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American Institute of Aeronautics and Astronautics

1

Asymmetric Stiffness Pitch Control - Transonic Pitch-Up Mitigation for the EF2000

M. Hanel*, W.Neuhuber†, R. Osterhuber‡ and G. Hofinger§ EADS Military Aircraft, Munich, Germany

and

M. Barrio** EADS Military Transport Aircraft, Madrid, Spain

This paper presents the control law functionality for mitigating the transonic pitch-up of the Eurofighter EF2000 aircraft. First, the aerodynamic problem of the transonic pitch-up on Eurofighter is outlined and solution strategies based on feedback control are discusse d. Predicting the pitch-up from model information and measurements in theory allows a more complete pitch-up reduction but is very sensitive to model and measurement errors. Detecting the pitch-up when it affects the aircraft leads to a late control surface response but is robust with respect to model and measurement errors. Then, the design of the Asymmetric Pitch Stiffness Feedback (a detection based control law measure), which is the core of Eurofighter's transonic pitch-up mitigation functionality is presented in detail. The linear and non-linear stability assessment approach for this function is reviewed. Additional features of the transonic pitch-up mitigation functionality for Eurofighter are discussed. Finally, flight test results are presented. The solution implemented reduces the pitch-up transient to 1.5 g and constrains the maximum vertical load factor to respect the structural load limits.

Nomenclature α angle of attack AoA angle of attack ADS Air Data System

mC pitching moment coefficient

mC& time derivative of mC FBS Full Back Stick FCS Flight Control System g acceleration due to gravity G(s) transfer function k feedback gain nz vertical load factor Ma Mach-number q pitch rate ω frequency (rad) TPDM Transonic Pitch Down Moment TPMC Transonic Pitching Moment Compensation

*Control Law Specialist. † Deputy Head of Flight Dynamics, Eurofighter Flight Control System Joint Team, Munich. ‡ Control Law Specialist. § Head of Flight Dynamics, Eurofighter Flight Control System Joint Team, Munich. ** Control Law Specialist.

AIAA Guidance, Navigation, and Control Conference and Exhibit16 - 19 August 2004, Providence, Rhode Island

AIAA 2004-4752

Copyright © 2004 by EADS Military Aircraft. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

AoA limit: "avoid Pitch Up"

Pitch Up Asymmetric stiffness: "kick in PitchUp"Nz,max

Mach

0.9 1.0

ground avoidance problemaltitude

Example Manoeuvre:Full back stick pull out of dive

nz <2g4-5g

0.87 1.05

<2g

Figure 1. Schematic of a full-back-stick (FBS) pull-out of a dive

I. Introduction On aircraft with swept-back wings, the centre of pressure is more aft for supersonic Mach numbers than for

subsonic Mach numbers. Consequently, it moves forward when the aircraft decelerates from super- to subsonics, thereby generating a nose-up (positive) pitching moment. In addition, at certain combinations of (transonic) Mach-number and angle of attack, flow separation occurs on the outboard wing and destroys lift behing the c.g. thereby generating a violent pitch-up transient. Both effects together generate uncommanded vertical load factor transients that jeopardize the flying qualities of the aircraft, threaten the pilot's health and lead to violations of the aircraft's structural load limits.

A transonic pitch-up problem is present on many fighter aircraft and various measures intended to control the flow-breakdown on the upper surface of wings with swept leading-edges are known. Fences, notches, saw-cuts, sawteeth, trips, Gurney-flaps, and vortex generators are examples of aerodynamic measures installed on existing fighter aircraft11. Whereas a certain limited pitch-up mitigation can be expected from such measures, no single measure solving the phenomenon completely is known.

After initial flight tests had revealed the extent of the transonic pitch-up problem on EF2000, later control law software releases simply limited the AoA-authority to values below the pitch-up AoA for transonic Mach-numbers. This approach however resulted in a severe limitation of aircraft performance which was not acceptable for service release (see Fig. 1).

Concluding from the aerodynamic analysis that a flow breakdown is causing part of the pitch-up problem, an unloading measure was investigated and tested in flight. This measure was called "split flaps", i.e. the downward deflection of the outboard flap was reduced and the pitching moment com-pensated by larger deflection of the inboard flap. The net result was not very promising.

