(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

AIAA 2000-0829 Wind Tunnel Based Virtual Glenn Gebert Joy Kelly Juan Lopez

Flight Testing

Sverdrup Technology, Inc. TEAS Group, Eglin AFB, FL

Johnny Evers Air Force Research Laboratory (AFRL/MN), Eglin AFB, FL

38th Aerospace Sciences Meeting & Exhibit

1 O-1 3 January 2000 / Reno, NV

.’ L’

A0046669

-For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191

(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

Wind Tunnel Based Virtual Flight Testing

Glenn Gebert’, Joy Kelly+, and Juan Lopez+ Sverdrup Technology, Inc., TEAS Group, Eglin AFB, FL

Johnny Evers+ Air Force Research Laboratory (AFRL/MN), Eglin AFB, FL

It is desired to develop a ground-based facility that could mimic flight-testing. The facility would allow for dynamic testing and parametric studies in a controlled environment with significant cost saving from conventional flight- testing. The Wind Tunnel Based Virtual Flight Test (WTBVFT) would provide this capability. The WTBVFT environment calls for a specialized test article support system, which allows for free rotational motion. Actual flight hardware could be mounted in the test article and “virtually fly in the wind tunnel” under its own flight control. Augmenting the rotational motion of the test article with “simulated translational motion” may produce the desired similarity to free-flight trajectories. Current approach for design and evaluation of control systems use digital and Hardware-in-the-Loop simulations. The WTBVFT is considered an intermediate step between simulations and flight test, providing a pseudo free-flight environment in a controlled ground facility. This paper discusses the WTBVFT concept, its challenges, and potential use. Description of a high-fidelity mathematical model for analysis of the WTBVFT environment is included. Preliminary results are presented showing the concept ability to mimic free- flight.

INTRODUCTION Generally, aircraft and missile control system design is

achieved using aerodynamics gathered from static wind tunnel test at a limited number of flight conditions. This method neglects the effects of dynamic transients and unsteady flow phenomena, and due to the cost of wind tunnel testing, is limited to a small set of Mach/angles of attack conditions. The Wind Tunnel Based Virtual Flight Test (WTBVFT) ground test methodology proposes a dynamic testing technique in the wind tunnel. The approach could provide a better characterization of aerodynamics and the potential for early identification of airframe control problems prior to flight test.

Currently, investigations of airframe/autopilot system response transition from simulations based on static aerodynamics, to flight-testing. Flight-testing is extremely expensive, time consuming, and in most cases limited in scope. It is hoped that the WTBVFT methodology can better bridge the gap between modeling and testing. In doing so, it could mitigate the risk and reduce cost of testing by reducing the test sorties required for weapon system development and evaluation.

The basic WTBVFT concept is to mount the test article on a specialized wind tunnel support system, allowing for airframe rotational motion. The test article will be able to freely experience all rotational motion while a computer simulation augments the translational motion. This facility

would allow for the closed-loop testing of actual flight hardware (rate gyros, autopilot, control fin actuators, etc.) prior to the first flight test. The autopilot and control system performance may be better understood by including the transient flow effects. A study was conducted to develop a simulation of the WTBVFT environment. The simulation indicated the way to make best use of a WTBVFT facility and identify any implementation problems.

This paper presents a mathematical model of the WTBVFT environment suitable for 6-DOF simulation. Several methods of utilizing the WBTVFT are evaluated in their ability to free-flight motion. This comparison provides the basis for a preliminary assessment of WTBVFT capability. The WTBVFT was modeled as a rigid test article mounted on a flexible support system.

A preliminary assessment of WTBVFT was conducted using 3-DOF models employing linear aerodynamics and assuming an ideal support system with the objective of identifying any fundamental deficiency in the WTBVFT approach. The analyses included open-loop and closed-loop autopilot controlled test cases. Preliminary results for typical autopilot-controlled cases indicate good correlation between predicted free-flight and the WTBVFT response.

