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FLEXIBLE AIRCRAFT FLYING AND RIDE QUALITIES Irving L. Ashkenas, Raymond E. Magdaleno, and Duane T. McRuer Systems Technology, Incorporated Hawthorne, California First Annual NASA Aircraft Controls Workshop NASA Langley Research Center Hampton, Virginia October 25-27, 1983 REPORT CONTENTS This presentation covers some of the highlights of IJASA CR-172201, "Flight Con- trol and Analysis Methods for Studying Flying and Ride Qualities of Flexible Trans- port Aircraft." The report itself contains the chapters listed in Fig. 1, and we'll follow this order in our discussion.
Of course, we'll have to limit ourselves to the more significant aspects and forego many of the details that are in the report.
We'll start: with a block diagram representative of a generalized FCS, go into a brief analytic exposition to illustrate a central principle in flexible mode con- trol, list and discuss some of tile pertinent pilot-centered requirements, expose the desired features of the control methodology, and select the methodology to be used.
Then we'll discuss the example Boeing-supplied characteristics and show how we approxlnated these with a reduced-order model and a simplified treatment of unsteady aerodynamics. The closed-loop flight control system design follows, along with first-level assessments of resulting handling and ride quality characteristics.
Some of these do not meet the postulated requirements and remain problems to be solved possibly by further analysis or future simulation.
I, INTRODUCTION
II, GENERAL ASPECTS OF FLEXIBLE VEHICLE CONTROL
III, SYSTEM DESIGN REQUIREMENTS AND DESIRES
METHODOLOGY CONSIDERATIONS FOR FLEXIBLE AIRCRAFT
IV,
CONTROLS AND FLYING QUALITIES ANALYSIS
V, FLEXIBLE AIRPLANE CHARACTERIZATION AND SIMPLIFICATION
VI I FLIGHT CONTROL DESIGNAND ASSESSMENTS
VII, CONCLUSIONS AND RECOMMENDATIONS
REFERENCES
Figure 1 GENEKALIZED FLIGHT CONTKOL SYSTEM FOR TRANSPORTAIRCRAFT INCLUDING FLEXIBLE MODES This block diagram (Fig. 2) illustrates primarily the multiple feedback paths acting on the sensor array and the possible use of secondary control points and limited for- ward loop elements. The primary FCS design task, of course, is to formulate the sensor equalization complex to yield a stable, robust system which meets the direct and implied requirements.
External Disturbances, Flexible Modes Generalized Coordinates i Elevator E Elevator - Forward Loop - Actuation - Equalization I / I System 6e Aircraft Attitude, '8 _ Secondary Dynamics Pitchin Control Secondary -TzG+-- Point Control a, Actuation Acceler- 6, Svstem ation Sensor/Equalization Complex Figure 2 ELEMENTARY FLEX MODE CONSIDERATIONS These equations (Fig. 3) constitute a simplified treatment of the considerations involved in synthesizing a suitable sensor-equalization response.
The first equation represents the rigid-body attitude rate response; the second is the slope of the first is the first oscillatory flexi.ble mode response where $I' bending mode at the sensor station.
Adding these responses yields the third equation with the simplified numerator/ The point is that selection of the sensor location and denominator ratios shown.
corresponding mode slope 4 can be used to directly affect these ratios or the.
equivalent pole-zero ordering.
+;ws Qflex 6,- s2 + 2(&),," + b,; K[s2 + 2q,~qs + ~$1 G(s) = " = s[s2 + 2t3',0@3+ $1 Figure 3 SYSTEM SURVEY FOR QUADRATIC DIPOLE CONTROL the root locus progresses into the right If the zero is greater than the pole, half-plane as in a); if less, it stays in the left half-plane as in b) and the proper choice of feedback gain will then provide enhanced structural mode damping.
This is a simplified explanation of a well-known general principle of flexible mode control, i.e., the desirability of synthesizing a sensor-equalization charac- teristic which exhib-its an alternating numerator/denominator ordering of quadratic pairs (a sawtooth Bode) which creates leading phase "blips" for those modes which are to be controlled. For those modes which are to be largely ignored by the con- trol system, appropriate notch or low-pass filtering might be considered if the modes are not so high in frequency relative to actuator and other dynamics as to make them insignificant anyway. (See Fig. 4.)
