of the
classical algorithm and optimal algorithm are larger than the phase shiRs of the UTIAS
adaptive algorithm and NASA adaptive algorithm. The NASA adaptive algorithm has a
response with much smaller magnitude.
The optimal algorithm resulted in the largest jack extension costs. The UTIAS
adaptive algorithm and the NASA adaptive algorithm resulted in jack extension costs
smaller than the classical algorithm and the optimal algorithm.
73
AIC and Simu. Sensed Angular Rate• -
• 2_ #j \\\ /_ \\_,i 1I ___S_'_]_ " /_E_;_m_l_ _ /_
0 1 2 t (sec) 3 4 5
8 ,A/C and Simu. Sensed Angular Rate.
L t
/t
"30 1 2 3 4 5
t (sec)
Line with no marks - Aircraft response.Line with marks - Simulator response.*- Classical o- NASA Adaptive +- UTIAS Adaptive x- Optimal
Input: Sinusoidal roll acceleration input, magnitude = 0.05 rad/sec 2, ¢o= 3 rad/sec.
Figure 6.3. Aircraft and Simulator Angular Rate Response.
74
6.3. Conclusions and Recommendations
At the current stage, in translational input eases the optimal algorithm and the
NASA adaptive algorithm perform better than the classical algorithm and the UTIAS
adaptive algorithm. In rotational input cases, the UTIAS adaptive and the NASA
adaptive algorithm perform better than the classical and the optimal algorithm.
The classical algorithm is a type of linear algorithm distinguished by the fact that
the washout output is proportional to the input. This is an undesirable attribute because
the duration of the onset cue is then limited by the maximum amplitude input case.
Therefore in lower amplitude case the onset cue cannot be sustained any longer even
though the hardware motion resource is quite available. The classical algorithm is
therefore not recommended.
The NASA adaptive algorithm has been improved by eliminating unwanted
spikes and excessive oscillations. The NASA adaptive algorithm currently performs
well.
The UTIAS adaptive algorithm is expected to perform better than it does
currently. It has also been improved by eliminating unwanted spikes and excessive
oscillations. Some more improvements are needed such as increasing the slow tilt
response by fixing or restricting the tilt adaptive parameters, thus changing some
parameters to make the translational response be sustained for a longer time. With these
further improvements implemented, the UTIAS adaptive algorithm might be attractive.
For the optimal algorithm, if selecting another washout frame can decrease the
actuator extensions, this algorithm will be very attractive. Currently the optimal
75
algorithm performs washout in the pilot head frame. As discussed in the UTIAS report,
this frame selection results in some extra jack extension costs when the simulator rotates.
A washout frame whose origin lies on the simulator centroid is desired. But the
desired frame will cause some cross coupling in the pilot specific force sensation. This
cross coupling might make the generation of the optimal transfer functions much more
complicated or even not practically feasible. Further study on the optimal washout in the
simulator centroid frame is recommended.
76
7. Phase2 OptimalAlgorithm Redevelopment
In Phase2, furthercomparisonsaremadebetweentheNASA adaptivealgorithm
anda redevelopedoptimal algorithm. The classicalalgorithmwill not beevaluateddue
to the undesirableresults obtained in Phase 1. Since the adaptive algorithms are
fundamentallysimilarwith theNASA adaptivealgorithmhavingmoredesirablefeatures
than theUTIAS algorithm, theUTIAS adaptivealgorithmwill not beevaluatedin Phase
2.
The optimal algorithmwill be revisedwith the centerof rotation redefinedand
utilizing a new cost functionwith additionalterms. In addition,a new designapproach
thatintegratesFORTRAN/MATLAB/SIMULINK is developedin which a setof selected
parameterscanbe testedin 30 secondsascomparedto 15minuteswith a conventional
approach.Therevisedoptimalalgorithmalsoincludesanewvestibularmodel.
Two generalproblemsthat wereunresolvedin Phase1 areaddressedin Phase2.
The In'stproblemwas that for inputs with largemagnitudesall the algorithmstendedto
drive the simulatorbeyondits motion limit. A nonlineargain algorithmwas developed
sothat the simulatorwould not reachits motion limit for mostinput cases. The second
problemwasthat whenthe simulatorreachedits limit analgorithmwasneededto brake
thesimulatorto afull stopandreleasethebrakeat apropertime to allow the simulatorto
againfollow the washoutalgorithmoutput. For this problem a braking algorithmwas
developedin Phase2.
77
7.1. New VestibularModels
The semicircular canals have been well studied by many researchers. A model
that was more consistent with the results of recent research could be found through a
review of the reports written by those researchers. The construction and justification of
this proposed model is discussed in detail in Appendix A. The revised model for
practical usage (neglecting the short time constant) can be expressed as:
" _ (l+ZoS)(l+Tps)(7-1-1)
where _ is the input angular acceleration and 03 is the sensed angular velocity. _o, ¢t,
and Xpare time constants. %, = 30 sec, ZL = 0.06 Sec, and %v = 5.7 see.
The UTIAS report [3] suggested a simplified otolith sensation model that ignored
the short time constant term (ZsS + 1) in Equation (2-1-2) for practical usage:
_. K ('c,s + 1)w
f ( Ls +1)(7-1-2)
where f is the input specific force and _f is the sensed specific force.
Human sensation models (7-1-1) and (7-1-2) are used in the revised development
of the optimal algorithm.
78
7.2. Redefinition of Center of Rotation
In Phase 1, the optimal algorithm resulted in significantly_ larger actuator
extensions than the other algorithms. It was found that this problem arose from the
different selection of the center of rotation. If the center of rotation is selected at the
centroid of the simulator, there are several cross-couplings:
pitch -') surge, pitch -') heave, roll -') sway, roll -) heave, yaw "-) sway, yaw "-) surge.
This can be shown in Figure 7.1:
O___'___RsPh (Pilot's head)
Ct (Centroid of the simulator)
Figure 7.1. Phase 1 Optimal Algorithm Center of Rotation
An angular velocity c0_ with respect to the centroid of the simulator always generates a
translational motion at the pilot's head.
If the pilot's head is selected as the center of rotation and the vestibular system is
considered as the only motion sensation organ of the pilot, all the cross-couplings will
disappear. This is the reason for which the UTIAS report [3] chose the pilot's head as the
center of simulator rotation. Unfortunately, this selection resulted in excessively large
actuator extensions in some input cases. This can be shown by an example in which the
simulator has both translational and rotational displacement.. For example, in the
pitch/surge mode the same tilt angle 0 and the same linear displacement Sx are generated
in two different systems, one of which has the pilot's head and the other has the centroid
of the simulator as the center of rotation. The motion of the simulator is shown in Figure
79
7.2. Figure 7.2 shows clearly that the different selections of center of rotation will result
in different amounts of actuator extensions.
The adaptive algorithms selected the cenlxoid of the simulator as the center of
rotation. However, cross couplings were ignored in the algorithm development. Test
results showed that some undesirable spikes were generated due to the cross couplings.
Some effort was spent on reducing or eliminating the magnitudes of the spikes in Phase
1. The spikes were reduced but not eliminated. The spikes may generate some negative
motion cue to the pilot's sensation or at least cause some delay on the pilot's sensation on
the positive motion cue. In Phase 2, a new optimal algorithm that chooses the centroid of
the simulator as the center of rotation was developed. Cross couplings were handled
explicitly and the spikes were eliminated in the new optimal algorithm.
8O
Originalsimulator
position
With
angulardisplace-mcm
Withboth
anglerandlinear
displace-me_t
ComparefmaIactuatordisplace-mcnls intwodifferent
systems
Centroid of simulator is the center of rotation Pilot's head is the center of rotation
P
C
//°l, /
x
,,/-:Y J/5// !1
,Y t
c/
x
, .j-_/ ! // "" l !,," ..'"b-'_ U /
/ ."/ !i/1 ..."/ /i/
/ ..t" / !/.'....'/." ///// //_// ¢?/i
,/
/L"
/_ - Actuator Extension relative tothe original position
E_ and EB have the centroid of thesimulator as the center of rotation
E2 and E4 have the pilot's head as thecenter of rotation
Figure 7.2. Actuator Extensions for Different Centers of Rotation
81
7.3. Revised Development of Optimal Algorithm
7.3.1. Construction of the System Equations and Cost Function
The optimal filters for the four modes, pitch/surge, roll/sway, heave, and yaw are
designed separately in the optimal algorithm development. This design technique was
also employed in the development of the other three motion-base drive algorithms.
In Phase 2 only the pitch/surge mode is redefined. The roll/sway mode filter
design was based on the pitch/surge redevelopment. The heave and yaw modes are
unchanged from Phase 1. The revised development for the pitch/surge mode is as
follows:
(a) Rotational Motion Sensation
Input:
Eul U = =ax u2
The semicircular canal sensation model given in Equation (7-1-1) is then used to obtain
the rotational sensation c]"
z.s(1 + XLs) T2s2 + T3s
= (1 + -c.sX1 + -CpS)u, s2 + 1.1s + To u 1
1 "Cl + q:_
where To- x_, T, - z,x. , T_= x_.To, T_= x.To
Now expressing the above in state space notation yields the following equations:
Define xl_ 2 [x I x T= _] , then
X_-2 = A=¢xI~2 + B,,,¢u_q = C_xl_ 2 + D=c u_
(7-3-2)
(7-3-3)
82
where
I71 B..= ,A.. = To ' L-ToT_
c., 0], =IT.0]
(b) Translational Motion Sensation
The otolith sensation model given in Equation (2-1-2) can be rewritten in terms of the
break frequencies Ao and Bo:
_ Go(s+A°) (7-3-4)f (s + Bo)
where f is the input specific force and _ is the sensed specific force. Go = 5.86,
Ao = 13.2 see, Bo = 5.33 sec.
Input "
U_ .--
- ax u2
The center of simulator rotation is set at the centroid of the simulator. Then
f= a x + gO- Rs_O (7-3-5)
where Rsz is the z-component of the Vector from the centroid of the simulator to the
pilot's head. Equation (7-3-5) can also be expressed in the LaPlace domain:
1
f(s) = u2(s) + (g _-- Rsz)U,(S)(7-3-6)
83
Specific force sensation:
= Go s +A----_o fs+B o
= GoS+Ao(u2 +( 1 _Rsz)Ul)s+Bo g_T
= Go s +A_° [(g sl-f- Rsz ) 1]us+B o
= Go [- Rs_s 3 - Rs_Ao s2 + gs + gA oS3 + Bo s2
-Ao)S 2 +gs +gA o
Go[ Rs_(B° s3+Bose
s+A o
s+Bo ] u
A_o.-Bo]s+B o u + Go[-Rs_
State-space model:
Define _x_ = [x3 x 4 x 5 x6] T, then
--X3-6 = A_x-_6 + Bmu_f = C_x3_ 6 + D_u
where
A_ _
1]u_
-_,o,o]oooo °]00 1 0 0 ' B_ -G O o 0 '
0 0 0 -B o Ao-Bo
C.-I1 0 0 11, D_=GoI-r, 11
(c) Combination of Both Rotational and Linear Motion Sensation
_~6 = Av x-1_6+ Bvu
-Yl = Cv xl_6 + Dv_u
(7-3-7)
(7-3-S)
(7-3-9)
84
where
E°Ix,_, = [x, x: x_ x, x_ x_]_, _, = _, .
o] >-7 o] >-l¢ Bv = Cv = " Dv =Av= A.. ' LB.J' c_ ' LV.j
It is assumed that the same human motion sensation model can be applied to both
the pilot in the aircraft and the pilot in the simulator. Define the input to the pilot in the
aircraft as u, = = and the input to the pilot in the simulator as- La_d LUA2
Us _ "_- •
asx LUs2J
and then define the pilot's
To reduce the order of the system equation, define x c = x s - x A ,
sensation error as _e= -Y,s -_,A' then
x_c = X_s--X_A = AvXs+BvUs-(AvXA+BvU_A)
= Avx_ +Bvus -BvUA (7-3-10)
_e= Cvx e + Dvu s - DvU_ A (7-3-11)
(d) It is necessary for the control algorithm to explicitly access some motion states, such
as the linear velocity and displacement of the simulator, which are desired to appear in
the cost function. For this purpose some additional terms were grouped and included in
the system equations.
X d = _axdt'l x71 axd,2/ x,
a:tjx9Xlo
- .X_lj
(7-3-12)
85
where
X--d= Aj x d + B e u_u_
0 1
0 0
Ad=O 0
0 0
0 0
0 00-
I 0 0
0 0 O,
0 0 1
0 0 0
(e) Input _u consists of filtered white noise.
equation
where
_x. = A. x. +B. wu_=x n
[: oI [1.o]An= -I.0 ' B.= 1.0
(f) Assemble system equations.
The desired system equation can be obtained:
IcJ_x= x d
n
Define
-0 O"
0 0
B_= 0 1
0 0
.1 0
This can be expressed by the state-space
(7-3-13)
86
then
where
IA_ 0 -By ] IBBiA= Ae , B=
0 A__J
C= vI , D= .
with the cost function
(7-3-14)
tl T T -t-
The cost function implies that three variables are to be constrained: _e, _Xd,and us.
_eis the sensation error. Xd, which is a group of terms, along with us define the rotational
and linear motion of the simulator. The cost function constrains both the pilot sensaiion
(7-3-16)
error and the simulator motion.
7.3.2. Transformation to Standard Form
The system equations and cost function can be transformed to the standard form
by the following equations:
System equation: _x = A'x + Bu-- + H n
[" t'tl r T t }Cost function: J= E/J,o[XRlx+u' R,u_']dt (P, -0) (7-3-17)
87
where
7.3.3.
°1,R x=CTGC,R u=C_GD,R z=R+DTGD,G = Rd
= - u' _ +RzIR_2x, R;=R 1-R,2R]1R_2 ,A' A BR_1R_2, __=u.
Solution of the Optimal Control Problem
The standard form solution to the optimal control problems can be applied since
both the system equations and the cost function are in standard form. Therefore,
u' = -R_' B T P(t) x_
where P is the solution of the algebraic Riccati equation:
0 = R'I - P B R21 BTP + A'TP + PA'
From (7-3-17) and the definition of u', it is obvious that
u s =-[R]'(BTP + R_2)_
F = R_'(BTP + R_2 )
Define
(7-3-18)
Therl
(7-3-19)
(7-3-20)
(7-3-21)
u s = -F_x (7-3-22)
Partition F corresponding to the partition of x =
x_
_ Ixel,. =-[F, F_ F, x_=-[_, .k__.j-_.,_.Lx-.J
(7-3-23)
88
Eliminate x_', from the system equations:
Ix[z] - -x_ 0 v
d Ad Xd
LX_
[Bv]u s (7-3 -24)+ Bd
After taking the Laplace transform of (7-3-23) and (7-3-24) and making some
substitutions, the following equations are obtained:
us(s) = @(s). u.(s) (7-3-25)
where
sl- A v + BvF 1 BvF2 1-'r,,,,o-,-,,-,,]_/(s)=[r, F2 BdF, sI--Ad +BdFzJ L B,F, -F,
Note that the filter matrix W(s) is not identical to the filter matrix W(s) described
in Section 4 and implemented in the UTIAS report. The revised design of "_¢(s) was
based on control inputs of angular acceleration and linear acceleration, while the design
of W(s) was based on control inputs of angular displacement and linear acceleration. A
revised on-line Fortran development was not implemented; the pitch/surge and roll/sway
filters W(s) developed in Section 4 were simply replaced with the revised filters _/(s) in
the Phase 1 on-line development.
7.3.4. Solution of the Washout Filter Coefficient
_/(s) is solved by Maflab functions and Fortran programs. All the system
matrices were constructed in Matlab functions. First, the weighing matrices Q, R, and Ra
in the cost function were selected. These matrices were adjusted several times in a trial
and error procedure. Then the system matrices Av, Bv, Cv, Dv, RI, Rz, Rm A', and R_
were constructed in a proper order. The algebraic Rieeati equation was defined in the
89
Madab function. The definition was transported to a Fortran environment in which the
algebraic Riccati equation would be solved by Fortran programs. The solution of the
algebraic RJccati equation was transported back to the Maflab environment and F1, F2,
and F3 could then be defined.
After all matrices in (7-3-25) were defined, the solution of XTV(s) still required
symbolic calculation since there was the Laplace variable s. A series of fairly.
complicated Fortran programs were presented in the UTIAS report to solve "¢¢(s). The
solution required manual cancellation of common poles and zeros. It was found that the
problem could be solved more efficiently by Matlab after a careful observation of
Recall that a linear control system can be expressed in state-spaceEquation (7-3-25).
form:
= +fluCx + Du
where A, B, C, D are system matrices.
Equation (7-3-27) determines a transfer function between X and u:
y= [C(sI - ,_)-! _ + fi] u
(%3 -27)
(7-3-28)
By an observation of the similarity between (7-3-26) and (7-3-28), it was found that the
state-space model that had U_Aas the input and u_.sas the output could be obtained directly:
'x_ = Ax + Bu A (7-3-29)u_s = Cx_ + Du__A
9O
where
I -BvF -BvF 1 =/Bv(I+F3)]A= AV_BdF Ad-BdFJ' B k BdF3 , C=[F,v2], D -v3
This state-space model could be converted to the transfer function model by the Matlab
function ss2ff easily. A Matlab function was also written to cancel common poles and
zeros and yield some transfer functions in reduced order. A simulation setup that reads in
the transfer functions automatically was constructed in Simulink. The effects of W(s)
are visualized with the simulation. If "_YC(s) is not satisfactory, the procedure of the
design of "vV(s) is repeated by selecting some new cost function matrices Q, IL and Ra,
until a satisfactory result can be finally approached. The procedure for the solution of
"vV(s) is illustrated in Figure 7.3.
91
Adjust weighting matrices tL Rd, Q i
(Matlab function: ric.m) r1
Define parameters: g, An,
vestibular parameters.
(Matlab function: ric.m)
1Construct system matrices:
As, Bs, Cs, Ds.
Other matrices: R1, R2, R12, RI', As'
(Matlab function: ric.m)
Output RI', BRB', As' toriceq.dat. End of ric.m
Read data from ricc.dat. Solve the algebraic
Riccati equation. P is the output.
(Fortran routine: optproj.exe)I
Output P to psol.m.End of optproj.exe
Read data from psol.m. Construct F. Calculate
state-space expression of the optimal filter.
(Maflab function: wsol.m)
1Transform to zeros and poles.
Cancel common factors.
Transform to transfer function form
with reduced order.
(Matlab function: wsolm)
Simulation result
not satisfactory
Perform simulation in
Simulink to verify the filters
are successfully designed.
(Simulation Setup: sopt.m)
Simulation result
satisfactory
Output optimal filtersto tfns.dat
Figure 7.3. W(s) Solution Procedure.
92
7.4. Nonlinear Gain Algorithm
It is desirable to maximize the magnitude of the motion cue while remaining
within the operational limits of the motion system. Although it is very difficult to restrain
the response within hardware limits all the time, it was found feasible to restrain the
response successfully during most of the simulation time by implementing a nonlinear
gain in the simulator motion-base driving software.
When the magnitude of input to the simulator motion system is small, the gain is
desired to be relatively high, otherwise the output may be below the pilot's perception
threshold when it should be perceptible. When the magnitude of input is high, the gain is
desired to be relatively low otherwise the simulator may go beyond the hardware limits.
Define the input as x and the output as y. Define Xm,x as the expected maximum input
and ym_, as the maximum output, and So and S_ as the slopes at x = 0 and x = x_
respectively. Four desired characteristics for the nonlinear gain can be expressed as:
(1) x=O =:, y=O;
(2) x = Xm_ ::_ y = y_._ ;
(3) Y'L-o=So;
(4) = ;
A third order polynomial can be employed to provide functions with all the desired
characteristics. This polynomial will be of the form:
y = c3x 3 + c2x: + c_x + co
93
where
Co=O
C1 = S O
-2c: = Xm_" (3Ym_ -- 2Soxm_ - SiXm_ )
C3 = X_-3. (Sox _ _ 2Ym_ + Slx,,_ )
One example of this nonlinear gain is shown in Figure 7.4, with parameters set as Xm,x =
10, ym_ = 6, SO= 1.0, Sl = 0.1.
5
4.5
4
3.5
3
y2.52
1.5
1
0.5
0
Nonlinear Gain
I : : : : : : : : : : 1 t t I t 1 i I0 1 2 3 4 5 6 7 8 9 10
Figure 7.4. Nonlinear Gain.
1
II
The nonlinear gain developed by NASA for its motion-base drive software results
in a high probability of reaching system limits for accelerations higher than 3 m/sec 2,
which is common in aircraft simulation. When the new nonlinear gain as shown in
Figure 7.5 was implemented in the software, in most input cases the simulator motion
was within the hardware limit.