THE WTBVFT CONCEPT A candidate implementation for the WTBVFT concept is illustrated in Fig. 1. The key elements are the support system, the high bandwidth balance equipment, the test

’ Senior AIAA member f Associate Fellow, AIAA This paper is a work of the U.S. Government and is not subject to copyright protection in the United States

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 2000-0829

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(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. , 1 -

article, and the simulation. The test article will likely be 0 guidance loops would be simulated in the 6-DOF with the mounted on a near frictionless bearing. This test article guidance filter model computing the acceleration would include the actual flight autopilot, control fin actuation commands to be telemetered to the autopilot in the test system, and inertial rate sensors. The test article is integrated article, to the digital simulation to form a Hardware-in-the-Loop l actual airframe accelerations originate from the simulation (HWIL) simulation capability. Ideally, the concept is to fly and are telemetered to the autopilot in the test article, the airframe real-time in the wind tunnel, allowing for free l accelerations are constructed from the wind tunnel rotation in response measured loading by dividing the forces by the mass, to the moments produced by the control tins, and closing the l the acceleration and rate feedback signals are used by the loop for guidance and control system testing. autopilot to calculate the fin deflection commands,

Stabilization of the test article in the wind tunnel could l the test article is free to rotate in response to fin deflections be achieved by closing the autopilot rate loops and using commands generating the angle of attack producing forces actual inertial rate sensors. While the measured angular rates and moments on the test article, of the test article are used for stabilization, the test article . the test article is stabilized using the on-board inertial rate angle of attack in the tunnel is controlled by telemetered sensors measuring the test article attitude rate of change,

IC

t

rarget Dynamics

IC

AC 6, 6 “j,PM Missile Guidance -r,

f+DOF

Filter I Autopilot --, Actuator - AW3 Force& - Position/

Mode, ---* Moments Ve,ocity _ Truth Data

0 .

Eqs Motio” pj-+ R. V.f .y I ’ I I I !

t I I - Replaced by VFT - 0 0 VFf 6 0 Corrections

, Eqs. Of Motion

I 0 , FJ , 4 S=M+wp-ur+g, 4 I

:.. --._

and Rate Gyros

NOTE: Frictionless support system Outputs: Forces and angular rates

I Close Loop: Telemetry A, and A, from 6-DOF to autopilot

2. Use w Model Rate @r =d,) for Stabilization of test article in VFT

_ IRU in missile, or signal from support system

A c and A M (acceleration commands and achieved acceleration

Forces, AoA rates, and roll rate from test article to 6-DOF

3. Support System Concept: Free to rotate in pitch and roll with limited motion in yaw for evaluation of cross coupling.

Figure 1. Candidate WTBVFT Implementation

acceleration signals. Acceleration commands and actual accelerations of the free flying airframe are computed in the simulation and sent to the autopilot in the test article. These guidance acceleration commands and actual accelerations close the loop around the Six Degree-of-Freedom (6-DOF) simulation to produce a guided trajectory. Aerodynamic forces and angular rates are fed back to the simulation to close the loop around the simulated engagement.

Two types of simulated flights are envisioned, 1) closed- loop guidance simulation of a target intercept, 2) preprogrammed acceleration commands for testing of the airframe/autopilot control. For the closed-loop guided engagement,

l measured forces and rates are sent to the simulation for updating the equations of motion and closing the loop around the guided trajectory.

For the pm-programmed acceleration flight, l there are no requirements to close the loop with the rest of

the simulation, l a pre-programmed series of acceleration commands will be

loaded in the test article computer, l acceleration feedback to autopilot could be calculated on-

board by scaling the measured force with the mass, l on-board rate sensors provide for pitch/yaw and roll

stabilization of the test article allowing for closed-loop testing of the autopilot.

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In addition to providing a new capability for research on the effects of unsteady aerodynamics, the WTBVFT is envisioned as a test tool supporting the DT&E process. The WTBVFT facility could likely be used as a risk reduction tool prior to the expensive, highly-visible first flight test, and to reduce costs by requiring fewer flight tests.

By being able to integrate hardware and software subsystems into a controlled, realistic flight environment, the WTBVFT can provide useful data for the initial validation of airframe design and guidance and control software. Without expending costly hardware, the airframe, autopilot/inertial sensors and actuator subsystem can be tested under simulated flight load and in the presence of unsteady aerodynamic effects. This is not feasible in conventional wind tunnel facilities. In addition some of the integrated subsystems and electrical interfaces between the autopilot processor, the actuator, and possibly the inertial rate gyro sensors could be further tested prior to flight.

