Ride quality sensitivity to SAS control law and to handling quality variations

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RIDE QUALITY SEI;SITIVITY TO SAS CONTROL LAW AND TO KINDLING QUALITY VARIATIONS Philip A. Roberts, David K. Schmidt, and Robert L. Swaim School of Aeronautics and Astronautics, Purdue University SUMMARY (0 State variable techniques are used to generate the vertical and lateral f-:selage loadfactor distributions for the B-52H and B-1 bombers. A compari- son of loadfactors resulting from cruise turbulence excitation, reveals that n M rive quality is not significently improved by increasing the control law ba{ complexity. Control law complexity is meant to imply rate feedback in com- parison to full state feedback. Handling quality parameterizations show

N

pronounced effects on the loadfactors. Finally variations under, relaxed static stability implementation show that the ride quality is degraded by ^!

restoration of handling characteristics to original short period values.

U

INTRODUCTION HHM O u .

Hw •y H co Control Configured Vehicle (CCV) technology is ,just beginning to affect m °

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the design, and manufacture of aerospace vehicles. Current technology pp, N;= craft like the F-16 fighter and B-1 bomber are utilizing concepts such as- a ride control, Relaxed Static Stability (RSS), and fatigue reduction. Future vehicles will certainly incorporate active controls, maneuver load control, H m direct lift, flutter mode control, and gust load alleviation concepts'.- These future vehicles will be optimized under many manifalds to include Ride a E Qu a lity (RQ).

- W FA •N The objective of this c paper in to discuss the RQ trends-which large J flexible aircraft exhibit under various parameterizations of control laws pa a a and handling qualities. The information was generated as a data base for „ENO research supported by NASA Dryden Flight Research Center under grant NSG 4003. The ultimate aim of the project is delineation of handling qualities N opt s p ecifications for highly flexible CCV vehicles. This paper contains a $z H summary of the assumptions and solution technique, a control law parameter- k ization review, a discussion of ride sensitivity to handling qualities, and a a V 00 finally the RQ effects generated by implementing relaxed static stability V to H configurations.

y N w SYMBOLS

Oj

A7>

ti^A^ 6

A' Transpose of the A matrix <' sia.

JUL 1976

M WEI, ► ED On NASA STI FACILITY INPUT BRANCH ti

C Mean aerodynamic - chord length cg Center of gravity } E{ Expected value HQ Handling Qualities I Distance from cg along fuselage centerline, positive forward x Distance between the tail and wing-body aerodynamic centers t N Loadfactor at a particular body station; z'Y z'denotes vertical y denotes lateral rms Root mean square RQ Ride Qualities RSS Relaxed-static stability S Wing planform area St Tail planform area Up Averaged Steady State Flight Velocity u Control(s) vector; elevator, aileron, and/or rudder V Tail volume coefficient x State vector; usually associated with physical outputs in thfis paper a Perturbation angle of attack slip 9 Perturbation side angle Damping value Scalar unit white noise n a Perturbation pitch angle g, ith elastic mode generalized displacement ¢i (R Y ) ith orthogonal elastic mode shape value at body station Z y Perturbation roll angle

Perturbation yaw angle w Natural frequency PROBLEM FORMULATION Equations of Motion for Flexible Vehicles Time domain representations for the flexible vehicles were decoupled into longitudinal and lateral state variable formats.

The Gaussian white noise representation of turbulence was modeled as a state vector system as suggested in reference 1. The gust state vector was appended to the vehicle state equations resulting in the familiar control form.(1).

x(t) = Ax(t) + Bu(t) + Gri(t) (1) where: x (n+p) X, i

u 'mX 1

n number of physical vehicle states - m number of controls p number of gust states a, n X 1

( +p )

A ' '(u`+p. X (n+p)

B (n+p X : ut

Loadfactor Expression The major contributions to vertical and lateral loadfactors at cruise "t conditions can be represented by equations ( 2a) and (2b). T w KK N Z x k x

(k ,t) _ ^CUQ(e-a) + PO 0 i ( ) g i ]' (2a)

E i=1 Ny(Rx,t) _ [ (2b)

g o -`U004) - A- ^ i (kx) g i 1

^

x where: K is the number of elastic modes included in the model.