94
7.5. Actuator Extension Limiting
There is a possibility that the output of the washout algorithm will drive the
simulator beyond its hardware limit. It is obvious that any hardware shut down due to the
simulator's excessive excursion should be avoided. This raises the requirement that the
simulation software should be able to handle the situation that the simulator may need to
be arrested before encountering the system limit. This necessary software subroutine is
called the braking algorithm. When necessary, the braking algorithm takes over the
control of the simulator from the washout algorithm. It is also desirable that when the
washout algorithm would begin to drive the simulator toward smaller excursions, the
braking algorithm returns control to the washout algorithm. In other words, the braking
algorithm should release the system to resume regular simulation at the proper time. The
logic of the braking algorithm is shown in Figure 7.6.
The algorithm makes a series of decisions to determine when to brake the
simulator and while braked to determine when to release the brake. The first decision is
based on an evaluation of the expression (2.%-a b .s-v 2) for each actuator at each
simulation cycle, where v is the velocity of the actuator, s is the available actuator stroke,
ab is the acceleration/deceleration by which the braking algorithm will stop the actuator,
and Co is a coefficient less than or equal to 1 that is described below.
ab should not be larger than the maximum actuator acceleration which is a
hardware parameter. The simulation software sets a software limit position that is before
the simulator hardware limit position. If the simulation cycling rate is infinitely high,
when Co = 1, the actuator will be stopped exactly at the software limit position; when
95
co< 1, the actuator will be stopped before the software limit position. Since the real
system always has a finite cycling rate, it is possible that the actuator may go a little
beyond the software limit position even though a braking algorithm is implemented. For
this reason, the software limit position should be set slightly before the hardware limit
position. When one actuator reaches the braking region defined by (2-c0.a b -s - v 2 < 0)
at time to, it will be decelerated by a_. At the same time, all other actuators will be
decelerated proportionally to their respective velocities at time to.
The second decision is based on a comparison between the actual simulator states
and the washout algorithm output. The simulator states refer to the simulator's linear and
angular positions. When the simulator has been completely stopped by the braking
algorithm, the comparison begins. When the washout algorithm output states are smaller
than the corresponding actual simulator states, the simulator will begin to follow the
washout algorithm output again.
When the braking algorithm releases the brake, the washout algorithm output may
have large velocities while the simulator has small velocities at that instance. To avoid
the regular simulation being resumed with any excessively large simulator acceleration,
an algorithm which allows the simulator to follow the washout algorithm output
gradually was designed. The algorithm expresses the linear and angular position
command to the simulator as:
96
where
Xco= = a(t)-XA_ + (1 - f(t)). (Xw._ - XA,,)
Xco _ is the commanded position which drives the simulator;
X^_ is the current actual position of the simulator;
Xw. _ is the current output of the washout algorithm.
a(t) is a function of time. It increases from 0 ton / 2 gradually.
(7-5-1)
97
SSI(3), BETAS(3)i DEGREE OF
. FREEDOM TO : L(6)i
r_ ACTU_'OR ! ••j COORDINATES ]
NO
• r
11 ,. " FLAG2.0_,,...._
---_ RELEASE_) -f
<-2. m=o
I=I+
FLAG(I) = l
NO I/"I
<:. ,> 6 :':
SUMFLAO FLAOO)
e.1 / -_
V-] BRAKE L(1)BY A) FRACTION OF
AMAXL
YES
. FLAG(1)=I 7 .>
BY ]!
1 !
_ j7
FLAG2 = 0
rt RL0_L0{
INDICATES THAT THE OLrFFUT OF THE
WASHOUT FILTER IS TOWARDS SMALLER BETAS
AND SSI. ID IS DETERMINED IN THE MAIN Ro[Pr[NE.
J
alto L(1)) < AMA DT "'._-_
)i L(1);O
! t
I=I+
Figure 7.6. Braking Algorithm in the Actuator Driving Subroutine.
98
8. Phase 2 Results
8.1. VitclVSurge Mode and Roll/Sway Mode
The pitch/surge mode and the roll/sway mode have similar characteristics with
both employing the simulator tilt to provide sustained specific force cue, and both having
the cross-coupling from the simulator tilt to the pilot's head translational motion. Both
half cycle sinusoidal inputs and ramp to step inputs were employed to test the pitch/surge
and roll/sway channel of the NASA adaptive washout algorithm and the optimal washout
algorithm.
When a 0.1 Hz half cycle sinusoidal translational acceleration was employed as
the input, the output of the NASA adaptive algorithm and the output of the optimal
algorithm were similar. The specific forces at the simulator pilot's head generated by the
two algorithms had similar magnitudes and shapes. The actuator extensions resulted
from the two algorithms were also similar. One difference with the NASA adaptive
algorithm was that the specific force generated went to a wrong direction at the beginning
of the input and had an extra hump besides the sinusoidal hump corresponding to the half
cycle sinusoidal hump of the input. The specific force output of the optimal algorithm
did not have these two deviations from the shape of the input. The outputs are shown in
Appendix C, Figures C.1, C.2, and C.3.
When a 0.5 Hz half cycle sinusoidal translational acceleration was used as input,
the shape of the specific force at the simulator pilot's head generated by the NASA
adaptive algorithm had some significant distortion. The specific force in the wrong
direction at the beginning of the input had a magnitude which was about half of the
magnitude of the onset of the specific force cue and a duration which was about one half
99
of the time by which the input reached its maximum. The specific force onset had some
more wiggles than the input and the washout of the specific force had a large overshoot.
Stimulated by the same input, the optimal algorithm generated a specific force at the
simulator pilot's head with significantly smaller shape distortion. There was no negative
cue at the beginning of the input The overall shape of the output was similar to the
input, with a small washout overshoot. The outputs are shown in Appendix C, Figures
C.10, C.11, and C.12.
When a ramp to step acceleration with a ramp slope of 3 m/sec 2 was employed as
the input, the specific forces at the simulator pilot's head generated by the two algorithms
had similar magnitudes and shapes. The actuator extensions resulting from the two
algorithms were also similar. The specific force generated by the NASA adaptive
algorithm went in the wrong direction at the beginning of the input. The specific force
generated by the optimal algorithm reached its maximum earlier as compared to the
adaptive algorithm and then slowly decreased. The outputs are shown in Appendix C,
Figures C.4, C.5, and C.6.
When a ramp to step acceleration with a ramp slope of 5 m/sec 2 was employed as
the input, the shape of the specific force at the pilot's head generated by the NASA
adaptive algorithm had some significant distortion. The specific force in the wrong
direction at the beginning of the input had a magnitude about one half of the magnitude
of the onset of the specific force cue with its duration almost equal to the input ramp
duration. The onset of the specific force was followed by a sag. Stimulated by the same
input, the optimal algorithm generated specific force at the pilot's head with significantly
smaller shape distortion. There was no negative cue at the beginning of the input. The
100
overall shape of the output was similar to the input. The outputs are shown in Appendix
C, Figures C.7, C.8, and C.9.
8.2. Heave Mode
A pulse acceleration with a magnitude of 3 m/seJ and duration of 5 seconds was
employed as the input. The onset of the specific force at the simulator pilot's head
generated by the NASA adaptive algorithm was similar to the one generated by the
optimal algorithm. When the specific force at the aircraft pilot's head decreased, the
optimal algorithm generated a corresponding drop of the specific force at the simulator
pilot's head, while the NASA adaptive algorithm did not generate an obvious drop of the
corresponding output. The drop of the specific force at the simulator pilot's head
generated by the optimal algorithm was followed by a washout with a large overshoot.
The outputs are shown in Appendix C, Figures C.13, C.14, and C.15.
8.3. Pitch Mode and Roll Mode
A doublet angular acceleration with a magnitude of 0.1 rad/sec 2 and a duration of
5 seconds was employed as the input to the pitch channel and roll channel. For the pitch
test runs the shape of the specific force generated by the NASA adaptive algorithm was
nearly the same as the shape of the input, while the specific force generated by the
optimal algorithm slowly decreased. For the roll test run the specific force generated by
the NASA adaptive algorithm was nearly the same as the shape of the input, while the
specific force generated by the optimal algorithm required more time to settle during
washout. Some distortion with the simulator angular velocity relative to the input was
also observed with the optimal algorithm. The outputs are shown in Appendix C, Figures
C.16, C.17, C.18, C.19, C.20, and C.21.
101
8.4. Yaw Mode
A pulse angular acceleration with a magnitude of 0.05 rad/sec 2 and duration of 5
seconds was employed as the input. Both the outputs generated by the NASA adaptive
algorithm and the optimal algorithm have the characteristic that the simulator yaw rate
and yaw angle were washed out toward zero when the aircraft yaw rate was rising up to a
constant value and the aircraft yaw angle was always increasing. The simulator yaw rate
generated by the NASA adaptive algorithm dropped much earlier as compared to the
aircraft yaw rate. The optimal algorithm generated a yaw rate following the aircraft yaw
rate for a longer time but also resulted in larger actuator extensions as compared to the
NASA adaptive algorithm. The washout of the simulator yaw rate generated by the
optimal algorithm had a larger overshoot than the one generated by the NASA adaptive
-algorithm. The NASA adaptive algorithm produced a distorted specific force curve with
an onset greater than the aircraft which decreased too rapidly, while the optimal
algorithm was closer in shape to the aircraft but with a large amount of overshoot in
washout. The outputs are shown in Appendix C, Figures C.22, C.23, and C.24.
8.5. Braking Algorithm
A y-acceleration pulse with a magnitude of 10 m/see 2 and duration of 10 seconds
was employed as the input. The optimal algorithm was employed as the washout
algorithm. The simulator reached its motion limit once and was successfully braked.
Some large specific force spikes were generated when the simulator was being braked.
The brake was then released when the washout algorithm output was driving the
simulator toward smaller excursions. The outputs are shown in Figure C.25.
102
9. Conclusions
When the pitch/surge or roll/sway channel was tested, the specific force output of
the NASA adaptive algorithm otten went in the wrong direction at the beginning of a
translational acceleration input. The specific force in the wrong direction resulting from
the cross-coupling from the simulator tilt to the simulator pilot's head translational
motion was reduced but not completely eliminated in the first phase of this project. It
was found that both the magnitude and duration of the specific force in the wrong
direction were still too large to be ignored when the input contained some frequency
components near or higher than 0.5 Hz. As discussed in Section 1, negative motion cues
should always be avoided if possible and when the motion cue onset has high importance.
The specific force in the wrong direction may generate a bad motion sensation which
happens at the motion onset, therefore it was desired to eliminate it completely. It was
found that the optimal algorithm successfully handled this problem. The cross-coupling
was explicitly expressed in the construction of the system equations when the new
optimal algorithm was developed. Results showed that the specific force in the wrong
direction was completely eliminated. The optimal algorithm also generated specific force
outputs with significantly smaller shape distortions than the NASA adaptive algorithm
did in the pitch/surge and roll/sway test eases.
In the heave test case, the NASA adaptive algorithm did not generate an obvious
specific force drop when there was a large drop of the input while the optimal algorithm
generated one, which was obviously desired.
103
When the pitch channel and the roll channel were tested, the NASA adaptive
algorithm generated simulator angular velocity outputs with very nice shapes while the
outputs of the optimal algorithm had some visible distortion. The optimal filters for the
pitch channel were designed in the pitch/surge channel design. The filters were tuned
mainly according to test runs with surge inputs. If the filters for the pitch channel are not
satisfactory, it may be necessary to re-tune those pitch filters without changing the filters
for the surge channel. This is also true for the filters for the roll channel.
When the yaw channel was tested, the output of the NASA adaptive algorithm
and the optimal algorithm were different. If the nonlinear gains for the two algorithms
are adjusted so that the two algorithms drive the simulator to the same amount of
actuator extensions, the simulator angular velocity output of the NASA adaptive
algorithm will have higher magnitude but be sustained for shorter time than the output of
the optimal algorithm. It is not clear which output will result in better simulation effects.
It was found that in most input cases, to generate the specific force at the
simulator pilot's head or the simulator angular velocity with the same magnitude, the
NASA adaptive algorithm and the optimal algorithm would result in about the same
amount of actuator extensions. The advantages of the optimal algorithm over the NASA
adaptive algorithm are that the optimal algorithm eliminated the negative motion cues,
generated outputs with better shapes in many simulation cases, and did not lose some
desirable motion cues while the NASA adaptive algorithm did in some input cases.
104
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Effects of Vestibular and Visual Motion Perception on Task Performance, Delft
University of Technology, Department of Aerospace Engineering, Delft, The
Netherlands, April 1978.
106
Appendix A.
Vestibular Rotation Sensation Model Construction and Analysis
1. Introduction
The purpose of this study is to find a vestibular semicircular rotation sensation
model that is most consistent with experimental results and can be justified by theoretical
analysis, thus providing a reliable approximation to the rotation sensation function. This
study is based on the reports presented by the many researchers who worked on the
semicircular canal and rotation sensation function analysis. The model is first
constructed step by step. The model parameters are then determined and then the model
is carefully justified.
2. Model Construction
The vestibular rotation sensation model has been well studied by several authors.
Steinhausen [A1] fast developed a linear second order model of canal dynamics to
explain the observed characteristics of vestibular induced eye movements in fish (pike) in
1931. This model was further refined by the "torsion-pendulum" model of Van Egmond,
et al. [A2] in 1949, and is later developed from a systems approach by Mayne [A3]. The
differential equation for this model is
IO'_ +cO, +kO. = Ia (A-l)
where I = Moment of inertia of the endolymph
c = Moment of viscous damping of the endolymph
k = Moment of elastic restoring force of the endolymph
O= = Angular displacement of the endolymph with respect to the head
= Angular acceleration of the head with respect to an inertial axis
107
The following transfer function is obtained from Equation (A-l):
0,(s) 1a(s)
I
k
c k I +-s+lS 2 +--S +- S2 CI I k k
For an overdarnped system, Equation (A-2) can be written as
(A-2)
I
0,(s) _a(s) (1 +x,s) (1+x:s)
c I
wherex2 =k -'xz ="c andxn > xu.
(A-3)
Schmid, et al. [A4] show that eupula deflection dp_
where
and the endolymph angular displacement 0= are related by
_ 2 RA_- - -- -a0,h A_
R = Central radius of the canal
A_ = Cross-sectional area of the canal
A_ = Cross-sectional area of the cupula
h = Height of the eupula
(A-4)
is equal to the K in the numerator in the transfer
and a is a nondimensional number. Substituting (A-4) into (A-3) results in the transfer
function relating eupula angular deflection to an angular acceleration input:
_o(s) _ ax,_a(s) (1 +xls_l +xzs ) (A-5)
The numerator in Equation (A-5)
function given by Zacharias [A5].
Further studies showed that a complete vestibular rotational perception model is
more complex than the torsion-pendulum model. Young and Oman [A6] formulated an
108
adaptation operator and cascaded it with the torsion-pendulum model to resolve the
conflicts between the sensed response predicted by the torsion-pendulum model and the
perceptual response measured in experiments. The addition of adaptation results in the
following transfer function:
_b_(s) _ K, "CoS 1 (A-6)
ct(s) l+ZoS (l+'clsXl+xzS)
Zacharias [A5] noted the following in regard to an additional lead component of
tile form (1 + xbs):
"ln addition to the adaptation just discussed, there appears to be evidence of
lead sensitivity in vestibular processing of angular velocity information. In studying
postural reactions to induced body tilt in 1970, Nashner found it necessary to augment
the torsion pendulum model with a lead term having a 17 msec time constant, in order to
fit reflex latencies to large amplitude disturbances. As noted by Ormsby, this type of leadbehavior is not inconsistent with the vestibular nystagmus frequency responses reported
by Benson, in which a high frequency gain rise was noted, consistent with a lead
operator having a 60 msec time constant. Finally, in their investigation of primary
afferent response of squirrel monkeys to rotational stimuli, Fernandez and Goldberg
found that the population average frequency response could be best fit with the inclusion
of a lead term having a 50 msec time constant."
A model representing both the semicircular canal and the peripheral neuron
transduetion dynamics is now established:
the(s) - K. XoS I+zLs (A-7)or(s) 1 +xos (1 +%s)(1 +x2s )
Fernandez and Goldberg [A7] determined the vestibular parameters for the squirrel
monkey by direct measurement of the afferent nerves due to various angular acceleration
inputs of different amplitudes and frequencies. Their transfer function relates the afferent
firing rate of the vestibular nerve to the angular acceleration input:
AFR(s) _ k XoS I +xLs (A-S)oL(s) 1 +XoS (1 +xls)(1 +x2s)
109
where the sensitivity k is different than the sensitivity K given in Equation (A-7).
3. Parameter Determination
Fernandez and Goldberg [A7] determined the average transfer
parameters for the squirrel monkey as
AFR(s) = k. 80s 1 + 0.049s
ct(s) 1 + 80s (1 + 5.7s)(1 + 0.003s) (A-9)
where the sensitivity k was estimated as 3.44 spikes sec'_/deg see "2 for a constant
acceleration input. Parameters for man are more difficult to measure because direct
detection of the afferent nerve outputs of the vestibular system cannot be done and
therefore most experiments were based on subjective responses or nystagmus tests.
The objectives of several researchers were to determine the values of the
parameters based on the subjective response of humans. Van Egmond, et al. [A2]
reported that x_ and x2 had values of about 10 seconds and 0.1 seconds respectively for
man in 1949. The values were based on the verbal response of highly trained subjects
subjected to various motion inputs in both a rotating chair and a torsion swing. Meiry
(from Zacharias [A5]) measured detection latency as a function of angular acceleration
step size, and found a long time constant of 7 seconds for roll-axis rotation about the
earth-vertical axis. Guedry (from Zacharias [.4,5]) used a short period rotational stimulus
consisting of an acceleration pulse doublet, and a response measure of apparent
displacement, and found values of 16 seconds and 7 seconds in yaw and pitch,
respectively about an earth-vertical axis. Malcolm and Melvill Jones (from Zacharias
[AS]) investigated the response to earth-vertical rotation about all three body axes by
using a velocity step as the stimulus, and measured the elapsed time to zero perceptual
response. They also measured the slow phase velocity (SPV) nystagmus of vestibular
function
11o
induced compensatory eye movements, thus providing two separate measures of canal
function. They were able to derive two sets of long time constants for the three axes with
the torsion pendulum model driving both perceived angular velocity and eye velocity.
Their results are summarized in Table A. 1.
Table A.1. Torsion Pendulum Long Time Constants (from Zacharias [A5]).
Yaw Pitch Roll
subjective sensation 10.2 + 1.8 5.3 + 0.7 6.1 + 12
nysta_mnus SPV 15.6 + 122 6.6 + 0.7 4.0 + 0.4
It should be noted that all the above estimations were based on the model expressed as
the transfer function in Equation (A-5).
Young and Oman [A6] later fit these measured parameters to a more complex
model. Young and Oman's model also resolved the apparent inconsistency between the
nystagmus and subjective response measures for yaw rotation. Figure A. 1 shows Young
and Oman's model. The torsion-pendulum model of the canals drives both perceptual
and nystagmus response channels. Each channel has its own adaptation time constant. A
single long time constant of 16 seconds is used for the torsion-pendulum model. A
combination of the torsion-pendulum model and the adaptation mechanism generated a
different response to a step input for each channel. When the model is stimulated by step
inputs, the apparent time constant of the nystagmus decay is 16 seconds, whereas the
apparent time constant for sensation decay is 10 seconds. This model predicts a result for
earth-vertical yaw rotation consistent with the data given in Table A. 1, but was never
extended for roll and pitch rotation.
It can be inferred that the long time constant z_ measured by Van Egmond, et al.
[A2], Meiry and Malcolm and Melvill-Jones (from Zacharias [AS]) does not actually
111
represent the semicircular canal parameter in the model, but is an overall dynamics
parameter representing the decay speed of the rotational sensation to a step angular
velocity input. Zacharias [A5] suggests each axis of rotation has an equivalent "body
axis" canal pair with a distinct time constant. These "body axis" time constants can then
be transformed into the three physical canal pairs. The psychophysical results show each
of the three canal pairs having a distinct value for "q, especially for yaw. However,
physiological results based on afferent responses by Fernandez and Goldberg [A7] show
the same value for x] for all three canal pairs. Zacharias [A5] suggests the differences
shown in the psychophysical results may occur at a central origin at the perceptual level.