Therefore, in summer 2001 a study was initiated to define a control law concept for mitigating the transonic pitch up. The goal was to achieve a carefree handling12 clearance in the transonic Mach-number range, accepting handling deficiencies (e.g. 2g pitch-up transients) in rapid decelerations. An early non-linear FCS-feature was known from work on the Northrop-Dornier project N/D1021 and provided the basis for the Control Law research.

The concept derived featured a combination of • Modifications to the Air Data System (ADS) to improve the Mach accuracy in transonics. • A feedback redesign exploiting the improved ADS accuracy to increase the bandwidth and the damping

of the short period motion. • The implementation of the asymmetric stiffness control law function described in this paper.

Given the ambitious time scales of the Eurofighter programme, an experimental software load was created for providing the asymmetric stiffness functionality for flight test on the basis of the existing ADS in order to de-risk the development ("proof of concept"). The function was successfully flight tested in March 2002 and subsequently the three components of the concept above were realized for service release. The combined solution was successfully flight test demonstrated in May 2003.


3

M=0.9

M=0.95

M=0.975

M=1.05

M=1.1

10 20 300-20

80%

60%

40%

20%

0.00

-20%

-40%

-60%

-80%-10 40

AoA [deg]

Cm

norm

alis

ed

Figure 2. Aerodynamic Characteristic in the transonic flight envelope

0.0 2.0 4.0 6.0 8.0

0.0

0.80

0.90

1.00

10.0

nz

0.0 2.0 4.0 6.0 8.0 10.0

1.10

Ma

time [s]

0.95

nznz Auth.

Figure 3. Simulation of unconstrained transonic pitch-up in a dive pull-up

II. Transonic Pitch-Up The basic aerodynamic phenomenon behind the transonic pitch-up is flow separation, involving shock /

boundary-layer interaction, on the outboard wing. It abruptly destroys lift behind the c.g., thereby genera ting a large pitch moment. How the flow separation is caused is not yet fully understood. Several sources of disturbance could be identified and complex interactions were observed. But understanding how they work is not easy and a simple modification of the aircraft structure that would remove the pitch-up could not be identified.

Over the years wind tunnel measurements and flight test identification were used to analyze the pitch response in transonics. However, the pitch characteristics vary, in detail, from model to model, from tunnel to tunnel, and from model / tunnel to flight. Differences of scale and geometry, and differences of environment (turbulence and uniformity, wall constraints, and measurement accuracy) all contributed to this situation. The aerodynamic dataset that has evolved allows repredicting flight data with acceptable accuracy and is fit for control law design but aerodynamic uncertain-ties (represented by tolerances on the aerodynamic derivatives) always have to be considered.

On Eurofighter (no noseboom installed), the Mach-number measurement accuracy is reduced in the transonic flight envelope. Mach-number offsets are varying strongly in both magnitude and potentially sign over a small Mach range. The challenge for control law design efforts in the transonic flight envelope is given by the combination

• of aircraft aerodynamic characteristics that are strongly depending on both Mach and AoA (see e.g. Fig. 2) and varying from highly unstable to stable over small Mach (0.01 Mach grid required) or AoA ranges and

• of measurement inaccuracies in Mach-number and AoA that do not allow to identify the expected aircraft dynamics and make compromise feedback gain values necessary.

Compromised (i.e. low) feedback gain levels alone however result in an underdamped system at the pitch-up Mach / AoA combination. The non-linear response then shows large transients in load factor


4

Figure 4. Simplified Pitch Control Structure

phase [deg] -200 -180 -160 -140 -120-220 -100

gai

n [d

B]

-10

-5

0

5

-15

10

Ma = 0.940 - 0.960, VEAS = 500.00 [kts], AoA = 6.0 [°]

3.05 < nz < 4.60[g]

-2.70 < -1/Ti <-0.18 [rad/s]

2.79 < wnsp <9.78 [rad/s]

0.070 < zsp <0.839

0.224 < zfcs <0.365

radius = 0.036

-200 -180 -160 -140 -120-220 -100

-10

-5

0

5

-15

10

Ma = 0.930 - 0.975, VEAS = 500.00 [kts], AoA = 6.0 [°]

3.72 < nz < 4.35[g]

-1.67 < -1/Ti <-0.19 [rad/s]

6.10 < wnsp <9.75 [rad/s]

0.669 < zsp <0.832

0.224 < zfcs <0.365

radius = 0.036

phase [deg]

gai

n [d

B]

Figure 5. Example critical case selection using Nichols-plots

Fig. 3 shows the vertical load factor response for a dive pull -out at low altitude. The peak nz levels shown would threaten the pilot's health and risk to induce overstress on the aircraft. Therefore, non-linear control law measures are necessary to avoid or at least mitigate the pitch-up to a tolerable overshoot level.