Throughout this paper the standard right hand stability axis system is utilized with the x axis positive forward from the eg`as shown in figure 1. 2 The sign conventions for the vertical and side bending elements are shown in figures 2 and 3.

b The loadfactor expressions can be reformulated as functions of the physical state variables by simple substitution.

x (P ,t) = P x (3a) (t) z X z z (3b) NY (Ax ,t) = Py xy (t) the IX(n+p) row vectors, P are deterministic for a given vehicle Z, equation of motion set, specific gontrol, and specified gain value.

Equa- tions (3) can be manipulated into a mean square value expression for the loadfactor.

E(N2 p E(XXI) (4) P, zV y zl y z0y Z'y Assuming a stationary, zero mean process for the state differential system (1) leads to an algebraic matrix Riccati equation.

This equation can be solved for the symmetric covariance matrix, E{xx l ).

Utilizing one algorithm suggested by Gelb in reference 2, convergence can be obtained within 35 seconds on a CDC for a 16xl6 Hiccati system. A simple matrix multipli- cation routine completes the solution utilizing equation (4).

Study Vehicle Descriptions and Flight Conditions The B-52H and B-1 were chosen for ttis study because they exemplify the trend toward more elastic structures for future large vehicles. The B-52, and commercial derivatives thereof, was a member of the first generation of elastic vehicles. Since that era, improved structural design techniques and composite materials have made possible vehicles like the highly plastic B-1.

The flight conditions were chosen because they represent cruise condi- tions which are mission essential because turbulence encounters at low and altitudes must be included in future design considerations.

The B-52H is used by the US Air Force as a long range bomber., It is meters long and has a wing span of 56.4 meters. Originally designed 47.55 as a high altitude bomber, it must now cope with penetration problems by Table 1 describes the flight condition combined high/low altitude profiles.

for the B-52H.

Mass = 158,75T kilograms (350,000 lbs.)

Mach = .55 y = 185-56 meters/see (608.8 fps) Velocit eg at 25% mean aerodynamic chord Altitude - 609.6 meters (2000 ft) TABLE 1: B-52H Flight Condition The B-1 is currently being test flown in a major pre-production effort by Rockwell International and the USAF. It is designed as the replacement vehicle for the aging B-52 fleet. The advanced structures and integrated technology make this vehicle an outstanding example for loadfactor

is 46 to elasticity. The overall length of the H-1 contributions due Table 2 utilized at the flight condition in meters`. The reference wing span is 41.8 meters.

(227,770 lbs) Mass = kilograms 103,315 Mach = . 85 fps) Velocity =289.4 meters /sec (949.45 40.67 (meters) cg is at fuselage station meters (100 feet) Altitude = 30.48 TABLE 2: B-1 Flight Condition CONTROL LAW VARIATIONS the Both vehicles were modeled as stable, unaugmented systems in ' B -52H which required a,': vertical and lateral cases with the exception of the - - Each vehicle small roll subsidence mode stabilization before proceeding.

model was theoretically modified utilizing pitch rate', yaw rate, pitch rate/ pitch attitude, blended pitch rate with acceleration, and full state ,feed- No significant differences in RQ were generated by these back control laws.

variations for identical (or nearly equivalent) handling quality values.

It should be mentioned here thsa the B-1 Structural Mode Control System" utilized because this study is involved with was purposely not included or general control design, parameterizations and not the specific RQ optimize- For both aircraft studies, only the primary control tion of the B-1.

surfaces (elevator, rudder, and aileron) were used for RQ determinations.

load- To establish a basis for comparison, the unaugmented vehicle meter/sec (1 fps) rms (root mean square) factors were computed for .3048 gust velocities.

-52H. The.< depicts the loadfactor curves for the unaugmented B Figure 4 nearly linear loadfactors labeled "rigid body only" include all terms except Hence any interactive rigid body the summations in equations (2a) and (2b).

and elastic dynamics from the Riccati solution are included in this output.

more pronounced curvature includes all the modes The second line which has a at this flight condition, For the B -52H that were utilized in the model.

is about 15% of the vertical loadfactors the maximum elastic contribution to this data were primarily aft- (The lateral fuselage modes used in total.

