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HANDLING QUALITIES OF LARGE FLEXIBLE CONTROL-CONFIGURED AIRCRAFT Grant No. NSG 4018 Final Technical Report for Period January 1, 1979 - June 30, 1980
(NAS.A-CR-163206) HA G NSO - 25344
NDLIN QUALITIES O F
LARGE FLEXIBLE CONTROL-CONFIGURED AIRCRAFT
Final Technical Report, 1 Jan. 1979 - 30
Jun. 1980." , (Oklahoma State Un1v., Unclas
Stillwater.) 13 p HC A02/MF A01 CSCL 01c G3/00 21475 I Principal Investigator: Dr. Robert L. Swaim Division of Engineering, Technology and Architecture Oklahoma State University 111 Engineering North Stillwater, OK 74078 NASA Technical Officer: Mr. Glenn B. Gilyard Vehicle Dynamics and Control Division 17 ^16^b,^^ ^^ NASA Hugh L. Dryden Flight + fi r , Research Center y P.O.. Box 273 JUN 1980 ^w Edwards, CA 93523 N
RECEIVED
NASA STI FACILM_ ACCESS DEPT.
G Introduction This Is a final report on Grant No. NSG 4010. The project began on was to have terminated on December 31, 1979. A no- January 1, 1979 and cost time extension was requested and approved extend Og the termination date to June 30, 1950.
has devoted ten percent Dr. Robert L. Swaim, Principal Investigator, tine throughout the project. OnePh.D. student, Mr, Supat Poopaka, has
time throughout the project. Mr. Poopaka is
been employed fifty percent it and
completing his Ph.D. thesis on the project and expects to complete
take the final examination, where he defends the thesis, in September 1900.
Three copies of the thesis will be submitted to the Technical Officer, Mr.
Glenn Gilyard, and two copies to the NASA Scientific and Technical Infor- mation Facility in late September.
As the details of the research will be documented in the thesis, this final report on the project will be just a brief summiary.
Problem Statement The effects on handling qualities of low frequency symuetric elastic of a large flexible air-
mode interaction with the rigid body dynamics
craft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies .
, modes made to induce varying of the two lowest frequency symmetric elastk amounts of mode interaction.
A sununary of our mathematical formulation of the problem is contained is a paper presented by Mr. Poopaka at the Eleventh
in Attachment 1, which
-2- Southwestern Graduate Research Conference in Applied Mechanics held April 11-12, 1980 at Oklahoma State University.
Results Our approach of relating numerical performance index values associated with the frequency variations used in several dynamic cases to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task. The detailed presentation of these results will be contained in the forthcoming Ph.D. thesis by Mr. Poopaka. An outline of the thesis content is presented below.
Thesis Outline I. Introduction A. Handling Qualities and Pilot Ratings B. Pilot Rating Assessment Techniques C. Background on the Effects of Dynamic Aeroelasticity on Handling Qualities D. Objectives and $cope of Study E. Plan of Presentation II. Literature Survey A. Past Results on Elastic Airplane Research III. Equations of Motion Longitudinal Equations of Motion for a FleXible Airplane A.
Turbulence Model B.
C. Attitude Director Equations D. B-1 Flight Condition IV. Pilot Modeling A. Manual Control and Pilot Models B. Optimal Control Model C. Internal Model D. Closed-Loop Performance Equations E. Hess's Pilot Rating Method
i
-3-
t
Thesis Outline (cont.1 V. Effects of Elastic Mode Interaction on Handling Qualities Define Controllable Boundary A.
B. Controllable Boundary Based on Open-Loop Parameters VI. Conclusions and Recommendations VII. Selected Bibliography VIII. Appendix A. Numerical Values of Stability Derivatives and Equations of Motion IX. Appendix B. Derivations Related to Singular Perturbation Theory X. Appendix C. Computational Algorithms Project Reports and Presentations A list of the reports and presentations generated on the project is given below.