III. EF 2000 Pitch Feedback - Control Law Structure The (simplified) basic EF2000 pitch feedback control structure is a PID controller, featuring a pitch damper (D),

an AoA (stiffness) feedback (P) and an integral feedback (I) of either AoA, nz or pitchrate q. For centre stick up to about half forward/back stick, a pitch rate demand system is realized (for optimum tracking performance). For large stick inputs, AoA (low speed) or nz (high speed) are used as control variables (AoA / nz protection). A derivator/integrator feedback system has been realized, where the integral control error and the time-derivatives of the proportional feedback signals are multiplied by the respective feedback gains, then summed up and integrated in a single ("bottle neck") integrator. This allows to schedule the feedback gains with angle-of-attack, dynamic pressure and Mach-number while avoiding to introduce additional feedback loops. The output of the integrator represents the commanded pitching moment Cm, which is then distributed on the control surfaces (foreplane and flap). Fig. 4 shows the simplified pitch feedback control structure.

IV. Mach-Number Accuracy and Linear Stability Margins In the transonic regime, the aircraft characteristics change dramatically for small differences in Mach-number or

angle-of-attack (see Fig. 2). Whereas the aircraft is open-loop unstable at high subsonic Mach-numbers, it is stable when it approaches Mach 1. The feedback gain levels required to ensure stability and performance vary accordingly. Consequently, the feedback gains have to be scheduled with Mach-number. Further, if linear stability margin requirements are to be satisfied over all configurations and c.g. variations, a minimum Mach-number accuracy level has to be achieved. The required accuracy level to achieve carefree handling characteristics for the Eurofighter aircraft in the transonic regime was determined in an iterative worst case design case selection and control law design process. See Fig. 5 for an example critical case selection for the Mach-number accuracy level prior to the ADS modification and Fig. 6 for the stability margin improvement achieved by the feedback redesign on the basis of the modified ADS.


5

phase [deg] -200 -180 -160 -140 -120-220 -100

gai

n [d

B]

-10

-5

0

5

10

phase [deg] -200 -180 -160 -140 -120-220 -100

gai

n [d

B]

-10

-5

0

5

10

Ma = 0.930 - 0.975, VEAS = 500.00 [kts], AoA = 6.0 [°]

aft c.g.

fwd c.g.

fwd c.g.

aft c.g.

before redesign

after redesign

Figure 6. Stability Margin Improvement achieved by the Feedback Redesign

V. Transonic Pitch-Up Mitigation Concepts - Detection versus Prediction The initial pitch-up mitigation concept on Eurofighter featured an open loop transonic pitching moment

compensation (TPMC) function. The idea behind the TPMC is • to predict the pitch-up from Mach-number and AoA measurements and • to compensate the pitching moment by adequate control surface deflection.

Given an exact model and ideal Mach and AoA measurements, the pitch up can - in theory - be completely eliminated using suitably phase-advanced feedback signals. In the transonic part of the flight envelope however, both the measurements of Mach and Mach-derivative with time and the model data are subject to errors. Therefore, the onset of the transonic pitch-up cannot be predicted accurately.

For small offsets in Mach-number, the pitching moment compensation can - instead of compensating the pitch-up - increase the subsequent pitch-down.

Consequently, all techniques that use Mach-number measurements and model data to predict and compensate the transonic pitch up will ultimately fail unless the Mach-number measurement is almost perfect. A less ambitious function that generates a pitch-down moment in fast decelerations through the transonic Mach-range could however be realized.

