Aircraft load alleviation by robust yaw-lateral decoupling

Available online at www.sciencedirect.com

Automatica 39 (2003) 1885 – 1891 www.elsevier.com/locate/automatica

Brief Paper

Aircraft load alleviation by robust yaw-lateral decoupling
Michael Kordta;∗ , J*urgen Ackermannb b Deutsches

a Airbus Deutschland GmbH, Kreetslag 10, D-21129 Hamburg, Germany Zentrum fur Luft- und Raumfahrt, Institute of Robotics & Mechatronics, Oberpfa'enhofen, D-82234 Wessling, Germany

Received 15 April 1999; received in revised form 22 August 2002; accepted 18 May 2003

Abstract In an engine out/engine failure of an aircraft the human pilot has to compensate a yaw disturbance torque. Because of a delayed reaction possibly followed by an overreaction the pilot may cause high loads (shear forces) at the vertical tail. These shear forces determine the static design of the vertical tail in some areas and its structural weight. Such a situation and a corresponding weight increase can be avoided by an automatic yaw control system. It achieves a precise and early yaw moment compensation faster than the pilot can do it. To tackle both the load alleviation and the handling problem within the controller design, the yaw rate is made robustly non-observable from the lateral acceleration at a decoupling point and approximately from the shear force at the vertical tail. The parameters of the robust controller can be derived analytically. Nonlinear high precision simulations show that a signi4cant load alleviation at the vertical tail is achieved and that the handling and the passenger comfort are improved. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Aircraft; Robust decoupling; Engine out; Load alleviation

1. Introduction Engine out (Fig. 1), abbreviated by EO, is a designcondition for an aircraft from the viewpoint of 9ight handling, robust design of the electronic 9ight control system, comfort, structural dynamics (structural loads) and static aircraft structure design. As the EO constitutes a yaw disturbance torque (Fig. 1) for the stable lateral aircraft motion, the EO by itself is not harmful to the aircraft. Nevertheless, large magnitudes of the yaw rate, the sideslip angle and the roll rate occur. Favre (1996), McLean (1997), Bennani, Magni, and Terlouw (1997) and Lambregts (1983) have revealed the potential of modern control system to increase the already high safety standards and to ful4ll stronger requirements than those which the above-mentioned disciplines impose
This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Xiaohua Xia under the direction of Editor Mituhiko Araki. ∗ Corresponding author. Tel.: +49-40-7437-3364; fax: +49-40-7437-4187. E-mail addresses: [email protected], [email protected] (M. Kordt), [email protected] (J. Ackermann).

0005-1098/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0005-1098(03)00218-8

today. Favre (1996) discusses the integration of the EO problem into the design of the standard lateral command and stability augmentation system (CSAS). The CSAS is based on the measurement or the observation of the yaw and the roll rate, the bank angle (Etkin & Reid, 1995) and, optionally, the sideslip angle. The aircraft is safely stabilized after the EO. The corresponding equilibrium condition is characterized by signi4cant magnitudes of the yaw rate, the sideslip and the bank angle, which clearly indicate the EO condition and cause the pilot to interact early, but without overreaction in order to stabilize the aircraft with zero yaw rate and low bank angle and to recover the original 9ight path. McLean (1997) uses a standard controller design methodology to design a second CSAS, which is activated after the detection of the EO. The system is therefore termed EO controller. In contrast to Favre (1996), no signi4cant magnitudes of the yaw rate, the sideslip and the bank angle occur. Bennani et al. (1997) and Lambregts (1983) integrate the EO control problem into the autopilot design. As the autopilot is based on more measured or estimated quantities than the CSAS (e.g. quantities characterizing the 9ight path), good performance can be achieved more easily than in case of the CSAS. The above authors already cover the requirements of the intially mentioned disciplines handling,

1886

M. Kordt, J. Ackermann / Automatica 39 (2003) 1885 – 1891

Disturbance Yaw Moment NzD

Shear Force Q y,vt vt

Engine Out Fig. 1. Disturbance torque from an EO results in a shear force at the vertical tail.

