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Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
FLIGHT TEST OF A TRAJECTORY CONTROLLER USING LINEARIZING
TRANSFORMATIONS WITH MEASUREMENT FEEDBACK
Robert F. Antoniewicz*and Eugene L. Duke*
NASA Ames Research Center
Dryden Flight Research Facility
Edwards, California
and
P.K.A. Menon**
Georgia Institute of Technology
Atlanta, Georgia
Abstract
The design of nonlinear controllers has relied on
the use of detailed aerodynamic and engine models
that must be associated with the control law in the
flight system implementation. Many of these controllers have been applied to vehicle flightpath control
problems and have attempted to combine both innerand outer-loop control functions in a single controller.
This paper presents an alternate approach to the design of outer-loop controllers. The approach simplifies the outer-loop design problem by separating the
inner-loop (stabilization and control) f;om the outerloop (guidance and navigation) functions. Linearizing
transformations are applied using measurement feedback to eliminate the need for detailed aircraft models
in outer-loop control applications. Also discussed is
an implementation of the controller. This implementation was tested on a six-degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Proof of the
concept is provided by flight test data which is presented and discussed.
CAS
command augmentation sytem
CLC
control law computer
FTTC
flight test trajectory control
HIDEC
highly integrated digital electronic
control
PCM
total automatic flight control system
WATR
Western Aeronautical Test Range
body axis normal accelerometer output
x-axis body accelerometer output
y-axis body accelerometer output
z-axis body accelerometer output
total aerodynamic drag
error signal
gravitational acceleration
altitude
altitude rate
linear control law gains
total aerodynamic lift
Mach number
pulse code modulation
Copyright 0 1990 by the American Institute of Aeronautics
and .4stronautics, Inc. No copyright is asserted in the
United States under Title 17, U.S. Code. T h e U.S. Government has a royalty-free license to exercise all rights under
the copyright claimed herein for Governmental purposes.
All other rights are reserved by the copyright owner.
TAFCOS
an
Acronyms
augmentor wing jet STOL research
aircraft
short takeoff and landing
Symbols
Nomenclature
AWJSRA
STOL
JAA.
518
rn
mass
P
Q
body axis roll rate
body axis pitch rate
7
body axis yaw rate
T
t
V
thrust; linearizing transformations
velocity
v
velocity rate
V
linear control or pseudocontrol
W
inverse linearizing transformations
XT
thrust along the x-body axis
Y
total sideforce
time
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
thrust along the z-body axis
measurement form
angle of attack
proportional control term
angle of attack rate
plant
angle of sideslip
reference trajectory
angle of sideslip rate
function of input vector
commanded incremental load factor
function of state vector
engine orientation angle
angle of attack
throttle
body reference frame Euler roll angle
rlCOm
commanded throttle
initial condition; zero altitude
8
body reference frame Euler pitch angle
e
Introduction
body reference frame Euler pitch
angle rate
b
body reference frame Euler roll angle
4
body reference frame Euler roll
angle rate
The problem of aircraft trajectory control is generally thought of as an “outer-loop’’problem, that is, the
aircraft is assumed to have a stabilizing, “inner-loop”
command augmentation system. Often, the inner-loop
problem is called the control problem, while the outerloop problem is called the guidance problem. For simple trajectories, outer-loop control may be provided
by an autopilot that maintains altitude and velocity or
performs somewhat more complex tasks such as automatic landing.
Vectors and Matrices
error signal vector
plant vector function
input vector function
measurement vector function
The fundamental objective of trajectory control
research at NASA Ames Research Center, Dryden
Flight Research Facility (Ames-Dryden),is to define a
generic approach for designing guidance laws that will
command an aircraft to fly precise flight test maneuvers to obtain accurate, repeatable flight data. The intent is to use modem control theory design techniques
to establish a method of designing flight test trajectory
controllers for various aircraft at Ames-Dryden to improve data collection performance.