While this Transonic Pitch Down Moment (TPDM) function only slightly reduces the pitch-up transient it helps to avoid overstressing of the aircraft structure. If the onset of the transonic pitch up cannot be predicted using the combination of

• Mach number and AoA measurement and • model data,

then it has to be detected once it occurs. The detection has to be based on the reliable measurements, i.e. pitch rate, (inertial) angle of attack and vertical acceleration (nz). It is evident immediately that although the detection is independent of Mach-accuracy it has two major disadvantages:

• A successful detection is only possible after the pitch up has started. Consequently, any contro l action based on detection will feature a non-negligible delay and a certain transient overshoot in AoA (and nz) will always have to be accepted.

• As the detection is to be model-independent, it cannot distinguish between pitch acceleration caused by the transonic pitch-up and pitch acceleration caused by other disturbances (turbulence etc.). Therefore, any action triggered by the detector must be equally applicable to the pitch up (change in Mach, only positive pitch acceleration) and a random disturbance (at constant Mach, pos. and neg. acceleration).

In addition to concepts relying exclusively on prediction (such as TPMC) or such ones relying exclusively on detection, a wide range of combinations can be imagined. The Eurofighter solution consists of a detection based function, the asymmetric stiffness, for mitigating the pitch-up transient combined with a load factor authority rate limit (see below) and the above mentioned TPDM function at high speeds to ensure that structural load limits are respected.


6

VI. Asymmetric Stiffness

A. The General Principle The basic ideas behind the asymmetric stiffness concept4 are

• detection of the transonic pitch up from the AoA/nz -measurement. • activation of an additional AoA feedback loop (increasing the overall AoA feedback gain) when the

pitch-up is detected. • restriction of the additional AoA feedback to pitch-down only, so that the handling qualities from the

linear feedback design will prevail as soon as the upward pitching motion is stopped. Below, a more detailed description of the asymmetric stiffness function is given.

B. Detection of a Pitch-Up from Angle-of-Attack The detection of the transonic pitch-up is based on a calculation of the dynamic overshoot in angle of attack. An

estimate of aircraft angle of attack response is derived using the following procedure. The stick-derived AoA command signal cα represents the steady state AoA-demand value. A second order filter is used to represent a crude dynamic model of the closed loop aircraft dynamics:

1275.0025.0105.0)( 2 ++

+−=

ssssGm

(1)

The zero in the right half plane represents the overall system lag and the non-minimum phase characteristics of the nz response. Sending the AoA command signal through the filter )(sGm and taking the maximum of the output and

cα delivers the estimate eα :

[ ]cmce G ααα ,max=

(2)

of the AoA response. The measured angle-of-attack signal and the angle-of-attack signal derived from nz are blended into a common measurement signal mα . The difference between AoA measurement and AoA estimate is used for the detection of overshoots in positive AoA. Consequently, the overshoot is set to zero if either mα or eα are negative. Further, the overshoot calculation is faded out in pitch-rate demand. For that purpose the activation factor acts ( 0.10.0 ≤≤ acts ) is defined. The overshoot in angle of attack oα is then obtained from

( ) actemo sααα −=

(3)

An uncommanded pitch up is detected if oα and α& are positive. Using

)0,max(αα && =pos

, (4)

the asymmetric stiffness feedback will be activated by the product posoαα & .

C. Asymmetric Stiffness Feedback Gain The asymmetric stiffness feedback generates a signal commanding a pitch down moment as

lim),min(, Mabasposasm kkkC ⋅⋅⋅= α&&

, (5)


7

kas 2.0

1.0 0.5 αe/αl 0.0

1.0

Figure 7. Asymmetric Stiffness Gain Factor

0.8 0.9 1. 1.1

1.0

0.0 0.0 Mach

kM

a

Figure 8. Mach-Fading

αl

1/pd [1/kPa] 0.01 0.03 0.1 0.025 0.02

2.2 2.5 2.8

2.3

7.5

Figure 9. mC& limit (dyn. pressure dependent)

Figure 10. Control Law Structure including asymmetric stiffness feedback

where • bk denotes the basic AoA feedback gain, • posα& denotes positive α& and

• ask the asymmetric stiffness gain factor (function of distance to the AoA-limit, see Fig.7) adding up to twice the "normal" pitch down AoA feedback if close to the AoA/nz-limit αl.

• kMa is fading out the asymmetric stiffness function outside of the transonic region (Fig. 8)

• lim is a dynamic-pressure-dependent

mC& output limit (Fig. 9).