Hence the rise in elastic effects near the tail.') body modes.

Figure 5 shows an impressive increase in the elastic contribution to will The discerning reader vertical loadfactors on the unaugmented B-l.

4 The and 5.

immediately note the changes in vertical scale in figures different flight conditions and elastic contributions to ride on the separate vehicles dictated these scale changes.

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I6m. 1600.

BOO Y 'SYFlTION Figure k: .` H-52H Unaugmented Loadfactors RQ SENSITIVITY TO HMLING , CHARACTERISTICS Under each control law studied, the gains were changed so that a range - f handling characteristics and their resulting loadfactors - could be cata- loged.

The values used for the handling characteristics were restricted to the acceptable ranges ` ` given in MIL SPEC 878511.- Hence the following boundaries: 7_

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Figure 5= 8-1 Unaugmented Loadfactors REPRODUCIBILITY OF IDRIGW" PAGE IB

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Longitudinal. Shor. Period{ £.0 { a sp s 10.0 n n Lateral Dutch Roll i :- ^ wD l - n It is important to reiterate at this juncture that the study goal was RQ sensitivity to feasible controls, not the design of an optimal control for either vehicle.

Pitch Rate Feedback (B-52H) Figure 6 shows the perventage change in loadfactor for various handling characteristics. The baseline In all these cases is the unaugmented vehicle loadfactors from figures b or 5, whichever is appropriate. As shown, the increase of damping and frequency for higher stabilizing feedback 'gains produced better RQ.

45.00 B-52H , MACH .55 , 6iO METERS PITCH RATE 6 so.aG 16.00 .00^I8889J¢011tL^^C. ^liLl0.^ SIi.S2 '^"-------.___.-,^3.0 i-15.00 6 10 10 CO .. iPS ]IL^_^35 4U. ... 4G -90,00 [METERS) r_ +. '70_11 G. 300. 500.

1500. 1500. IINCMEFI " W 00' soov srrtae Figure 6: Pitch Rate SAS Changes I Yaw Rate Feedback (B-1) Figure 7 shows the loadfactor curves for the B-1 lateral dynamics.

Notice the effect is similar; increased damping produces better RQ.

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.OA Mfr 1 or 114,4101, K' \P MITERS

A

INCH![

O * p

uss t ti BOOM BTAT/ON RATS SAS WITH YAW 8-1 LATERAL o.

Figure 7: B-1 Yaw Rate SAS Loadfactore Blended Pitch Rate and Acceleration (C O ) (B-1) Figure 8 shows the percentage changes in loadfactor under the C* control policy with variations in handling characteristics.

Again the same general trends appear.

, w.oe B-1 MACH .85 , 30 METERS BLENDED PITCH RATE p T UIIGY'T•AT/J Vahid, ^-16.00 ?.

[ w-36.60 ,10 I6 20 26 00.

-46 006 40 46 IMETE881 0^- ho.

6W8011.

0, 15^ Y p 0. IINCHE81 - HOOP SMRTION Figure 8: B-1 C* SAS .

Full State Feedback (B-52H) The trend expected by control experts would show that higher frequency and higher damping beget better RQ. This expectation was validated using full state feedback pole placing capacility. Figure shows the results as percentage changes in loadfactor compared to the unaugmented vehicle. The by relatively low baseline forward fuselage percentage changes were distorted loadractor values. Hence the higher damping/frequency loadfactor curves represent better rides overall. The asterisk cases in fiWwe 9 deserve \ ^Special mention. In these two cases the elastic mode damping was artifi- cially increased through the elevator feedback control policy. Vote that both cases generated appreciably worse RQ. This occurred because of the increased elevator excitation of the rigid body parameters in equations (2).

Breakdowns of the elastic contributions to the loadfactors showed the three elastic modes chosen for increased damping actually did 2ontribute less to the rms loadfactor.