nonlinear control vector
state vector
state derivative vector
linear system state vector
i
linear system state derivative vector
Y
observation vector; reference trajectory
State
z
measurement vector
A
linear system plant matrix
B
C
I
linear system input matrix
Previous work at Ames-Dryden justifies the usefulness of outer-loop controllers which command the aircraft to fly precise trajectories.’ In addition, having
trajectory tracking capabilities available allows the researcher to design experiments to test other outer-loop
functions such as optimal trajectories, intercept trajectories, navigation functions, or even automated approach and landing flightpath control.
linear system observation matrix
identity matrix
Subscripts
corn
commanded
D
derivative control term
e st
estimated
h
altitude
I
k
integral control term
M
Mach number
In flight test trajectory control the requirement is to
provide precise, repeatable control of an aircraft during maneuvers used to gather aerodynamic, structural,
propulsion, and performance data. For conventional
flight regimes these maneuvers are fairly straightforward and, in general, easily modelled. Typical of
these maneuvers are level-accelerations/decelerations,
pushover/pullups, and windup turns.
kinematic
519
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
Numerous approaches to the flight test trajectory problem were taken including cut-and-try techniques on a nonlinear simulation? linear optimal
contro~,~
optimal cooperative c o n t r o ~ eigenstructure
,~
a~signrnent,~
and classical control theory.’ Although
both open-loop and closed-loop systems were successfully developed and utilized in flight, each of these approaches had limitations. The use of nonlinear control
simplifies many of these problems, although some cutand-try tuning may still be required because of modelling assumptions.
Meyer and Cicolani5 describe a formal structure for
advanced flight control systems that provides the basis for the results described in this paper. This formal structure, the total automatic flight control system, has been applied in detailed nonlinear simulations
of the de Havilland C-8A Buffalo augmentor wing jet
STOL research aircraft (AWJSRA),6 a vertical attitude
takeoff and landing aircraft? and others. Excellent
results were achieved in all of these studies, and the
claim made by Meyer, et al.* that “the method is effective for a large class of dynamic systems that require multiaxis control and that have highly coupled
nonlinearities, redundant controls, and complex multidimensional operational envelopes” can be taken as
thoroughly validated.
jectory design. Since the trajectories to be flown are
standard flight test maneuvers, time scale separation
will be achieved through gain selection.
To do this, the aircraft plant is analyzed for the slowest dynamic characteristics in the flight regime over
which the guidance law is to be used. Gains can then
be selected using any appropriate linear design technique so that the outer-loop dynamics are sufficiently
separated in time scale from the slowest plant dynamics. The plant can then be considered by the outer-loop
controller as having no apparent dynamics.
A flight test trajectory controller (FTTC) was designed using this approach and was tested on a realtime, six-degree-of-freedom, full-envelope, nonlinear
simulation of an F-15 aircraft and subsequently in
flight on a preproduction F-15 aircraft. Flight testing
covered a subset of the maneuvers tested in the simulation. The results are presented and discussed.
An Alternate Approach to the Nonlinear
Control Problem
This paper presents the theory for and an application of an approach that provides a solution to the flight
test trajectory control problem meeting the stated objective. This approach eliminates the need for inverse
aerodynamic models by using measurement feedback.
The elegance of the approach is that no inherent aerodynamic models are used, so it is easy to apply the
controller to different aircraft. The use of nonlinear inverse transformations and time scale separation
presents a single linear system covering a large portion of the envelope to the designer. Only simple
linear proportional-integral or proportional-integralderivative guidance laws need be designed for the
outer loop. The nonlinear inverse transformationsmap
the linear trajectory command to the nonlinear input
required by the plant. Time scale separation provides
the justification to ignore the plant dynamics which are
fast relative to the outer-loop commands. Put simply,
the dynamics of the outer loop are designed to be slow
enough so that the plant achieves the commanded input prior to the guidance law computing a new command. This can be done through gain selection or tra-
520
The use of detailed aerodynamic models in an outerloop, nonlinear controller can be eliminated by using
aircraft accelerometer, rate gyro, and other sensor outputs. This simplifies the nonlinear controller in two
ways: by eliminating aerodynamic coefficient calculations, and by making the nonlinear controller “model
independent” given the same command paths into the
inner-loop control system.