1. R. L. Swaim and Wen-Yo Yen, "Effects of Dynamic Aeroelasticity on Aircraft Handling Qualities," Journal of Aircraft, Vol. 16, No. 9,
Sept. 1979, pp. 635-637. Also presented at AIAA Oklahoma Section
Mini-Symposium, University of Oklahoma, Feb. 24, 1979.
2. R. L. Swaim, "Handling Qualities of Large Flexible Aircraft," presented at AIAA Oklahoma Section Mini-Symposium, Oklahoma State Univer5ity, Feb. 23, 1980.
Supat Poopaka, "Handling Qualities of Large Flexible Aircraft," 3.
Ph.D. Thesis Research Proposal, Oklahoma State University, Nov. 21, 1979.
4. Supat Poopaka, "Handling Qualities of Large Flexible Aircraft," presented at Eleventh Southwestern Graduate Research Conference in Applied Mechanics, Oklahoma State University, April 11-12, '1980.
5. R. L. Swaim, "Handling Qualities of Large Flexible Control-Configured Aircraft," Semi-Annual Status Report on Grant No. NSG 4018, June 22, 1979.
6. R. L. Swaim, "Handling Qualities of Large Flexible Control-Configured Aircraft," Semi-Annual Status Report on Grant No. NSG 4018, Dec. 31, 1979.
-4- R. L. Swaim, "Handling Qualities of Large Flexible Control-Configured 7.
Aircraft," Final Technical Report on Grant No. NSG 4018 0 June 30, 1980.
8. Supat Poopaka, "Handling Qualities of Large Flexible Aircraft," Ph.D.
Thesis, Oklahoma State University, School of Mechanical and Aerospace Engineering, to appear Sept. 1980.
9. Supat Poopaka and R. L. Swaim, "A Mathematical Pilot Model for Appli- cation to Highly Elastic Aircraft Handling Qualities Studies," under preparation for submission to the Journal of Guidance and Control in Se p t. 1980.
rz
i
i HANDLING QUAL I T1 CS OF LAR FLEX IBLE AIRCRAFT GE Sopat Poopak School of Mechanical aiid Aerospace Engineering Oklahoma State University
Aprt l / W
Sunana rX The effects on handling qualities of elastic mode interaction with the rigid-body dynamics of a large flexible aircraft are discussed. An extension of the optimal control model for the human operator is made so that the mode interaction effects on-the pilot's control task can be assessed.
Introduction The handling qualities &re the flying qualities of a piloted air- craft. They are the characteristics of an aircraft that govern the ease and precision with which a pilot is able to perform the control task required in support of the aircraft mission flight phase. The pilot's subjective opinion on the handling qualities is called a pilot rating and usually based on the Cooper-Hiper pilot rating scale C1].
The effects of elastic mode interaction on the handling qualities have been reported recently in Reference 2 based on a ground-based pilot- flown simulation. In this report we develop an extension of the optimal control model for the human operator so that the mode interaction effects on handling qualities can be easily assessed.
Problem Statement The dynamics of an aircraft to be controlled by the human pilot are described by a set of small perturbation equations of motion:
+ ^ acaW + E & WI)
xa,,^t ) o)
Aa f Ct W
+ D u.Ct) Go, ?Cot ffl
y a
•2- F.
x where x col. (x ,x ,x j, y is a turbulence state vector, x a ag ^^) ar
ar ae
is a rigid body states, is an elastic body states, u is a control xae input, y is a displayed output, and w is a zero-mean, gaussian, white noise process with autocovariance.
a(+,-t (2)
Z )
w
;Stt,)I -
E j
`YUd
For a cruise,, level fo ighft condition, eqn. (1) represents the a longitudinal equations of motion and y It) is an attitude director equa,, tion.
n i
(XP ) , . 0) dCl) .. ee ^^^
^ m
Vi a (#) = 60)--
1 (3)
j.