WTBVFT CHALLENGES There arc many technical issues associated with the

WTBVFT environment; some of them are mentioned here: l Characterize the impact of the support system

hardware. i Support system interference of test article

aerodynamics. i Support system/test article flexure effects i High data rate balance system compatible with real-

time simulation. + Effect of test article structural dynamics change due

to mounting system on the autopilot. l Center of gravity movement during flight. l Develop method to simulate realistic flight conditions.

; Rapid changes in Mach number and Reynolds number

i Absence of plunging dynamics in wind tunnel test article

WTBVFT MOUNTING OPTIONS Several test article mounting configurations are possible

for the WTBVFT environment. Currently, four have been examined. They are the following:

Air BearinP Mounting System with a Solid Strut - The air bearing would be able to move in all three rotational directions, but would have constrained motion (physical stops) in two of the three directions. The inner ball of the air bearing, which constrains the translational motion of the test article, would be rigidly attached to the tunnel by means of a solid cantilevered beam. Tension Wires Mounting System - The concept is extremely similar to the solid strut except the test article would be held in position by taunt wires extending to the wind tunnel ceiling, floor, and walls. Actuated Sting -The sting is mechanically controlled and positioned rapidly to mimic the flight. The required position of the actuated sting would be determined by the predicted attitude in a full 6-DOF simulation. The simulation determines the desired flight attitude using real-

time measurements of forces and moments acting on the wind tunnel.

l Hybrid Mounting Svstem - A combination of an actuated sting in one axis together with an air bearing in other axes could be utilized to extend the range of motion of the air bearing and mrther model complex free-flight dynamics.

Preliminary analysis and cost indicated that the wire support system is the most likely candidate.

Any mounting system for the WTBVFT will only approximate free-flight. The WTBVFT is not capable of modeling the effects of flight path rate of change. Consider a planar motion. In flight, the azimuth Euler angle 8 is the sum of the angle of attack a and the flight path angle y as is shown in Fig. 2. In the wind tunnel, the flight path angle does not change, making y always equal to zero. Thus, when a missile is maneuvering, the test article in the tunnel will always make a and 8 equal to each other. The plunging effect of the flight path rate of change cannot replicated in the wind tunnel. Part of this work was to determine the best way to implement the WTBVFT in light of this physical limitation.

Mounting systems that allow free rotation of the test article place restrictions on the mass properties of the test article. The use of flight hardware requires the flight dynamic pressures. Thus, the flight moments of inertia are required to produce proper airframe response. Fully actuated stings do not require the test article’s mass properties to match the flight hardware. All mounting systems will disturb the flow and alter the body aerodynamics. It is a significant design effort to minimize this impact.

Flig& Path

z/l v Figure 2. Schematic of a Typical Airframe Trajectory

WTBVFT NOMENCLATURE The modeling of the WTBVFT environment requires the

use of several coordinate systems. Points and vectors arc referenced in multiple coordinate systems and this can lead to a confusing set of variables. In order to facilitate the nomenclature, a logical naming convention has been adopted. All four sub/superscript positions around a variable are utilized to identify the variable and specify the coordinate system to which it is referenced.

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(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. .

Consider the general symbol, D E A B C

representing a typical variable. The present adopted nomenclature assigns the following attributes. A - Identifies the type of variable. The following

assignments are made P - Point F - Force M - Moment V-Velocity 0 - Angular Velocity 8 -Angular Position I - Moment/Product of Inertia e - Quatemion Element r - Position Vector Some Others

B- Identifies the coordinate system to which the variable is referenced. The following coordinate systems are used in this analysis. f - Inertial Coordinate System (Fixed) b - Body Fixed Coordinate System s - Sting Coordinate System FF - Free-Flight Coordinate System

C - Identifies the variable component. The following possibilities exist, x, y, 2 - Cartesian Components 1,2,3 ,4 - Quatemion Components

D - Descriptor of the variable, which will identify the nature of the variable. 0- Origin of a Coordinate System A - Attachment Point R - Reference Location

E - Power to which a variable is raised. As an example, the notation leads to the following

interpretation of the variable

which identifies the square of the Cartesian x component of position for a body fured attachment point referenced in the sting coordinate system. Note that the descriptor, preceding superscript, has its own subscript, further describing it. In this case, the b subscripted off the A indicates that it is an attachment point on the body.