While both of these features provide the potential
for major design, implementation, and execution time
benefits, the model-independence feature is perhaps
the most significant contribution. It offers the possibility of designing a generic, general-purpose outerloop guidance law that, for similar types of aircraft,
is independent of the aircraft to which it will be applied. Obviously, complete model independence can
only be achieved by representing vehicles with identical models.
Linear and Nonlinear System Formulations
The plant around which the FTTC is designed includes the aircraft, the flight control system, and the
instrumentation system. This plant is modelled by
the equation
putes the real input to the nonlinear system. The T-map
shown in the same figure is the mapping from the plant
states to the linear system outputs described in previous formulation^.^ In this formulation it is the identity
matrix. Implicit in equation (9) is the assumption that
gm(z) r f o .
Given this plant model, it is desired to develop a system of the form
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
in the Brunovsky canonical form. This system is
known as the apparent linear plant. Development of
this system is achieved throughlinearizing transformations and time scale separation The state vector x contains all necessary states of the nodinear system state
vector, %, as well as all necessary integral states.
Linear Guidance Law Design
In the formulation of the FITC, the linear control
law is a simple tracker as opposed to the explicit model
follower used by Meyer et aL9 The linear control law
or pseudocontrol receives its input, e , from the feedback of the linear system, y , and the reference or command trajectory, ysef. so that
Derivation of the Linearizing 'handormation
The input to the apparent linear system is derived
from equation (2) to be
% = V
e = Yref - Y
(3 )
For the tracker, the first step of the design is to determine the nature of the command to be used (that is,
step, ramp, parabola, and so forth). The designer can
then determine the number of integrators required to
achieve adequate tracking performance. Once this has
been established, the pseudocontrol gains can be determined using appropriate modem or classical control techniques.
This equation and equation (1) are then combined
so that
v = fp(x) + & ( X ) U
(4)
This is the linearizing transform for state feedback.
Note that the number of states and controls are the
same so that gp( x) is a square matrix function.
Next, the terms fp(x) and gp(x) in equation (1)
must be transformed into terms that are functions of the
measurement vector z , which includes all necessary
accelerometer, rate gyro, airdata, and so forth, measurements.
fp(x) = fm(z)
( 5)
g p w = gm(z)
( 6)
( 10)
Nonlinear System Equations
For the F- 15 aircraft on which this approach is to be
tested, the aircraft can be represented by a nonlinear
system equation with the form
so that equation (1) becomes
It is this transformation which eliminates the need
for aerodynamic models in the linearizing transformations of systems developed previously. The linearizing transformation as a function of measurements is
given by
v = fm(z) + gm(z)u
( 8)
The controls for this system are the inputs to the innerloop controller, and are defined for this application
tobe
[ ;;][ ]
A%,
The real control input into the plant can then be determined by solving equation (8) for the nonlinear input~
sothat
u=
=
(13)
where
A%-
= a,
-1
( 14)
The nonlinear system state equations used are the
standard wind axis equations of motion which corre-
This equation represents the inverse linearizing transform, referred to as the W-map (Fig. 2). which com-
521
spond to the states in the state vector and can be found
in Ref. 10. They are
ti=
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
&=
AX
1
= -{cos
am
P[gm(a, cos a - a,, sin a)
- XTestcos a1
+gma,sinp+ XTCOSCYCOS~
+ -mg(cosacospsinO
- sin p sin 4 cos 6
- sin a c o s pcos +cos e ) }
1
-[-Dcosp+Ysinp+XTcosacosp
m
+ ZT sin a c o s p - mg( cos a c o s /3 sin 0
- sin p sin 4 cos 8
- sin a c o s pcos COS e ) ]
(28)
1
[ - L + ZT cos a - XT sin a
v m cos p
+ mg(cosacos4cose
+ sin a s i n e ) ]
+g - tan p ( p cos a + r sin a)
&=
1
v cos p [ -g(
an COS
+ a,
sin
aces 4cos e
- sin a sin e ) ]
+q-tanp(pcosa+ rsina)
-COS
h = a, sin 0 - a y sin 4 cos 0
+a,cos &cos e - 1
1
i;= -[
sin e(xT- D cos a + L sin a)
Equations (17), (18), and (28) through (30) are
used to derive the inverse transformations for the
guidance laws.