safety and comfort. Bennani et al. (1997) and Lambregts (1983), moreover, tackle the robustness requirements. Here, we investigate whether the aspects of structural dynamics (load alleviation at the vertical tail) and thereby of the static aircraft structure design can be integrated into the design of an EO controller. During an EO and the corresponding corrective pilot action, large loads, i.e. shear forces, bending and torsion moments occur at the vertical tailplane. The EO case may be a structural sizing case for some areas of the vertical tail. A considerable saving in structural weight of the vertical tail is possible if the maximal loads are robustly reduced in the whole operating domain. The main contribution to the loads at the vertical tail are the aerodynamic forces due to the sideslip, the rudder de9ection and the inertia term (Lomax, 1995). Consequently, a worst case rudder de9ection commanded by the pilot and a worst case sideslip have to be considered for the design of the vertical tail. According to the Joint Aviation Requirements JAR 25.367 (Joint Aviation Authorities, 1994), the pilot begins to react at the 4rst maximum of the yaw rate, but not earlier than 2 seconds after the EO. Consequently, a large sideslip has been built up. The pilot reaction is then to reduce the yaw rate by a high rudder de9ection rate until the derivative of the sideslip angle passes zero. This can lead to high rudder de9ections. Thereby, the essential characteristics of a human controller in a disturbance rejection problem are covered: 1. He is possibly too slow due to his reaction time. 2. In a delayed corrective action, he may even overreact. The same aspects can be observed in a yaw moment disturbance rejection in case of a car. Examples are skidding on an icy road or side-wind. The driver reacts when already a considerable yaw rate has been built up and an overreaction may drive the tire force into saturation. Such a situation can be avoided by an automatic yaw control system, with feedback of the yaw rate to a corrective steering angle that is added to the driver-commanded steering angle. This control system will compensate the disturbance torque faster and more accurately than the human driver (Ackermann, 1997, 1995). This control concept is transferred to the EO problem of the aircraft, consisting of a feedback of the yaw rate to the rudder: due to the early feedback of the yaw rate which is

induced by the EO, such a system can react faster and more accurately to the disturbance torque than the pilot. The essential aspect of the control concept is that the eHect of a yaw disturbance torque is compensated so fast in the planar lateral motion that in the closed-loop system the coupling into other degrees of freedom is small, in particular, the yaw rate (which is an unavoidable initial consequence of the EO yaw disturbance torque) should not in9uence the lateral acceleration. The planar lateral motion consists of the lateral translational motion and the rotational (yaw) motion, which are bidirectionally coupled. In the controlled system, there is only a coupling from the lateral acceleration to the yaw rate, but not vice versa. The system is unilaterally decoupled in the sense that the yaw rate is made non-observable from the lateral acceleration at the decoupling point (Ackermann, 1997, 1995). Hence, the yaw rate in consequence of the EO will not in9uence the lateral acceleration. Exploiting the design freedoms in the controller allows us to achieve a yaw rate that has approximately no in9uence on the shear force. An important requirement for both the car and the airplane application is the robustness of the unilateral decoupling controller. 2. Robust unilateral decoupling For cars, it is usual to describe the steering motion in a plane on road surface level. For an aircraft, the planar motion is strongly coupled with the roll motion due to the vertical tail and the diHerent lift of the left and right wing due to diHerent velocities under a yaw motion. This coupling is important for stability and maneuverability (Etkin & Reid, 1995). The disturbance torque of an EO and the compensating torque from the rudder de9ection occur essentially in the body-4xed (x; y)-plane. A design goal is to prevent the energy resulting from the unbalanced engine from being transferred from the yaw motion into the roll motion. To achieve this, the coupled yaw and lateral translational motion resulting from the EO has to be kept small. That means the disturbance is already compensated within the planar lateral motion after having induced only small deviations from the reference yaw rate. If this goal is achieved, then this is an aposteriori justi4cation for using a planar model to derive the controller structure. If the disturbance only induces small amplitudes in the closed-loop system even nonlinear eHects (Etkin & Reid, 1995) can be neglected for the controller design. Such a linear planar model allows to design a simple controller for the aircraft in detailed analogy to the car. To ensure the distinction between a yaw motion (yaw rate) which has been commanded by the pilot and a yaw motion due to an EO, the EO controller has to be combined with a pre4lter generating the reference yaw rate rref from the pilot command. Due to the superposition principle of linear system theory, the pre4lter can be designed after the