The mC& signal is fed into the integrator "bottle neck" of the pitch control law. Summarising the above, the asymmetric stiffness feedback is activated with positive α& and oα , adding a pitch down AoA feedback untilα& changes sign. The magnitude of the pitch down

mC& signal is constrained to reduce the sensitivity to turbulences and gusts.

Following the argument above, it seems only logical to activate an "asymmetric" damping increase similar to the asymmetric stiffness. The pitch damper however potentially interacts with the structural dynamics of the aircraft. Therefore, limits are imposed on the pitch damper to avoid exciting aeroservoelastic reactions. The pitch damper was increased to this limit and non-linear measures were avoided.

D. Asymmetric Stiffness - Control Law Structure Fig. 10 illustrates the control law structure associated with the asymmetric stiffness feedback. A block diagram

of the asymmetric stiffness feedback is given in appendix.


8

- k b

k b k a ∆ k b +

t ω 2 /2 π π π

f(x)

VII. Stability Assessment

E. Linear Stability Assessment In the linear stability analysis, the asymmetric stiffness functionality can be represented as increase of the AoA

feedback gain7. As the function is active only for AoA overshoots (positive oα ) and positive α& , applying the full gain in the linear analysis would be very conservative. Around a trim condition trα with the asymmetric stiffness active, the resulting AoA feedback gain can be represented by

end

else

then0)( and ) i.e.,0(if

b

ab

tro

kk

kkk

=

∆+=>>> αααα &

(6)

where kb denotes the basic AoA feedback gain and

Maasba kkkk =∆

(7)

denotes the gain increment due to the asymmetric stiffness function. For a sinusoid input, the following output results:

}{{ }ππ

π

2|,sin0|,sin)()(

2

2

≤<⋅≤≤⋅∆+=

xxxkxxxkkxf

b

ab

(8)

A Fourier series expansion to the first harmonic approximation

xbxaxf a sincos)( 1121

0 ++= (9)

with

∫

∫

=⋅=

=⋅=

π

πν

π

πν

νν

νν

2

02

1

2

02

1

...,2,1,sin)(

...,2,1,0,cos)(

dxxxfb

dxxxfa

yields coefficients 4

,2

, 110a

baa kkbkaka ∆

+=∆

=∆

=ππ

. Table 1 shows resulting amplitude and phase shift

of the equivalent representation )sin()( 210 ϕ+⋅+= xAxf a with 2

121 baA += ,

1

1arctan ba=ϕ for different

asymmetric stiffness gain factors.


9

Table 1. Resulting amplitude and phase shift for different asymmetric stiffness gain factors

Maasba kkkk =∆∆ / A [ ]°ϕ 0.5 1.12 4.0 1 1.26 7.3 2 1.53 12.0

Asymmetric Stiffness Functionality

Linear Feedback Contribution

Pitch Stability Nichols Plot

Phase [deg]

Gai

n [d

B]

-220. -200. -180. -160. -140. -120. -100. -80. -60. -15.

-12.

-9.

-6.

-3.

0.

3.

6.

9.

12.

1.0 Hz

2.0 Hz

3.0 Hz

1.0 Hz

2.0 Hz

3.0 Hz

Asymmetric Stiffness offAsymmetric Stiffness on

Mach = 0.95, H = 15000.0, ALPHA = 6.0

Figure 12. Nichols plot for a critical Mach/AoA combination with and without AS stiffness feedback applied

From these results, it can be concluded that the 1b -term constitutes the dominant contribution to the feedback gain, whereas the main effect of the 1a -term is found in the phase shift. It should be noted however that the phase shift in the overall closed loop frequency response (pitch damper, integral feedback and other contributions included) is significantly smaller.

For the linear stability assessment of the transonic flight envelope, only the 1b -term is considered directly (i.e., 25% of the asymmetric stiffness feedback gain is applied). Less than 3dB gain and 25° phase margin for the feedback system with the increased feedback gain applied would be rated unclearable. For cases with less than 4.5dB gain margin or 35° phase margin an additional non-linear (non-compliance) assessment is performed (see below).

Fig. 12 shows a Nichols plot for a critical Mach / AoA combination (pitch up) with and without 25% asymmetric stiffness gain applied. For the case shown, the asymmetric stiffness feedback improves the upper gain margin but reduces the phase margin. It should be noted that such stability margin violations can only be tolerated at isolated AoA values if they are respected for neighboring AoA values (local non-compliance).