If we define that a maneuver begins at the trim condition t = t o = 0 so that x = 0 , then equation (11)
can be written as
Equations (17) and (18) are already in the form
needed since all of the terms can be measured on the
aircraft. Equations (15), (16), and (19) need to be
transformed to functions of observed variables. This
is done using the equations relating accelerometers and
states also found in Ref. 10. They are
1
a,&= - ( x T - D c o s a +
gm
- gmsin 0 )
ay,k
=
X(0) = o = f ( x ( 0 ) )
and as we also define that for the initial trim condition
Ui(0) = O f o r a = 1,3,thenitfollowsthat
f(x(0)) = 0
Lsina
Guidance Laws
1
-(Y+ grnsindcosd)
The guidance laws for the nonlinear FITC are
driven by error signals obtained by computing the difference between the reference state vector prescribed
by the desired aircraft trajectory and the aircraft measurement feedback. The output of these linear control
laws are pseudocontrols which are transformed, using the W-map, into commands for the aircraft/innerloop system.
gm
1
az,k = -( ZT - Dsin a - Lcos a
gm
+ gm cos 4 cos e)
a,,k = a, - sin 0
ay,k = ay + sin +cos 0
a,,k = a,
+ g(x(O))u(O)
The guidance laws used for the implementation discussed later in this paper are derived here. There
are three command loops available for control by the
FITC. These are pitch, which is controlled by incremental load factor command, A%-; roll, which is
controlled by roll rate command, pcm; and thrust,
which is controlled by throttle command, qcm.
+ cos 4 cos 8
The measurement feedback form of equations (IS),
(16). and (19) are
522
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
Three different trajectories were desired to be flown:
a level acceleration maneuver, a pushover/pullup maneuver, and an excess-thrust windup turn maneuver.
The level acceleration maneuver is defined as a wings
level, constant altitude maneuver with Mach number
increasing (or decreasing) at a specified rate. The
pushover/pullup maneuver is a wings level, constant
throttle maneuver with angle of attack varying at a
specified rate from trim to a minimum value, then to
a maximum value, then back to trim. The excessthrust windup turn is a constant altitude Mach maneuver, with angle of attack increasing at a specified rate
to a specified value.
computed using the inverse linearizing transformation
g,
+ tan P(pc0s a! + r sin a!)
1
--[ - g( a,, cos a! + a, sin a!)
v cos p
= iu,
+ g(cos a!cos 4cos e
+ sin a sin 0) ]
(34)
The pitch rate command qcm is then used to determine the A &. using the following inverse lineanzing transformation:
An,.
The linearizing inverse transformations are also derived from Ref. 10.
= -1
v cos p
+ a,, + (Pcm
g cos a
- Q)
( 35)
These two transfornations could be combined into one
transformation; however, the pitch rate command generated by equation (34) must be filtered because of
noise and system delays. This effect is discussed in
the Implementation Experience section.
Pitch Guidance Laws
The pitch command for the F?TC is computed using
two different guidance laws and transfornation equations. The level-acceleratioddeceleration maneuver
uses reference altitude and altitude rate to compute
a vertical acceleration command; the excess-thrust
windup turn and the pushover/pullup maneuver use
reference angle of attack to compute an angle-of-attack
rate command.