M. Kordt, J. Ackermann / Automatica 39 (2003) 1885 – 1891

1887

9ap-/slat-setting (Etkin & Reid, 1995). In that sense, FY; wfp is an uncertain function. FY; tail (x; R ) depends on both the state x and the input of the system, i.e. the rudder de9ection angle R , cf. Fig. 2. In analogy to Eq. (1), FY; tail is given by FY; tail (x; R ) = Y ; tail + (b=VTAS )Yr; tail r + YR R : R

The lever arm of FY; tail is ltail . The derivatives Y ; tail , Yr; tail and YR approximately depend only on velocity and altitude. In that sense, FY; tail is an uncertain function. Ideally, the desired balance of torques would be achieved by choosing the rudder de9ection angle R such that

l

FY; wfp (x)lwfp − FY; tail (x; R )ltail + NzD = 0

l

l

or the front tire angle  such that

lR

lF

− FY; R (x)lR + FY; F (x; )lF + NzD = 0:

lDP

aY,DP

FY,R

NzD CG

FY,F

decoupling point

Fig. 2. Planar model for the compensation of a yaw disturbance torque NzD by a rudder de9ection angle R /front tire angle .

controller design (Kordt & Ackermann, 2001) so that the case rref ≡ 0 is only considered here for brevity. The planar model is illustrated by Fig. 2. In case of the car, the starting point of the controller design are the lateral forces between the tires and the road (Ackermann, 1997, 1995). They are concentrated on the front and the rear axles, FY; F and FY; R in Fig. 2. The corresponding lever arms are lF and lR . In case of the aircraft, such a pair of forces in the (x; y)-plane can be introduced by discretizing the distributed aerodynamic forces and summing them up for wing, fuselage and pods: FY; wfp and for the tail: FY; tail , cf. Fig. 2. FY; wfp depends on the state x of the aircraft and has a lever arm lwfp with respect to the center of gravity (CG). The state x = [ r]T consists of the yaw rate r and the sideslip angle . Within linear aerodynamic theory, FY; wfp (x) can be expressed by aerodynamic derivatives FY; wfp (x) = Y ; wfp + (b=VTAS )Yr; wfp r;

(2)

(1)

where b is a reference length like the half span length and VTAS is true airspeed (Etkin & Reid, 1995). The force derivatives Y ; wfp , Yr; wfp result from a nonlinear trimming computation and linearization at the trimming point. These derivatives depend on several varying parameters: velocity, altitude and wing con4guration parameters like

(3)

(4)

The forces and the disturbance torques are unknown, however, so that a robust implementation of the control laws resulting from Eq. (3) is impossible. An alternate approach was very successful in the automotive application and is applied to the aircraft here. The idea is to split the vehicle dynamics robustly into two subsystems. A 4rst order subsystem with output lateral acceleration should not be in9uenced by the yaw rate, because the disturbance torque NzD primarily enters into the yaw acceleration and the yaw rate. A simple choice would be the decoupling of the lateral acceleration at the CG. Then, however, the yaw rate r as part of the state x enters into aY; CG via both unknown forces FY; wfp (x) and FY; tail (x; R ), cf. Eq. (6), and again the ideal robustness cannot be achieved. Therefore, we 4rst de4ne a decoupling point DP in a distance lDP from the CG so that FY; wfp (x) does not enter into the lateral acceleration aY; DP at the decoupling point. With mass m and moment of inertia Iz of the aircraft, the distance lDP is calculated from the condition aY; DP = aY; CG − lDP r: ˙