If a position around the variable is left blank, it was not required to describe the variable without ambiguity.

FREE-FLIGHT EQNS. OF MOTION The equations of motion for a rigid body require the use of

two coordinate systems, a body fixed, and an Earth fixed. The quatemion formulation of relating the body fixed coordinate system with the Earth fixed was used for this analysis and is documented in Ref. 1. Using the quatemion formulation, the free-flight equations of motion are given by

.Ph+2dFFe2 FFe4-FFel FFe3>

+

(1)

FF”p FF’x-FFwx FF&

where ?’ V FF x ’ FF y 9 and FFVZ are the velocities of the body

in the body futed directions, FFFX, FFFY, and $‘F are z the aerodynamic and propulsive forces in the body fixed F@, ,=Fy, and ,C,CZ directions, FF o I, FF~ y , and FF o _ are the roll, pitch and yaw rotation rates about the body axes, ,+I, ,+?2, F,N?3, F@4 are the elements of the quatemion, m is the instantaneous mass of the body, g is the acceleration due to gravity, and a dot over a variable indicates time differentiation.

The moment equations are the following, -I - FF I 1.v -FF I: I

I -FF ,c I 1 FF >

I -FF p I FF :

where the FF’,,FF’y,FF’-,FF’xy,FF’yr, and FFIrare

the typical moments and products of inertia about the body fixed axes, and F;MX,FFM,,, and FFA4- are the aerodynamics and propulsive moments about the FF x9 FFY, and FF z axes, respectively. The quatemions and inertial positions are updated in the typical way.

+

(2)

A Six Degree-of-Freedom (6-DOF) simulation was constructed and used as a “truth-model” for comparison with the WTBVFT.

WTBVFT EQNS. OF MOTION Due to the flexible support system, the equations of

motion are considerably more involved for the WTBVFT environment than for free-flight. The elastic motion of the sting needs to be modeled, and the interaction between the sting and the test article needs to be addressed. The motion of the test article in the wind tunnel is related to a free flying body. In modeling free-flight, two coordinate systems were required, the body fixed and the Earth fixed. In general, WTBVFT requires four coordinate systems. The four systems are shown in Fig. 3, and are labeled in the following manner:

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1) The Inertial (Fixed) Coordinate System (shown in Blue). coordinate directions. The free body diagram for the test Assumed to be attached to the wind tunnel wall. article is shown in Figure 4.

2) The Sting Coordinate System (shown in Green). Assumed The aerodynamic, gravitational, and propulsion forces to be oriented in the set direction of the sting, but not and moments on the test article act at its center of gravity in necessarily attached to a particular point on the sting. the usual way. However, due to the mounting system, there

3) The Body Coordinate System (shown in Red). Assumed are additional forces and moments located at the point of to be attached to the test article center of gravity. attachment.

4) The Free-Flight, Body Fixed Coordinate System (shown The test article is treated as a rigid, body capable of in Violet). Taken to be attached to the free flying body’s experiencing motion with six degrees of freedom. Damped center of gravity.

The Origi nFme Flight Coordinate System Must be the Airtkme’s Center of Gravity.