Roll Guidance Laws
The lateral commands for the FTTC are computed using two different guidance laws and transformations. For the level-acceleratioddeceleration and
pushover/pullup maneuvers, the reference roll attitude
brei is known and dCm is computed using the linear
control law
Vertical acceleration is computed in the altitude
command pitch loop using the following linear guidance law:
where
with
ej, =
href - h
and p , , is computed using the inverse linearizing
transformation equation
eh = href - h
Then A%,, is obtained from hCmusing the inverse
linearizing transformation equation
A%,,,
= -1 +
h,,,-a,sinB+a,sin+cosB+
COS e cos 4
pCm= (bco,-tan8(qsin++
= k,,e,
+ k,,
6’
e,dt
( 33)
where
4,,f
e , = a,,f - a
From ,ut
( 37)
The guidance law computation for the excess-thrust
windup turn requires the use of two layers of outerloop controllers. Each outer loop must be slower than
its inner loop. For this control loop, the outer-loop linear guidance law computes an h,, using the same
linear control law shown in equation (31). Roll attitude command is then computed using the following
inverse linearizing transformation equation:
1
( 32)
The second pitch control is the angle-of-attack command loop. The linear control law for this loop is
dr,,
rcos+)
an intermediate pitch rate command is
523
= -cos-1
a, sin 8 - hcm/g -
(
cosq-
This intermediate command is used in the linear control law
and to describe drawbacks which had or were expected
to have noticeable impacts on the results.
Flight Test System Description
The F-15 highly integrated digital electronic control
(HIDEC) aircraft and the remotely augmented vehicle
(FL4V) system'' shown in Fig. 1 were used to flight
test the guidance laws. The F-15 HIDEC is a preproduction F-15 aircraft with Pratt & Whitney 1128 engines, a digital command augmentation system (CAS),
and a digital electronic engine control. The RAV system has both downlink and uplink capabilities, and has
a ground-based minicomputer in which control laws
may be implemented for flight test. This system eliminates the need for large computational capabilities onboard the aircraft.
from which p,, is computed using the inverse linearizing transformation shown in equation (37)
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
Thrust Guidance Laws
Two throttle commands were required for the maneuvers defined. The first command holds the throttle
position constant at the current or at some predefined
position, qc,
= qref.
The throttle command for all other maneuvers is a
Mach number controller. The commanded Mach rate
is computed using the linear control law
hi,, = kMDen;r + k M p e M +
6'
kMIeMdt
The RAV system is designed so that software developed and tested on the Ames-Dryden simulation system may be transported directly and run on identical
computers in the RAV system. This enables the engineer to cheaply and easily perform verification and
validation tests on the simulation before using the aircraft and RAV system.
(39)
where
e& =
eM
&ref
- n;i
= Mref - M
which is used to establish a thrust command T,, from
the inverse linearizing transformation equation
Tc,
The drawback to the RAV system is that an additional 80 to 100 msec of pure delay are added to the
control loop. The time added to an aircraft system delay as a result of the asynchronous systems of up to
three frames (or up to 150 msec) can make the control
task much more difficult. For the outer-loop guidance
problem, this delay was expected to cause a noticeable
problem in the lower dynamic pressure ranges.
= {maucm
-gm[ ay sin /3
+ cos p( a, cos a - a, sin a)]
- XT cos CY cos p
+ mg( cos a c o s psin 6 - sin psin C#J cos 6
- sin COS /3 COS COS e)}/
The allowable command ranges for the controller
were set at *150.0 dedsec in roll rate, -0.75 to 4.0 g
in incremental load factor (0.25 to 5.0 g normal acceleration), and full range for both throttles. The only
problem foreseen resulting from the command range
limits was in the incremental load factor command.
(cos E cos a cos p + sin E sin a cos /3) (40)
with E being the angle between the x-body axis and the
direction of thrust. The actual throttle setting is determined by using a model of the thrust-throttle relationship and inverting it so that
Flight Test Pajectory Control Software Program
The linear control laws and nonlinear inverse transformations described in previous sections, along with a
command generator to produce the reference time histories of the states to be tracked, were implemented
in FORTRAN in a computer program called the flight
test trajectory controller or FTTC (Fig. 2). An operator interface to the controller was developed to input
maneuver specifications, and to monitor the F " C and
flight test system.
The thrust term XT in equation(40) is obtained using the same model with a simple lag to emulate the
engine lag.
Discussion
These sections describe the system and software
used to flight test this approach. No effort is made to
give an in-depth description of the system used. Instead, descriptions are given to provide adequate information regarding how the experiment was performed,
The basic frame time of the program is 12 msec.