(5)

Here, aY; CG and r˙ are expressed in terms of the pair of forces: aY; CG = r˙ =

FY; wfp + FY; tail ; m

FY; wfp lwfp − FY; tail ltail + NzD : Iz

(6) (7)

This yields aY; DP =

FY; wfp + FY; tail m

FY; wfp lwfp − FY; tail ltail + NzD Iz
 lDP lwfp 1 = FY; wfp − m Iz
 1 lDP lDP ltail + FY; tail − NzD : + m Iz Iz − lDP

(8)

1888

M. Kordt, J. Ackermann / Automatica 39 (2003) 1885 – 1891

NzD yaw dynamics

dynamics of lateral acceleration at decoupling point

r

and in aerodynamics due to variations in velocity and altitude (Etkin & Reid, 1995). These variations are equivalent to variations in lwfp , ltail , m, FY; tail and FY; wfp (Etkin & Reid, 1995). Physically speaking, the yaw rate r grows rapidly after the EO and induces a large acceleration aY; DP and large shear forces at the vertical tail. This dominating eHect is directly compensated by the r.u.d. EOC. Detailed numerical simulations in Section 3 reveal that the remaining immediate eHect of the EO on aY; DP in terms of (1=mlwfp )NzD (cf. Eq. (10), Figs. 3 and 4) has an acceptable level from the viewpoint of structural dynamics and handling. Next, the requirement for low shear forces Qy; vt at the vertical tail (load alleviation) is incorporated into the controller design. Qy; vt is approximately given by Lomax (1995)

aY,DP

Fig. 3. Bidirectional coupling between the lateral acceleration aY; DP at the decoupling point DP and the yaw rate r in the planar lateral aircraft motion in case of an EO disturbance torque NzD .

The location lDP of the decoupling is calculated from the condition that the factor of FY; wfp is zero, i.e. Iz lDP = (9) mlwfp and for this choice of lDP we have lwfp + ltail 1 aY; DP = FY; tail (x; R ) − NzD : mlwfp mlwfp

Qy; vt ≈ −mtail aY; tail + FY; tail ;

where mtail is the mass of the vertical tail. As the decoupling point is close to the vertical tail for all operating conditions of the aircraft, the lateral acceleration at the decoupling point aY; DP approximates the lateral acceleration aY; tail at the vertical tail. The yaw rate is made robustly non-observable from FY; tail and aY; tail and by Eq. (11) also from Qy; vt . Hence, the controller design approach covers the requirement to alleviate the loads at the vertical tail. Next, the r.u.d. EOC is symbolically derived. The rudder angle is composed of a reference part R; pilot and a feedback part R; control resulting from the r.u.d. EOC:

(10)

For the complete physical analogy to the car see Ackermann (1995). Eq. (9) corresponds to a representation of the mass and the moment of inertia by two masses in the positions lwfp and lDP from the CG, see Fig. 2, Ackermann (1997, 1995). The position lDP of the decoupling point is close to the vertical tail and varies only slightly with the distribution of the mass, which is changed by the payload and the fuel consumption. For controller design, it is therefore assumed to be constant. The induced error has to be analyzed by nonlinear high precision simulations of the closed-loop system. According to Eqs. (10) and (2) the lateral acceleration aY; DP at the decoupling point depends on the yaw rate r only via the uncertain function FY; tail ( ; r; R ) = Y ; tail + (b=VTAS )Yr; tail r + YR R . The crucial step for robustly eliminating the in9uence of r on aY; DP by a robust unilateral decoupling EO controller (abbreviated by r.u.d. EOC) is to choose the rudder de9ection angle R such that it cancels r in the argument of the function FY; tail ( ; r; R ), see Figs. 3 and 4. More precisely, aY; DP shall be robustly decoupled from the yaw rate by a controller, i.e. the yaw rate should be not observable from aY; DP for all variations in mass NzD

yaw

δR

dynamics

r

r

dynamics of lateral acceleration at decoupling point

This effect is cancelled by the EO Controller k r1 sS + kψ sS

(11)