AngularVelocityof Skull
(s+25)(s+0.0625)
Torsion-PendulumCanal Dynamics
Nystagmus 120sec
Gain Adaptation
s Dynamics
(s + 0.0083) _ 1 ty
l (Slow Phase)
CentralNervousSystem
Tnne Delay
3.8 deg/secThreshold
s + 0.033
30 see
Ad_talion
Long TermThreshold
Habituation
1.5 deg/se¢ Sensation ofThreshold Vdocity
Figure A.1. Adaptation Model for Earth-Vertical Rotation (from [A3] ).
Fernandez and Goldberg [A7] made the following observation in regard to the
short time constant x2:
112
"Our observations, since they extended only to 8. 0 Hz, are insufficient to provide
a direct experimental measure of xz Some estimate of this constant can, however, be
made from hydrodynamic considerations. What seems to be required is a solution of the
Navier-Stokes equation for the complicated geometry represented by the canal, the
associated ampulla, and the utriculus. No one to our knowledge has accomplished this,
though Steer has solved the equation for a straight tube in 1967. The approximate value
of the time constant, so derived, is "c2 = (p r 2 / 11 [52), where [3 is the first zero of the
zeroth-order Bessel function of the first kind; p and _ are, respectively, the density and
viscosity of the endolymph, and r is the internal radius of the tube, in this case the radius
of the membranous carnal. This radius has been measured by Igarashi and leads to a
value of x2 equal to 0.005 seconds in man and 0.003 seconds in the squirrel monkey. "'
Several authors did experiments to determine the value of "[L" Their findings are
sunimarized in Table A_2.
Table A.2. Lead Sensitivity to Rotational Stimuli (From Zacharias [A5]).
x L (see) Measure Source
0.017 (man) posture control Nashner
0.06 (man) nystagmus Benson and Ormsby
0.05 (squirrel monkey) primary afferent Fernandez and Goldberg
From experiments with human subjects, Van Egmond, et al. [A2] showed that the
perceived angular velocity 6 is proportional to the cupula deflection _bcby the long time
constant x_, resulting in the transfer function
6(s) _ x,s (A-IO)o(s)
As shown in Equation (A-9), Fernandez and Goldberg [A7] show a gain sensitivity k
between the input stimulus and the afferent firing rate that was estimated at 3.44 spikes
see 4 / deg sec "2. Ormsby (from Zacharias [A5]) proposed that the perceived angular
velocity o5 is proportional to the afferent firing rate. While no one to date has
experimentally obtained this parameter, Zacharias [AS] noted that Curry, et al. provided
an estimate of the overall gain between perceived and input angular velocity based on
angular acceleration thresholds.
113
From subjective pilot measurements of angular acceleration thresholds on a
moving base platform, Hosman and van der Vaart [A8] show the perceived input
threshold am_ as
Dram
a_m -[H(o_ )] (A-I 1)
where bmm = Minimum sensed amplitude of the afferent firing rate
[H(o) l = Modulus of the vestibular transfer function
From the measured frequency response of atom the following transfer function is obtained,
neglecting gain sensitivity and adaptation:
I + 0.1097 sH(s) = (A-12)
(1 + 5.924 s)(1 + 0.005 s)
These results are based upon roll and pitch acceleration thresholds; yaw thresholds were
not measured. The value for z_ agrees well with the value obtained by Fernandez and
Goldberg The value obtained for % is nearly twice the nystagmus value obtained by
Benson and Ormsby as given in Table A.2.
From the results reported by the authors mentioned in this section, a transfer
function that can best describe the vestibular rotational sensation system is proposed:
AFR(s) 80s 1 + 0.06s
ct(s) = 3.44--- (A-13)1 + 80s (1 + 5.73s)(1 + 0.005s)
It should be noted that the parameters in the above transfer function are by no means
exact, but are of the correct order of magnitude, thus making the transfer function a
meaningful approximation to the real dynamics of the vestibular rotation sensation
system. The frequency response of the transfer function given in Equation (A-13) with
114
gain k = 1 is shown in Figure A.2. Both the torsion-pendulum model and the complete
sensation model with lead and adaptation mechanisms included are both shown.
e_
© -50
"EIu:Z -100
Bode Plot of Rotational Sensation TF w/Ang Accel Input
10 -3
100
! ! i
i t t i
Sensation Model w/Lead & Adaptation [Torsion-Pendulum Model I
100
Frequency (Hz)
-20010 .3
Figure A.2.
I I I | i
10 .2 10 "I 10 ° 101 102 103
Frequency (Hz)
Frequency Response of Vestibular Rotation Sensation System.
The sensory function of the semicircular canal can be described by observing the
frequency response of the torsion-pendulum model. In the range of normal head
movement from 0.05 to 5.0 Hz (Mayne, [A3]), the gain response decreases by 20
dB/decade with the phase close to minus 90 degrees. In this frequency range the canal
functions as an "integrating accelerometer" or an angular velocity transducer. At very
low frequencies less than 0.01 Hz, the phase approaches zero degrees, thus functioning as
an accelerometer. At very high frequencies greater than 100 Hz, the phase approaches
minus 180 degrees, thus functioning as an angular displacement transducer. The effects
115
of adaptation and lead on rotational sensation are apparent, adaptation influences low
frequencies below 0.01 Hz while lead influences high frequencies greater than 10 Hz.
4. Physiological Interpretation
Modem theories of the operation of the semicircular canal receptors are based on
the assumption that the nervous impulses are generated by deflection of the hairs in the
sensory cells as a result of the cupula displacement. Input acceleration is fast
transformed into cupula deflection by the cupula-endolymph system. Then the cupula
deflection is further transformed into electrical impulses by the mechano-neural
transduction system consisting of sensory hair cells, afferent nerves and efferent nerves.
The cupula-endolymph system was likened to an overdamped linear torsion-
pendulum by Steinhausen [A1] in 1931. A rigorous analytical evaluation of the dynamics
of the endolymph motion in the semicircular canals was made by Steer [A9] in 1967.
The torsion-pendulum model is well accepted by different authors without controversy
upon the form of the model.
Besides the torsion-pendulum dynamics there are some additional terms in the
complete transfer function in Equation (A-8). These terms could be grouped as
kzas (1 +xLs) (A-14)(1 +_o s)
representing an adaptation-lead mechanism. Controversy occurred when different
authors tried to interpret this adaptation-lead mechanism primarily because the precise
mechanism of hair cell stimulation is not yet understood.
The first controversy is whether the adaptation arises in the mechanics of the
cupula-endolymph system or in the mechano-neural system. Goldberg and Fernandez
[AS] presented a good discussion of the origin of the adaptation:
116
"'Two observations tend to suggest that the adaptation arises in the mechano-
neural system. The first is the clear adaptation seen by Lowenstein when polarizing
currents were applied to the vestibular nerve of the thornback ray. Presumably, the
currents acted directly on the nerve terminals. The second is the fact that units differ
greatly in their adaptive properties. Were adaptation of mechanical origin, one wouM
have to assume that hair cells differ in the way they are mechanically coupled to the
motion of the cupulcL An assumption which appears to us more reasonable is that the
adaptation reflects the physiology of the hair cells and�or of the afferent nerve terminals.
Another, perhaps unlikely, possibility is that the adaptation results from the activation of
the efferents innervating the sensory epithelium."
Controversy arose again about the origin of the lead operator. Since no
mechanism was found in the cupula-endolymph -system that could provide a reasonable
interpretation for the lead operator, most authors suggested that the lead operator arose
from the mechano-neural system. Fernandez and Goldberg [A7] suggested that the lead
operator implies the sensory hair cells are sensitive to both the displacement and the
velocity of the cupula. The time constant ZL reflects the relative sensitivities to these two
aspects of the cupular motion. They further suggested that the adaptation-lead
mechanism represents the transfer function between the discharge frequency F and the
cupula deflection _:
F(s) _ kx os(1 + _ L)
(S) 1 + S_(A-15)
This expression implies that both adaptation and lead arise from the mechano-neural
system.
Schmid, Buizza, et al. [A4] gave two other plausible interpretations for the
adaptation-lead mechanism. One is based on the observation that there are two types of
sensory cells in the vestibular sensory epithelia of mammals. All the sensory cells are
assumed to be characterized by a transfer function of the type
117
Fl(s ) _ K*T*s
t_(s--")"- 1+ T*s (A-16)
where F_ is the afferent nerve output, qb is the cupula deflection, KI is the sensitivity
factor and T* is the time constant of the transduction process. It is further assumed that
the two different types of sensory cells work in parallel with a different T*. Then the
overall transfer function of the mechano-neural transduction system can be expressed as
F(s) K2,T_s K=T:s
_(s) - 1 + T_s + 1 + T2s (A-l'))
By simple manipulation the following transfer function can be obtained:
F(s) K:,Tls (1 + T3s)
t_(s) - (1 + T,s) (1 + T2s ) (A-18)
where T_ >> T2 and T3 _ 21"2. If T2 is assumed negligible, then the transfer function can
be reduced to an adaptation-lead operator and give a good interpretation to the origin of
the adaptation-lead mechanism. A very small T2 implies that a group of sensory cells
have a very small adaptation time constant. Experiments have shown that the adaptation
time constants of the vestibular mechano-neural system of squirrel monkeys range
approximately from 30 seconds to infinitely long. The fact that no group of sensory cells
with a small adaptation time constant were found experimentally conflicts with the first
interpretation presented by Schmid, et al. [A4].
The second interpretation presented by Schmid, et al. [A4] is based on the
existence of efferent pathways descending from the vestibular nuclei to the sensory
epithelium, possibly with an inhibitory function. These efferents may represent a
negative feedback that modifies the characteristics of the mechano-neural transduction.
The average dynamics of all sensory cells is assumed to be
118
r,(s) K*T*s (Aq9)w
_(s) I+T*s
The dynamics of the inhibitory process is described by means of a first order system with
a time constant T_ much smaller than T*. The complete mechano-neural transduction
system can be represented by the block diagram in Figure A.2.
¢<s) dK.v,s [ u(s)+=0. "1 I+T*s ]
Dynamics of the_L_y cells
Dynamics of theeffezent pathway
Figure A.2. A Closed-loop Interpretation of the Mechano-neural System.
The closed-loop transfer function can be obtained:
K*T*s
F(s) l+T*s K*T*s(1 + T#)
- K*T*s K i_s) 1 +I+T*s I+T#
I+(K*K i + 1)T*s +Tis + T* T_s2(A-20)
By introducing the simplifications suggested by the condition T, << T*, it follows that
F(s) K*T*s (l+Tis)i
_(s) [I+(K,Ki +I)T,s ] Ti(l+K,_i +1 s)
(A-21)
If T_ is small enough to be considered negligible,K*K i +1
function can be further reduced to the form of Equation (A-15).
then the above transfer
119
4. Conclusion
The vestibular rotational sensation system has been well studied. Its model
consists of a second order torsion-pendulum operator and an adaptation-lead operator.
The torsion-pendulum operator arises from the cupula-endolymph system and functions
as an angular velocity transducer in the range of normal head movement. The model is
then augmented by the adaptation-lead operator that arises from the mechano-neural
transduction system. The adaptation-lead operator most likely represents a closed-loop
dynamic system consisting of sensory cells, afferent nerves as feed-forward path and
efferent nerves as negative feedback path. Based upon the model parameters reported in
the literature a transfer function best approximating the rotational sensation system is
proposed.
120
5. References
A1. Steinhausen, W., Observations of the Cupula in the Ampullae of the Semicircular
Canals of the Labyrinth of a Living Pike, Pfluger's Arch. ges Physiol., vol. 232, pp.
500-512,1933, NASA Technical Translation NASA TT F-13, 665, May 1971.
A2. Van Egmond, A. A. J., Groen, J. J., and Jongkees, L. B. W., The Mechanics of the
Semi-circular Canal, Journal of Physiology, vol. 110, 1949, pp. 1-17.
A3. Mayne, R., A Systems Concept of the Vestibular Organs, Handbook of Sensory
Physiology, Vestibular System, vol. 6, part 3, pp. 493-560.
A4. Schmid, R., Buizza, A. and Zambarbieri, D., Applied Physiological Mechanics,
vol. 1, OPA, Amsterdam, B.V., 1979, pp. 779-893.
A5. Zacharias, G. L., Motion Cue Analysis for Pilot-Vehicle Analysis, Department of
Defense Report AMRL-TR-78-2, May 1978.
A6. Young, L. R. and Oman, C. M.; Model for Vestibular Adaptation to Horizontal
Rotation, Aerospace Medicine, vol. 40, no. 10, 1969, pp. 1076-1080.
A7. Fernandez, C., and Goldberg, J. M., Physiology of Peripheral Neurons Innervating
Semicircular Canals of the Squirrel Monkey. II. Response to Sinusoidal Stimulation
and Dynamics of Peripheral Vestibular System. Journal ofNeurophysiology, vol.
34, no. 4, 1971, pp. 661-675.
AS. Hosman, R. J. A. W. and van der Vaart, J. C., Vestibular Models and Thresholds of
Motion Perception. Results of Tests in a Flight Simulator. Delft University of
Technology, Department of Aerospace Engineering, Report LR-265, April 1978.
A9. Steer, R. W., The Influence of Angular and Linear Acceleration and ThermalStimulation on the Human Semicircular Canal, So. D. Thesis, Massachusetts
Institute of Technology, Cambridge, MA, 1967.
121
Appendix B.
Phase ! Rotational Output Figures
Figure B. 1. Classical Algorithm Roll Doublet Pulse Input.
I m/s 2 peak, 10 second duration input.
Figure B.2. Optimal Algorithm Rol Doublet Pulse Input.
1 m/s 2 peak, 10 second duration input.
Figure B.3. NASA Adaptive Algorithm Roll Doublet Pulse Input.
1 m/s 2 peak, 10 second duration input.
Figure B.4. UTIAS Adaptive Alg0fithm Roll Doublet Pulse Input.
1 m/s 2 peak, 10 second duration input.
122
CLASSICAL ROLL "FI_T CASE
DOUBLET INPUT
I
09
oo<_
0
Cq
8<
-I0
Icq
09
E ov
NO _
<-10
NC Accel. at Centroid of NC
<09
Ev
X6(3
03
0.1
0
Simu. Accel. at Centroid of Simu.
, , , -01. ' ' '5 10 15 20 0 5 10 15
t (sec) t (sec)
20
CN
09
E
>-,O
03
0.05
0
, ' ' 43.055 10 15 2O 0
t (sec)
5 10 15
t (sec)2O
O,04om_
('M
Q30.02
E
N, 0
03, , ' -0.025 10 15 2O 0
t (sec)5 10
t (sec)
I
15 20
Figure B.1. Classical Algodthm RollDoubletPulse Input.
123
0.2
g3
Ev
x 0I
.m
3>CO
-0.2'0
.-. 0.2
>.,. 0
Simu. Velocity in Inertial Coord.
L ., i |
5 10 15
t (sec)
CO-0.2.H
0
2O
0.2
¢tJ
Et,,j 0
!,i
CO
-0.2.0
i J i
5 10 15
t2O
i
5, ! i "
10 15 20
t (sect
Ev
OCOcOX
!
¢tJ
Desired & Actual Simu. Displacement0.2
0
-a -0.2tmCO 0 5 10 15 20
t (sec)
E
>-,CO
o_>..
!
¢tJ(9
OCO
Ev
NI
CO
o_r,,,J
I¢o(9
CO
0.2
0
-02-. , , ,0 5 10 15 20
0.2
0
-02 • , i i .io
0 5 10 15 2O
t (see)
Figure B.1. Classical Algorithm Roll Doublet Pulse Input.
124
CLASS[CAL ROLL I_ST CASE
DOUBLET INPUT
40
(D
v
"_ 20n
I
rn<
00
..-..1
_0¢-
I--I
rm
<-10
1
"_ 013.
I
133<
-10
Aircraft Angular Position
I
5I |
10 15
t (see)2O
| I I
5 10 15
t (sec)2O
-o 40
t-Q_
I
m 20O3
CO
"o 0mo3
v I
t-
I I 1 !
5 10 15 2O 5
t (sec)
Desired & Actual Simu. Anglar Position
0 15 20
rf_09
o5
"_ 0en03
G9
!
m009
o5
(D"a-1m 009
5 10
t (sec)
I I
5 10
t (sec)
|
15 2O
" ,¢ ,.
I
10
t (sec)
I
15 2O
Figure B.1. Classical Algorithm Roll Doublet Pulse Input.
125
-15
00
1
,.Q"-'0
-10
1
--.-0!
-10
Aircraft Angular Rate
5I I
10 15
t (sec)
2O
-102O 0
Simulator Angular Rate
| I |
5 10 15
t (sec)
2O
L
5i !
10 15
t (sec)
1t,/]
t_
"-'0
oO-1
2O 0 5 10 15
t (sec)2O
!
5i !
10 15
t (sec)
1
c_
"ov0
O9-1
2O 0I , |
5 10 15
t (sec)2O
Figure B.I. Classica}Algorithm goU Doublet Pulse Input
126
CLASSICAL ROLL TEST CASEDOUBLET INPUT
•'Aircraft Specific Force at Pilot Head1
<
E oX
!
LL<
-10
I
5I !
10 15
t (sec)
2O
1..--=,,
<
E ov
X!
LI.CO
Simu. Specific Force at Pilot Head
-10
i I !
5 10 15 20
t (sec)
5
>', -5I,<
-100
!
5i !
10 15
t (sec)2O
5
>;', -5LI._O
-100
i i |
5 10 15
t (sec)
2O
_7.
<
E
N, -9LL<
-100 5
i i
10 15 20
t (sec)
-8A
<
E -9N
!
Ia_O3
-100
| I
5 10
t (sec)
|
15 2O
Figure B.1. Classical. Algorithm Roll Doublet Pulse Input.
127
_NC(r) & Simu.(g) Sensed Specific Force@3
E
X!
"LI.ca009
-1 ' ' 'co 0 5 10 15 20
< t (sec)
<mA/C(r) & Simu.(g) Sensed Specific Force03---5E
v
u_0
>-,LL "51 ' ' 'o_ 0 5 10 15 20< t (sec)
_NC(r) & Simu.(g) Sensed Specific Force03 - .
E 5N
!
L_60060
JcO. 5N
| • ILL60 0 5<
03
E_
,o.
3
2ONC(r) & Simu.(g) Sensed W
60 0od
3 -lo , , ,60 0 5 10 15< t (sec)
03 NC(r) & Simu.(g) Sensed W1
"t3
!
3o6060
oO
3-1 ' ' '60 0 5 10 15< t (sec)..._" A/C(r) & Simu.(g) Sensed WO3
1"1o
t,=!
3o6060
, , 3-110 15 20 60 0
<t (sec)
5 10
t (sec)
!
15
2O
2O
2O
Figure B.1. Classical Algorithm Roll Doublet Pulse Input
128
CLASSICAL ROLL TEST CASEDOUBLET INPUT
E
Z 0.10
0ZLU_-0.1XUJ
O
E 0.5
Zo
0ZUJI---X,,,-0.5
0
Jack 1
! I
5 10
t (sec)Jack 3
• I !
5 10
t (sec)Jack 5
!
15 20
E 0.5
Zo
0ZLLI
;_ -0.5LLI
0
!
15 20
| i !
5 10 15 20
t (sec)
Ez 0.1O
0ZLU
_-0.1LLI
0
E---- 0.5Zo
0ZuJI--x-0.5U.I
0
E O.5 !
0ZLU
-0.5-XLU
0
Jack 2
I I i
5 10 15
t (sec)Jack 4
I
5b I
• 10 15
t (sec)
Jack 6
I I
5 10
t (sec)
|
15
Figure B.1. Classical Algorithm Roll Doublet Pulse Input.
2O
2O
2O
129
OFIiMAI ROLL TEST CASEDOUBLET INPUT
IA
oq<
E"_0X
!
oo<
-I0
I
O3
_0N
o<
-10
• NC Accel. at Centroid of NC
! I I ,,,
5 10 15
t (sec)2O
0.1
E"-" 0x,o0O3
Simu. Accet. at Centroid of Simu.
• i |
5 10 15 20
t (sec)
5 10 15
t (sec)2O
_0.2
o_-0.2O3
0I !
5 10
t (sec)
i " I I
5 10 15
t (sec)
2O
0.2¢N
E"-" 0
(/3-0.2
0 5|
10
t (see)
Figure B.2. Optimal Algorithm Roll Doublet Pulse Input.
h
15 20
,,! ,-,
15 2O
130
0.2
03
E
x, o
03
-0.20
,, 0.2
>., o°_
> -0.203
0
0.2A
Ev
N, 0
(,,9
-0.20
Simu. Velocity in Inertial Coord.
I I |
5 10 15
t
I I
5 10
t Csec)
I
.15
2O
2O
Ev
XI
r_co
X!