Due to the inherent non-linear nature of the asymmetric stiffness function, the linear stability assessment alone does not constitute sufficient evidence for clearance. It is mainly used for critical case selection. A non-linear assessment for selected (worst-case) configurations is finally used to generate the clearance evidence.

F. Non-Linear Stability Assessment For selected configurations in general and the non-compliance cases in particular, a non-linear stability

assessment of the closed loop system is required. Gain margins are tested by applying a factor to the integrator output ( mC -demand). For testing the phase margin, a delay is introduced at the same point. For generating a phase shift of ϕ∆ =25° at 1Hz, a delay of ∆t=0.069s (from t∆=∆ ϖϕ ), corresponding to 11 frames at 160Hz iteration rate is required.

For the stability assessment of the asymmetric stiffness function the following strategy was followed: Worst-case manoeuvres (max. deceleration through transonics encountering the pitch-up) and generic cases (e.g. const. Mach) were simulated without delay, with 11 frames (25° phase shift at 1Hz, 50° at 2Hz) and 15 frames delay (34° phase shift at 1Hz) applied. Load factor transients were compared to judge the degradation of the system8,9. This approach allows to analyze the robustness to phase shifts of the closed loop system with all (modelled) non-linear effects included. Fig. 13 shows a comparison of a simulated 4g deceleration at constant altitude with and without delay in the system. The system becomes unstable for the 15 frame delay case and a 1.3Hz oscillation builds (phase shift is 44° at 1.3Hz).


10

4g Constant Altitude (10000ft) Deceleration

EF 2000: 15 ton twin-seat aircraft

no delay _1 11 frames delay (25° at 1Hz) _2 15 frames delay (34° at 1Hz) _3

0.0

2.0

4.0

6.0

8.0 NZ._1NZ._2NZ._3

ETA._1ETA._2ETA._3

0.850

0.900

0.950

0.000 2.000 4.000 6.000

TIME

MACH._1MACH._2MACH._3

0.0

-5.0

-10.0

vertical load factor Nz

foreplane position η

Mach number

Figure 13. Comparison of simulated 4g constant altitude deceleration manoeuvres with and without delays

1.0

0.9 1.05 0.93 1.0

0.0 0.0

Ma 0.0 -0.01

1.0

0.0

dMa/dt

kMa kdecel

Figure 14 (left) and figure 15 (right). Mach and dMa/dt dependency

VIII. Nz-Authority Rate Limit Even with the asymmetric stiffness function active, the transonic pitch-up will generate a load-factor transient of

1.0 to 1.5g in fast decelerations with constant stick input. Consequently, structural

load limits can still be violated in decelerations at FBS.

In addition, it should be noted that for Eurofighter, the full back stick g-authority is considerably ( 2≈ g) higher in subsonics than in supersonics. Therefore, in fast decelerations, the g-transient caused by the transonic pitch-up is aggravated by the increase in nz-authority. Similarly, by implementing a reduction in nz-authority coinciding with the transonic pitch up, the g-transient can be mitigated. As the magnitude of the g-transient depends strongly on dMa/dt, i.e. it is most disturbing at fast decelerations, such a reduction in nz -authority needs to be a function of dMa/dt (no reduction for accels and higher reductions for faster decels). It is obvious that such a measure is helpful only in the full back stick cases.

The implementation chosen here consists of rate limiting the nz-authority increase from supersonics to subsonics with time as follows:

[ ]g/s)0.1( Madecelmax kkRRL −=

(10)

with maxR , the maximum rate of change in the nz-authority (set to 1g/s) and decelk and Mak read from the

interpolation in Figs 14 and 15: Thus the rate

limit is a function of dMa/dt (approaching zero for high neg. dMa/dt), virtually keeping the nz-authority constant through transonics on fast decelerations.


