For review for publication in 1EEE Transactions on Aerospace amt Electronic Systems ROBUST DAMAGE-MITIGATING CONTROL OF AIRCRAFT FOR HIGH PERFORMANCE AND STRUCTURAL DURABILITY _ Jeffrey Caplin Asok Ray t, Senior Member, IEEE Mechanical Engineering Department The Pennsylvania State University University Park, PA 16802 Suresh M. Joshi, Fellow, IEEE NASA Langley Research Center Hampton, VA 23681-0001 "["Corresponding Author: Tel: (814) 865-6377; Email: axr2(,:t_psu.edu Kevwords: Damage-Tolerant Systems, Robust Control, Structural Durability ABSTRACT This paper presents the concept and a design methodology for robust damage-mitigating control (DMC) of aircraft. The goal of DMC is to simultaneously achieve high performance and structural durability. The controller design procedure involves consideration of damage at critical points of the structure, as well as the performance requirements of the aircraft. An aeroelastic model of the wings has been formulated and is incorporated into a nonlinear rigid-body model of aircraft flight-dynamics. Robust damage-mitigating controllers are then designed using the H_ -based structured singular value (g) synthesis method based on a linearized model of the aircraft. In addition to penalizing the error between the ideal performance and the actual performance of the aircraft, frequency- dependent weights are placed on the strain amplitude at the root of each wing. Using each controller in hun, the control system is put through an identical sequence of maneuvers, and the resulting (varying amplitude cyclic) stress profiles are analyzed using a fatigue crack growth model that incorporates the effects of stress overload. Comparisons are made to determine the impact of different weights on the resulting fatigue crack damage in the wings. The results of simulation experiments show significant savings in fatigue life of the wings while retaining the dynamic performance of the aircraft. :_The research work reported in this paper has been supported in part by: NASA Langley Research Center under Grant No. NCC-1-249; National Science Foundation under Grant Nos. DMI-9424587 and CMS-9531835; National Academy of Sciences under a Research Fellowship award to the second author. https://ntrs.nasa.gov/search.jsp?R=19990116705 2020-03-30T02:09:29+00:00Z
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For review for publication in 1EEE Transactions on Aerospace amt Electronic Systems
ROBUST DAMAGE-MITIGATING CONTROL OF AIRCRAFT
FOR HIGH PERFORMANCE AND STRUCTURAL DURABILITY _
Jeffrey CaplinAsok Ray t, Senior Member, IEEE
Mechanical Engineering Department
The Pennsylvania State UniversityUniversity Park, PA 16802
Thestatevectorusedforsynthesisof thelateralcontrollerincludesboththelateralrigid-bodystatesandthestatesof the antisymmetric aeroelastic model. Since the spiral mode is not of interest during the controller synthesis
phase, it is possible to neglect the role angle state without significantly altering the dynamics of the other modes.
Thus, by considering the first three degrees of freedom for generalized displacements and eight additional
aerodynamic states of the antisymmetric aeroelastic model in Eq. (8), the plant state vector of lateral motion
becomes:
xt,,=[p r f3 q, r12 r13 r_l ri2 fi3 Y,, "'" Y,8] r (11)
where p is the roll rate;
r is the yaw rate;
_3 is the sideslip angle;
T1k, k = 1,2, 3 are the coefficients of the first three antisymmetric modes of structural deformation;
rl k, k = 1,2, 3 are the time derivatives of rl k, k = 1,2, 3, respectively;
Yak, k = 1,2,..., 8 are the eight aerodynamic states chosen for the antisymmetric aeroelastic model.
The generalized plant used for synthesis of the lateral controller is shown in Figure 6. The ideal model contains
two blocks; one is a first order system representing the desired roll mode time constant, and the other is a second
order linear time-invariant system with the desired frequency and damping ratio of the Dutch roll mode. The
performance weighting function Wp (s) contains three blocks. The first two blocks penalize the differences in roll
rate and sideslip responses of the aircraft model and the ideal model. The third block penalizes the difference in
bending strain between the left and right wings. Although the wings are subjected to both bending and torsional
displacements, the magnitude of the torsional strain is about two orders of magnitude lower than the bending strain.
Thus, the principal strain is essentially equal to the bending strain, and only the bending strain is penalized during
controller synthesis. However, both values are used as feedback signals for control purposes. The strain weighting
functions are selected for the damage-mitigating controller design based on the information generated from
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extensivesimulationruns.The transfer function W c(s) represents the frequency-dependent weights placed on the
antisymmetric stabilator deflection and its rate. These weights are constant over the frequency range of interest, and
are chosen to be the inverses of the maximum position and rate. The low-pass filter on the reference signal is
included to make the D-matrix of the generalized plant zero, which is a requirement of the MATLAB function
sdhfsyn for sampled data controller design. The transfer function Wde I(s) is the uncertainty weight. In an actual
design case, it would be desirable to characterize the uncertainty in the plant model based on the known dynamic
behavior of the aircraft, preferably from experimental data. In this case, since the model [Brumbaugh, 1991] does
not represent any specific aircraft, no such data was available. Therefore, we have chosen an uncertainty weight of
2000O(s+loo)(s + 2000Xs + 10000) ' which represents -10% uncertainty at low frequencies increasing to -200% uncertainty at
high frequencies. For the lateral model it is found that good results can be obtained when the ideal models are also
used as the low-pass filters on the reference signals. This choice slightly reduces the order of the generalized plant.