E3cO
E
>-,
mo3
Desired & Actual Simu. Displacement
0.2
E
N,E3cO
N,
Oo9
0
-02". , i ,
0 5 10 15 2O
t
0.2
0
0.2
0
-02,
5 10 15 20 0
• t (sec)
5 10 15 20
t (sec)
i I |
5 10 15 2O
t (sec)
Figure B.2. Optimal Algorithm Roll Doublet Pulse Input.
131
OFTIMA_ ROLL TEST CASEDOUBLET INPUT
4O
00
.--.1
"_0
l:0'==:-1
0
{3)
"{3V
"_ 013.
I
I=,==:
-10
Aircraft Angular Position .
i
5| |
10 15 20
t (sec)
,,, .t,
5! I
10 15
t (sec)2O
.t. ; I =,
5 10
t (sec)
Figure B.2.
!
15 20
Optimal Algorithm Roll
Desired & Actual Simu. Anglar Positior40"10 _,_
.m
t-_-, 20O0O0o_ 0
(I1"_ -20 ' 'm 0 5
"-'1
e-
"_ 0m
(DV
!
mO
I13
| |
10 15 20
t (sec) .
I
5! I
10 15
t (sec)
=, °
2O
5L
10
t (sec)15 20
Doublet Pulse Input.
132
15
00
1@3
"10---0
-10
1
¢:O
"O---0,-¢,
-10
. Aircraft Angular Rate
,5 10
t (sec)
15 20
2OSimulator Angular Rate
O9-10
0 5I i
10 15
t (sec)
2O
1
(D
"---"0
O9I I I ,. el i i I
5 10 15 20 0 5 10 15
t (sec) t (sec).20
1o=
(D"0vO
O9, i i -1 ,
5 10 15 2O 0 5
t (sec)
L !
10 15
t (sec)
2O
FigureB.2. Optimal Algorithm Roll Doublet Pulse Input.
133
OPTIMAL ROLL TEST CASEDOUBLE1" II_PUT
Aircraft Specific Force at Pilot Head1
E oX
I
<--1 I | •
O. 5 10 15 20t (sec)
1c'q
E o
xLL.CO
Simu. Specific Force at Pilot Head
-10
I t I
5 • 10 15 2O
t (sec)
• 5¢',q
0E>;', -5u.
-100
I . , I I
5 10 15 20
t(.sec)
5
;o_', -5U.03
-100
I
5&, ,, !
10 15
t (sec)
20
-7A
¢q
--8
N,-9
-100 5
-7A
C'q
= -8E
v
N, -9LI.00
I I | I
10 15 20 10 15
t (sec) t (sec)
/-10
0 5 __0
Figure B.2. Optimal Algorithm RollDoubletPulseInput.
134
_NC(r) & Simu.(g) Sensed Specific Force _ NC(r) & Simu.(g) Sensed W_1 _20
x, . co 0
X' ._ , , , _:-10 ' ' '
-'0 5 10 15 20 _ 0 5 10 15
t(sec) <.. t (see)_NC(r) & Simu.(g) Sensed Specific Force NC(r) & Simu.(g) Sensed W
5 {-1oo 0 5 • 10 15 20 ¢n 0< t (sec) <
_A/C(r) & Simu.(g) Sen._-_:t Specific ForceO'3
N!
(nO
_-5N,
<
i i !
0 5 10 15 20
t (sec)
Q3
c:_ 1(D"O
I
5o03(,0
0<
20
i I i
5 10 15
t (se c)
NC(r) & Simu.(g) Sensed W• ". ,. . . .
2O
j i |
5 10 15
t (sec)
2O
Figure B.2. Optimal Algorithm Roll Doublet Pulse Input.
135
.OPTIMAL ROLL TEST CASEDOUBLET INPUT
E 0.4
z 0.20
w --0.2
_ -0.4.W '
0 5
E 0.5
ZO
0ZW
_' -0.5W
0
7-0ZWI--X-1W
0
Jack 1
|
10
t (sec)Jack 3
E_.I
| , i,,
5 10
t (sec)Jack 5
i
5
W
' W15 2O 0
Ev
z 0.5
, LU15 20
E
Z 0.5O
0ZLU
_ --0.5LLI
0
Jack 2
! , I
5 10
t (sec)Jack 4
|m i
0 5 10
t (see)Jack 6
|
15 2O
I
15 20
i . i I I I
10 15 20 5
t (sec)
I
10
t (sec)
|
15 2O
Figure B.2. Optimal Algorithm Roll Doublet Pulse Input.
136
NASA ROLL TEST CASEDOUBLET INPUT
1
E 0v
X!
O
-10
A
¢N
8-1
.0
E 0v
N!
OO
-1-0
A/C Accel. at Centroid of NC Simu. Accet. at Centroid of Sirnu.0.1
04
69
E---- 0x,OO
-0.10
| I i ! I , I
5 10 15 20 5 10 15
t (sec) t (sec)
2O
I I I I I I
5 10 15 20 5 10 15
t (sec) t (sec)
0.10,1
o_
E-0
0
-0.1,0
i
2O
0.1C_
E--" 0N,OO(D
,0.1.0
I I I I I I
5 10 15 20 5 10 15
t (sec) t (sec)2O
Figure B.3. NASA Adaptive Algorithm RoU Doublet Pulse Input.
137
.0.2A
E
x, oGO
-0.20
0.2
{_, o
-0.20
0.2A
E
N, 0t.O
-0.2
0
Simu. Velocity in Inertial Coord.
-- ,, I,, I i
5 10 15 20
t (sec)
I ! I
5 10 15
t (sec)2O
5 lo i5t (sec)
A
E
x,E3
od
x,_B
"10tmO3
E
Desired & Actual Simu. Displacement
0.2
0
-0.2"I, I I
0 5 10 15 20
t (sec)
_', 0.2
20
03(D
"a -0.2
0 5 10 15 20
" t (sec)
EN 0.2
!
Q
i |
10 15
t (sec)
20
Figure B.3. NASA Adaptive Algorithm Roll Doublet Pulse Input.
138
NASA ROLL TEST CASE
DOUBLET IN'PUT
40
_ 20!
en<
00
.-.1
¢U"-0¢-
|
en
<-10
1
v
"_ 0
!
en<
m 1 , ,
0
Aircraft Angular Position
5I |
10 15
t (sec)
2O
"_ Desired & Actual Simu. Anglar Position
5/0
0 5
.m
.c:nl0
!
rr_CO
o5Gr)a)
t_CO
(D
v 1aJd)¢-
_o123CO
o5
•u 0I:GCO
a) ••u 1
10 15 20
t (sec)
I I ! I ] !
5 10 15 20 5 10 15
t (sec) t (sec)
0
2O
n!
t_CO
o5co
d)"Ot_CO
I I I --1 I !
5 .10 15 20 0 5 10 15
t (sec) t (sec)2O
Figure B.3. NASA Adaptive Algorithm Roll Doublet Pulse Input
139
Aircraft Angular Rate15
00 5
t/)i ,, 0
10 15 ' 20 0
t (sec)
Simulator Angular Rate
5i i
10 15
t (sec)
2O
109
¢30
"10"---"0
1A
"-'0,o"
03I ' 'i ' I -1 , , a
5 10 15 20 0 5 10 15
. t (sec) t (sec)
2O
"- 1
tZ)
(D"O---0
<-1
"1eo
¢30
"10---0V
O3
I I I _1 | i I
5 10 115 20 "0 5 10 15
t (sec) t (sec)
2O
Figure B.3. NASA Adaptive Algorithm Roll Doublet Pulse Input.
140
NASA ROLL T_.ST CASE
DOUBLET INPUT
Aircraft Specific Force at Pilot Head1
,<e"J-
E oX
I
U..<
-10
1¢q
E oV
x,iit,O
Simu. Specific Force at Pilot Head
I ! ! --I I I I
5 10 15 20 0 5 10 15 20t (sec) t (sec)
A sI_4
< .10/0 5
|
1CN<
=0E
>;,-1U.
-20
I I | I
10 15 20 5 10 15
t (sec) t (sec)
2O
-7A
O4
= -8E
N -9LL</
I-100 5
-9.6
N, -9.8LLt._
I I i I i
10 15 20 0 5 10 15
t (sec) t (sec)
Figure B.3. NASA Adaptive Algorithm Roll Doublet Pulse Input.
2O
141
<m_A/C(r)& Simu.(g) Sensed Spec_c Force1
E
x,Itoo00O
=5
-1 ....oo 0 5 10 15 20< t (sec)
<m_A/C(r)& Simu.(g) Sensed Specific ForceO3
5E
v
It
.,-50 5 10 15 20
< -. t (sec)"_NC(r) & Simu. (g) Sensed Specific Force
_5N,ItcoO03
0_-5N
!
Itc,o :0<
/
A
O3
20
-10_ 0
v
$
_0
_-1¢n 0,<
!
_0
, , , _-15 10 i5 20 oo 0
t (sec) <
NC(r) & Simu.(g) Sensed W
,/ \
1 I i
5 10 15
t (sec)
A/C(r) & Simu.(g) Sensed W
2O
,_= _ |
5 10 15
. t (sec)NC(r) & Simu.(g) Sensed W
2O
i , i a ,,.
5 10 15
t (sec)
2O
Figure B.3. NASA Adaptive Algorithm RoU Doublet Pulse Input
142
NASA ROLL TEST CASEDOUBLET INPUT
-Ev
z 0.10r- 0ZW__.-0.1XW
0
E 0.2
Z0
0ZW
:_ -0.2w
0
E
ZW
..0.2XW
0
Jack 1
J
5 10
t (sec)Jack 3
!
15
5 10
t (sec)Jack 5
15
2O
2O
E
'0.1
0ZLU_- -0.1XW
0
E 0.2
Jack 2
I
5.
ox -0.2,UJ
0 5
E
z 0.20
0ZW
:_ --0.2W
0
!
10
t (sec)Jack 4
I
10
t (sec)Jack 6
!
15
!
15
| l a i I
5 10 15 20 5 10
t (sec) t (see)
|
15
2O
2O
2O
Figure B.3. NASA Adaptive Algorithm Roll Doublet Pulse Input.
143
ADAPTIVE ROLL TEST CASEDOUBLET ]IN'PUT
._.I
oO
<-1
0
1A
_0
-10
'iA
<¢0
E---0
0<
-10
NC Accet. at Centroid of NC
I I I
5 10 15 20
•t
0.1
0X
OO0
-0.10
Simu. Accel. at Centroid of Simu.
I | |
5 10 15 20t (sec)
A£N<¢/)
F:
>-|
8
0.1
0
' -0.15 10 15 20 0
t (sec)
5 10 15 20
t (sec)
L'N<GO
E
N,30
oO
0.1
0
I I , i
5 10 15 20 "0"10
t (.sec)
! ! )-
5 10 15 20
Figure B.4. UTIAS Adaptive Algorithm Roll Doublet Pulse Input.
144
E
X!
.m
0.2 ¸
0
Simu. Velocity in Inertial Coord. ,E-- Desired & Actual Simu. Displacement0.2'
0.2
E
>;., 0
-0.20
x,Oo3
0.2
w
Ev
N o
oO
0xO3
"10Q_0
, ' ' -02. '5 10 15 20 0 5
t (sec)
! !
10 15
t (sec)
E---- 0.2
I i I t i i
5 10 15 20 5 10 15
t (sec) t (sec)
2O
>-!
E3
0
.>;.(D
13-0.2
r.n 0
E--- 0.2N
I
0N,
i
' ' ' _-02. ' ' '5 10 15 20 m 0 5 10 15
t (sec) t (sec)
20
20
Figure B.4. UTIAS Adaptive Algorithm Roll Doublet Pulse Input.
145
ADAFrIVE ROLL TEST CASEDOUBLET INPUT
4O
_,2o_o
0
(3
_3V
(U_0t-
<-10
1A
"1oV
"_ 0
-10
Aircraft Angular Position
/i I I
5 10 15
t (sec)
2O
I I |
,5 10 15
t (sec)2O
I I I
5 10 15 20
t (sec)
Figure B.4. UTIAS Adaptive Algorithm
"_ Desired& Actual Simu. Anglar Positior
°_
r-n
I
ml060
05
®
mcD
A
/0
0
"10"-'1
| , | !
5 10 15 20
t (s_)
(D.E
|
{13CO=0e3
DQ03
o
0
-10
I I I
5 " 10 15 20
t (sec)
°_
I
m0O3
=Oo_
-{3.1 , ,m 0 5 10¢,O t (._)Roll Doublet Pulse Input.
I
15 20
146
15
_5
00
1O'3
t_
"1o"-'0ET
-10
1e3
"1o----0,-¢,
-10
Aircraft Angular Rate
5 10 15
t (sec)
I I I
5 10 15
t (sec)
10
_5
O90
20 0
1A
t3_
"o"_0
-120 0
Simulator Angular Rateq .... ,
5 10 15
t (sec)2O
I | I
5 10 15
t (sec)
2O
1
"1o----0
oO, , , -1 ' ' '
5 " 10 15 20 0 5 10 15
t (sec) t (sec)
2O
Figure B.4. UTIAS Adaptive Algorithm Roll Doublet Pulse Input.
147
ADAPTIVE ROLL TEST CASEDOUBLET II_UT
Aircraft Specific Force at Pilot Head1
03
E o
x,<
-1 i , ,0 5 10 15
t (sec)
2O
Simu. Specific Force at Pilot Head1
O4
03
E o
x,LLCO
-10
i i i
5 10 15 20
t (sec) ..
-100 5 10 15
t (see)2O
_.2
>7,-2LL¢./'3
-40
|
5i |
10 15
t (sec)
2O
O3
E
NI
LL<
-7
-9
-100 5
i I
10 15
t (sec)
•Figure B.4.
2O
-9A
E-9.5LI..
-100
L
5I ,., r
10 15
t (sec)
UTIAS Adaptive Algorithm Roll Doublet Pulse Input.
2O
148
<_'NC(r) & Simu.(g) Sensed Specific Force(D
v
x,u.mO
-1 ' ' '¢n 0 5 10 15 20< t (sec)
<m'-'NC(r)& Simu.(g) Sensed Specific Force5.
E
o"J
C_• 20"o
_ 10
ff'j
NC(r) & Simu.(g) Sensed W
"oV
!
5o
/,,,
o-10 ' ' '
0 5 10 15
t (sec)NC(r) & Simu.(g) Sensed W
09
00 0
"10
t.--.!
5o0"J03
o_
5-1<
2O
I i " I
5 10 15
t (sec)
NC(r) & Simu.(g) Sensed W
2O
i i I
5 10 15 20
t (sec).
Figure B.4. UTIAS Adaptive Algorithm Roll Doublet Pulse Input.
149
ADAPTIVE ROLL TEST CASEDOUBLET INPUT
A
E 0.1
Z0_- 0ZUJF-X-0.1UJ
0
A -
E
z 0.2oF- 0ZuJ
_ --0.2
0
Jack I
J
E 0.1v
Z0
0ZUJ
:_ -0.1
0
Jack 2
J ] ,, I | !
5 10 15 20 5 10
t (sec) t (sec)Jack 3 Jack 4
/
5 10 15 20 0 " 5 10
t (._=c) t (sec)Jack 5 Jack 6
E
z 0.20F- 0ZLU .0.2I-XLU
0
/
!
15
15
I, I I
5 10 15 20 5 10
t (sec) t (sec)
|
15
Figure B.4. UTIAS Adaptive Algorithm Roll Doublet Pulse Input.
2O
2O
2O
150
Appendix ¢.
Phase 2 Test Run Output Figures
Figure C. 1.
Figure C.2.
Figure C.3.
Figure C.4.
Figure C.5.
Figure C.6.
Figure C.7.
FigureC.S.
Figure C.9.
Figure C. 10.
Figure C. 11.
Figure C. 12.
Optimal Algorithm Surge Half Sinusoidal Pulse Input.0.1 I-Iz half cycle, 1 m/s 2 peak x-acceleration input.
NASA Adaptive Algorithm Surge Half Sinusoidal Pulse Input.0.1 Hz half cycle, 1 m/s 2 peak x-acceleration input.
Surge Pulse Input Specific Force Comparison.
Comparison of the specific forces for both algorithms.
Optimal Algorithm Surge 3 m/s2/s Ramp-Step Input.3 m/s2/s slope, 5 m/s 2 peak x-acceleration input.
NASA Adaptive Algorithm Surge 3 m/s2/s Ramp-Step Input.
3 m/s2/s slope, 5 m/s 2 peak x-acceleration input.
Surge 3 m/s2/s Ramp-Step Input Specific Force Comparison.
Comparison of the specific forces for both algorithms.
Optimal Algorithm Surge 5 m/s2/s Ramp-Step Input.
5 m/s2/s slope, 5 m/s2 peak x-acceleration input.
NASA Adaptive Algorithm Surge 5 m/s2/s Ramp-Step Input.
5 m/s2/s slope, 5 m/s 2 peak x-acceleration input.
Surge 5 m/s2/s Ramp-Step Input Specific Force Comparison.
Comparison of the specific forces for both algorithms.
Optimal Algorithm Sway Half Sinusoidal Pulse Input.0.5 Hz half cycle, 1 m/s 2 pea k y-azz, eleration input.
NASA Adaptive Algorithm Sway Half Sinusoidal Pulse Input.0.5 Hz half cycle, 1 m/s 2 peak y-acceleration input.
Sway Pulse Input Specific Force Comparison.
Comparison of the specific forces for both algorithms.
151
Figure C. 13.
Figure C. 14.
Figure C.15.
Figure C.16.
Figure C. 17.
Figure C.18.
Figure C. 19.
Figure C.20.
Ftgure C.21.
Figure C.22.
Figure C.23.
Figure C.24.
Figure C.25.
Optimal Algorithm Heave Square Pulse Input.
3 m/s 2 peak, 5 second duration z-acceleration input.
NASA Adaptive Algorithm Heave Square Pulse Input.
3 m/s 2peak, 5 second duration z-acceleration input.
Heave Square Pulse Input Specific Force Comparison.
Comparison of the specific forces for both algorithms.
OptimalAlgorithmRollDoubletPulseInput.0.I rad/sec'peak,5 seconddurationinput.
NASA Adaptive Algorithm Roll Doublet Pulse Input.0.1 rad/sec 2 peak, 5 second duration input.
Roll Doublet Specific Force Comparison.Comparison of the specific forces for both algorithms.
Optimal Algorithm Pitch Doublet Pulse Input.0.1 rad/sec 2 peak, 5 second duration input.
NASA Adaptive Algorithm Pitch Doublet Pulse Input.
0.1 rad/sec x peak, 5 second duration input.
Pitch Doublet Specific Force Comparison.Comparison of the specific forces for both algorithm_.
Optimal Algorithm Yaw Doublet Pulse Input.
0.1 rad/see 2 peak, 5 second duration input.
NASA Adaptive Algoritlma Yaw Doublet Pulse Input.0.I rad/sec2peak,5 seconddurationinput.
Yaw DoubletSpecificForceComparison,
Comparison ofthespecificforcesforboth algorithms.
Sway PulseInputBrakingAlgorithmTest.I0 m/s2peak,I0 seconddurationy-acx_erationinput.
Specific force comparison figures are labelled as follows:Line with no marks - aircrat_ response.
Line with marks - simulator response: o - NASA Adaptive; * - Opttm
152
A/C Accel. at Cent_oid of A/C
0.5
o_-0.5<
-1
11
10 20 30t(_
m -0.1
40 0
0.1
0, _ 0.05
o,_ -0.5 m -0.05
-1 -0.10 10 20 30 40 0
t (sec)1 0.1
0.5
_o'2<_ -0.5
0.05go'2m -0.05
-1 ' ' ' -0.10 10 20 30 40 0
t (see)
Simu. Accel. at Centroid of Simu.
i
10i I
20 30t (sec)
i
10i i
20 30t (see)
10 20 30t (sec)
4O
40
40
Figure C.I. Optimal Algorithm Surge Half Sinusoidal Pulse Input.
153
Aircraft Angular Position0.1
Simu. Anglar PosWon
0.5
e)
oe-
n..0.5
-10
,-, 0.5ol6
t oI- -0.5
-10
. m.. i
10 20 30t (sec)
40
I I i
10 20 30t (sec)
4O
0.05
0
CL-0.05
-0.10 10
2
e_.o
0 10
i i
2O 30t (sec)
i I
20 3Ot (sec)
4O
40
0.5A
60
I1.-0.5
-10
0.5
0
;_ -0.5
.I ]I i | i i |
10 20 30 40 0 10 20 30t (sec) t (sec)
4O
Figure C.1. Optimal Algodthm Surge Half Sinusoidal Pulse Input.