Lyate the Origiy Postions oflhe Body Fixed, ~~~~~~ Stmg, and Free blight Coordmate Systems Referenced to the Inertial Coordinate Axes-q-q . -.

kigin of the Body Fixed Coordinate System lust be the Center of Gravity of the ‘kst Article

C h T

The Origin of the Sting Coordiite System Should Probably be the Base of the Sting

Figure 3. Coordinate Systems for WTBVFT Simulation

The body, sting, and free-flight coordinate systems are springs affect the motion in the inertial directions, but all related to the inertial coordinate system. The vectors translational motion is still allowed for the wind tunnel

“;T, of?, and o’; r’ , respectively locate the origins of the mode1. The equations of motion for the test article are

body, sting, and free-flight systems in the inertial coordinate essentially the typical equations for a 6-DOF simulation.

system. Additionally, the body, sting, and free-flight

coordinate system are related to the inertial coordinate system through independent (quatemion based) rotation matrices. Vectors in the body, sting, and free-flight frames can be readily rotated to the inertial frames. Vectors in the non-inertial coordinate systems can be related to one another by first using the inertial coordinate system as an intermediate system.

The equations of motion are determined for a rigid test article on a flexible sting mounting system. Thus, the mounting system is taken to be a series of damped, Hooke springs constraining the translational motion in the inertial

Figure 4. Free Body Diagram for the Test Article

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The accelerations acting on the body are given by

+

(3)

where a dot over a variable indicates time differentiation; ,,Vx, bVy, and *V, are the body velocities in the body fixed g, hy. and g directions; hi,, be+, and & are angular velocities about the body fixed g, hy, and bz axis; i F, , i F,, , and i Fr are the aerodynamic and propulsive forces in the G, ,J, and hz directions; m is the mass of the test article; g is acceleration due to gravity; tFx, f F,, , and l F- are forces exerted on _ the test article by the sting mount transformed from the sting coordinate system to the body fixed g, hy, and hz directions; and heI, f12, be), and be4 are the elements of the quatemion associated with the body fixed to inertial rotation matrix.

The generalized moment equations describing the angular accelerations are given by

(4)

where the JX,, J,,, JZ, dxy. dP, and d,, are the typical moments and products of inertia about the body fixed axes;

hUKWp _ and :M- are the aerodynamics and propulsive moments about the ,,x, hy, and hz axes, respectively; p4, ,;MY ,y z are the moments exerted on the test article by the sting mount, transformed from the sting coordinate system to the body fixed g, hy, and hz directions, respectively; are coefficients of friction about the ,,x, G, and g axes are bp,, &, bu,, respectively, and the position of the sting attachment point on the body is given in the body coordinate system as *lPx, *iP,,,and *“P h 2’

Although several mounting systems were examined, only the tension cable system is discussed here. Figure 5 shows a schematic of the cable system retaining the wind tunnel model. Equations are developed for an arbitrary number of cables fixed at general points on the test article and the wind tunnel walls.

The point of attachment on the tunnel wall is defined as yPx, YP, and :P,, and the points of attachment on the

test article as defined as :; P,, T Py and $P-, where the i indicates the ith mounting cable. Each cable is assumed to have its own stiffness and damping, respectively defined as ‘lk, and “c. The unstretched length of each cable is

defined as OS d . The length of each cable is given as

The total forces acting on the body due to a total of ‘N cables in the inertial p, p’, andg are given by the following,

(6b)

Each cables can only exert tensile forces, and exert no load if they go slack. Thus, the MUX function is utilized Eqs. (6a-c).

in

I

Figure 5. Diagram of Cable Support System

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The points on the body where the cables are attached 2 P may be related to the inertial frame for use in Eqs. (6a- c) by the following formula

“;ij=“;F+,J&g (7) and the cable forces can be related in the body fixed frame by means of,

;Eb+/ IQp ;P (8) The moments associated with the cables are then

,“M,=;P, ,‘F;-?q. ;Fv (94

The cables were assumed to be massless, damped springs. All that is required is to track the positions of the ends of the springs, and use of the equations of this section to determine the applied forces and moments on the test article.

The aerodynamics of the WTBVFT article are driven by the wind. Typically, the motion of the body through stagnant air drives the aerodynamics. The WTBVFT test article moves a relatively small amount, but the wind tunnel blows a mass of air around it, which leads to the aerodynamic loading. Therefore the wind must be accounted for.

The direction and velocity of the wind is known in the inertial frame of reference and is given the component values of/W,, /WY, and ,Wz in the p, p, and p directions, respectively.