OdB Lines for Neutral Stability o 1 Lag- Lead Dipole b) Lead- Log Dipole (2 c I) Figure 4 I I I II I I III I llll1lllllllllllllllllllllllllll1lllllllIIIlII PILOT-CENTERED COMMAND KEQUIKEMENTSAND FLYING QUALITIES In addition to the Foregoing implied requirement, there are direct requirements for minimum satisfactory flying and ride qualities. The flying qualities list shown here pertains to pilot's attitude and acceleration response to elevator input (Fig. 5).
The first two headings refer primarily to attitude control and reflect the pos- sible use of either frequency- or time-domain assessment criteria.
The third heading relates mostly to unwanted acceleration responses which can be self-excited by feedthrough to, and ampli- excited directly by the pilot's remnant, fication resulting from, the pilot's body-arm-controller induced motions, or directly excited by normal closed-loop piloted operation.
The final heading generally relates to either attitude or acceleration responses, although attitude is the more common culprit.
goth synchronous behavior and the PI0 syndrome are assessed later for the derived system, as are pertinent aspects of the preceding items.
FREQUENCY DOMAIN M~b+I/T~E)e-TS f (s) = EQUIVALENT s(s2+2&JJs +w21 BANDWIDTH CLOSED LOOP TINE DOMAIN ENVELOPE BOUNDED TIME PARAHETERS TRP FLEX I BLE MODE EFFECTS REMNANT EXCITATION VIBRATION FEEDTHROUGH PILOT CLOSED-LOOP EXCITATON OF FLEX MODES PI0 CONSIDERATIONS SYNCHRONOUS BEHAVIOR PI0 SYNDROME Figure 5 FQ AND FLEX A/C CONTROLCONSIDERATIONS GOVERNING CONTROL DESIGN TECHNIQLJRSELECTION The summation of certain of the foregoing and of the more complete considera- tions in the report as they pertain to the selection of appropriate design method- ology is listed here (Fig. 6).
In the first place, we have to consider uncertainties and variations in the air- frame poles and zeros due to changes in flight conditions and loading.
Second, we have to utilize and consider many elements which are basically expressed i.n frequency-domain formulations.
Third are the direct and implied control design criteria which can be in time- or frequency-domain formulations, or simply expressed as desirable qualities.
8ased on these and other considerations, the basic control methodology selected comprises conventional, classical, multivariable, frequency-domain analysis tech- niques.
1, KEY AIRCRAFTPARAMETERS WIDE RANGING (LO FREQ) POLES, ZEROS NARROW RANGES (HI FREQ) 2, FREQUENCY DOMAIN FORMULATIONS .
PILOT I/O CONTROL ACTIVITIES, REMNANT, VIBRATION FEEDTHROUGH, PI0 BEHAVIOR .
UNSTEADY AERODYNAMICS .
MODAL FORMULATIONS -FREQUENCY-IDENTIFIED POLES AND ZEROS .
CONTROL ACTIVITY RANGE .
RIDE AND HABITABILITY CONSIDERATIONS AND CRITERIA .
RANDOM GUSTINPUTS 3. CONTROL SYSTEM DESIGNCRITERIA .
FLYING QUALITIES REQUIREMENTS .
FLEX m)DE POLE, ZEROSEQUENCING FOR CONTROLLED MODES .
GAIN STABILIZATION FOR IGNORED MODES .
ENHANCED DAMPING FORm)DESPOSSIBLYCAUSING EXCESSIVE REMNANT PILOT FEEDTHROUGH, PILOT SYNCHRONOUS BEHAVIOR .
PI0 SUSCEPTIBILITY .
CONTROLLER SIfiPLICITY .