^ ) the slop% of the ath
where xp indicates pilot fuselage station, (x p symmetric elastic mode at that station, F j (t) the generalized displace- merit; ©(t) the rigid body pitch angle, and 0 M the elastic contribution to total pil;ch angle (see Fig. 1).
right 1--- tangent
ai cmkpi
U
o orreon Titch Angle at Cockpit The task of the pilot is to keep the rigid pitch response following the command director, Since only the total pitch response is shown to the pilot, therefore he has to distinguish rigid body motion from the total motion. We want to establish the boundary between when the pilot can visually separate the rigid body piotion from^he total motion in terms I of undamped natural freyuencie of the elastic modes. The rigid body r ^3^ E
mock ► parameters will be ma i n to i nod at the values known to give good
. • , d, haiidlinil qualities by" the mole-plar.ement technique while the elastic mode frequencies will be parametrically varied to introduce the mode in- teraction. The pilot model developed for computer simulation of this task is presented in the next section, The Pilot Model The optimal control model for the human operator developed here is a modified version of the standard optimal control model(3,4]. The model structure is illustrated in Fig. 2.
Ot )
Airtra(+ 'Xow
yA^^^ pis lq
—.^p yr ► AMhlc^ u4tl`^^P .^
ODERATOR MODEL r + '+ HUMAN i Go ^ ► N¢^ r molar s _ I Delay ► "lk) +trol() Es/i Ma ii
^)
Y orl ros t try ^ f Fig, 2 Optimal Control Model for Human Operator The relation v(t) = r(t-T) is approximated by a first-order Padd' approximation which can be expressed in the state variable form as z (a) r(f) u ct) (4) (f7 ^ I aCt) + ^4 The perceived information y p (t) is a noisy version of y a (t), i.e.,
+ 1^y cf)
yF^1) = yq M)
(5)
-4- g where vy(t) is a zero-mean, gatevJ in, white noise with autocovariance
(8)
dlt, V, i and Vy is known to scale with mean square of yas
yQ'i W 1 (7)
'Vyti I= eye E 1 11
where the observation noise/signal ratio e y. = 0.0171.
The pilot generates a command control input m(t) which is then transformed to r(t) via the relation
T„ rC^) + rCt) - mCi)
+ v',"66)
(8)
where T n is the neuromotor lag matrix and
v m (t) is a zero-mean, gaussian, white noise, with autocovariance ..t
-j”, J Cis
E f a,Ct ') et'/at)I -
Z) (9) and V is known to scale with E(mi(t) 2 ), i.e., s L
►►►
E ^ct^
e„,, V^,,
(10)
V, a where the motor noise/signal ratio eni^ = 0.003n.
Equations (4) and (8) may be augmented to (1) to define an aug- mented system of equations
?CU mCi) + E c WL(0
ac.( t ) = Ae 4 f3,, (11) n xC,C{J
C C
yulf) —S- I when ► A„'
A« Qq -8„ o
r .
T.
O Q TR i
[Ca DA ^ E: r -
Cc = p . x MO`
DA ^^ O TN The aircraft dynamics of eqn, (1) can be written in the form
+ 13 U(f) WW
?C LH) _N Alz 4E 1 xiti) `f Art ii(f) +
Azz, ?c & M + Ez+' O
8z u cI)
,M. ,W - A 21 ?c 1 (1) t
(l2)
b(4) _ C1 x110 Cz Wz.(07 + D
Lt(f)
where x 1 is a vector of the rigid body state varia0 es, x 2 is a vector of the elastic mode state variables, and is a small positive scalar U constant which can be unknown in this study.
In performing estimation and control command generation, it is nec- essary for the pilot to have 5 knowledge of the aircraft dynamics, the human limitation parameters (T,T n ,Vy,Vm ) and weighting coefficients of the performance index. This knowledge is called the internal model. In our aircraft dynamics model, the display consists of a slowly varying part due mainly to the rigid body dynamics and a high frequency oscillation part from the elastic mode. From the past experiment [2) it is evident that the pilot ignores the low amplitude high freugency oscillation part of the display. Therefore, in the pilot model, we will I the slowly varying dynamics subsystem as the internal model.