The aerodynamics are calculated in the body frame of reference, and therefore, the wind velocity must be transformed to the body frame, such that,

/wx /WV

1

/w- I

(10)

The total velocities of the relative air in the body frame of reference, ,,‘Vx, hTVy, and bTVz are then given by,

(11)

These velocities, bTVx, ,,‘I’,,, and hTVz are then used to calculate the dynamic pressure, angle of attack, side-slip angle, etc. for the calculation of the aerodynamic loading in the typical way.

INITIAL RESULTS The equations were developed for a 6-DOF simulation.

However, for a first look at the behavior of the system, and 3- DOF analysis was performed. This analysis was used to examine the WTBVFT environment and determine the best methodology for implementation.

The 3-DOF model involves the case of allowing translational motion in the inertial p and /z directions, and

rotations about the p axis producing changes in the Euler pitch angle 8. This type of simplistic model is appealing since it represents a reduced set of governing equations, while still providing insight into the WTBVFT capability to simulate the flight trajectory problem.

Several variations of 3-DOF simulations were developed to examine the best implementation of the WTBVFT. These included open-loop airframe and autopilot controlled cases. Several of the results from those simulations are presented here.

The open-loop airframe response was the first examined. A missile is initially trimmed at a zero cx and zero 8 and y. At time f equals 0, the control surfaces are deflected to 10” causing the missile to pitch up. For this example, there is no autopilot and the following linear aerodynamics are used,

where L, is the reference length, and the aerodynamic coefficients in the matrix, mass properties, and thrust level were chosen for a typical short range air-to-air missile to represent a typical missile.

Two 3-DOF simulations were performed, one to model free-flight (truth model), and the other to model the WTBVFT. The WTBVFT model simulated a one degree of freedom (I-DOF), where only pitch rotations were allowed. The 3-DQF modeled the actual motion of a missile that is moving in only one plane, and the l-DOF modeled the wind tunnel WTBVFT environment which is able to rotate, but not translate.

The aerodynamics and flight conditions used in each model are identical and the sting mount is assumed to be rigid and frictionless. Figure 6 shows the angle of attack history of both the 3-DOF and the WTBVFT l-DOF simulations. There is a significant difference seen by the two difference simulations. The difference in the two systems arises due to the ability of the 3-DOF to experience translational motion, and the l-DOF does not. Immediately, the 3-DOF-simulation experiences smaller fluctuation in angle of attack, and the differences between the two simulations increases in time. The translational motion of the 3-DOF has a significant impact on the airframe angle of attack, and subsequently, its aerodynamic loading and predicted trajectory.

The conclusion is that the open-loop response of an airframe in the WTBVFT wind tunnel model with a free mounting sting would not be able to duplicate the actual angle of attack and aerodynamic loading.

A far better correlation between the WTBVFT and free- flight simulation is obtained if the proper closed-loop autopilot control is used. Analyses were performed on several different closed-loop systems, using several different autopilot architectures and employing several different feedback signals. Only two of the examined autopilot

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(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. . - r -

systems will be presented here. A tail controlled short range used directly without delays to stabilize the test article. There missile airframe with linear aerodynamics was used for this are subtle differences between the two techniques, therefore, preliminary analysis. both were examined using the 3-DOF simulation.

“..rm*r.gLotA~skn,DtY Figure 7 shows a block diagram of the implementation of the acceleration autopilot using the test article AOA rate (oi ) feedback signal in a WTBVFT simulation. For this ideal case, the total acceleration in the body frame of reference is determined by scaling the measured aerodynamic force with the mass. Since the aerodynamic force is measured directly in the wind tunnel, there is no need to feedback signals from the trajectory simulation shown in the green block of Fig. 7

The WTBVFT simulation controls the angular rate of the wind tunnel test article by feedback signal of the wind tunnel AOA rate rather than the pitch rate of the body.

Figure 6. Angle of Attack History Coulparrst the WTBVFT and T---‘” nx-~-’

To control the airframe a QrIUUL Jm.vvY yI. feedback autopilot was used. The three-loop! loop, the synthetic stability loop, and the acce‘ As shown in Fig. 7, the 3-100~ autopilot uses act rate feedback signals. The actual accelem+inn

Figure 6. Angle of Attack History Comparison Between A set of pre-programmed acceleration commands was

the WTBVFT and Truth Model. used for this test. Since the accelerations are preprogrammed

To control the airframe a typical 3-100~ acceleration/rate this autopilot requires no information from the trajectory

feedback autopilot was used. The three-loops are the rate simulation. This does lead to a physical difference between

loop, the synthetic stability loop, and the acceleration loop. the WTBVFT environment and an actual flight test.