R = R; pilot + R; control :

(12)

In the closed-loop system, the diHerential equation of FY; tail should not depend on the yaw rate r, i.e. it should have the general form F˙ Y; tail = f(FY; tail ; R; pilot ; ˙R; pilot ; NzD ):

(13)

FY; tail can be diHerentiated according to Eq. (2). Next, it is shown that already a 4rst order controller structure is suOcient for ful4lling the condition (13): ˙R; control = k r + kr r˙ + Kpre4lter R; pilot ; R = R; control + R; pilot ; N zD

aY,DP modified yaw dynamic

(14)

dynamcis of lateral acceleration at decoupling point

a Y,DP

= equivalent block diagrams

Fig. 4. Robust unilateral decoupling of the lateral acceleration aY; DP from the yaw rate r by a dynamic feedback of the yaw rate to the rudder in case of an EO.

M. Kordt, J. Ackermann / Automatica 39 (2003) 1885 – 1891 robust unilateral

-100

/|Q

y,vt

0

| in [%]

y,vt,max

| in [%]

z,vt,max

0

-100

/|M

-50

Q

/|Q

y,vt

-40

0

| in [%]

y,vt,max

design

-60 relevant critical region region

z,vt

/|M

-50

Q

design -60 relevant critical region region

z,vt

design -60 relevant criticalregion region

robust unilateral r. u. d. EO controller decoupling controller detection time: detection time: 0.50.5s s

-20

-40

M

| in [%]

0 -20

-40

z,vt

/|M

-20

M

r.decoupling u. d. EO controller controller detectiontime time: 20ms detection < 100 ms

z,vt,max

z,vt,max

0

M

| in [%]

conventional controller + corrective action normal lawpilot + pilot

1889

-100

-50

Q

/|Q

y,vt

0

| in [%]

y,vt,max

Fig. 5. Phase diagram: shear force Qy; vt against torsion moment Mz; vt at the vertical tail, comparison of the CC and r.u.d. EOC for eleven operating conditions at mach = 0:2 and 0:35 at the most critical altitudes. In case of the r.u.d. EOC, detection times of 20 ms (center) and of 0:5 s (right) are considered.

with free controller parameters k and kr . To show this, the diHerential equations for and r are expressed in terms of FY; wfp and FY; tail : (15)

˙ r˙ and ˙R by the DiHerentiating Eq. (2) and substituting , expressions in Eqs. (12), (14) and (15) yields: 
b F˙ Y; tail = (YR k − Y ; tail )r + YR kr + Yr; tail VTAS ×

lwfp FY; wfp − ltail FY; tail + NzD Iz

+Y ; tail

FY; wfp + FY; tail mVTAS

+YR (Kpre4lter R; pilot + ˙R; pilot ):

3. Application to aircraft load reduction (16)

Then requiring the explicit terms in r, i.e. (YR k − Y ; tail )r, to be cancelled, allows us to derive the controller parameter k symbolically: k = Y ; tail =YR :

conventional controller + corrective pilot action

(17)

However, r-dependent terms also implicitly enter in Eq. (16) via the terms in FY; wfp . By choosing −1 (lDP Y ; tail + bYr; tail ); (18) kr = YR VTAS all terms in FY; wfp cancel. Herein, Eq. (9) has been used. With this choice of controller parameters, the diHerential equation for Fy; tail is 
−ltail Fy; tail + NzD b ˙ F y; tail = Yr; tail + YR kr VTAS Iz Fy; tail + Y ; tail mVTAS + YR (Kpre4lter R; pilot + ˙R; pilot ):

For an instantaneous outer left EO at t = 0 s, Fig. 7 compares the r.u.d. EOC (upper aircraft with the light grey vertical tail, the corresponding shear force Qy; vt is illustrated

(19)

This equation shows that the yaw rate r of the controlled system has no in9uence on FY; tail and by Eq. (10) also no in9uence on aY; DP . Hence, the choice of the controller structure is adequate to derive a robust gain-scheduling controller, which makes FY; tail independent of the yaw rate for all

