Document
NASA Contractor Report 170411 NASA-CR-170411 19840016525
Optilmall Cooperative Control Synthesis
Applied to a Control-Configured Aircraft
D. K. Schmidt and M. Innocenti
•.
I.fBRARY COpy
Grant NAG4-1 January 1984 i .'t 1\1 r:z -I 19 o .'t, 'I ui., 04.
r I' I' LANGLEY RESEARCH CENTER Ii ~~ LIBRARY, NASA Hl·\MPTON, VIRGINIA 111111111111111111111111111111111111111111111 NF02564
Nl\Sl\
NatiQnal Aeronautics and Space Administration NASA Contractor Report 170411
Optilmall Cooperative Control Synthesis
Applied to a Control-Configured' Aircraft
D. K. Schmidt and M. ~nnocenti School of Aeronautics and Astronautics, Purdue University, W. Lafayette, Indiana 47907 Prepared for Ames Research Center Dryden Flight Research Facility under Grant NAG4·1
NI\5;/\
National Aeronautics and Space Administration Ames Resean:h Center Dryden Flight Research Facility Edwards, California 93523 This Page Intentionally Left Blank I. INTRODUCTION Quantitative handling qualities specifications are almost non existE~nt for flight vehicles exhibiting non conventional dynamiG charac- teristics. Examples include vehicles in completely foreign operating environments, or radically new aerodynamic and flight control designs such as Control Configured Vehicles (CCV's). Furthermore, higher order- system dynamics or even augmentation itself, have been found to signifi- cantly alter pilot opinion ratings so that the existing handling qualities specifications, based on conventional modes, are not appropriate for use with such systems.
J\ methodology that would effectively take into account both aug- mentation system design and the human evaluation in a single analytical framework was proposed in Reference [lJ. Optimal control theory was used to synthesize the augmentation control law as well as to model the human pilot control input. More recently. the methodology was extended to include a more complete pilot model and the restriction that the augmentation is a linear combination of selected system meaSU1"ements [2J.
The aim of the present paper is to apply the extended approach to the synthesis of an augmentation system, consisting of a control law of simple structure, for a control-configured flight vehicle similar to the AFTI/F-16 [3J, and to compare the resulting controller with two alternate control designs - a rate command system and a simplified, linearized version of this AFTI/F-16 air-to-air combat mode control law.
II. METHODOLOGY REVIEW At this point, a brief review of the methodology is appropriate - the complete derivation can be found in Reference [4J.
The aircraft dynamics, linearized about a steady state level flight condition ;s expressed by the following linear time invariant system (1) - n - - m - with xsR , up and u sR. The vector w is a zero-mean Gaussian white- A noise process with intensity W. In addition to (1), we assume that measurements or outputs available to the two "controllers" up and u A are
y
=Cx+v
P P P (2)
YA = C x + C U
'. x u p respectively. The vector Vp is also a zero-mean Gaussian white-noise process (with intensity V ) representing the error in the pilot's p observation, and Y are the measurements for feedback augmentation.
A A schematic diagram of the aircraft plus control dynamics is shown in Figure 1.
- The input up represents the human operator component of the
total control vector U, or for example, control surface deflections
associated with the pilot's stick input. The mathematical model for the pilot has been chosen to be similar to the optimal control model
of Kleinman and others [5J. The input u ' associated with the aug-
A mentation system, is constrained here to be the direct feedback of - u AIRCRAFT YSAS
-
u SAS AUGMENTATION + + PILOT MODEL up LoeR Block Diagram Fi gure measured outputs, or (3 ) (Note that this is consistent with the desire for simple~ easy to implement control laws).
Solut'ion for up
- * The optimal controller up is chosen to minimize the performance index J ' the pilot's objective in the task. Now J is taken to be p p T T
J = E{lim ~ ( (xTQx + u R u + d T R
(4) P T+oo I '0 P 1 P P 2 up) dt} where E{'} indicates the expected value operator~ and the weighting matrices are Q ~ 0, R1 ~ 0, R2 > O. Since the pilot controls the augmented aircraft, the minimizing control policy for up must be found subject to the dynamic constraint (5) where G is the matrix of augmentation gains yet to be found. Now
T
defining x = exT ... up] the pilot's optimal control input ;s given by
A
U = Kx
P (6 ) -1 K = - R2 [0: I] P
where X is the best estimate of X obtained from the Kalman filter
A .
x =
a o
(7) T -1
M = L:C Vp
p Finally, P and L are obtained from their respective Ricatti equations T i-I A+BAGC : Bp+BAGC - x u ---------~---------- ! 0 0 L -0'
- P --- R2 -1 [o! IJ P = 0 (8)
+ I~-+-~
r I 0 I R1 L ; and I iT ! J\+BAGC ' Bp +BAGC i x u 2:+2:1 !
o 0
,.... T-' j DWOT , V -1 [C : OJ -----_ .... - ... - -2: = + 2: 0 I Y pi ,
lC~J
Vm_ : - Now, consistent with the human operator model [5J the control input is modified to the (sub-optimal) relation or A :.* Kx+K u +v
U =
x U p m P (9) or for scalar up gx - u + v' p m where 'n is the human's neuromuscular lag time constant and vm is a zero-mean Gaussian white-noise process with intensity Vm that represents the error contaminating the pilot's commanded control.