154
_" 0.5
< ..0.5
Aircraft Angular Rate0.1
o.05_
0
_-0.05
Simulator Angular Rate
I I i | 2=0 i-10 10 20 30 40 -0.10 10 30
t (sec) t (sec)
'k-1 -1 , , ,
0 10 20 30 40 0 10 20 30t_ t_
1 0.1
= I i
-10 10 20 30 40 -0.10 10 20 30
t (sec) t (sec)
40
40
4O
Figure C.I. Optimal Algorithm Surge Half Sinusoidal Pulse Input.
155
1
o.sx,
00
Nrcra_ Specific Force at Pilot Head0.3
-8
-10
-110
__"0.2
0.1
o
Simu. Specific Force at Pilot Head
, ., -0.1 ' ' '10 20 30 40 0 10 20 30 40
t (sec) t (sec)0.05
-0.05 ' 20 '10 20 30 40 0 10 30 40t (sec) t (sec)
t t 30 i i t10 20 40 10 20 30t (sec) t (sec)
-8
-1o[
-14 I
0 4O
Figure C.1. Optimal Algorithm Surge Half Sinusoidal Pulse Input.
156
A/C(..)& Simu.(-)SensedSpecificForce
_0.5/ \
" 0_ / '_ .....
I0
_-0.5
i . i i
0 10 20 30t (sec)
0.5
o(/)u).,P -0.5074:
"1 i , | i
0 I 0 20 30t (see)
Ev
N -3.9u.u)(/)
-4ILO)< -4.1
0
oO.O5
offl
-0.os
_ -0.140 0
10.5
< -140 0
1
_0.5
0)¢9
A/C(..) & Simu.(-) Sensed angular rate
i i i
10 20 30t (sec)
10 20 30
_" -0.5
i i i -1 i
10 20 30 40 0 10 20 30
t (sec) t (sec)
40
40
40
Figure C.1. Optimal Algorithm Surge HalfSinusoidal Pulse Input.
157
Simu. Transla'donal Velocity Simu. Translalional Displacement0.3
O,2
I | !
0 10 20 30 40t (sec)
U)
0.2
0.1
0
-0.10
1
i
10i b
20 30t (sec)
_0.5 __, 0.5
-0 u) -0.5
-1 -10 10 20 30 40 0
t (sec)
0.05
N 0
O)-0.05
10 20
t (sec)
L
30
i i
20 30
t (sec)
4O
4O
40
Figure C.I. Optimal Algorithm Surge Half SinusoidalPulse Input.
158
0.1
"- 0J¢0¢8
.-j-0.1
0
Jack Extension
-0210 20 30 40 0 10 20
t (sec) t (sec)
10 20 30 40 0 10 20
t (sec) t (sec)
10 20 30 40 0 10 20
t (sec) t (sec)
Jack Extension
30 40
3O 40
30 40
Figure C.1. Optimal Algorithm Surge Half Sinusoidal Pulse Input.
159
1
0.5E
-0.5
-1
0
0.5Ev 0>-6
-o.5
-1 o
0.5Ev 0
o< -0.5
-10
A/C Accel. at Centroid of A/C
10 20 30 40t (sec)
Simu. Accel. at Cenlzoid of Simu.
I
-0.2 _ ...........10 20
t (sec)0
0.1
0.05"" 0
o_ -0.05
.... 0.1 , '10 20 30 40 0 10 20
t (sec) t (sec)
3O
0.1
0.05E
,3 -o.os
-0.1010 20 30 40 10 20
t (sec) t (sec)
i
30
t
3O
4O
40
4O
Figure C.2. NASA Adaptive Algorithm Surge Half Sinusoidal Pulse Input
160
0.5A
o)IB
.0e-
n-0.5
-10
o..o.5
-I0
0.5
0
-,0.5
-10
AJrcraRAngular Pos_on
I1.
0.1
0.05
0
-0.05
Simu. Anglar Position
, , , -01. ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)3
18
"-1I--
00
i b i i |
10 20 30 40 10 20t (sec) t (sec)
0.5
0
-0.5
3O
| | | _1 i
10 20 30 40 0 10 20 30
t (sec) t (sec)
4O
4O
4O
Figure C.2. NASA Adaptive Algorithm Surge Half Sinusoidal Pulse Input.
161
AircraftAngularRate0.1
0.5
<_-0,5
, i i i
"10 10 20 30
t(sec)1
40
0.05
_ -0.05
-0.10
Simulator Angular Rate
i I i
10 20 30t (sec)
-10 10 20 30 40 0 10 20 30
t (sec) t (sec)1 0.1
, i i i | i
10 20 30 40 10 20 30t (sec) t (sec)
0.05
_ ._.05
.-0.10
e_0.5
0
<_-0.5
-10
40
40
40
Figure C.2. NASA Adaptive Algorithm Surge Haft Sinusoidal Pulse Input
162
_05x,"
00
Aircraft Speci_c Force at Pilot Head
| |
10 30
0.6
-8
V
N_: -10
-110
0.40.2
x,o
Simu. Specific Force at Pilot Head
, -0.2 ' ' '20 40 0 10 20 30
t (sec) t (sac)0.05
0
tn
005 ! i I
10 20 30 40 0 10 20 30
t (sec) t (sec)-8
N, -12u..(/3
-14• ! i i i
10 20 30 40 0 10 20 30t (sec) t (sec)
4O
4O
40
Figure C.2. NASA Adaptive Algorithm Surge Half Sinusoidal Pulse Input.
163
A/C(..)&Simu. (-) Sensed Specific Force
0
O.S0
-10
0.1
0.05
_'-0.05
,,N-3.9¢J)¢/J
(/)<: -4.1
0
A/C(..) & Simu.(-) Sensed angular rate
-0.1 , , ,10 20 30 40 0 10 20 30
t (sec) t (sec)
10 20 30 40 0 10 20 30t (sec) t (sec)
1
_0.5
't-o
¢0U)
-0.5
| | I ml I ,,, ! I
10 20 30 40 0 10 20 30t (sec) t (sec)
4O
40
40
Figure C.2. NASA Adaptive Algorithm Surge Half Sinusoidal Pulse Input.
164
-0.5
-I0
0.1
0.050N
-0.10
Simu. Translational Velodty
10 20 3Ot (sec)
i i i
10 20 30t (sec)
v
40
4O
0.6Simu. Translational Displacement
0.4
-0_0 10
0.5
i i
20 30
t (sec)
(/3-0.5
-10
0.1
i i
10 20 30t (see)
0.05
(0-0.05
' ' ' -0.1 _ '10 20 30 40 0 10 20
t (sec) t (sec)
3O
4O
40
4O
Figure C.2. NASA Adaptive Algorithm Surge Half Sinusoidal Pulse Input.
165
0
Jack Extension
10 20t (sec)
30 40
O.2
E 0.1
00
m -0.1
-O.2
0
Jack Extension
10 2Ot (sec)
30 4O
0.1
0j_,(,1
-0.1
0*-- m ,
10 20 30 40 0 10 20 30
t (sec) t (sec)
10 20 30 40 0 10 20 30
t (sec) t (sec)
40
40
Figure C.2. NASA Adaptive Algorithm Surge Half Sinusoidal Pulse Input.
166
1.2A/C & Simu. Spedfic Force at Pilot Head
i I I I I | t I !
0.6
_n 0.4
0(
-O.20
0.8
0.6
0.4
o.2
-O.20
I ] I i I I 1 I t
2 4 6 8 10 12 14 16 18 20t (sec)
A/C & Simu. Sensed Specific Force at Pilot HeadI I I I t I
i I i I I 1 I I I
2 4 6 8 10 12 14 16 18 20
Figure C.3. Surge Pulse Input Specific Force Comparison.
167
5
x, °
-5 _0
0.50
u< -.0.5
-10
ArC Accel. at Centroid of NC
l , • ,
i i I
10 20 30 40t (sec)
Simu. Accel. at Centmid of Simu.
°'IO.2
!or-0.4
0
0.1
i
10 20 30t(_ ..
10 20 30
t (sec)
i I I
10 20 30t (sac)
0.050
o¢n .0.05
-0.14O 0
0.1
0.05
-0.1
4O 0
4O
| | i
10 2O 3O 40t (sec)
i .... I ....... i
10 20 30t (sec)
Figure C.4. Optimal Algorithm Surge 3 m/s2/s Ramp-Step Input.
4O
168
0.5A
Q
0me-
13.-0.5
-10
0.5
oJ=
-0.5
-10
0.5
0
-0.5
-10
Aimmft Angular Position Simu. Anglar Position0.1
0.05
0J¢a.
-0.05
' ' ' -01. ....10 20 30 40 0 10 20 30
t (sec) t (sec)
_6
J¢i-2
i " I i O i i i
10 20 30 40 0 10 20 30t (sec) t (sec)
0.5
0
-0.5
| I | --1 _ i
10 20 30 40 0 10 20t (sec) t (sec)
Figure C.4. Optimal Algorithm Surge 3 m/s2/s Ramp-Step Input.
30
40
4O
40
169
._ 0.5O
!
<_-0.5
-10
0.5
-10
0.5
-10
Aircraft Angular Rate0.1
0.05
0
_ -0.05
Simulator Angular Rate
' ' ' -01. , , ,10 20 30 40 0 10 20 30
t (sec) t (sec)
i | |
10 20 30 40 0 10 20 30t (sec) t (sec)
0.1
0.05
0
-0.05
....... -0.1 ' '10 20 30 40 0 10 20 30
t (see) t (see)
Figure C.4. Optimal Algorithm Surge 3 m/s2/s Ramp-Step Input.
40
4O
4O
170
6AimrattSpecificForceatPilotHead
i i I
0 10 20 3O 4Ot (see)
_0.5
¢/)
;
0
0.05
Simu. Specific Force at Pilot Head
i i ,
10 20 30t (sec)
4O
0
I -005 ' ' '0 10 20 30 40 0 10 20 30
t (sec) t (sec)..8 -8
4O
N,-10
-11 ' ' '0 10 20 30 40
t(_
N, -12iiO_
-14
0| , i
10 20 30t (sec)
4O
Figure C.4. Optimal Algorithm Surge 3 m/s2/s Ramp-Step Input
171
V
Xu. 0¢0
,,x.2
0
0.5
0o_m.
-0.5¢0<
-10
,,N-3.9
A/C(..) & Simu. (-) Sensed Specific Force
/
10 2O 3Ot (sec)
m i t
10 20 30t (sec)
o)w.N -4I1.
_-4.1
0
0.1
0.05
3 oo}
O)
< -0.14O 0
1
® 0.5
'1"3 oo')¢/)
7-0.5
A/C(..) & Simu.(-) Sensed angular rate
I " i i
10 20 30t (sec)
40
10 20 30 40
t(_
C/)<C
.10 20 30 40 0 10 20 30
t (sec) t (sec)
4O
Figure C.4. Optimal Algorithm Surge 3 m/s2/s Ramp-Step Input.
172
'0.5
o_-0.5
-I
0
1
co-0.5
-I0
0.1
m -.0.05
-0.10
Simu. Translalional Velodty Simu. Transla6onal Displacement
10 2O 3Ot (sec)
4O
0.5
u) 0
-0.50
i i J
10 20 30
t (sec)
i i i
10 20 30t (sec)
0.5
(0-0.5
-140 0
0.1
10 20 30
t(_
10 20 30t (sec)
0.05
_, oa
-0.05
-0.140 0 10 20 30
t (sec)
Figure C.4. Opdma/Algorithm Surge3 nYs2/sl_.mp-Step _put.
40
40
4O
173
F-_ -0.2
-0.4
om
i)
Jack Exten_on
A
Ein.1¢om
-,j
i i
10 20t (sec)
i
30 40
Jack Extension
E °sl
-0.5 _ , , ,0 10 20 30
t (sec)
0.2
0
-0.2
0
0.5
0
i i
10 20
t (sec)
i t
10 20
t (sec)
i
30 4O 0 10 2O
t (sec)
J , d
30 40 0 10 20
t (sec)
30
I
30
40
4O
Figure C.4. Optimal Algorithm Surge 3 m/s2/s Ramp-Step Input.
174
NC Accel. at Centmid of NC Simu. Accel. at Centroid of Simu.
0 10 20 30 40 0 10 20 30
t (sec) t (sec) •1 0.1
0.5
-o.s
_I i | i
0 10 20 30t (sec)
1
0.5
o
-05
-10
40
¢)to -0.05
i i i
10 20 30t (sec)
0.1
O3-0.1
i r ! I i
10 20 30 40 0 10 20 30t (sec) t (sec)
Figure C.5. NASA Adaptive Algorithm Surge 3 m/s2/s Ramp-Step Input.
4O
40
40
175
0.5
0"F" -o.51
-10
j o.0.s
-10
0.5
0
-0.5
-10
AJrcmttAngular Position Simu. Anglar Pos#don0.1
0.05
_ 0
11.-0.05
' ' ' -01. ' ' ,10 20 30 40 0 10 20 30
t (sec) t (sec)15
_10
__5
f
i | i 0 I I I
10 20 30 40 0 10 20 30t (sec) t (sec)
0.5
0
-0.5
i i i I1 i i t
10 20 30 40 0 10 20 30t (sec) t (sec)
Figure C.S. NASA Adaptive Algorithm Surge 3 m/se/s Ramp=Step Input.
4O
40
4O
176
Q
0
_-0.5
-10
1
0.5
0
<_-0.5
-10
-10
Aircraft Angular Rate Simulator Angular Rate0.1
0.05
, , , -01. ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)
I | i I i i
10 20 30 40 10 20 30t (sec) t (sec)
_0
0
0.1
0
_ -0.05
, , , -01. '10 20 30 40 0 10 20 30
t (sec) t (sec)
Figure C.5. NASA Adaptive Algorithm Surge 3 m/sZ/s Ramp-Step Iaput.
40
4O
40
177
6
V
,,X,2<
00
'1
-8
-10<C
-110
Aircraft Specific Force at Pilot Head
10
2
V
0o)
Simu. Specific Force at Pilot Head
' 11 i ,
20 40 0 10 20 30t (sec) t (sec)
0.05
0O_
-0.05 .....10 20 30 40 0 10 20 30
t (sec) t (sec)-8
10 20 30 40 0 10 20 30
t (sec) t (sec)
40
4O
40
Figure C.5. NASA Adaptive Algorithm Surge 3 m/s2/s Ramp-Step Input.
178
_,4
i2X
(n..><-2
-40
-10
E
N -3.9it.0"J0)
"_ -4.1
A/C(..) & Simu. (-) Sensed Specific Force
J i a
10 20 30t (sec)
40
i i |
10 20 30t (sec)
40
A/C(..) & Simu.(-) Sensed angular rote0.i
0.05
_ -0.05
<: -0.1 ' ' '0 10 20 30
t (sec)
,0 10
1
_0.5
Y
_--0.5
I i
20 30t (sec)
(0,<
t t . "1 :
10 20 30 40 0 10 20 30t (sec) t (sec)
40
40
40
Figure C.5. NASA. Adaptive Algorithm Surge 3 m/s2/sRamp-Step Input.
179
._o(/)
-1
Simu. Translational Velocity
0.5
(_ 0
Simu. Translational Displacement
, , , -0.50 10 20 30 40 0 10 20 30
t (sec) t (sec)
,0.5
o;_ -0.5
1 1
" 0.5
_o(t)
-0.5
t , , I I
-10 10 20 30 40 -10
t (sec)0.1 0.1
._o.o5 _ o.o_t
I I _, I
-0.10 10 20 30 40 -0.10
t (sec)
I i .... k
10 20 30t (sec)
10 20 30t (sec)
40
40
40
Figure C_. NASA Adaptive Algorithm Surge 3 m/s2/s Ramp-Step Input.
180
Jack Extension
0.5
" 0JIe0m
-0.5
0
0.4
,-- O.2
0
el-0.2
10i |
20 30
t (sec)i
0.4 | | I
0 10 20 30t (sec)
0.5
an 0
v |
0 10 20t (sec)
40
40
I
30 40
Jack Extension
0.5
V
0
-0.5|
0 10 20t (sec)
0.4
0 10 20 30t (sec)
¢D
el
0
-0.5|
0 10| |
2O 30t (sec)
4O
40
40
Figure C_S. NASA Adaptive Algorithm Surge 3 m/s2/s Ramp-Step Input.
181
A/C & $imu. Specif¢ Force at Pilot Head
! /
ooV!
0 1 2 3 4 "5 6 7 8 9 10t (sec)
A/C & $imu. Sensed Specific Force at Pilot Head
1' / _.e--eoocoocoocccc.c oocoooooocoo,_
-1 i, i i i.., i i i I i0 1 2 3 4 5 6 7 8 9 10
t (sec)
Figure C.6. Surge 3 m/s2/s Ramp-Step Input Specific Force Comparison.
182
"5
A/O Accel. at CentToidof A/O, , ,
_5 i | i
0 10 20 30 40t (sec)
Simu. Accel. at Centzoid of Simu.
0.5
co
-0.5-
1 0.1
I
10i i
20 30t (sec)
-1 _.10 10 20 30 40 0
t(_
0.5
,_ 41.5
-10
0,1
0.05
v
-0.1
10 20 30t (sec)
i _ , i i :
10 20 30 40 0 10 20 30t (sec) t (sec)
Figure C.7. OptimalAlgorithmSurge5 m/s2/sRamp-Step Input.
4O
40
4O
183
0.5Sm_
0J::n
-0.5
-I0
A
_, o.s
_ 0o
i- .0.5
-10
0.5
-0.5
-10
Nrcrafl Angular PosiUon
131ID
n
Simu. Anglar Posi'don0.1
0.05
0
-0.05
-0.10
8
i i J i m |
10 20 30 40 10 20 30t (sac) t (sec)
_6
e-_'2
i i I 0 I I ill i
10 20 30 40 0 10 20 30t (sec) t (sec)
0.5
-0.5
' ' •, -1 ' '10 20 30 40 0 10 20
t (sec) t (sec)
3O
l_i_re C.T. OptimalAlgori',J_SurSe5 m/s2/s_St_p T,.,p_.
4O
4O
4O
184
-10
1
o
0
<_-0.5
Aircraft Angular Rate
10 20 30t (sec)
=1 = = t
0 10 20 30
t(se_1
0.5Q
_-0.5
Simulator Angular Rate0.1
-10
0r,
"_ -0.05
-0.140 0
t i t
10 20 30t (sec)
-540 0
0.1
10 20 30
t (sec)
i | t
10 20 30t (sec)
0.05
o_ -.0.1_
-0.140 0
, t
10 20 30t (sec)
Figure C.7. Optimal Algorithm Surge 5 m/s2/s Ramp-Step Input.
40
40
4O
185
00
1
0.5
_-0.5
-10
-8
N_. -10
-110
NrcraR Specific Force at Pilot Head
10 20 30t (sec)
4O
x,u.¢0
00
0.05
Simu. Specific Force at Riot Head
t t , i
10 20 30t (sec)
2b10t (sec)
4O-0.05
0
-8
t i i
10 20 30t (sec)
10 20 30t (sec)
._-10
..N-12
U)
-14
40 0| i |
10 20 30t (sec)
Figure C.?. Optimal Algorithm Surge 5 m/s2/s Ramp-Step Input.
4O
=
40
4O
186
4
,,xo
-40
_"-0.5
-10
A/C(..) & Simu. (-) Sensed Specific Force
i I I
10 20 30t (sec)
i i I
10 20 30t(_
N -3.9It.¢0
N -4U.
-4.1
0i i i
10 20 30t (sec)
0.1
0.05?.
o"-0.05
<_ -0.14O 0
'. ID_2
<-4
40 0
1
_0.5
_: oU)U)
-0.5u)<:
-14O 0
A/C(..) & Simu.(-) Sensed angular rate
i I i
10 20 30t (see)
40
10 20 30 40t (sec)
10 20 3O 40t (sec)
Figure C.7. Optimal Algorithm Surge 5 m/s2/s Ramp-Step Input.
187
0,5
0-0.5
,0.5
o_-0.5
Simu. Translational Velocity
-1
0 10
-1 ''0 10
Simu. TmnslalJonal Displacement
0.1
0,5
(n 0
• -05. .....20 30 40 0 10 20 30
t (sec) t (sec) .
0,05
_ -0,05
I"0°1 , I
0 10
0.5
m -0.5
I l _I I i |
20 30 40 0 10 20 30t (sec) t (sec)
0.1
0.05A
E
N, oau)
-0.05
' ' -0.1 ......20 30 40 0 10 20 30
t (sec) t (sec)
Figure C7. Optimal Algorithm Surge 5 m/s2/s Ramp-Step Input.