CONTROLLER ROBUSTNESS Figure 6 THREE VIEWS OF SUPERSONIC CRUISE AIRCRAFT Before applying these techniques, it was necessary to derive a simplified repre- sentation of the Boeing-supplied data base for the delta wing supersonic cruise air- craft (SCRA), shown in Fig. 7, which included: Modal equations of motion (EOM) - 25 x 25 a.
b. Computer printouts of EOM matrix elements for 6 reduced-frequency sets of unsteady aerodynamics for each of 4 flight conditions C. Mode shape data in a variety of formats: tabulated, interpolated displace- ments and slopes at selected locations on the fuselage centerline; pictorial or perspective views; and contour plots for wing relative displacements out- of-plane d. Numerical frequency response data at 149 discrete frequencies supplied on magnetic tapes for four flight conditions. These "data" are the result of interpolation among the 6 reduced-frequency sets of unsteady aerodynamics SPAN 141.67’ P II !I LENGTH 293.33’ Figure 7 MODE SHAPES FOR TAKEOFF WEIGHT DISTRIHUTION To afford an appreciation for the scope o.f the complete model Eormulation, the total set of centerli.ne elastic mode shapes for the take-off case is shown in.
Fig. 8 in the form of displacement normalized to maximum deflection. In general, the modes are 3-dimensional, and Fig. 8 shows just the cut along the fuselage centerline.
In many cases the maximum deflection is not along the centerline, and there is no corresponding unity value shown for those modes.
Modes one and two (Fig. 8) are rigid-body modes, respectively heave and pitching motion. Mode three is the first structural (bending) mode, and the struc- The i.n-vacua tural modes go up in complexity and frequency as the numbers go up.
frequencies in Hz are as follows.
Mode Frequency (Hz) Mode Frequency (Hz) Mode Frequency (Hz) 3 9 4.44 15 6.44 1.14 4 1.60 10 4.82 16 6.89 5 2.49 11 5.15 17 7.06 6 2.95 12 5.45 18 7.24 7.44 7 3.81 13 5.92 19 8 4.28 14 6.11 20 7.56 For a transport aircraft, this list has a remarkably large number of low-frequency closely spaced modes which can interfere, in one way or another, with piloted con- trol.
Y 11 I. 1, w I I I mm CG -SENSOR- I?::; I I I IL iI- 0 SW moo 1500 2OW 2506 3000 3500 lincherl Figure 8 I II II I I I I lllllllll1lllllllI Ill1 I I II I llllllllll MODE SHAPES FOR TAKEOFF WEIGHT DISTRIBUTION (CONCLUDED) Various body centerline stations and physical poi.nts are identified along the bottom of each plot. The "sensor station" is one chosen by Boeing as being in a fairly stiff region as evident by the fairly flat shape of the various modes in this area. The open circle symbols in Fig.
8 show that there is little change in mode three for the start cruise condition.
Modes nine through fourteen in Fig. 9 are characterized by more lumps and bumps than the first set, and modes fifteen through twenty in Fig. 9 are even lumpier and include some very large spikes. These anomalies appear to be due to ill-conditioned the mass and stiffness elements chosen for the analysis lumped parameters, that is, are not necessarily well conditioned and apparently lead to local resonances which give rise to the discontinuities shown.
However, notice that the area in the "sensor" region, where the structure is relatively stiff, is pretty smooth for all modes.
la- .?5 - = .50- m 8, .25 - it .
o- 1’ -.25 -30 I I .I .I I I II 0 500 1000 1500 2000 2500 3000 3500 I inches I Figure 9 - - COMPARISONOF MODEL C WITH.COMPLETE DISCRETE ROEING DATA The number of elastic modes selected for final retention in .the simplified model underwent a gradual increase from three to seven to ten largely to account for the acceleration response shown in Fig. 10. The reduced-order (10 mode) model "C" shown retains modes 3 to 6, 8, and 11 to 15, and is effected through progressive elimination of successive elastic modes by neglecting dynamic (s2 and s) terms relative to (constant) stiffness terms in each successive modai column. The generalized coordinate to be eliminated, now characterized by only a stiffness term, is expressed in terms of the remaining coordinates. Notice that some' of the retained modal equations are for higher frequency modes than those eliminated. This poses no mathematical problem, the progressive elimination of the equations in question proceeds as described above. However, there is no good physical rationale for neglecting the dynam1.c and s) terms of certain lower frequency modes and retaining those for some (6 higher frequency modes, except that it produces an excellent match as illustrated in Fig.
10, where the high-frequency behavior is reproduced with sufficient fidelity to permit accurate Klde quality analyses to proceed on the basis oE the reduced- order model.
This match is also based on simplified, "distributed" unsteady aerodynamics, meaning that for each degree oE freedom, or matrix column, the corresponding flexi- ble mode frequency was used to assign constant aerodynamics consistent with that value of reduced Erequency.