11

0.9 1.0 Mach

nz at FBS

fast decel (dotted)

slow decel (solid)

Figure 16. Full-Back-Stick (FBS) Vertical Load Factor (nz) Authority

F279 15kft LEVEL TURN DECELERATION AT FBS

0.9 0.95 1.0

4.0

5.0

6.0

0.9 0.95 1.0

-8.0

-6.0

-4.0

MACH

MACH

Asymmetric Stiffness (solid)

Asymmetric Stiffness (solid)

AoA-limit + TPMC(dashed)

AoA-limit + TPMC (dashed)

Vertical Acceleration

Foreplane Deflection

Figure 17. Asymmetric Stiffness Flight Test Results ("proof of concept")

The nz-authority MAXzN , is then obtained from

),(MIN ,,,,1,, tRLNNN nMaxznauthznMAXz ∆+=+

(11)

It should be noted that this change will only affect manoeuvres where the pilot commands more than the supersonic g-authority during decelerations through transonics (the Eurofighters' constant-stick-force-per-g stick concept generates an aft stick deadzone in supersonics) whereas the feedback system will not be modified for accelerations or constant Mach and for decelerations with commanded nz below the supersonic g-authority.

Judging from simulation and flight test results the measure does not lead to nz -underachievements but - together with the asymmetric stiffness – removes the nz-overshoots over MAXzN , otherwise seen in fast decelerations.

IX. Experimental Software and "Proof of Concept" Flight Test Program In order to de-risk the FCS development for the transonic regime, an experimental software load was created for

providing flight test with the asymmetric stiffness functionality ("proof of concept"). The software was ready within 3 months and a 1-week flight-test campaign out of Moron AFB (Spain) was organized in March 2002. Using the (twin-seat) DA6 prototype aircraft, 6 sorties were flown in 4 days by 5 pilots, allowing to perform 61 deceleration manoeuvres5,6. The main objectives of the flight test were

first, to prove the safety of the additional feedback (the software allowed to select different levels of AS feedback gains).

second, to check the performance of the AS function (g-transients compared to simulation).

and third, to get a pilot opinion about aircraft handling in the presence of the remaining g-transients.

The experimental software allowed to select / deselect the asymmetric stiffness function in flight. In addition, an instinctive-cut-out (ICO) capability was provided for the pilot to instantaneously disengage the function.

For transonic Mach-numbers a reduced load factor authority limit was implemented to give some


12

Asymmetric Pitch Stiffness Feedback - Flight Test Results

Const. altitude (7500ft), const. stick deceleration at 4g (dashed) Const. altitude (7500ft), const. stick deceleration at FBS (solid)

IPA1 Flight 49

2.0

4.0

6.0

8.0NZ._4G

NZ._FBS

-8.0

-6.0

-4.0

0.85 0.90 0.95 1.00MACH

ETA._4G

ETA._FBS

vertical load factor (g)

foreplane deflection (°)

Figure 18. Flight Test Results - Transonic deceleration at constant altitude and constant stick, 4g and FBS.

margin against overstressing. With this setup it was possible to compare the asymmetric stiffness function to the previous protection system (AoA limit below pitch-up AoA and TPDM function). The flight test focused on dive pull-up manoeuvres and constant-altitude decelerations. Fig. 17 shows the results obtained in FBS level turn decelerations at 15kft. With the asymmetric stiffness function engaged, it is possible to fly to the AoA value where the pitch-up is most pronounced. The foreplane time-history shows how the control law reacts to the emerging pitch-up, limiting the transient to 7.0≈ g. The lower load factors in the asymmetric stiffness case below Mach 0.95 are due the reduced nz authority. The results allowed to conclude that the AS functionality

• mitigates uncommanded pitch-ups • provides the necessary protection against overstressing • leaves noticeable nz-transients in fast decelerations, which pilots however did not rate as major handling

problem. On the basis of the flight test results achieved it was decided to implement the solution concept for the transonic

flight envelope outlined above, i.e. concerning ADS accuracy and subsequent linear feedback redesign plus asymmetric stiffness functionality, TPDM at high speed and nz-authority rate limit.

X. Flight Test Results with the Service-Release Standard The modifications to the FCS design for the transonic flight envelope were incorporated into the Eurofighter

entry into service (EIS) software standard. Flight data was gathered on an instrumented production aircraft (the British IPA 1 aircraft) as clearance evidence for demonstrating carefree handling10. 8 sorties on the British IPA 1 (twin seat) aircraft in both a symmetric and an asymmetric (700kgm missile asymmetry) air-to-air configuration were flown by 6 pilots. Three types of manoeuvres, constant altitude deceleration, dive pull-ups and sustained wind-up turns, were tested in order to assess the transonic flying and handling qualities.