4O
4C
4<
188
0.4
"-" 0.2E
"" 0
w_ -11.2
-0.4
0
Jack Extension
i
10|
2O
t (sec)
A
gt_4
0m
"3
0.5
0
, -0.530 40 0
Jack Extension
i i
10 20
t (sec)
i
30 4O
0.2
EV
0..1¢¢)¢l
--)
-0.2
0.5
,n 0
m"3
i *
10 20t (sec)
i
30 40
i *
10 20
t (sec)
02
E
_" 0om
"3
-0.2
0
|
30 40 0
i i
10 20
t (sec)
10 20t (sec)
lrgure C.7. Optimal Algorithm Surge 5 m/s2/s Ramp-Step Input.
30 4O
30 4O
189
5
-50
0.5
0
-o.5
-10
A/C Accel. at cen_roid of NC
0.50
Simu. Accel. at Centroid of Simu.
¢0 -0.5
0
0.1
0._ 0
_ -0.05
-0.10
I I I I b i
10 20 30 40 10 20 30t (sec) t (sec)
I ! J I | |
10 20 30 40 10 20 30
t (sec) t (sec)
0.10
m_.l
i I i
10 20 30 40 0 I 0 20 30t (sec) t (sec)
Figure C.8. NASA Adaptive Algodthm Surge 5 m/s2/s Ramp-Step Input.
4o
4o
4O
190
0.5G)
0m..ca.
-0.5
-I0
"_ 0.5
;:o,.cv- -0.5
-10
0.5
=00
O.-0.5
-10
Aimmlt Angular Position Simu. Anglar Position0.1
I ! I
10 20 30t (sec)
4O
0.05
0J_I1.
-0.05
-0.10
15
I i
10 20t (sec)
t
3O
i t i
10 20 30t (see)
4O
10 /
00
I I
10 20
t (sec)
I
3O
0.5
-0.5
| i |
10 20 30 40 "10
t(sec)10 2O 3O
t (see)
Figure C8. NASA Adaptive Algorithm Surge 5 m/s2/s Ramp-Step Input.
4O
4O
4O
191
Aircraft Angular Rate Simulator Angular Rate1 0.1
_= 0.5
0
<_-0.5
0.05
-1 ........ -0.10 0 20 0 40 0
t
0.5 to_ _ o_ _-
< -0.5
-1 " -50 10 20 30 40 0
t (sec)1 0.1
| i i
10 20 30t (sec)
i i I
10 20 30t (sec)
0.5
o<:-0.5
i I | I ,_ i
"10 10 20 30 40 10 20 30
t (sec) t (sec)
0.05
o_ -0.05
-0.10
Figure C.8. NASA Adaptive Algorithm Surge 5 m/s2/s Ramp-Step Input.
40
I
4O
40
192
6
x,,2<C
00
-8
N,u. -10<
-110
Aircraft Spedfic Force at Pilot Head
E
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Simu. Specific Force at Pilot Head
i i I D1 i " I i
10 20 30 40 0 10 20 30t (sec) t (sec)
0.05
(n
-005. ' ' '10 20 30 40 0 10 _
t(=_ t(_-8
-10
-12
i i i i i
10 20 30 40 0 10 20 30t (sec) t (sec)
Figure C.8. NASA Adaptive Algorithm Surge 5 m/s2/s R,_mp-Step Inpm.
4O
40
4o
193
4
_0U)
-40
(o<
0
N -3.9IL.(/)(0
A/C(..) & Simu. (-) Sensed Specific Force
L i |
10 20 30
t (_)
b i 1
10 20 30t (sec)
0.1
0.05
I
o(/)
< -0.140 0
1
_0.5
O_
A/C(..) & Simu.(-) Sensed angular rate
i i i
10 20 30t (sec)
i i i
10 20 30t (sec)
• _-0.5
i i | _1 i i i
10 20 30 40 0 10 20 30
t (sec) t (sec)
40
i40
40
Figure C.8. NASA Adaptive Algorithm Surge 5 m/s2/s Ramp-Step Input.
194
2Simu.TranslationalVelocity
1.5Simu.TranslationalDisplacement
i
10
0.5
_-0.5
-10
0.1
0.5
_o0) -0.5
! I i "1 I ! i
10 20 30 40 0 10 20 30t (sec) t (sec)
0.1
0.05
,_ o_-0) -0.05
-0.1 '0 10
0.05
-0.05
-0.10
i |
20 30 40 10 20 30
t (sec) t (sec)
Figure C.8. NASA Adaptive Algorithm Surge 5 m/s:/s Ramp-Step Input.
40
40
40
195
Jack Extension
0"5 t_"-
-° t-0.5
I
0 10
iv).I¢
m
I i
20 30t (sec)
4O
Jack Extension
0.5 '
-0.5/__ , . ,
,q.
oIu
0 10 20t (sec_
0.5
0
-0.5 -0.5
0 10 20 30 40 0 10 20t (sec) t (sec)
0.5
o(B
-'3
-0.5
i .
0.5
-0.5
3O 40
|
3O 40
on
a ! | |
0 10 20 30 40 0 10 20
t(_ t(_
I
30 40
Figure C.8. NASA Adaptive Algorithm Surge 5 nds2/s Ramp-Step Input.
196
2
1.5
i 1
" 0.5ffl
<
_.5-
-10
5
A/C & Simu. Specific Force at Pilot Head
I J ! I I I
b I I
O00000OOOOOOO
L I I I 1 I I I1 2 3 4 S 6
t (sec)
I
7 8 g 10
AJC& Simu. Sensed Specific Force at Pilot Headi I I I I i I I I
. IL_,_
_3
u._2¢0.6" 1¢0<
O_
-10
l I I I I l I I I
1 2 3 4 5 6 7 8 9t (sec)
10
Figure C.9. Surge 5 m/s2/s Ramp-Step Input Specific Force Comparison.
197
O.2
0.10
-0.1
-O.20
00
-10
A/C Accel. at Centroid of A/C0.1
0.050
u
Simu. Accel. at Centmid of Slmu.
' ' , -01 , ,10 20 30 40 0 10 20 30
t (sec) t (sec)
02
0.10
_-0.1O)
-O.2i I ..L.. J t |
10 20 30 40 0 10 20 30t (sec) t (sec)
0.1
0.05
o
-o.os
.... -01 , , ,10 20 30 40 0 10 20 30
t (sec) t (sec)
4O
40
4O
Figure C.IO. Optimal Algorithm Sway Half Sinusoidal Pulse Input.
198
0.5
_,_ 0J_n
-0.5
-10
! o-.0.5
-10
0.5
0
-0.5
-I0
Aircraft Angular Podtion
i , |
10 20 30t (sec)
0.5
l)
0.J=gZ.
-0.5
40 0
0
-o.s
Simu. Anglar Position
i i i
10 20 30t(_
' ' ' -1 ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)
0.5
0
-0.5
i i i "1 i i ,
10 20 30 40 0 10 20 30
t (sec) t (sec)
40
4O
4O
Figure C.10. Optimal Algorithm Sway Half Sinusoidal Pulse Input.
199
0
_-0.5
-10
1
-10
1
0.5
Z- o_-0.5
-10
Aircraft Angular Rate
0.5[
0a.
uJ -0.5
Simulator Angular Rate
| ' ' , I
10 20 30 40 0 10 20 30 40t (sec) t (sec) -
0.1
_' 0.05
0
_'_-0.05
' ' ' -01. ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)0.1
i i i J I I
10 20 30 40 10 20 30t (sec) t (sec)
0.050
_ -0.05
-0.10
Figure C.10. Optimal Algorithm Sway Half Sinusoidal Pulse Input.
40
40
200
AimraRSpecificForceat PilotHead. Simu.SpecificForceat PilotHead1 1
_, _ 0.5E ox, x,
-o.s -o.s
-1 -10 4010 20 30
t (sec)
_0.5
i i
0 10 20 3Ot (sec)
-8
4O
-8
i i
0 I 0 20 30t (sec)
i
10 20t (sec)
3O
-110
-10
-12 ¸
-14, i i |
I0 20 30 40 .0 10 20t (sec) t (sec)
3O
4O
4O
40
Figure C.10. Optimal Algorithm Sway Half Sinusoidal Pulse Input.
201
A/C(..)& Simu.(-)SensedSpecificForce0.1
_, o _ okl "_-"_--
"0"10 1'0' 2() 30 40 < 0I" 1'0 20
t (sec) t (sec)
0.6 . _ 0.1o._ _ o.o_?.
W
-O20
E
,,N-3.9 ___U)
_ .4.1
NC(..) & _mu.(-) Sensed angular rate
I
3O
0
..... "_ =0.1 ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)1
_0.5
'1"
o(¢)
_" 41.5
• i .1 i .... i i
10 20 30 40 0 10 20 30
t(se_ t_ec)
Figure C.10. Optimal Algorithm Sway Half Sinusoidal Pulse Input.
40
40
40
202
0.1
0.05
u) .0.05
-0.10
0.1
0.1_
gom .0.05
-0.10
0.1
0.05
fo) -0.05
-0.1 •0
Simu. Translational Velocity Simu. TransJa'donalDisplacement
0.5
rn -0.5
| J J ml
10 20 30 40 0
t (sec)0.1
_ -0.05
,, , ' -0.110 20 30 40 0
t (sec)0.1
| l
10 20 30 40t (sec)
10 20 30 40
t (sec)
10 20 30 40t (sec)
0.05
_. o-0.05
i i
10 20 30 40t (sec)
Figure C.IO. Optimal Algorithm Sway Half Sinusoidal Pulse Input.
203
0.1
_" 0om
.-j
-0.1
0.1
A
o.o5,n 0
lib-_ -0.05
Jack Extension
l i
10 20t (sec)
I
3O 4O
0.1
o.o5
m_ .0.05
Ex n on
| | ,
10 20 30t (sec) ..
40
10!
2O 30
t (sec)4O
0.1
V
0
m
10 20 30t (sec)
4O
0.1
V
0.tooQ
-0.1
i I | i i
10 20 30 40 0 I 0 20 30t (sec) t (sec)
4O
Figure C.IO. Optimal Algorithm Sway Haft Simsoidal Pulse Input.
204
A/C Accel. at Cen_oid of A/C0.2 0.1
Simu. Accel. -atCentroid of Simu.
"O'20 ' 1(3 ' 20 0
t c) 15 i
1 . • • 0.4
< 0 -0.4, ,
0 5 10 15 20 0 5
0.5
-o.s
t (seo)0.1
0.05
g_-o._"O'.1
0
"1 , I |
5 10 15
t (sec) .
i I
10 15
t (sec)
_1 h , i i i
0 5 10 15 20 5 10 15
t (sec) t (sec)
2O
2O
2O
Figure C.11. NASA Adaptive Algorithm Sway Half Sinusoidal Pulse Input.
205
0.5
0
-0.5
-10
0J:
-0.5
-10
0.5
0
-0.5
-10
Aircraft Angular Position
I
6
_0.i.
a.
-1
Slmu. Anglar Position
I i i ._ | i
5 10 15 20 0 5 10
t (sec) t (sec)
| I | ul i |
5 10 15 20 0 5 10
t (sec) t (sec)
0.51
0
-0.5
i i i _1 L I
5 10 15 20 0 5 10t (sec) t (sec)
I
15 2O
i
15 2O
!
15 2O
Figure CA1. NASA Adaptive Algorithm Sway Half Sinusoidal Pulse Input.
206
AJrcmttAngular Rate
0.5
0
_5
2
"1 | I I
0 5 10 15 20 0t (sec)
1 0.1
Simulator Angular Rate
i i i
5 10 15
t (sec)
-1 -0.1 ' ' '0 5 10 15 20 0 5 10 15
t (sec) t (sec)0.1
0.050
_ -0.05
-1 , , , -0.1 ' ' '0 5 10 15 20 0 5 10 15
t (sec) t (sec)
2O
20
2O
Figure C.11. NASA Adaptive Algorithm Sway Half Sinusoidal Pulse Input.
207
Aimrafl Specific Force at Pilot Head Simu. Specific Force at Pilot Head
_,_ 0.50
< -0.5
_I | "' | !
0 5 10 15t (sec)
1
0.5
0
2O
0.5
¢0
-0.5
5|
10 15t (sec)
0 5 10 15 2O 0t (sec)
-8 -8
-1o -12-14
-110 5 10 15 20 0
t (see)
5 10 15
t (see)
i i i
5 10 15t (sec)
Figure C.11. NASA Adaptive Algorithm Sway Half Sinusoidal PulseInput.
2O
2O
2O
208
0.1A/C(..) & Simu. (-) Sensed Specific Force
o.os
o(¢)
-0.10
0.6
E 0.4
A/C(..) & Simu.(-) Sensed angular rate'_ 'I T
i ! I ..,
5 10 15 20 5 10 15
t (sec) t (sec)
N-3.9
-4.1
Q0.05
9"
o'-0.05
-0.1 ....5 10 15 20 0 5 10 15
t (sec) t (sec)0.1
_0.05
Y
-o.os-0.1
0I . * i * i i
5 10 15 20 5 10 15t (sec) t (sec)
2O
20
2O
Figure C.11. NASA Adaptive Algorithm Sway Half Sinusoidal Pulse Input.
209
Simu.Tmnsla_onalVelocity0.1 0.1
o.ost _ o.os_ o _ o
• _ io _s 2o "°Io st (sec)
o, / °'_/_o._ " _ o.ltg /
g o \/_ _o.o_i/_o oI _f,'_-o.os L/
-0.1 ' ' ' -0.050 5 10 15 20 0 5
t (sec)0.1 0.1
Simu. Tmnsla_onal Displacement
| i
10 15t (sec)
I |
10 15
t (sec)
20
20
m -0.05
0.05
N 0Do)
-0.05
-01. ' ' ' -01. ' ' ,0 5 10 15 20 0 5 10 15
t (sec) t (sec)20
Figure C.11. NASA Adaptive Algorithm Sway Half Sinusoidal Pulse Input.
210
0.1
o.os"" 0
f_ -0.05
-0.1
0
0.1
o.os0
m -0.05
-0.1
0
Jack Extension
i | i
5 10 15
t (sec)
5 10 15t (sec)
20
20
Jack Extension
0.1
E
Om
,-j
-0.1
0|
5
0.1
I i
10 15 20t (sec)
_" 0(,>¢1
,-)
-0.1
i |
10 15
t (sec)
2O
i I I
5 10 1.5 20 0 5 10 15t (sec) t (sec)
20
Figure C.11. NASA Adaptive Algorithm Sway I-Ialf Sinusoidal Pulse Input.
211
A/C & Simu. Specific Force at Pilot Head1
0.8
-O.2
-0.4 .L 2_ 1 .L 1 J. L .L J
0 1 2 3 4 5 6 7 8 9 10t (sec)
A/C & Simu. Sensed Specific Force at Pilot HeadI I $ I I ! I I I
(nu)
0.2LL
r.o 0.1<
0
-0.10
/
I
J
I
a
I I I I _, I t I
2 3 4 5 6 7 8 9 10t (sec)
Figure C.12. Sway Half Sinusoidal Pulse Input Specific Force Comparison.
212
o_
0.10
-0.1
-10
3
2
0
A/C Accel. at Centroid of A/C Simu. Accel. at Centroid of Simu.0.1
0.050
-o.o5
' ' ' -01 , , ,10 20 30 40 0 10 20 30
t (sec) t (sec)0.1
4O
i i i
10 20 30t (sec)
4O
0.05
tO -0.05
-0.10
0.4
0.2
0
-O.2
' ' ' -0410 20 30 40 0
t (sec)
J ! i
10 20 30
t (sec)
• i
10
4O
i i
20 30t (sec)
4O
Figure C.13. Optimal Algorithm Heave Square Pulse Input.
213
1
0.5
0J:I1.
-0.5
-10
-10
0.5
0
-0.5
-10
Aircraft:Angular Position
|
10
i'
J:
i
10
i i I
20 30 40 10t (sec)
2O 3O 4Ot (sec)
10
0.1
0.05
0
-0.05
-0.10
1
10
" 0J:
-0.5
-10
1
0.5
_ 0"Wa.
-0.5
-10
Simu. Anglar Position
2O
t (sec)
I
30
i
20 30 40 10t(_
i a
20 30
t (sec)
20
t (sec)
i
30
Figure C.13. Optimal Algorithm Heave Square Pulse Input.
40
4o
40
214
I
0
_<-0.5
-10
1
0.5
0
<_-0.5
-10
1
-10
Aircraft Angular Rate •Simulator Angular Rate'0.1
i
10I , I
20 30t (sec)
I
10i |
2O 3Ot (sec)
40
4O
_" 0.05
o_ -0.05
-0.10
0.1
t
-0.1 /0
0.1
t i i
10 20 30t (sec)
4O
I i i
10 20 30t (sec)
40
t
10
0.05
oo) -0.05
' ' -01. ..........20 30 40 0 10 20 30
t (sec) t (sec)4O
Figure C.13. Optimal Algorithm Heave Square Pulse _put.
215
-°
Aircraft Specific Force at Pilot Head Simu. Specific Force at Pilot Head
_ 0.50
x,-0.5
-10
I | |
10 20 30t (sec)
4O
0.50
m -0.5
-10
0.05
i i t
10 20 30t (sec)
4O
0.5
Eo>r,_ ..0.5
_1 i i I
0 10 20 30t(se_
_-7
40
-10 __-0 10 20 30 40
t (sec)
(n
0
-8
u.N,-12
(0
-14
i t !
10 20 30t (sec)
i40
i
0 10I I
20 - 30t (sec)
40
Figure C.13. Optimal Algorithm Heave Square Pulse Input.
216
0.1
_0.05
X
o¢/)
_ -0.05¢/)<
--0.10
0.5
o) 0
._"-0.50'3<
-10
N"-3¢0
Nu.-4
0
A/C(..) & Simu. (-) Sensed Specific Force
i i , i
10 20 30t (sec)
4O
i i , i
I 0 20 30
t (sec)40
| i
10 20t (sec)
30 40
Q0.05
D.!
_ oif)
"-0.05
-0.10
9"0
(n
0)
< -0.10
1
13b6
0.5
_ oif)
_ -0.5
<-1
0
A/C(..) & Simu.(-) Sensed angular rate
i i i
10 20 30 40t (sec) .
i i i
10 20 30t (sec)
40
| ,i i
10 20 30t (sec)
40
Figure C.13. Optimal Algorithm Heave Square Pulse Input.
217
0.1•Simu. Translational Velocity
•-. 0.05
_.1_
! i
10 20 30 40t (sec)
,,_ 0.50
_-0.5
-10
0.5
i I I
10 20 30t (sec)
40
o-0.5
0
0.5
(n-0.5
-10
0.5
u).0.5
-10
Simu. Translational Displacement
| I I
10 20 30t(_
l I I
10 20 30t (sec)
4O
' ' ' -05.10 20 30 40 0 10 20 30
t (sec) t (sec)
40
4O
Figure C.13. Optimal Algorithm Heave Square Pulse Input.
218
0.4
•-').0.:
..0._0
0.4
02
:o-O2
-0.40
0.4
O.2
-0_
Jack Extension
i
10
t (sec)
i i
10 2O
t(_c)
411I i
10
0.4
O.2E
0
m
_ .0.2
0.4
0.2
_ .0.2
' -0.43O 4O 0
0.4
_, O.2
-'_ -0.2
Jack Extension
i i
10 20t (sec)
i
10
30
i
20t (sec)
i
3O
' ' -04• i
20 30 40 0 10t(_
i
2O
t (sec)
i
3O
Figure C.13. Optimal Algorithm Heave Square Pulse Input.
4O
40
4O
219
0_.
IX, 0
<E.0.1 .
-O.20
0< -0.5
-10
00
A/C Accel. at Cenboid of A/C
i i I
10 20 30t(_
i | h
10 20 30
t (sec)
I | I
10 20 30t (sec)
4O
4O
4O
0.1
_,,_0.050
0m -0.05
.0.10
0.1
0.050
(.1U¢o -0.05
-0.10
Simu. Accel. at Cenkoid of Simu.
| i i i
10 20 30 40t (see) ..
I
, .k i
10 20 30t (sec)
4O
10 20 30 40t (sec)
Figure C.14. NASA Adaptive Algorithm Heave Square Pulse Input.
220
0.5o
0mJ=D.
-0.5
-10
J_I- ..O.5
-10
0.5
0
-0.5
-10
Aircraft Angular Position
A
(D
D.