By the singular perturbation technique [5,6], we can d9compose the 4.
slowly varying part from the system (12) by letting u-o , from which we get CQ, ?C t(f ) 4 Dd, WO (13) y^ (f) _.,.. r k w6- N Az& Alz 13L where A ll AoL ,w Ass — AftL Ate "I -1
D p .. M 6
Cs, A X c , - G 1, cA Air Ail Es
Ea, : E, — Ass A ii
The pilot control task is assumed to be adequately reflected in the choice of a control • that minimizes the performance index
r( )
+ r' Ct 1 he" ' ] dt
9 d (^) 4r
OL I") a y J t 10) " r-# C Y ( 1 4) go T I conditioned on the perceived information y p (-). The command control m(t) of eqn. (8) is then given by
xs lf) ^-l i (15)
rA .-Lori xt(f) i --t 1 r where s xs [nd,
x t r;j
Tn P , C x ,`^, it P,a.
elua4terf
fl,s
J s^ hh^ies . ^ L 0] Q o P - ^ L! ' [ ► 1 i ., Lop}, - P u. r ,, 'i p ..
+?A o
P + Gp go P=
Ao C O
" C ' M ir (16) O
0b
o A e^ 8 &— Bac , _ D
o LC a
D^, a
= 0
A O o -&,,r
4/T t 8 O o o = is chosen such that the resulting T n is equal to 0.1 The weighting Q r second, which is a typical value for the human neuromotor lag.
a Kalman (t) is the best estimate of x t (t) generated by The state x t filter, B, W(+)4- zC" v^ ' [Lj pH)-Cc,X j 0, X t M)+^ ?C t f+) A t (17) S.
Y r7- where 1: satisfies the equation co V^j Es COX o z Aj (18) TWO G D 0N., TN
r wI Q
r
Wow
1 0'.
Combining egns. (5) with (11), (15) and (17) yields the closed loop system W d + Qc L, Ec, IXc W -- We f l Ice w Ac . .
Cp X6.^w^C^^^
6(i) +Y_ co
(Ak- t3 6 vy^[ ,x^
(1^) The covariances E(y a (t) 2 ) and E(m i (t) 2 ) for egns. (7) and (10) can be obtained by solving egns. (19) for cov.(x.c'xt)' Conclusion The technique developed here is being applied to determine the handling qualities of a large flexible aircraft of Reference 2 in a longi- tudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency, symmetric elastic modes made to induce varying amounts of mode interaction. The pilot rating is found by using the technique of Reference 7.
Acknowledgement A The author wishes to thank Dr. Robert L, Swaim of Oklahoma State University for his guidance and support. This work is supported by the NASA Dryden Flight Research Center under Grant NSG 4018.
a M A
4-
References
1, Chalk, C. R,, et al. "Background Information and User Guide for
MIL S-F-87858(ASG), Military Specification - Flying Qualities of
Piloted Airplanes." AFFDL-TR- -72, Air Force Flight Dynamics
Laboratory, Bright-Patterson AFB, Ohio, 1969, 2.
Swaim, R. L. and Yen, W. Y. "Effects of Dynamic Aeroelasticity on
Handling qualities and Pilot Ratings." AIAA paper 78-1365.
Proceedings of the ALmospheric Flight Mechanics Conference, Palo Alto, CA, August 7-9, 1978.
3. and Levison, W. H, "A Control Theoretic Kleinman, D. L., Baron, S, IEEE Trans. Auto.
Approach to Manned-Vehicle Systems Analysis."
Contr., Vol. AC-16 (1971), 824-832.
Baron, S. and Berliner, J, "MANMOD 1975: Human Internal Models 4.
Perception Models." Army Missile Research, Develop-
and Science-
ment and Engineering, Redstone Arsenal, A1., 1975.
5. Chow, J. H., Allemong, J, J. and Kokoktovic, P. V, "Singular
Perturbation Analysis of Systems with Sustained High frequency
Oscillations." Automatics, Vol. 14 (1978), 271-279.
6. Haddad, A. H. "Linear Filtering of Singularly Perturbed Systems."
IEEE Trans. Auto, Contr., Vol, AC-21 (19*), 515-519.
7, Hess, R. A. "A Method for Generating Numerical Pilot Opinion Ratings." NASA TM X 73101, 1976.
PAC A .r