However, only the maneuver selection logic and the
524
to 240 msec were examined over a matrix of maneuvers simulated at Mach 0.75 and 1.20 and at altitudes
from 10,OOO to 40,OOO ft. The controller performed
acceptably at all conditions.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
linearizing transformations run at this rate. The command generator and pseudocontroller run every other
frame. This is done because the command generator and the pseudocontroller represent the outerloop or slow controller, while the linearizing transformations and the aircraft CAS represent the innerloop controller.
The FTTC was flown between May and August 1989. During these flights, pseudocontroller gains
were adjusted and minor changes were made in the
guidance law to improve performance of the Controller.
Four of the maneuvers flown are presented in Figs. 3
through 6 and are discussed here.
The frame time was selected because it was the
fastest that the software could run without getting
frame overruns. A slower frame time would have
added to the overall loop delay of the system, so it
was desirable to minimize the frame time. However,
the controller sees constant values of sensed data between downlink data frames which have the same rate
as the aircraft system (50 msec). This could be a problem during very dynamic maneuvers.
The first of the four maneuvers shown in Fig. 3
is a level acceleration maneuver from Mach 0.70 to
Mach 1.20 at a rate of 0.01 Mach numbedsec. Roll
attitude is held to within f2.0" of wings level. Mach
number increases at a constant rate except for a short
time around Mach 1.0. This effect is caused by the aircraft pitching rapidly to correct altitude error resulting
from the shock wave forming at the tip of the noseboom. The effect is also evident in the altitude, altitude
rate, and commanded incremental load-factor plots.
Results
Note that in the nonlinear guidance laws defined by
equations (31) through (41), none of the equations use
aerodynamic terms and, therefore, none of these guidance laws require aircraft-specific aerodynamic models. In fact, no aircraft-specific models are required
except for the simple thrust-throttle mapping shown in
equation (41). These results are significant in their differences from the results reported by previous authors.
The pushover/pullup maneuver shown in Fig. 4 was
flown at Mach 0.90 and 10,OOOft with angle of attack
varying between 0" and 2.5" at a rate of 0.5 deg/sec.
Tracking of reference angle of attack is affected noticeably by sensor noise. This effect is discussed in
more detail later in this paper.
During simulation and flight test, controller performance was measured by the ability to keep aircraft parameters within specified tolerances. These
tolerances are AO.01 Mach number, 6100 ft altitude,
and f0.3" angle of attack. In addition, the controller
must have smooth transitions from the capture of initial conditions to the beginning of the maneuver itself.
Also, when parameters to be tracked are ramped, the
controller must maintain the tolerances while ramping those parameters smoothly. The large tolerance
in angle of attack is caused by the noise and accuracy problems associated with the measurement of
that parameter.
Figures 5 and 6 show excess thrust windup turns.
The first windup turn is flown at Mach 0.65 and
25,000 ft, while the second one is flown at Mach 1.20
and 25,000 ft. The maneuver at Mach 0.65 tracks altitude poorly with an error of approximately 150 ft before rolling out to straight and level. This maneuver
also has a difficult time tracking Mach number with an
error of approximately Mach f0.025. This is partially
caused by a 1.5-sec delay built into the throttle command to eliminate the problem of the throttle toggling
between core power and afterburner.
The second excess thrust windup turn performed at
Mach 1.20 does not show this problem. Altitude is
kept to within f25 ft within Mach f0.008. Here, however, angle of attack is not ramped smoothly to the desired value of 5", and even though the commanded incremental load factor is at its maximum value, the angle of attack measured is just over 3". The problem of
the unknown scaling effect in the flight control system
occurred in both the pitch and roll command paths.
Simulation evaluation was conducted for all three
maneuvers across a Mach number range of 0.60 to 1.20
and across an altitude range of 10,OOOto 40,000 ft with
acceptable results, except at the high and slow conditions. While the results at the high and slow conditions did not fall within the specified tolerances, the
controller was still able to perform the maneuver.