As shown in Fig. 7, the 3-100~ autopilot uses acceleration and To achieve a closed-loop time constant of 100 msec, a

rate feedback signals. The actual acceleration is sensed by damping of 0.8, and a frequency crossover of 50 radisec, the auto P a

ilot ains are k DC = 1.049, kA = 0.02279 radlscclftlsec’,

Translational Motion

I I I

Figure7.Block Diagram for Acceleration Autopilot Using AOA Rate Feedback

the accelerometer and the body rate is sensed by the rate oI = 10.76 per set, and kR = 1.45 see. The accelerometer was gyro. The rate signal is added to the acceleration error signal assumed to be located at the center of gravity. and integrated to form the rate command out of the synthetic Figure 8 shows the acceleration history of the stability loop. The same body rate feedback is further WTBVFT and free-flight simulations. The blue line shows combined for control of the response and for damping the commanded accelerations, the green line shows the augmentation. The gain koc maintains a unity gain in the acceleration experienced by a free flying body (truth acceleration control loop. The control actuation system model), and the red line shows the accclcration calculated response was neglected. by the WTBVFT simulation. The initial acceleration in the

For the WTBVFT two options are available for opposite direction is due to the typical rcsponsc of tail implementation of the angular rate feedback loops. One controlled missiles. approach is to use the pitch/yaw rate gyro signals after they Note that there is a difference in the steady state are reconstructed in the simulation. The reconstructed response between the free flying simulation and the pitch/yaw rates in the simulation are obtained by combining WTBVFT simulation. The reason for the difference lies in the AOA rate (measurement of test article angular rate in the the fact that during a maneuver, the free flying body trims at tunnel), with the simulation estimate of flight path rate of a slightly difference AOA than the WTBVFT model, and change (the translational effect). The second approach is to only part of the body pitch rate (ci ) rather than the total body feedback directly the AOA rate as measured by the on-board rate gyro on the test article. In the latter there is a

pitch rate ( h~ y = ci +f ) is fedback to the autopilot.

discrepancy with actual flight, however, there is no need to During a steady maneuver a free flying body eventually reconstruct signals. Furthermore, the sensor outputs can be trims at a given AOA and its oi vanishes. However, since it

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(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. _ * * -

is maneuvering, its ,,cJ+ term does not vanish since it is the flight model and the color red to the WTBVFT sum of oi and the rate of change of the flight path angle v , simulation. In all figures, there are only very slight which is clearly non-zero. The wind tunnel mode1 is differences between the free-flight simulation and the constrained in translational motion, and therefore, its flight WTBVFT simulation.

ath anple never changes.

Acceleration History AccaRntlon A

Figure 8. Acceleration History for an Acceleration Autopilot with AOA Rate Feedback for WTBVFT and Free-Flight Simulations

Figure 9. Angle of Attack History for an Acceleration Autopilot WTBVFT Simulation

During a steady maneuver, the moments go to zero. Therefore, at trim,

Angie of Attack History Accelaratlon Autopilot VFT Slmulatlon

Elevator Deflection History

O=,C, =Cmo +C,a+C,6+““‘C, i 1

L, hay 2v

In a free flying body, the last term is non-zero during a steady maneuver. In the WTBVFT environment, the last term settles on zero. Therefore, to achieve equilibrium, the free flying body and WTBVFT model set the control fins at different deflections, resulting in different trim angles of attack. In the case shown, the difference in the trim AOA and elevator is approximately 0.15%.

Figures 9 and 10 show the angle of attack and elevator T-W

deflection histories for the simulations. Both charts show the Figure 10. Elevator Deflection History for an greatest differences between the WTBVFT simulation and truth-model during the large, steady state maneuver. The differences are due to the physical difference between the free flying body and the constrained wind tunnel model. The free flying body continues to rotate, but the rotation rate of the wind tunnel model vanishes in steady state.