10

r / rref in [%]

r˙ = (lwfp FY; wfp − ltail FY; tail + NzD )=Iz :

5 0 -5

-10 0

5

10

15

t in [s]

robust unilateral decoupling EO controller 10

r / rref in [%]

˙ = ((FY; wfp + FY; tail )=mVTAS ) − r;

variations of the mass and the aerodynamics. Since the variations of the aerodynamic derivatives of the tail Y ; tail , Yr; tail and YR can be expressed in terms of the variations of the velocity and the altitude (Etkin & Reid, 1995) and as lDP is assumed to be constant, a gain-scheduling is only required in the velocity and the altitude, which can be easily measured. Remarkably, the controller does not depend on the aerodynamic derivatives Y ; wfp and Yr; wfp of Eq. (1). These derivatives cannot be exactly expressed in terms of the velocity and the altitude, cf. Etkin and Reid (1995). Hence, these derivatives would have induced an uncertainty in the gain-scheduling.

5 0 -5

-10 0

5

10

15

t in [s]

Fig. 6. Time histories of the yaw rate r for the comparison of the r.u.d. EO switched on after a detection time of 20 ms and the CC for the 9ight conditions of Fig. 5.

1890

M. Kordt, J. Ackermann / Automatica 39 (2003) 1885 – 1891

0s

1s

1.5 s

2.5 s

3s

3.5 s

Fig. 7. Aircraft and shear force dynamics at the vertical tail in an outer left EO for 6 time steps: EOC (upper aircraft with light grey vertical tail, corresponding shear force: right, light grey column at right bottom of each subplot) compared to the CC (lower aircraft and left column).

by the right, light grey column at the right bottom of each subplot in the six subplots) with a conventional controller (lower aircraft and left column in each subplot). The two controllers are abbreviated by EOC and CC. The EOC is switched on after a detection time of 20 ms. At 1 s, the early rudder de9ection angle of the EOC is more than 2 times larger than for the CC and the following subplots show the resulting early stabilization of the 9ight path. At 2:5 s the corrective pilot action (JAR 25.367) becomes evident. It is justi4ed by the signi4cant 9ight path deviation which the CC could not prevent. The induced shear force is reduced by more by than 50% by the EOC. The assumption of a linear planar model for controller design is justi4ed by the small roll angles, which ensure better passenger comfort than the CC.

The shear force at the vertical tail Qy; vt and the corresponding torsion moment Mz; vt at the vertical tail are usually analyzed in a phase diagram, see Fig. 5. Design relevant operating conditions are represented by regions in the phase diagram. Fig. 5 compares the r.u.d. EO (Fig. 5 center, right) with the CC (Fig. 5 left). Two detection times of 20 ms (Fig. 5 center) and 0:5 s (right) are considered. Fig. 5 indicates that the regions of simultaneously large shear force and torsion moment are avoided in a nearly ideal way in consequence of the EOC. The extreme values in shear force and torsion moment are nearly reduced to one half by the EOC compared to the CC. The achieved robustness is remarkable, i.e. the area covered by all the various phase curves corresponding to diHerent 9ight conditions is nearly condensed to one curve.