Tests were also conducted in the simulation with
varying amounts of pure delay in the uplink and downlink emulation. Total system delays ranging from 120
The effect during flight test which the pilots found
least acceptable, and in some cases unacceptable, was
the effect termed roll ratcheting which appears at the
525
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
not modelled in the simulation. The problem of roll
ratcheting warrants further investigation.
beginning of the roll into the turn. This effect, seen in
Figs. 5 and 6 , vaned in magnitude and frequency depending on the conditions of the turn. In the slower
or higher turns, the effect was not noticeable to the pilot. The origin of this effect is unclear. However, one
possible explanation is that the CAS seemed to scale
the command generated by the inverse transformation.
The gains in the linear control law were driven up to
account for this instead of simply scaling up the commands out of the inverse transformations. This may
have caused the linear gains to be too high in some
flight conditions, thus causing the ratcheting. This
problem does point out, however, that such scaling effects and nonlinearities in the inner-loop control system need to be accounted for in the inverse transformations. The transformations derived herein only account for aerodynamic nonlinearities and the nonlinearities in the equations of motion.
Conclusions
Research is ongoing at the Ames-Dryden Flight Research Facility to define a technique for designing
flight test trajectory controllers. Many techniques have
been investigated. The most promising technique of
the previous research involved the use of linearizing
transformations using state feedback.
An approach to the outer-loop trajectory control
problem for developing nonlinear guidance laws using linear controls with nonlinear transformations and
measurement feedback was presented. A controller
was designed which applies this approach specifically
to the problem of flight test trajectory control. Testing was accomplished on a full-envelope, nonlinear,
six-degree-of-freedom simulation and in flight using
an F-15 aircraft. Flight test results are presented.
The origin of the noise in the angle of attack
and commanded incremental load factor seen in the
pushover/pullup maneuver can be explained, at least
in part, by these two maneuvers. During both maneuvers, the commanded incremental load factor reaches
its maximum limit and is held constant for a short time.
However, noise in the angle-of-attack trace is significant (up to approximately 0.3") and is probably a result of either measurement noise, turbulence, or both.
Angle of attack provides the feedback for the linear
control law that computes the linear system input of
angle-of-attack rate (equation (33)), as well as heavily influencing the inverse transformation shown in
equations (34) and (35). The commanded incremental load factor computation seems to amplify the noise
on angle of attack. While not a divergent process, filtering sensed angle of attack is necessary to provide
smoother tracking of commanded angle of attack.
Simulation and flight test results indicate that the
flight test trajectory controller is capable of performing an acceptable job of controlling an F-15 aircraft through level accelerations, pushover/pullups,
and windup turns over a large portion of the flight envelope. Some problems are encountered at high and
slow (low dynamic pressure) conditions where time
scale separation between the fast and slow controllers
disappears as aircraft performance decreases. Another
problem for this controller was a ratcheting motion of
the aircraft that occurred when entering windup turns
at high dynamic pressures. This effect may be cleared
up by running the controller at a slower rate than the
tested rate of 83.3 Hz. Also in this application, certain
nonlinearities were not accounted for in the linearizing
transformations. It is likely that these nonlinearities
contributed to the problem of roll control.
The results of the flight test of the FTTC indicate
that the approach of using linearizing transforms with
measurement feedback is a valid approach for developing outer-loop controllers for nonlinear systems.
Tracking of reference trajectories is acceptable over a
large range of altitudes and Mach numbers using only
a single set of gains.
The approach for designing outer-loop controllers
for high-performance aircraft by using inverse linearizing transformations with measurement feedback
has been validated by the results in simulation and
flight testing. With the exception of a simplified engine model, this approach does not require implicit or
explicit aircraft models in the design. It may be easily
applied to other aircraft requiring similar inputs to the
control system.
In general, the flight test data matched the simulation data with the exception of sensor noise, which was
526
References
Smith, G. Allan, and Meyer, George, Application
of the Concept of Dynamic Trim Control to Automatic
Landing of Carrier Aircrafr, NASA ”-1512, 1980.
‘Duke, Eugene L., Jones, Frank P., and Roncoli,
Ralph B., Development and Flight Test of an Experimental Maneuver Autopilot f o r a Highly Maneuverable Aircraft, NASA TP-2618, 1986.