-100 - Figure 10 MODEL,D TAKEOFF B0DE.S OF PITCH ATTITUDE A final correction was applied ‘to eliminate perceived Inconsistencies in the supplied numerical elevator,fngrtlal properties and produce the "final" (Fig. 11) model "D" attitude responses for two locations.
The rear seat location provides the better sawtooth and is so labeled.
Z,DO wkadkc) .I0 10.00 I -I .I.
8Rear soot “Sawtooth” Bode 0) -8 et Senior b/ 7 cc Figure 11 , _ ,-,: : .. I ‘.. . .
MODEL D TAKEOFF BODE WITH PITCH RATE GYRO ~.r;,:.'. .,.
.,.:, - .'
Figure 12 shows the Bode for &rate gyro ; with' tippica dynamics, at the rear seat station with a:.suggested. clbiure. gain .of OW5. :c .- w(rad/sk) 10.00 0 dB for K,.= .5 - u
p -100 -
a
---.a------------------
-
Rate Gyro Loop T. E 400 o%ec.i soot “Sawtooth” Bode [.7,201 -a,, -( (Ride Quality Modes) Rate Gyro Dynamics : 3’ Figure 12 ROOT LOCUS PLOT OF FIGURE 12 SYSTEM 13 shows the resulting improved damp The corresponding root locus plot in Fig.
13, and 14, which are slightly degraded.
ing of all modes except 11, +o WI5 WI4 WI3
c
WI2 WII Actuator and Rate Gyro Root Locus “Sawtooth” Bode, Ride Quality Modes w4 w3 WSP Figure 13 e'pilot PILOT STATION AUGMENTED ATTITUDE RESPONSE TO ELEVATOR, T-- e feedbacks to 8 but they were not very effective in pro- We also looked at a, f requency modes.
viding additional damping of the lower In fact, the higher fre- quency modes, 6, 8, and 11 to 15, are essentially unobservable by a centerline acceler- ometer. Accordingly, vertical acceleration feedback to the elevator appears to be unnecessary to slightly undesirable; it was therefore eliminated as a pri.mary clo- The remaining basic elevator control loop structure shown below sure possibility.
is si.mple indeed (Fig. 14).
ec a2 8 8 et3 station - Vehicle - 87s L Rate Gyro %s s - Figure 14 ELEVATOR CONTROL LOOP STRUCTURE . ,: The basic FCS-augmented .attitude response at the.piiot's station to control 15. The effective bandwidth, set in this inputs using this system is given in Fig..
case by a 6 dR gain margin.requirement, is abo-ut 0.9 .to 1.0 rad/sec which corre- sponds to satisfactory handlfng ,for this flight ,condfti'on.
.I.
urn I - u(mdk'Y- %" Figure 15 8' RESPONSETO LO-DEG STEP ELEVATOR However, the pilot's station attitude response to a step input in Fig. 16 shows an effective time delay of about O-55 set, greater than allowable even using the most optimistic data. This quite large time delay is also apparent in the Fig. 15 phase characteristics (i.e., using the sLmple approximation 'cw - 90 deg = 1.57 rad where w N 4 = 180 deg, reff k 1.57/3.2 s 0.49). It is directly traceable to bending mode effects as shown at the bottom of Fig.
16, which shows only about a 0.10 set delay in the pitch response at ,the rear seat where the mode slopes are all either basically smaller than, or opposite in sign to, those at the pilot station. Thus the differ- ence is attributable to the natural change in sign .of the mode slopes in going from the rear seat to the pilot's station. The change in sign is a result of the In this sense, the inherent bending mode shapes of a slender flexible body.
associated additional time delay of the pilot's attitude response to a step control aft-surface input is fundamental. Before we decide what, if anything, can be done to eliminate or reduce such additional delay, we need to make further assessments.
l.O- 0; (de@ I I I I I 4 .6 .0 1.0 1.2 Time bed Al Pi/of Station I I I I I !a .6 .0 1.0 1.2 Time bed At f?eoi Seot Figure 16 "SYNCHRONOUS" PI0 POSSIBILITY Relative to PI0 proneness, the Fig. 15 pilot's attitude Rode is such that loop closure can be easily effected with pure gain adaptation on the part of the pilot.