Acceleration Simulation

Autopilot WTBVFT

Finally, the trajectories of the free-flight and WTBVFT simulations for the corresponding acceleration commands are shown in Fig. 11. The free-flight simulation trajectory is the green line, and the WTBVFT simulation trajectory is the red.

A WTBVFT environment with an acceleration autopilot and pitch rate feedback signal is shown in Fig. 12. The oi value obtained from measurements in the wind tunnel is augmented with the y term obtained from the trajectory calculations to calculate the airframe body pitch rate. This configuration mimics the actual autopilot, but requires rcconstructcd signals and additional interfaces.

Trajectory

The acceleration, angle of attack, and elevator Figure 11. Trajectory of an Acceleration Autopilot histories are shown in Figs. 13, 14, and 15, respectively. WTBVFT and Free-Flight Simulation These figures again assign the color green to the free-

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(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. a * _.

Translational Motion

Figure 12. Block Diagram for Acceleration Autopilot Using Pitch Rate Feedback.

-Iso J- .-..---.-..... L _._____.” ___...... I .- .- --. I. -. .-...- I-.- ,I.,.~

Fig Lure 13. Acceleration History for an Acceleration Autopilot with Pitch Rate Feedback for WTBVFT and Free-Flight Simulations

L

F

Angle of Attack History

‘“1 ...- Acceleration Aufop?l~~V~T Slmulatlon ..” “.-.‘“.-,-.-..--i -..- T.-.- i .._.. -

P, I I I I I ,I- ,.,

deflection angles is only approximately 0.15%, which is not observable on these graphs. Figure 16 shows that the two computed trajectories arc virtually identical.

Elevator Deflection History Jo.. 1

...... Acceleration htopilot VFf Simulation ~.-- - ~ .._.......... T .-...... Ii

I .4 1 I I.. I..... ..-.. I T--I.,

Figure 15. Elevator Deflection History for ai Acceleration Autopilot with Pitch Rate Feedback for WTBVFT and Free-Flight Simulations

igure 14. Angle of Attack History for an Acceleration Autopilot with Pitch Rate Feedback for WTBVFT and Free-Flight Simulations

The elevator deflection histories show some differences during the transients. The most notable difference occurs just before 1 second in the simulation. The steady state AOA and deflections are nearly identical. The pitch damping term is sufficiently small and does not significantly alter the trim attitude. The difference in the steady state AOA and elevator

Traiectorv

‘igure 16. Trajectories for an Acceleration Autopilol with Pitch Rate Feedback for WTBVFT and Free-Flight Simulations

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(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. . ‘. , ‘$ -

SUMMARY A mathematical mode l for 6-DOF simulation of the

W ind Tunnel Based Virtual F light Test (WTBVFT) is presented. This mode l accurately represents the motion of a constrained test article in the WTBVFT environment. Challenges and utility of the WTBVFT concept are discussed with the overall conclusion that WTBVFT should provide improvements to the test capabilities of wind tunnels and reduce the risk and cost of test and evaluation.

Preliminary simulation analyses using 3-DOF mode ls have been conducted with positive results. The objective was to compare the response of a free-flight vehicle with the WTBVFT environment simulation. Test cases investigated included open-loop airframe and closed-loop autopilot controlled cases. These results indicate that for typical autopilot controlled cases the WTBVFT environment is capable of reproducing the free-flight behavior within acceptable differences. As expected, due to the lack of translation in the WTBVFT, some discrepancies were noted, particularly for open-loop airframe.

ACKNOWLEDGMENTS This work was supported by the Air Force Armament

Laboratory (AFRL/MN) at Eglin AFB as part of a joint effort with the Arnold Engineering Development Center (AEDC). The Virtual F light Test program is an AEDC effort funded by the Air Force O ffice of Scientific Research.

REFERENCES ‘Robinson, A. C., “On the Use of Quaternions in Simulation of Rigid-Body Motion”, WADC Technical Report 58-17, Wright Air Development Center, WPAFB, Dec. 1958.

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