The trials confirmed the anticipated improvements: peak nz-levels and nz-transients were well within the bounds of acceptable aircraft behaviour and pilot comments were very favorable. Ride quality was judged to be quite smooth in comparison with earlier FCS standards and pitch transients were rated to be significantly smaller than those experienced at earlier FCS standards and also less than on other aircraft. In most turning decelerations pitch transients were accompanied by slight wing drops which required minimum lateral stick to correct. The aircraft behaviour in the asymmetric configuration was similar to the behaviour in the symmetric configuration.

Fig. 18 shows flight test results (symmetric aircraft) for constant altitude, constant stick decelerations at 7500ft. Time histories for a 4g deceleration and a FBS deceleration are given. The activation of the asymmetric stiffness functionality can be seen from the foreplane time history.


13

-0.05 s + 1

0.025s + 0.275s + 12 G =m

αc

αm

pos. nz - auth. αl

Max.αe αo

αo > 0?

1.0

2.0

αlαl/2 αc

+

-

Y N

kAS

0.0

1.0

0.0 0.0Ma0.85 0.9 1.1 1.15

kMaMACH-NUMBERPitch Rate DemandBlending 0.0 < kq < 1.0

0.0

Y

N

αm> 0 & αc > 0?

1 2

2

1

kbl

AoA-FEEDBACK GAIN Asymmetric Stiffness Gain

dα/dt

dα/dt (dα/dt)pos

7.5

2.2

0.01 0.1 1/pd(650kts) (250kts)

1/pd

limlim

lim Cm

α - measurement

α - command

nz - measurem.

nz - command

pos. α - auth.

blending /dyn. press.

inverse dynamic pressure

Figure 11. Bloc diagram of the asymmetric stiffness feedback

XI. Conclusion A transonic pitch up mitigation system for the Eurofighter EF2000 aircraft has been presented. The asymmetric

stiffness feedback detects uncommanded pitch-up motion in the transonic flight regime. The feature reduces the transonic pitch up transient to max. 1.5g. Together with a transonic pitching down moment function and a vertical load factor authority rate limit, the asymmetric stiffness functionality allows keeping the load factor nz within the structural load limits of the aircraft. In addition, the handling characteristics in the transonic flight envelope are considerably improved.

Appendix


14

References 1 Neuhuber, W et al., N/D-102 Operational Weapon System, Northrop/Dornier, December 1984 2 Neuhuber, W., Flugverhalten von Hochleistungs-kampfflugzeugen, Dornier-83-/14-EA, November 1983 3 Barrio, M., EF2000 Experimental Control Laws for Asymmetric Stiffness Evaluation - Flight Control Laws, Flight

Mechanics , Handling Qualities and Loads Assessment, EADS - CASA Technical Report NT-J-FVC-01068, February 2002.

4 Hanel, M. Asymmetric Stiffness Design, EADS-M - CL Design Note CL-P3-Design 58, Issue1, March 2002 5 Hanel, M. "Asymmetric Stiffness" Flight Test Results, EADS-M - CL Design Note CL-P3-Design 63, Issue1, March 2002 6 Haya, R., Fuentes, J., Flight Test Asymmetric Stiffness Campaign, EADS-CASA-MEM-JOC-0149-VP, March 2002 7 Petry, J., Linear Stability Analysis: Proposal on how to consider Asymmetric Stiffness; MEM-J-O-F-0789-FJ302, Oct.

2003 8 Barrio, M. Assessment Route for Asymmetric Stiffness Clearance , EADS-CASA MM-J-FVC-02099, May 2002 9 Barrio, M. Validation of the Assessment Route for Asymmetric Stiffness Clearance, EADS-CASA MM-J-FVC-02146,

July 2002 10 Skovlund, M., Rothnie, P., Eurofighter IPA1: Transonic Handling Characteristics with the FPSP1b+ Control Laws ,

BAe-WFt-RP-EFA-FTR-000090, Issue1, Alt. 1., June 2003 11 Doyle, P., Hunter, C. et. al., Analysis Report FC4PH22 Part A - Transonic Pitch Up Investigations , BAe- WAE-RP-

EFA-SAC-4198, November 2003 12 Orme, P., Carefree Handling Definition and Verification Concept, CD-J-462-F-2001-Issue2, August 2000

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