M. Kordt, J. Ackermann / Automatica 39 (2003) 1885 – 1891

The 9ight conditions are eleven operating conditions (different amount and distribution of mass) at mach = 0:2 and 0.35 and at the most critical altitudes. In consequence of the achieved load reduction, the vertical tail can become signi4cantly lighter in combination with the EOC. Fig. 6 shows that the corresponding amplitude variations of the yaw rate time histories in the 4rst peak are reduced by more than one half by the EOC (detection time 20 ms) compared to the CC (see also Fig. 7). 4. Conclusion A new pilot assistance control system for the yaw disturbance moment compensation has been transferred from cars to aircraft. The new pilot assistance system is characterized by a very early interference within man’s reaction time: obviously, an automatic system can master an EO situation in a much better way by avoiding any time wasting in consequence of the pilot reaction time and by avoiding any overreaction. Instead of 4rst letting the aircraft drift into an extreme 9ight situation, which then is hard to master and induces high loads at the vertical tail, the early yaw moment compensation keeps the aircraft in a moderate 9ight condition with low tail loads. Thereby, a task separation is achieved, which enables the pilot to concentrate on planning and performing long-term task or other tasks, e.g. in case of 4re. Here, man is superior to any automatic system. The short-term task, in particular within the reaction time where an automatic system is superior to man, is performed by the automatic system. In non-linear high-precision simulations, the control system turns out to be very robust to parameter variations (mass, aerodynamics). The physical design procedure yields analytical expressions for the two controller parameters. Acknowledgements Partial support by the German government (Flexible Aircraft project) is acknowledged. References Ackermann, J. (1995). Safe and comfortable travel by robust control. In A. Isidori et al. (Eds.), Trends in control: A European perspective (pp. 1–16). London: Springer. Ackermann, J. (1997). Robust control prevents car skidding. 1996 Bode prize lecture, IEEE Control Systems (pp. 23–31).

1891

Bennani, S., Magni, C. F., & Terlouw, J. C. (1997). Robust >ight control (pp. 13–21, 149 –397). London: Springer. Etkin, B., & Reid, L. D. (1995). Dynamics of >ight (pp. 101–114, 129 –154, 219 –256, 280 –295) (3rd ed.). New York: Wiley, Inc. Favre, C. (1996). Modern Flight Control System a Pilot Partner towards better Safety. In Proceedings of the second international symposium on aerospace, science and technology, ISASTI 96 (pp. 472– 481), Jakarta. Joint Aviation Authority JAA (1994). Joint aviation requirements JAR-25 large aeroplanes (pp. 1–C–8–10). Cheltenham: Printing and Publication Services Greville House, Change 14. Kordt, M., & Ackermann, J. (2001). Robust design of a structural dynamic engine out controller for a large transport aircraft. AIAA Journal of Guidance, Control and Dynamics, 24(2), 305–314. Lambregts, A. A. (1983). Integrated system design for 9ight and propulsion control using total energy principles. AIAA Aircraft design, systems and technology meeting, Paper no. AIAA-83-2561, Forth Worth, Texas. Lomax, T. D. (1995). Structural loads analysis for commercial transport aircraft: Theory and practice (pp. 42– 45, 143–160). Reston, Virginia: AIAA, Education Series. McLean, D. (1997). An Automatic Engine-Out Recovery system. In Proceedings of the international aviation safety conference, IASC 97 (pp. 763–776), Amsterdam.

Michael Kordt received the Dipl.-Phys. degree from University of Hamburg and the Dr.-Ing. degree from University of Bremen. From 1996 to 1999 he was research engineer at the German Aerospace research center. Since 1998 he is also loads & system engineer at Airbus Germany in Hamburg and Toulouse. Since 2000 he is head of several technology projects. Since 2001 he is also research & technology coordinator for loads & aeroelastics. His main research interests include aircraft dynamics and control, robust and nonlinear control. He is co-author of the book Robust Control (London: Springer-Verlag, 2002). Juergen Ackermann received the Dipl.-Ing. and Dr.-Ing. degrees from the Technical University Darmstadt, the M.S. degree from the University of California, Berkeley, and the Habilitation degree from the Technical University Munich. Since 1962 he has been with the German Aerospace Center (DLR) in OberpfaHenhofen, Germany. From 1974 to 2001 he was Director of the Institute of Robotics and Mechatronics. He is also Adjunct Professor at the Technical University Munich. His main research interests include parametric robust control and vehicle steering applications. He is author of books on Sampled-Data Control Systems (London: Springer-Verlag, 1985) and Robust Control (London: Springer-Verlag, 2002). Dr. Ackermann is a Fellow of IEEE and recipient of the Nichols-Medal from IFAC and of the Bode-Lecture Prize from the IEEE Control Systems Society.