Simu. Anglar Position0.1
0.05
0
-0.05
-0.10
1
i i i , , ,
10 20 30 40 10 20 30
t (sec) t (sec)40
o
_" -0.5
* J i _1 , I =
10 20 30 40 0 10 20 30
t (sec) t (sec)
4O
0.5
0
-0.5
r
i
10 20 30 40 0 10 20 30t(_ t(se_
40
Figure C.14. NASA Adaptive Algorithm Heave Square Pulse Input
221
0.50
<_-0.5
AircraftAngularRate
0 10 20 30 40t (sec)
1
0.5
0
< -0.5
-10
1
0.5
_<-0.5
-10
Simulator Angular Rate0.1
0.05
_ -0.05
-0.10
' ' ' -01.10 20 30 40 0
t (sec)0.1
| | |
10 20 30t (sec)
40
10 20 30t (sec)
40
I i | I i
10 20 30 40 10 20 30t (sec) t (sec)
0.05
0
_ -0.05
-0.10 40
Figure C.14. NASA Adaptive Algorithm Heave Square Pulse Input.
222
Aircmtt Specific Force at P,ot Head Simu. Specific Force at Pilot Head
-10 10 20 30 40
t (sec)
0.5
¢o -0.5
-10
0.05
i i !
10 20 30
t (sec)
-1O" 10 20 30 40
t (sec)mE T T r
-9
-10 . "0 10 20 30 40
t (sec)
U)
0
i : i
10 20 30t (see)
-8
_.,10 _--
_ -12
-14i ,
0 10i I
20 3Ot (sec)
Figure C.14. NASA Adaptive Algorithm Heave Square Pulse Input.
4O
4O
4O
223
0.1
0.05=K
o¢0
-0.05
-0.10
'_" 0
-0.5<
_.I0
N,,.3U_
0
A/C(..) & Simu. (-) Sensed Specific Force
| ! !
1O 20 30 40t (sec)
= ....... = i
10 20 30
t (sec)
1!
=
10
f
4O
0.1
_0.05
o¢/)
--0.05
-0.10
A/C(..) & Simu.(-) Sensed angular rate
0.1
_0.05
10 20 3O
t (see)
O9
-0.10 10 20 30
t (see)1
® 0.5
Y
_ oO)(tl
<
2o 3o 4o "_o _o_ 2o 3ot (sec) t (sec)
4O
4O
4O
Figure C.14. NASA Adaptive Algorithm Heave Square Pulse Input.
224
0.1Simu. Translational Velocity
_n -0.05
-0.10
I i I
10 20 30t (see)
0.5
_.5
| i I
"10 10 20 30
t (sec)0.5
-0.50 10
". •
4O
4O
Simu. Translational Displacement
I i i
10 20 30t (sec)
I I I
10 20 30t(_
4O
' ' -0.520 30 40 0 10 20 30
t (sec) t (sec)
40
40
Figure C.14. NASA Adaptive Algorhhm Heave Square Pulse Input.
225
._. O.2g"- 0(.1(g
'-3-O.2
0
Jack Extension
i
10
(,q
ee
Jack Extension
0.2
0
..0.2
0i |
|
20 30 40 20
t (sec) t (sec)
i
10i
3O 4O
0.2
I0 !0
,n 0,,1<¢)m
"3-O.2
|
10
.r 0
go
| ii
20 30 40 0 10 20t (sec) t (sec)
i |
20 30 40 20
t (sec) t (sec)
I
30
o-_ .0_
0 10i
30
Figure C.14. NASA Adaptive Algorithm Reave Square Pulse Input.
4O
4O
226
-6A/C & Simu. Specific Force at Pilot Head
I I I I I I I I I
-7
I1.O'J
-10 _
-110
-1
I I I I I t I I
1 2 3 4 5 6 7 8t (sec)
A/C & Simu. Sensed Specific Force at Pilot Head
• L- _I,
I
9
I I I ! I ! I I I
10
Eii{n-3¢/J
111
ii
•_ .4_
-5 1 i
0 1 2I I I I I I
3 4 5 6 7 8
t_
m
_ _ _._,
9 10
Figure C.15. Heave Square Pulse Input Specific Force Comparison.
227
-g.5A/C & Simu. Specific Force at Pilot Head
! ! ! I
(%1A
" -1(:U)
IL<:
-10.5 i I I I I J I I I0 1 2 3 4 5 6 7 IS 9 10
t (sec)
A/C & Simu. Sensed Specific Force at Pilot HeadI'3.5 t I I I I t i I
u) .4 _-
j=t5
L " I
U)
-4.5 ....... I f i j0 1 2 3 4 6 7 8 9 10
I
5t (sec)
Figure C.15. Heave Square Pulse Input Specific Force Comparison.
228
O.2
-10
1
0.5
LI .
-o.s
-10
A/C Accel.at Centroid of A/C
10 20 30t (see)
4O
0.1
0.05E"" 0
O¢o -0.05
-0.10
Simu. Accel. at Centroid of Simu.
i i |
10 20 30
10 20 30t (sec)
| i i
10 20 30
t (sec)
0.1
• _-0.1
40 0
0.1
0.05
0
-0.05
-0.1
40 0
10 20 30
t (sec)
. |
10 20 30t (sec)
Figure C.16. Optimal Algorithm Roll Doublet Pulse Input.
4O
4O
4O
229
• 40
3OO
_20Zn
10
00
o.1=
-0.5
-10
0.5
0
-0.5
-10
/Nrcr_ Angular Position
I | I
10 20 30t (see)
4O
Simu. Anglar Position
10t/_'_'''_'-
V-10[ ,
0 10 2O
t (sec)1
I
3O 4O
oJ:
• I- -0.5
' ' ' -1 ,10 20 30 40 0 10 20
t (sec) t (sec)1
|
30 4O
0.5
0
Z-0.5
i i wl i t
10 20 " 30 40 0 10 20t (sec) t (sec)
i
3O 4O
Figure C.16. Optimal Algorithm Roll Doublet Pulse Input.
230
15
00
1
0.5
0
< 4_.5
-10
1
o.s
0
< -0.5
-10
Aircraft Angular Rate
i
10I i
•20 30t (sec)
4O
5
o
(n
-50
0.1
Simulator Angular Rate
I i I
10 20 30t (sec)
I
10I J
20 30
t (sec)4O
|
10
0.05
0
_ -0.05
-0.10
0.1
0.05
0
_ -0.05
' ' -0.120 30 40 0
t (sec)
I | I
10 20 30t (sec)
i . i i
10 20 30
t(_
Figure C.16. Optimal Algorithm Roll Doublet Pulse Input.
4O
4O
4O
231
Aircraft Specinc Force at Pilot Head1 1
Simu. Spedfic Force at Pilot Head
-10 10 20 30 40 -10
t (sec)2
"( 0 10 20 30
t (sec)-7
40
10 20 30 40t(_. ..
-30
-9
10 20
• t (sec)
i
30 40
< -9
-100
-9.5
.... 10 ' '10 20 30 40 0 10 20
t (sec) t (sec)
i
J
30 40
Figure C.16. Optimal Algorithm Roll Doublet Pulse Input
232
A/C(..) & Simu.(-) Sensed Specific Force A/C(..) & Simu.(-) Sensed W
_. _ _1_t0.5 _ 10 t A
_.o_ _o I _ ....."1o lO 20 3o <% _ lo 20 30
A/C(..) & Simu.(-) S nsed Spec_c Force 40 NC(..) & Simu.(-) Sensed W
_0 0.5
°I - "=.el _ , _ .II , ,
! i
0 10 20 30 40 0 10 20 30NC(..) & Simu.(-) Sensed Specific Force
_5E
N" 0u)o)N"
0i i |
10 20 30
t (sec)40
A/C(..) & Simu.(-) Sensed W1
_' 0.5Y_: otn(n
_" -0.5
-10 10 20 30
t (sec)
40
4O
40
Figure C.16. Optimal Algorithm Roll Doublet Pulse Input.
233
Simu. Velocity in Inertial Coord. Desired & Actual Simu. Displacement.0.2 ,....,0,2
0.1 . _ 0.1
_; C ._ 0
o3 ..0.1-0.1
• "020 1() 2() 3() 40 o) .020 1() 20 30 40
t (sec) t (sec) -.
O2 I
o.1 >. o.2
O)I I I J i J
0 10 20 30 40 0 10 20 30t (sec) t (sec)
0.2 0.2
V
0.1(n•a 0
-0.1
0.1
-0.1
-020
o_i i i I I I
10 20 30 40 "0:_0 10 20 30
t (sec) t (sec)
4O
4O
Figure C16. Optimal Algorithm Ron Doublet Pulse Input
234
0:_
.-. 0.1
"- 0J¢oM
-_ -0.1
-0.20
0
w 0¢)m
,-.)
-0.5
0
Jack Extension
i i I
10 20 30
t(_
J¢om
0.5
0
-0.5
40 0
,q,
m.--j)
0.5
0
i
10I , I
20 30
t (sec) '
-0.5! I
10 20 30 40 0 10 20t (sec) t (sec)
O.2
Jack Exter_on
© 0
m-_ -0.1
I
3O
, , . -0.2 . ,10 20 30 40 0 10 20
t (sec) t (sec)
I
30
Figure C.16. Optimal Algorithm RollDoublet Pulse Input.
4O
4O
4O
235
0.2
0
-0.1
-O.20
1
0.5
A/O Acoel, at Centroid of A/C
i J i
10 20 30t (sec)
_1 i i i
0 10 20 30t (sec)
1
0.5
_-0.5
Simu. Accei. at Cer_oid of Simu.0.1
-10
i i i
10 20 30
t(_
4O
4O
4O
" 0.05
g o
,_-o.os
-0.10
0.1
0.05O_
o -0.05
-0.10
i i i
10 20 30t (sec)
i i i
10 20 30t (sec)
0.1
0.05
o_-
-0.1i
0 10, | i
20 30
t (sec)
]Figure C.17. NASA Adaptive Algorithm Roll Doublet Pulse Input.
4O
4o
40 °
236
; 40
3O
_20.I=(I.
10
00
| 0-o.s
-10
0.5
(1.-0.5
-10
Nrcra/t Angular Po_n
/I | i
10 20 30t (sec)
40
20
15
o_,,10
" .I=• (I.
5
Simu. Anglar Position
/0
0I i i •
10 2O 30 4Ot (sec)
! i i
10 20 30
t (see)4O
o-o.5.
I I I
:. -I0 10 20 30
...... t (sec)1
10 20 30t (sec)
0.5
0"WCl.
-0.5
-14O 0
| i i
10 20 30t (sec)
Figure C.17. NASA Adaptive Algorithm RoB Doublet Pulse Input
4O
40
237
Nrcratt Angular Rate Simulator Angular Rate -
• 5[/_ ,
i i i
15
,olA_5
0tl , , ,10 "500 20 30 40
t (sec)1 0.1
t_ 0 _
-1 ' ' ' -0.10 10 20 30 40 0
t (sec)1 0.1
Io_t Io_
_._
-1 -0.10 10 20 30 40 0
t (sec)
10 20 30 40t (sec) -
10 20 30 40t (sec)
! t i
10 20 30
t (sec)
4O
Figure C.17. NASA Adaptive Algorithm Roll Doublet Pulse Input.
238
AircraftSpecificForceatPilotHead Simu.SpecificForceatPilotHead1
_w 0.5
x,_: -0.5
_= 0.5
e o
u) -0.5
-1 .... 1 ....0 10 20 30 40 0 10 20 30
t (sec) t (sec)2 1
• 1() 2'0 30 ()
t (sec)
o-10 ..... 10
0 10 20 30 40 0 10t (sec)
| I
20 30t (sec)
i i
20 30t (see)
4O
4O
40
Figure C.17. NASA Adaptive Algorithm Roll Doublet Pulse Input.
239
A/C(..) & Simu.(-) Sensed Specific Force A/C(..) & Simu.(-) Sensed W
11 _15
× ,=. !_
o') f_(/') , .-.
"10 1'0 20 30 < "50 1'0 2'0 30
2 A/C(..) & Simu.(-) nsed Sloe c Force 40 A/C(..) & Simu.(-) Se W• ' 1 ' ' ,
_ _
'< -1 - ' '0 10 •. 20 30 40
A/C(..) & Simu.(-) Sensed Specific Force
_o(n(/)
0 10 20 30A/C(..) & Simu.(-) Sensed W
1
• 0.5
"ro
u)u'J
-0.5
<:. i , ,_,, , I1 [ i
10 20 30 40 0 10 20t (sec) t (sec)
i
3O
40
4O
40
Figure C.17. NASA Adaptive Algorithm Roll Doublet Pulse Input.
240
0.2Simu.VelocityinIner_l Coord.
_0.1
E 0
-0.1
-O.20
O.2
,0.1
o) -0.1
0.2_
_, 0.1
_02
0.1
-0.1
.021
Desired & Actual Simu. Displacement
! I i i I i
10 20 30 40 0 10 20 30 40t (sec) t (sec) ",
•E 0.2
0.I
,_ 0
-0.1
co -O2| I I i i |
10 20 30 40 0 10 20 30t (sec) t (sec)
02
r_ 0.1
_ -0.1
10i I ,_ I i i
10 20 30 40 0 10 20 30
t (sec) t (sec)
40
40
Figure C.17. NASA Adaptive Algorithm Roll Doublet Pulse Input.
241
0.1
E O.05"- 0
m ..0.05
-0.1
0.4
A
o_0
M"_ -02
-0.4
0.5
0om
-0.5
0
Jack Extension
0.4
o.2
0
m_ -0.2
•.0.4 -, I I | 4
10 20 30 40 0 10 20t (_) t (see)
* | i i m
10 20 30 40 10 20t (_c) t (=5¢)
0.5
E
"_ 0oa
-0.50
O.2
0.1E
V
0
m_ -0.1
Jack Extension
i
4O
i
3O 4O
, , , -0.2 ......10 20 30 40 0 10 20
t (sec) t (sec)
i
Figure C.17. NASA Adaptive Algorithm Roll Doublet Pulse Input.
242
A/C & Simu. Specific Force at Pilot HeadI I l I i J I i i
O_
(_ _1
-3
-5
..60
I i I i
2 4 6 8 10 12 14 16 18 20t Csec)
A/C & Simu. Sensed Sped_c Force at PSot Headi i I. i I i I i I
O_
¢.NI.'_
-4
-50
I I I I I I I i I
2 4 6 8 10 12 14 16 18 20t (see)
Figure C.18. Roll Doublet Pulse Input Specific Force Comparison
243
O.2
_ o.1
41.1
-.0.20
,,_ 0.50
<_-0.5
-10
0.5
!o._ -o.s
-10
°
NC ._cel. at Centmid of
I | |
10 20 30t (sec)
4O
i I i
10 20 30t(_
4O
Simu. Accel. at Centroid of Simu.0.1
0.050 _-'--
,go -0.05
-0.10
0.1
I I
10 20 30t (sec)
0.05
ooco -0.05
4O
-0.10
0.1
| i , !
10 " 20 30
t (sec)
0.05
0
uu) -0.05
4O
' ' , -0.1 , , ,10 20 30 40 0 10 20 30
t (sec) t (sec)0 _
Figure C.19. Optimal Algorithm Pitch Doublet Pulse Input.
244
0.5¢:bQ
02_r,
-0.5
-10
40
I"-10
00
0.5
0
-0.5
-10
Aircraft Angular Position Simu. Anglar Position0.1
0.05
0
O.-0.05
, , , -01.10 20 30 40 0
t (sec)15
/ -e
._ 5
I i I 0
10 20 30 40 0t (sec)
1
I i i
10 20 30 40t (sec)
I n i
10 20 30 40t (sec)
i i |
10 20 30t(_
0.5
O0
3_O.
-0.5
-10
i L
10 20 30t (sec)
40
Figure C.19. Optimal Algorithm Pitch Doublet Pulse Input.
245
Aircraft Angular Rate1 0.1
0.05
-1 ' ' ' -0.1
0 1,0 t 20 0 40 0
15 + ' 5
+_0
01 _ -50 10 20 30 40 0
t (see)1 0.1
0.50
0.05
o_ -0.05
I i i
"10 10 20 30 40 _'10
t(_
Simulator Angular Rate
10 20 30t (see)
10 - 20 30t (sec)
,I ,, | I
10 20 30t (sec)
4O
40
4O
Figure C19. Optimal Algorithm Pitch Doublet Pulse Input
246
AircraftSpecificForceat PilotHead
x,
-2 ,a i
0 10 20 30
t (sec)
'1
2
m 0
-140 0
Simu. Spedfic Force at Pilot Head
a 0 i
10 20 30t (sec)
40
0.5
(o -0.5
-1 -1 ' '0 10 20 30 40 0 10 20
t (sec)-7 -9.4 . ..c)
t (se
-9 u.-9.8 ,/ .C/)
-10 , , , -10 ' ,0 10 20 30 40 0 10 20
t (sec) t (sec)
m
30
a
30
40
40
Figure C.19. Optimal Algorithm Pitch Doublet Pulse Input.
247
A/C(r) 8, Simu.(g) Sensed Specific Force A/C(r)&Simu.(g)SensedW6 , 1
0 20 3'0 40 "10- 1'0 ..... 2'0
nsed CO _ ,' u.(!1 | A/C(r) & Simu.(g) . Specific Force _, 15 , •
_vO'5 t / _IOfA
<-5 '"_o" i'o 20 o 1o - 20
I
30A/C(r) & Simu.(g) Sensed W ..
A/C(r) & Simu.(g) Sensed Specific Force
I
30A/C(r) & Simu.(g) Sensed W
5
(,,)-5,<
0I I h
10 20 30t (sec)
40
1
I:D® 0.5
,;. ,_ oI¢1
U)<C
-10 10 20 30
t (sec)
4O
40
40
Figure C.19. Optimal Algorithm Pitch Doublet Pulse Input.
248
O.2
o) -0.1
--O.20
0.2
0.1
0.-0.1
.O.20
O.2
0.1
0-0.1
-O2.0
Simu. Velodty in Inertial Coord.
i i i
10 20 30t (sec)
40
t" , I i
10 20 30t(_
4O
t I I
10 20 30t (sec)
4O
,-, O.2g
0.1
-0.1
o) -0.20
,., O2.gg 0.1o)•a 0
;_ -0.1¢0
.-O.20
O.2
0.1O)•a 0
_-0.I
O)..O.2
0
Desired & Actual Simu. Displacement
i i i
10 20 30t (sec)
I | I
10 " 20 30
t (sec)
lC) ' '20 30t (see)
4O
4O
40
Figure C.19. Optimal Algorithm Pitch Doublet Pulse Input.
249
o(I
0.5
0
Jack Extension
a
10i
20t (sec)
3O 40
Jack Extension
0 10 20t (sec)
30
f .
4O
O.2
00m
-,j.O.2
0i |
10 20t (sec)
0 10
f
i
30 40
I
i i
20 30 40
t (sec)
O2
_r 0(.1m
-,,)-0.2
0 10., i
2Ot (sec)
g0
g
-0.5i
0 10t (sec)
Figure C.19. Optimal Algorithm Pitch Doublet Pulse Input.
4o
4o
250
A/C Accel. at Cerdxoid of A/C0.2
'0.1
s o
0 10 20 30t (sec)
0.1
_ 0.050
_ -0.05
o) -0.1
-10 10 20 30
t (see)1
40 0
,,_irnu.Accel. at Centroid of Simu.
i b i
10 20 30t(_
40 10 20 30t (sec)
10 20 30 40 0 10 20 30
t (sec) t (sec)
4O
4O
40
Figure C20. NASA Adaptive Algorithm PitchDoublet Pulse Input.
251
0.5
_, 0i-
n-0.5
-I0
4O
20
00
0.5
0
-0.5
-10
Aircratt Angular Posilion Simu. Anglar Position0.1
0.05
Q
_ 0
, , , -0.1 ' '10 20 30 40 0 10 20
t (sec) t (sec)3O
I "
3O
"_20 f10
, , , 0 _'_"'10 20 30 40 0 20
t (sec) t (sec)1
I
3O
0.5
-0.5
i i .... r O "1 i i10 20 40 0 10 20t (sec) t (sec)
I
3O
Figure C.2O. NASA Adaptive Algorithm Pitch Doublet Pulse Input.
4O
4O
4O
252
Aircraft Angular Rate
_1 i : I
0 10 20 30t (sec)
15
40
.00 10 20 30 40
t (sec)
0.1
o.osl
..0.1 i
0 10
_0
i
0 10
0.1
Simulator Angular Rate
f I '
20 30
t (sec)
i i
20 30
t (sec)
-1 ..... -0.I ....0 10 20 30- 40 0 10 20 30
t (sec) t (sec)
4O
t4O
40
Figure C.20. NASA Adaptive Algorithm Pitch Doublet Pulse Input.