Accordingly, there is no tendency for the "PI0 syndrome" which is characterized by required low-frequency lag adaptation for normal closed-loop operations. Such lag is an easy to accomplish, low-workload behavioral pattern described by pilots as a "smooth, trim-like control action." The trouble arises when, in an attempt to regain control after an upset or other stressful occurrence, the pilot regresses to a Then the pilot-vehicle (with the suddenly pure gain type of proportional control.
changed pilot equalization) may temporarily have too small a gain margin at a "high" frequency oscillatory mode (short period or conceivably a flexible mode).
The Lightly damped peak at about 16.5 rad/sec (Fig. 15) could conceivably be excited momentarily by "synchronous" pilot behavior at thLs frequency. The result- ing PI0 would not be unstable at the more probable lower gain shown in the fragmen- tary root locus of Fig. 17, but could have quite low damping. Of course, the level of pilot gain involved can only be sustained for a short tine before the system diverges at the lower frequency corresponding to the -180 deg phase crossover in Fig. 15. Thus, at best, synchronous PI0 would occur in "bursts" rather than in a sustained oscillation.
18.0 17.5
b
17.0 16.5 16.0 , -2.5 -2.0 -1.5 -1.0 -.5 o- Figure 17 PILOT STATION ACCELERATION (sip) RESPONSETO ELEVATOR INPUTS With respect to vibration feedthrough to the pIlot, the excitation at the pilot's station due to step and ramp elevator inputs is shown in Fig. 18. Clearly, the alleviating influence of a rate limIted surface input is desirable to avoid the high-frequency ringing at about 40 rad/sec and to reduce the amplitude and frequency for a lo-deg elevator ramped in at 30 deg/sec, the of the 16 rad/sec mode. However, effective time delay increment (half of the time to ramp to 10 deg) is 0.17 sec.
Therefore the effects of realistic surface rate limits wiL1 be to accentuate the A better solution effective time delay problem which is already possibly critical.
to the vibration feedthrough problem than Low surface rate saturation is desirable.
aI 10 deg Sfep 0.5 9 rod/xc sip
/-
(a 0.7 I I,, I Time &/ 30 deg/sec Romp Figure 18 ,
as
-
AMPLITUDES WITH SENSOR LOCATION w13 Turning now to ride qualities and Fig. 19, we have to recognize first that the usual Dryden turbulence spectra effectively flatten the asymptotic amplitude response to random gust inputs over almost the entire frequency range.
This is indicated by the long dashed lines in Fig. 19 which reprerient the zero dB line for a still leaving large spikes in the pilot's a, ow unity gust, response at about 16 and 36 rad/sec. As shown in the figure, these same spikes are generally evident along the entire cabin area. This means that ride quality is ageneral problem, not necessarily peculiar to pilot location. Accordingly, a general solution must be found. This could conceivably take one of two forms: use of a secondary control point to damp the offending modes or seat motion attenuation and damping.
The ride mode most evident in Fig. 19 is that at roughly 16 rad/sec, mode 6.
The largest amplitude spike above the zero dB gust lines at 16 rad/sec is about 34 dB (at the rear node) or an amplification factor of 50. This is far too large to be effectively damped by passive seat suspension and cushioning systems.
?lode 6's three-dimensional character is predominantly of a wing torsional nature so it's not surprising that a centerline control has no effect on it.
It is also clear that the wing lift due to such torsional deflection will apply more or less uniformly along the fuselage, which explains the Fig. 19 results. The obvious way to damp this motion is to use the outboard wing movable surfaces responding to motion also sensed at an outboard location. The Boeing data, unfortunately, do not cover symmetric aileron or flaperon inputs to the Longitudinal mode, so this option remains as a possible future exercise.