8-52H, MAW .65. 00 METERS FULL STATE7 6 30,00.

" 35 4s IMETERS) Is 20 215 30 4a .10 .5 -30.00 1 1 1 1 , INCHES) "1 1200. 1500. teoo^ ( 0. eba.

BODY STATION I:ncraased J'.P"ns ' constdotel4of., J* Figure 9: B-52 Full State SAS This result prompted a theoretical attempt to parametrically plot load^ Using a transfer function approach and factor versus frequency and damping.

9 J'he ioadfactor mean the Dryden power spectral density for Vertical gusts domain. The square value was computed as an integral over the fr'e : ,^,u'ency 9.

results support the numerical analysis shown in fi are e, ikewise da mping value frequency increases, the RQ gets better.,^^ As excursions from the coupled elastic mode eigenvalue at constant frequency A numerical example was run for the will adversely affect the loadfactors.

10 for two increased short period frequency B-52H and is shown in figure The elastic mode increased damping was not included in these cases.

cases.

OF THD, REPRODUCIBILM IS POOR ORIGINAL PAGE

,MJ^r 1,ll..^t 14°M°s,^ IagYlebK .6000 - 8-52H, MACH .55. 610 METERS

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FREQUENCY

EFF(:CT

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(INCNEB) BODY 06 TION Figure 10:

B-5211 Increased Short Period Frequency Effect

9-stH VERTICAL

S,e

.1t, m.6,

c9 rtrrd

_ man j .H, ,d °.t.r ^^

c $4 fail ..e ruad ^, cc cc ) F°ulye Sf^t:m 6 (Mctm) Figure 11:

B-52H Rigid Body Relaxed Static Stability

i

RSLA. X I , 'D STA'T'IC STABILITY (1185) 'No methods were used to simulate this effect on the study vehicles.

rirst the tail. volume coefficlent, was reduced.

& S t t (5) c S This h v.tis the effect of shifting the vehicle aerodynamic center toward the center Uf gravity. Static stability is thereby reduced..

The second method involves an artificial eg shift toward the tail.

This is the more practical of the two methods, as it has alreadybeen incorporated as a fuel transfer or management activity on a test vehicle (CCV B-52).

Figure 11 shows the effect of RSS on vertical ride for the rigid body B-52F vehicle. Essentially pitching moment effects are reduced until at neutral stability the loadfactors are constant and due only to the vertical accelerations. , This would logically follow front definition of the neu- tral point. The question now arises, what rides are inauced by restoring the original handling characteristics of the unaugmented vehicle with an - active control system4 ' Figure 12 shows these results in terms of percent loadfactor change. c;-^reral the restoration resulted in degraded RQ. ,''., TERS B L M ACIII ..,..

5 IMETEfl61 Z26 IO I6" •30.0 7INCME61 1600.

oopp U. IB00.

600. 0, 300. d BODY S'NION Figure 12: B-52H RSS, Restored Handling Qualities ].3

CONCLUSIONS 1. hide quality is particularly sensitive to the handling characteristics specifications.

Except in optimizing a particular vehicle's control capabilities, ride quality is not dependent ;n the type of ,:ontrol law chosen.

3.

Relaxed Static Stability has a favorable effect on D-1 ride quality in that less pitch acceleration mud/or velocity contribute to the loadfactor.

!,, Relaxed Static Stability with restored handling qualities generates higher loadfactors on the N-52H and B-1 at the flight conditions studied.

REFERENCES Beath, Robert E., II: State Variable Model of Wind Gusts, Air Force 1.

1 1 ,ight Dy namics Laboratory Technical Memorandum, AFFDL-FGC-TM-72-12, Wright-

Patterson AVB, Ohio, July 1972.

2. Applied Optimn'. Estimation, MIT Press, Cambridge, Gelb, Arthur, et al.: Mass. ,

1974-

Swnim, H. L., et a1.: An Analytical Method for Ride Quality of 3.

Flexible f.irplaaes, Proceedings of the 3rd AIAA Atmospheric Flight Mechanics Conference, Arlington, Texas, Jwie 1976.

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