253
Aircraft Specific Force at Pilot Head Simu. Specific Force at Pilot Head
20 30t (sec)
"20 10 20 30 40 lu__'
t (sec)1 t
o
_ 0.5
-0.5 "
-10
-7
0
m -0.5
10 20 30 40 0 10
t (sec)-8.5
I |
20 30t (sec)
N_, "8-,9
-100
! i I
10 20 30 40t (sec)
-9
-100 10
t, i
20 30
t (sec)
40
40
40
Figure C.20. NASA Adaptive Algorithm PitchDoublet Pulse Input.
254
A/C(..) & Simu.(-) Sensed Specific Force A/C(..) & Simu.(-) Sensed W
s .._ 1_4 F-. _o.s
_2 _ ogo
' ' ' < -1 .... " '"20 10 20 0 10 20 30 40
1 A/C(..) & imu.(-) S nsed S c Force40 A/C(..) & Simu.(-) Sensed W •
o. }o_ " •< -1_ 10 20" 30 30 ..... '
A/C(..) & Simu.(-) Sensed Specific Force A/C(..) & Simu.(-) Sensed W
s 8' o.5'1"
o)_o _ oO) (/)
| i I _1 i | i
0 10 20 30 40 0 10 20 30 40
t (_c) t (._.e)
Figure C.20. NASA Adaptive Algorithm Pitch Doublet Pulse Input.
255
Simu. Velocity in Inertial Coord.
02
'0.10
_.0.1
-02
0
02
0.1
-020
I I |
10 20 30
t (sec)
I I |
10 20 30t (see)
O.2
'0.1
o: -0.1
-02
0| | I
10 20 30t (sec)
4O
0 .
4O
E"-" 02x,r_u)• . 0
o-02Q
(0
CO
Desired & Actual 5imu. Displacement
i i" _ ,
o 1o 20 30t (see)
0.2
0.1
:_ .0.1
0'J|
"020 10
_, 0.4[
t •
(o .0.4 I-0 10
i I
2O 3Ot (see)
i
20 30t (sec)
4O
4O
40
Figure C.20. NASA Adaptive Algorithm Pitch Doublet Pulse Input.
256
_, 0.5V
"" 0(3tO") -0.5
-10 10
0.4
0
0.4
JackExten_on
0 10
! I
20 30t (sec)
40
a i
20 30t (sec).
4O
0o4
f-o.41 ' ,
0
Jack Exten_on
°.'I• 0.2
.Id0¢=
.0.2
10 20 30t(_ .
0,4 , i
0 10
40
--- 0.5E
0
n --_ -0.5
I
20t (sec)
"1 I,, .
10 20 30 40 0 10 20t (sec) t (sec)
I
30 40
i
3O 40
Figure C.20. NASA Adaptive Algorithm Pitch Doublet Pulse Input.
257
6
5
.62
-10
5
4
.1
I)
& _mu. S_c Fo_ _ Pil_ Head
I _ I ! t 1 I I I
__COOOOOO_OCOOOO_O000COOOOO0_OO00
i I I [ I I I I I
2 4 6 8 10 12 14 16 18 20
& _mu' _ S_c For_ _ Pil_ He_
I I I I I l I I I
. _v_v_v_v_
-10 •
I 1 I I t I I I 1
2 4 6 8 10 12 14 16 18 20t (sec)
Figure C21. Pitch Doublet Pulse Input Specific Force Comparison.
258
O.2
0.1"-" 0
<-0.1
-O.20
0.5
,_-O.5
-I0
0.5
._ .O.5
-10
A/C Accel. at Centmid of A/C Simu. Accel. at Cerrkoid of Simu.0.1
• _ 0.05
g 0
om -O.05
' ' ' -OI.10 20 30 40 0
t(=_0.1
i , i i
10 20 30t_ec)
_,_ 0.050
m -.0.05
' ' ' -0.1 ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)0.1
0.05
_ .O.05
' ' ' -01. ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)
Figure C22, Optimal Algorithm Yaw l?_ublet Pulse Input.
4o
4o
4O
259
0.5
0J=O.
-0.5
-I0
.1
_v
| o-o.s
-10
4O
3O
_20
00
Aircraft Angular Posmon
10 20 30 4O
10 20 30 40t (sec)
0.1
0.05
Q0
f..I1.
..0.05
-0.10
--- 0.5o
0o
_- -o.5
-10
2O
0
Z-10
Simu. Anglar Position:
| I i
10 20 30t (sec)
I I t
10 20 30t (sec)
....... -2010 20 30 40 0 10 20 30
t (sec) t (sec)
4O
4O
4O
Figure C22. Optimal Algorithm Yaw Doublet Pulse Input.
260
-10
o
0
_-0.5
-10
15
i,<
00
Aircraft Angular Rate
10 20 30t (sec)
40
i ! !
10 20 30
t(_
| i L
10 20 30t (sec)
-0.140 0
Simulator Angular Rate
| | i,
10 20 30 40
t (sec) ,
40 0
10 20
t (sec)
30 40
i i i
10 20 30 40t (sec)
Figure C22. Optimal Algorithm Yaw Doublet Pulse Input.
261
0.05
0.04
Aircraft Specific Force at Pilot Head
10 20 30 40t(_
-8
Simu. Specific Force at Pilot Head0.1
o.os
,,-o.,s[ V-0.1L , , ,
0 10 20 30 40
x 10"= t (sec) .15
_---10
* , i I iS I = I
10 20 30 .40 0 10 20 30t (sec) t (see)
-8
4O
-10<
-110
-°
i -9
N," -10¢9
.... 11 ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)
4O
Figure C22. Optimal Algorrt.hm Yaw Doublet Pulse Input.
262
0.1NC(..) & 8imu.(-) Sensed Specific Force
1
0.5
A/C(..) & Simu.(-) Sensed W
0
"0"10 1`0 2'0 30 40 <: "10 1'0 2'0 3'0
&A/C(..) & Simu.(-) Sensed Specific Force A/C(..) 8imu.(-) ,Sensed W .
-"°°21 t_ - ' g 11 ' "
0.01 t/A_ _0"5[
I ' _ .1 1 I '
"0.010 10 20 - 0 10 20 3`0
/VC(..) & $imu.(-) Sensed 8 c A/C(..) & $imu.(-) Sensed W
20 . ,
_-S ,=
N _ 10I\ "
.... 100 10 20 30 40 0 10 20 30
t (sec) t (sec)
40
40
40
Figure C22. Optimal Algorithm Yaw Doublet Pulse Input..
263
-O.20
0.2
_, 0.1
0
_-0.1
-0:_0
O.2
0.1
-O.20
Simu. Veloc_y in InerSai Coord.
10 20 30 40t (sec)
I .... i I I
10 20 30 -40t (sec)
O.2
_0.1U)•6 0
-0.1
¢n .-O.20
O.2
0.1U),_ 0
-0.1
(n -0.20
,., O.2
_0.1¢9.6
O)
Desired & Actual Simu. Displacement
i | i
10 20 30t (sec)
m i
10 2Ot (sec)
.... •0.2 ' ' '10 20 30 40 0 10 20 30
t (sec) t (sec)
40
40
40
Figure C22. Optimal Algorithm Yaw Doublet Pulse Input.
264
0.4
"- 0
m
-0,4
0.4
--- O.2E
0
m_ .0.2
Jack Ext.en_on
i I
10 20t (sac)
h i
10 20 "t (sec)
J¢ocO
0.5
0
, -0.530 40 0
I
30 40
tom
,-)
10 20 30 40t (sec)
qD
m
0.5
0
0.5
0
Jack Extension
i ! i
10 20 30t (sec)
| i ,, L
10 20 30t (sec)
| i i
10 20 30t (sec)
Figure C22. Optimal Algorithm Yaw Doublet Pulse Input.
4O
4O
4O
265
O.2
0.1
x,U
-O.20
_ -0.5 •
-10
-10
A/C Accel. at Centroid of NC Simu. Accel. at Cerr_oid of Simu.0.1
0.05
0_ -0.05
.... -01 _. •
10 20 30 40 0 10 20 30t (sec) t (sec) •
0.1
0.050
_ -0.05
, , , -0.1 _. ' '10 20 30 40 0 10 20 30
t (sec) t (sec)0.1
0.050
0_ -0.05
, , -01. ' '10 20 30 40 0 10 20 30
t (sec) t (sec)
Figure C.23. NASA Adaptive Algorithm Yaw Doublet Pulse Input.
40
4O
4O
266
0.5A
(D
0_=11.
-0.S
-10
E oJ=_- -0.5
-10
4O
,3°Ia'lO
00
Aircraft Angular Positiono_1
Simu. Anglar Position
i = i
10 20 30
t (see)4O
| i |
10 20 30t (see)
4O
0.05O}o
0Za.
-0.05
-0.10
1
I0.5
0==t- -0.5
-1 /0
15¸
_10
;f5
' ' ' 0
10 20 30 40 0t (sec)
i i i
10 20 30t (sec)
4O
I i i
10 20 30
t (sec)
10 20 30t (see)
4O
4O
Figure C.23. NASA Adaptive Algorithm Yaw Doublet Pulse Input.
267
0
<_-0.5
-10
Aircralt Angular Rate
! I !
10 20 30
t (sec)40
0.1
0.05
0
_-0.05
-0.10
0.1
Simulator Angular Rate
I | i
10 20 30t (sec)
0.5
0
_<_-0.5
-I0
15
o I0
|
10 2O 30t (sec)
I | |
10 20 30t (sec)
0.05
0
_o -0.05
-0,140 0 10
40
0
I
0 10
| |
20 30
t (sec)
I i
20 30
t (sec)
Figure C.23. NASA Adaptive Algorithm Yaw Doublet Pulse Input.
40
40
40
268
0.05
0
0.02
o
-0.020
-8
E
-10
-110
Aircraft Specific Force at Pilot Head•i ¢ _"
10 20 30 40t (sec)
Simu. Specific Force at Pilot Head0.1
x,u.o) -0.05
-0.10
i
10
x 10.310
i
20 30t (sec)
-S0
-8
i i i i i i
10 20 30 40 " 10 20 30t (sec) t (sec)
N, -10(n
.... 11 ' '10 20 30 40 0 10 20
t(_ t(_
3O
Figure C.23. NASA Adaptive Algofizhm Yaw Doublet Pulse Input.
4O
4O
4O
269
0.05
0
0.02
N
u)
(/3-5<
A/C(..) & Simu.(-) Sensed Specific Force
I i i
10 2O 30 40A/C(..) & Simu.(-) Sensed Specific Force
10 20 30 40A/C(..) & Simu.(-) Sensed Spec_ Force
| b i
10 20 30 40t (sec)
1
li0.5
¢1.I
_ o
< -10
1
oO.5
0
-0.5
< -10
A/C(..) & Simu.(-) Sensed W
i i
10 20 30NO(..) & Simu.(-) Sensed W
I |
10 20 30A/C(..) & Simu.(-) Sensed W
40
_,15
A# _
_" 0 _
_-50 10
40
i i
20 3Ot (sec)
4O
Figure C.23. NASA Adaptive Algorithm Yaw Doublet Pulse Input.
270
0_
0.I0
_-0.I
-0_0
O.2
,_,_0.I0
_-0.1
-0_0
0.2
,0.1
o_-_.1
-O.20
Simu. Velocity in Iner'dal Coord.,.,, 0.2E
V
x 0.1
¢0,,_ 0
_-0.1
_ -0.20
Desired & Actual Simu. Displacement
| | i i _, i
10 20 30 40 10 20 30
t (sec) t (sec)
I i | . i i i
10 20 30 _ 10 _ 30
o.11-
_ 41.2/0
... 0.2E
V
e_0.1(0
-o.ia(o
-O.20
| i i | i .... _ .
tO 20 30 40 10 20 30
t (sec) t (sec)
Figure C.23. NASA Adaptive Algorithm Yaw Doublet Pulse T-put.
40
4O
4O
271
"" 00m
") -0.2
O2A
g0
0m
-O2
0.20
UU
,.-)-O.2
0
Jack Extension
|
10i i
20 30t (sec)
4O
h
10i |
20 30t (sec)
40
i
10
0.4
,-. 0.2E
m
-0.4 ,
0 10
Jack Extension
A j
20 30t (see)
a
2O 3Ot (sec)
0.4
020
(.IM
"_ -0.2
' ' -04. , , - ,20 . 30 40 0 10 20 30
t (sec) t (sec)
Figure C.23. NASA Adaptive Algorithm Yaw Doublet Pulse Input.
4O
4o
4O
272
0.1A/C & Simu. Specific Force at Pilot Head
I I I I t I I I I
0.05
< ..0.05
-0.1 I I I I I I I I I
0 2 4 6 8 10 12 14 16 18 20
t (sec)
A/C & Simu. Sensed Specific Force at Pilot Head
0.04 _ , , , , , , , ,
"_ -0.04
-0_ 1 I I I I I 1 I I
•. 0 2 4 6 8 10 12 14 16 18
Figure C24. Yaw Doublet Pulse Input Specific Force Comparison.
273
0.2
"01
"I"oV p
-o.1
-0.20
10
E"" 5
00
_" 0.5
E"-" 0N<_-0.5
0
NC Accel. at Centroid of A/C
10 20 30
t (sec)40
..... f i
10 20 30
t (sec)
4O
10
Simu. Accel. at Centroid of Simu.
0.1
Ev 0X6(3
¢0 -0.1
v0>:,oo
0)
0
5
-50
10 20 30
t (sec)
10 20 30t (sec)
0.5Ev 0
¢o -0.5
i i
20 30 40 0 10 20 30t (sec) t (sec)
40
4O
4O
Figure C25. Sway Pulse Input Braking Algorithm Test.
274
0.5A
0
O.-4).5
-10
o1-I- -0.5
-10
0.5A
0
-0.5
-10
Aircraft Angular Pos_on
i i ..... I
10 20 30t(_
I I I
10 20 30
t (sec)
4O
40
Sirnu. Anglar Position
5
_0
I1.
-5
0 10 20 30 40
t (sec)
.2 ,- • •0.1 I
o r-V
.0.2_0 10 20 30 40
t (sec)0.3
0.2
0.1"Wa.
0
10 20 30 40 0 10 20 30t (sec) t (sec)
40
]Figure C2$. Sway Pulse Input Braking Algorithm Test.
275
1
0.5
_ ..0.5
-10
1
0.5
0
_-0.5
Alrctalt Angular Rate
I I I
10 20 30
t (see)
=1 i i I
0 10 20 30t (sec)
1
0.50
<_-0.5
-10
4O
40
i
10 20 30t (sec)
40
4
2
-40
0.5
0
¢n -0.5
1
0.5
0
_-0.5
-10
Simulator Angular Rate
J | i !
10 20 30 40t (sec)
_L__
0 10 20 30 40t (sec)
10 20 30 40t (sec)
Figure C2S. Sway Pulse Input Braking Algorithm Test.
276
< -0.5
-10
10
5
AircraR Specific Force at Pilot Head
| i i
10 20 30
t (sec)
O I i
0 10 2O 3Ot (sec)
,-8
-10
-110
i i i
10 20 30
t(_
40
4O
_2
go
-8
-10
-12o
-14
Simu. Specific Force at Pilot Head
10 20 30
t (sec)
0 10
40 0
i i
20 30t (sec)
10 20t (sec)
3O
40
40
40
Figure C2S. Sway Pulse Input Braking Algorithm Test.
277
A/C(..) & Simu, (-) Sensed Spec_ Force A/C(..) & Simu.(-) Sensed angular rate
Figure C25. Sway Pulse Input Braking Algorithm Test.
278
0.1
o.os0
_ -0.05(/)
.0.1
Simu. Translational Velocity5
o_-5(n -I0
-15
x 10_imu- Translational Displacement
0 10 20 30 40 0 10 20 30 40
1 . t (sec) . 2 . t (sec) .
>. _o
t I t | |
"20 10 20 30 40 "20 10 20 30 40
t (sec) t (sec)0.1
i
10
o° lo
(o -0.051
0.05
-0.10
, , -0.120 30 40 0
t (sec)
m
10|
2Ot (sec)
3O 4O
Figure C25. Sway Pulse Input Braking Algorithm Test.
279
Jack Extension Jack Extension
,-, 0.5
o.s i-,"-o.s i
-1: .......... -0.5 , , ,o _o 20 30 ,o o _o 20 30 4o., . t<_c_ . ", . t<=c_ .
_ ,-0.5 _ -_ -0.5
Jz¢o¢=
°1 _ I i
0 10 20 30 40t (sec)
0.2
0
-0:_
0 10 40, ! i
20 30t (sec)
_1 i I | |
0 10 20 30 40
t (sec)
_,o.s _-_
_ ,-0.5
m R i i i
0 10 20 30 40t(se_
Figure C25. Sway Pulse Input Braking Algorithm Test.
280
281
REPORT DOCUMENTATION PAGE I OM_N'N°"°z_saPublicrepodingburdenfor this colk)ctic_of information isestimated to average I hourper response,including the time for reviewingin,st_u.ctions,se_chi,-,0.existingdatasources,gatheringand mainta_tngthe data needed,and ¢ornplet_g and ..my_.wmg_ co/,l_t_n _ _forrn.at__Se_od_.commer_:ts_reg___=rag_ burc_ _r_enOr a_l otheraspectof thiscollectionof info.n_a!ion,includ!ngsuggest_nstot reducingm_souroen,_o,wa__.._glor_.H.eauqu_reur.=0%[.,,._=, _,,,=.,u,=_ -y, ,,j_!-,_,,_,.__w, ..... ......Reports,1215 Jefferson Davis H=ghway,Suite 1204, Arlington,VA22202-4302, and to the unce ot ManagememanD uuoge_.,P'aperwon_Meoucuon r'ru_uLtu.u._ u_ooj,Washington,DC 20503. •1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATE._ COVERED
March 2000 Contractor Report5. FUNDING NUMBERS4. TITLE AND SUBTITLE
Motion Cueing Algorithm Development: Initial Investigation and
Redesign of the Algorithms 992-30-11-01
s. 'AUTHOR(S)
Robert J. Telban, Weimin Wu, and Frank M. Cardullo
7. PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES)State University of New York
Binghamton, NY 13902-6000
9. S_)ONSORING/MONITORiNG AGENCY NAMF:(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Langley Research CenterHampton, VA 23681-2199
NAS 1-20454
8. PERFORMING ORGANIZATIONREPORT NUMBER
10 SPONSORING/MONITORING" AGENCY REPORT NUMBER
NASA/CR-2000-209863
11.SUPPLEMENTARYNOTESPrepared by the State University of New York - Binghamton for NASA Langley Research Center undersubcontract to Unisys Corporation, Inc. NASA Langley Research Center Technical Monitor: Jacob A. Houck
12a.DISTRIBIJTION/AVAILABILITYSTATEMENT
Unclassified-Unlimited
Subject Category 54 Distribution: StandardAvailability: NASA CASI (301) 621-0390
12b. DkST_iBUTION CODE
13. ABSTRACT (Max/mum 200 words)
In this project four motion cueing algorithms were initially investigated. The classical algorithm generated
results with large distortion and delay and low magnitude. The NASA adaptive algorithm proved to be weIl
tuned with satisfactory performance, while the UTIAS adaptive algorithm produced less desirable results.
Modifications were made to the adaptive algorithms to reduce the magnitude of undesirable spikes. The optimal
algorithrn was found to have the potential for improved performance with further redesign. The center ofsimulator rotation was redefined. More terms were added to the cost function to enable more tuning flexibility.
A new design approach using a Fortran/Matlab/Simulink setup was employed. A new semicircular canals model
was incorporated in the algorithm. With these changes results show the optimal algorithm has some advantages
over the NASA adaptive algorithm. Two general problems observed in the initial investigation required
solutions. A nonlinear gain algorithm was developed that scales the aircraft inputs by a third-order polynomial,
maximizing the motion cues while remaining within the operational limits of the motion system. A braking
algorithm was developed to bring the simulator to a full stop at its motion limit and later release the brake tofollow the cueing algorithm output.
14. SUBJECT TERMS
Flight Simulation, Simulators, Motion Systems, Cueing Algorithms
Motion Perception
17. SECURR'Y CLASSIFICATION 18. SEGURI]Y CLAS.StI'ICATION 19. SECURITY CLASSIFICATIONOF REPORT OF THIS PAGE OF ABSTRACT
Unclassified Unclassified Unclassified
NSN 7540-01-2a0-_SOO
282
15. NUMBE_ OF PAGES
• - 28716. PRICE CODE
A1320. LIMITATION
OF ABSTRACT
UL
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