Rmr Nodt,JIPS Figure 19 RESULTS AND CONCLUSIONS: GENERAL Systematically exposed all design-centered factors to consider (l)(Fig. 20) Control system'functions and roles Flexible mode control.principles ., FCS crkteria an4 desire& for " Pilot-centered command and flying qualities > Bide-qualitfes ,' Controller-centered requirements and deaign.implications Available design methodologies and selection of recommended methods Established fundamental requirements on effective vehicle characteristics (aircraft/controller combination) consistent with simple robust control- lers. -- i.e., pole-zero ordering (2) Translated above into system and subsystem requirements (1) Confirmed a simplified treatment of unsteady aerodynamics which compared very well with the complete treatment (3) ,Developed and demonstrated considerations for selective inclusion/deletion of significant/insignificant modes within reduced-order system8 (3) 0 Demonstrated systematic design/analysis methods to meet requirements; derived a very simple robust system (4)
(1) ASSEMBLED REQUIREMENTS AND DESIRES
(2) REITERATED A CENTRAL PRINCIPAL IN FLEXIBLE MODE CONTROL
(3) DERIVEDAND UTILIZED A SIHPLIFIED,FLEXIBLE AIRPLANE MODEL
(4) DEMONSTRATED SYSTEMTIC DESIGNKTHODS
(5) IDENTIFIED CERTAIN PROBLEMS ENDEflIC TO FLEXIBLE VEHICLES
OF TYPE STUDIED
Figure 20 CONCLUSIONS: SPECIFIC "PROBLEMS" The effective time delay in 0 response to elevator appears to be a generic FJ problem due to low-frequency ending mode(s) as seen at the pilot station (Fig. 21).
l Vertical acceleration feedthrough at the pilot's station can be reduced by lowering the saturation rate of the elevator. However, this adds to the 9 response lag and may not be a viable solution.
Vertical acceleration response to w is high in general and must be reduced for good ride qualities. Analysis ndicates that secondary, outboard sur- f and off-centerline located sensors offer a probable solution which face(s), should also decrease vertical acceleration feedthrough.
0 mode is also involved in "synchronous PIO" possibili- The above "prominent" ties, but these are evident in the pilot's pitch attitude response and may or may not be reduced by the above-suggested secondary control surfaces.
Because of its prominence in ride, synchronous PIO, and vibration feed- response characteristics similar to those of the "prominent" mode through, are likely candidates for simulation research.
Te IN 6p RESPONSE TO ELEVATOR -- A GENERICPROBLEM DUE TO LOW
FREQUENCY BENDINGMODE(S)
VERTICAL ACCELERATION FEEDTHROUGH AT PILOT'S STATION
VERTICAL ACCELERATION RESPONSE TO wg IS HIGH IN GENERAL AND
MUSTBE REDUCED FOR GOOD RIDE QUALITIES
THE ABOVE"PROMINENT"MODEIS ALSO INVOLVEDIN "SYNCHRONOUS
PIO" POSSIBILITIES
BECAUSE OF ABOVEEFFECTS, RESPONSE CHARACTERISTICS OF THE
'PROMINENT" MODE ARE LIKELY CANDIDATES FOR SIMULATION
RESEARCH
Figure 21 RECOMMENDATIONS Expand present study to include off-center line symmetric controls(Fig. 22) Plan and conduct moving base simulation to investigate: (a) LOW-freqUE!nCy tims delay8 in pilot station attitude response asso- ciated with fuselage bending mode8 (b) Motion feedthrough and potential synchronous PI0 due to high-frequency centerline motion Develop more-automated means to achieve simple controllers which exhibit robust characteristics demonstrated herein, e.g.: Automated numerator synthesis for minimum (fixed-form) sensor/ equalization complexes which assure desired zero, pole order, and per- mit maximum spacing between a limited (specified) number of zero, pole pairs Frequency domain optimal performance indices and procedure8 which pre- ordain an optimal controller/aircraft combination satisfying the saw- tooth Rode requirements
STUDYOFF-CENTER LINE SYMMETRIC CONTROLS
PLAN AND CONDUCT MOVINGBASE SIMULATIONTO INVESTIGATE:
(A) TIME DELAYSDUE FUSELAGE BENDINGMODES
(B) FEEDTHROUGH AND POTENTIALSYNCHRONOUS PI0 DUE TO HIGH-
FREQUENCY COCKPITACCELERATION
DEVELOP MORE-AUTOMATED f'iZANSTO ACHIEVE SINPLE, ROBUST
CONTROLLERS
Figure 22 BIBLIOGRAPHY Ashkenas, I. L., Magdaleno, R. E., and McRuer, D. T.: Flight Control and 1.
Analysis Methods for Studying Plying.and Ride. Qualities, of Flexible Transport Aircraft, NASA CR-172201, August 1983. . .