Smith, G. Allan, and Meyer, George, “Application
of the Concept of Dynamic Trim Control and Nonlinear System Inverses to Automatic Control of a Vertical Attitude Takeoff and Landing Aircraft,” AIAA 812238,1981.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
*Duke, Eugene L., Swann, Michael R., Enevoldson, Einar K., and Wolf, Thomas D., “Experience with
night Test Trajectory Guidance,” Journal of Guidance, Control, ana‘ Dynamics, vol. 6 , no. 5, Sept.Oct. 1983, pp. 393-398.
8Meyer, G., Hunt, R.L., and Su, R., Design of a
Helicopter Autopilot by Means of Linearizing Transformations, NASA TM-84295, 1982.
3Menon, P.K.A., Badgett, M.E., Walker, R.A., and
Duke, E.L., “Nonlinear night Test Trajectory Controllers for Aircraft,” Journal of Guidance, Navigation, and Control, vol. 10, no. 1, Jan.-Feb. 1987.
9Meyer, George, “The Design of Exact Nonlinear
Model Followers,” Proceedings of 1981 Joint Automatic Contro! Conference, Charlottesville, Virginia,
1981, pp. FA3A.
4Gary, Sanjay, and Schmidt, David K., Optimal Cooperative Control Synthesis of Active Displays, NASA
CR-4058,1987.
“Duke, Eugene L., Antoniewicz, Robert E, and
Krambeer, Keith D., Derivation and Definition of a
Linear Aircrajlt Model, NASA RP-1207, 1988.
’Meyer, George, and Cicolani, Luigi, A Formal
Structurefor Advanced Automatic Flight-Control Systems, NASA TN D-7940,1975.
“Petersen, Kevin L.,“night Experience With a Remotely Augmented Vehicle Test Technique,” AIAA
81-2417, NOV.1981.
Radar
antenna
900283
Fig. 1 Remotely augmented vehicle system used to flight test the F?TC.
527
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
Y,
Yo
Y
,
V
Command
generator
Pseudocontroller
WT-map
Fig. 2 Structure used for the FTTC.
528
i = f(x) + g(x)u
$7,
U
Aircraft plant
Pcom 1
deglsec
0
-10
I
I
I
I
I
I
I
I
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
4-
/'"
0
-4
~
Mach
21
-'
I
0
40
h,
ftlsec
0
=-
I
-40
25,100
h9
ft
25,000
I
I
I
I
I
;
24,900 0
10
30
Time, sec
20
40
60
50
900265
Fig. 3 Flight data of a level acceleration maneuver; Mach 0.70 to1.20,25,000 ft.
529
-
-0
-10
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
10 -
Pcom 9
deglsec
*
I
I
I
I
0-
I
/
1
I
I
I
I
1
-
com 8
g's
40
Mach
0
Time, sec
900266
Fig. 4 Flight data of a pushover/pullup maneuver; Mach = 0.9, 10,000ft, between a! = 0" and a = 2.5".
530
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
Start maneuver
End maneuver
P,
deglsec
-40
100
-
Pcom?
deglsec
-100
25,200
I
I
I
I
I
I
I
h’ 24,800
ft
24,400
*
com 9
g‘s
llLzlzk
-4
Mach
2oo
PLA
deg
corn ’ 100
0
4
8
12
16
Time, sec
20
24
28
900267
Fig. 5 Flight data of an excess thrust windup turn maneuver; Mach = 0.65,25,000 ft, from
531
atrim
to cy = 12’.
Start maneuver
4:Ft"-c.r,
I
-100
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3373
deglsec
PI
i
i
i
i
i
i
-40
Pcom
deglsec
,
-100
25,040
2
25,000
24,960
l
-4
l*L
1
Mach 1.20
1.19
com 9 100
deg
8o0
4
8
12 Time,
16sec 20
24
28
900268
32
Fig. 6 Flight data of an excess thrust windup turn maneuver; Mach = 1.2,25,000 ft, from CYtrim to CY = 4'.
532
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