3.2 Longitudinal Controller Synthesis
The state vector used for synthesis of the longitudinal controller includes both the longitudinal rigid-body states
and the states of the symmetric aeroelastic model. However, since the phugoid mode is not of interest, it is possible
to ignore the velocity, altitude, and pitch angle states without significantly altering the short period response of the
aircraft. Thus, by considering the first three degrees of freedom for generalized displacements and eight additional
aerodynamic states of the symmetric aeroelastic model in Eq. (6), the plant state vector of longitudinal motion
becomes:
go,. xo ]T
where q is the pitch rate;
a is the angle of attack;
k, k = I, 2, 3 are the coefficients of the first three symmetric modes of structural deformation;
_k, k = I, 2, 3 are the time derivatives of {k, k = 1,2, 3, respectively;
x ak, k = 1,2,..., 8 are the eight aerodynamic states chosen for the symmetric aeroelastic model.
The generalized plant used for synthesis of the longitudinal controller is shown in Figure 7. The ideal model is
a second order linear time-invariant system with frequency and damping ratio selected to match the desired short
period response of the aircraft. The performance weighting function Wp(s) contains two blocks. The first block
penalizes the difference in pitch rate response between the outputs of the aircraft model and the ideal model. The
second block penalizes the average bending strain of the left and right wings. The frequency-dependent weight
W c (s) penalizes the actuator positions and rates of the symmetric stabilator deflection and its rate. Similar to the
lateral controller, these weights are constant over the frequency range of interest, and are chosen to be the inverses
t3
of themaximumpositionandrate.ThetransferfunctionWdeI(s)is theuncertaintyweight,whichisthesameas
Remark3.2: Frequency-dependentweightingfunctionsarechosenfor penalizingtheaveragestrainandthedifferenceinstrainatthecriticalpointsof theleftandrightwings.Duetothenonlinearrelationshipbetweenstrainandfatiguecrackgrowthrate,thedesiredformsof theweightingfunctionsarenotknowna priori. The existing
literature with the exception of Holmes and Ray (1998) does not address this issue of strain weighting.
Unfortunately, Holmes and Ray have not considered the effects of crack retardation. Simulation results presented
later in this paper show that ignoring the effects of crack retardation under stress transients may lead to significant
errors.
4 EVALUATION OF THE DAMAGE-MITIGATING CONTROL SYSTEM
There are a few issues that need to be addressed for evaluation of damage-mitigating capabilities of an aircraft
controller. First, it is necessary to ensure that comparable rigid-body motions are executed with each simulation run.
For example, it would not be meaningful to compare crack growth for one maneuver having a peak load factor of 8g
with that from a almost similar maneuver in which the peak load factor is, say, 7g. The second issue is how to
compare the results of crack growth from different simulation runs with due consideration to the effects of variable-
amplitude cyclic stresses. The third issue is evaluation of crack growth due to multi-axial stresses resulting from
combined actions of the lateral and longitudinal controllers. Although the lateral and longitudinal dynamics of the
aircraft are very weakly coupled and the respective controllers are designed separately, the fatigue crack damage
depends on the total stress at the crack tip, to which both the symmetric and antisymmetric aeroelastic models make
contributions. The controller design procedure should be a three-step process from these perspectives:
Step#1: Evaluate all longitudinal Damage-Mitigating Controllers while the aircraft simulation model is executed for
purely longitudinal maneuvers. Alternatively, one could lift the restriction on pure longitudinal motion as
long as the same lateral controller is used in all cases.
Step#2: Evaluate all lateral Damage-Mitigating Controllers while the aircraft simulation model is executed for
combined lateral-longitudinal maneuvers using the same longitudinal controller. Limiting the maneuvers to
pure lateral motion would also be an option for aircraft that are not designed for aggressive maneuvers. For
fighter aircraft, however, the average stresses experienced under pure lateral motion would most likely be
too far below the maximum allowable stresses for any significant fatigue crack growth to be observed.
Step#3: After selecting one or more potential candidates from each of the previous two steps, the candidate lateral
and longitudinal Damage-Mitigating Controllers must be evaluated in pairs under combined lateral and
longitudinal maneuvering.
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In thispaper,however,nosignificantdamage-mitigationisachievedwiththelongitudinalcontroller.Therefore,Step#3is deemedunnecessaryforthisaircraft.Furthermore,sincethebendingstressesdominatethetorsional
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LIST OF TABLES AND FIGURES
Table I Dynamic Models of Actuators
Figure 1 Transformation from Vertical Axes to Body-Fixed Axes
Figure 2 Relationship Between Body-Fixed, Stability, and Wind Axes
Figure 3 First Three Symmetric Mode Shapes
Figure 4 First Three Antisymmetric Mode Shapes
Figure 5 Damage Mitigating Control System Schematic
Figure 6 Generalized Plant Model for Lateral Controller Design
Figure 7 Generalized Plant Model for Longitudinal Controller Design
Figure 8 Aircraft Performance and Damage under Turn Reversal Maneuver