Sblution for U A
For the input u ' we wish to find the controller u (or gain G)
A A as in (3) that minimizes the index of performance that includes J or p (l0) subject to the constraints of Equations (5) and (7). Thus, the augmentation is chosen to be "pilot-optimal" in the sense that its index of performance J incorporates J , which, as in [6J, [7J, and [8J, A p is taken to be correlated with the pilot rating.
Now in solving for u ' we must include the dynamics of the
A (pilot's) state estimator, Eqn. 7, in addition to the plant dynamics, Eqn. 50 Substituting Eqno 9 into the above two relations, and defin- -T [-T :::T
ing the augmented state vector q = x ; x ~ we may write the system
J dynamics in the form .
(11 )
q = A q + B uA + 0 W
with ",T -T -T -T [ w = J w vm vp
A B o o
p o o
A =
-----------r------------------------
o I A+BAGC -MC B +BAGC
I x P P u ~1Cp I K
o I Kx
u t T T,' , B = [6 .. 0 I ••• OJ A, ' --
o =
We may now express the objective function J as A T (l2)
J = E{lim t J (qTQq + uATFuA)dt}
A T-t-co 0 where Q
Q = 0
o
With the control law taken as the set of gains G that minimizes Eqn. 12, subject to Eqn. 11 may bE~ shown to be [2J ( 13) B T [8 T. .
where
OJ ·
OJ C = rCA = A: .. :
·
·
T .
~T = [0 0 8 OJ .
f = [0 CAJ A - -T with L = E{q q } satisfying the relation T [A + BG{C · O)]L + L[A+BG{C O)J A A (14 ) T
+ DWD = 0
and H satisfying
+ Q +
=0 III. APPLICATION In the following, we will apply the technique to the augmentation synthesis of a CCV vehicle similar to the AFTI/F-16 aircraft [3].
We will sepcifically have as the design objective that of optimizing pitch tracking performance. The vehicle state vector is taken as
- ----- .:...-.----
T x = [u, a, 8, 8] the perturbation forward velocity, angle of attack, A T
pitch rate, and pitch attitude angle. The control vector is u = [oE' of]'
where 0E is the elevator and of the direct-lift flap deflection. (Note that in the following, the forward velocity u is nondimensiona1ized with the reference velocity U and all the angular displacements and angular o rates will have units of degrees and degrees per second respectively).
The motion of the aircraft is referenced to the steady-state 1 eve 1 flight condition given in Table 1.
Table 1 Flight Condition Specifications
MACH M = 0.8
Altitude h = 23000 ft Trim Velocity U = 819.57 ft/sec o .
Trim angle of attack a = 2.345 deg
o Load factor LOg The attitude II command II signal to be tracked Bc is chosen consistent with previous pitch tracking studies [9J and is generated by a white- noise process Wc with zero mean and intensity 0 , passed through a Wc second order filter having a break frequency .5 rad/sec and a damping ratio of 0.5. In state variable form ;-0 - -
iOol
i
1. I (15 )
= A X + = = + Xc Xc Wc DCwC c c
l~C
e -.5 .....
L-·25
I1.J
c The covariance 0 is chosen in this case to yield 0 = 10.deg Wc Bc The information perceivE~d by the pilot, or his observation vector yp is chosen to be , E: ' .
E:
c = e - e
(16 )
Yp = e = C x + vp c
p
eJ
representative of a pursuit tracking task. Also the pilot's objective function for the pitch tracking task is taken as (17) This selection of weightings has been shown [9J, [10J to be consistent with experiment data on the modeled task for a wide variety of system dynamics. Likewise, the augmentation system objective function is (18 ) with F = pI > 0 the augmentation weighting matrix (I = identity).
Now in Eqn. 17, as with the complete pilot model [5J the parameter r is adjusted to produce a pilot's neuromuscular lag time constant (Eqn. 9) 't = 0.1 seconds.
n The measurements selected in this analysis for augmentation feed- T
back were simply YA = [a, e, 6J, or we are performing the optimization
assuming the control law G a + G· 6 + G e a 8 8
[::l ang =
(It should be noted that the augmentation measurements in this case do not include pilot control input, although this is admissible in the formulation. Finally, in this exploratory investigation a constant set of stick gains were selected, and the pilot control input was taken as I K i °E
I Est
= = u °stick °stick P ) LO F --.:
I KF
pilot st - - with KE = 1.0 and KF = 0.25. Further studies will address the pos- st st sibilities of letting the stick gains be free to be selected in the optimization, and whether to include pilot control input in the augmen- tation measurements).
Finally, the knowledge of the (observation and motor) noise intensities is required (or Vy and V ). The complete pilot model [5J m is developed on the basis of nearly constant noise to signal ratios, rather than constant noise intensities. Therefore, an iterative pro- cedure was used, beginning with the augmentation synthesis with assumed V and V , then the augmented system dynamics were evaluated with the m y complete pilot model (with time delays and attention sharing) to verify that the covariances (V and V ) utilized were consistent with a properly m y calibrated pilot model.
The synthesis procedure was performed in a parametric fashion by varying the scalar p in (18), or control energy weighting. In this way, E!ffects of different levels of augmentation authority on system perfoY'mance can be determi ned. Tabl e 2 revea 1s the parametri c optimi- zation results, obtained from evaluations of the augmented aircraft with the complete pilot model. The augmentation control gains are listed in Table 3. Finally the eigenvalue locus with increasing augmentation level (p) is shown in Figure 2. (Time responses are shown in the next section of the paperJ Table 2 Results Optimization g (de ) p r Cf (deg) Jp(cost) TN (\i sec E: p 0.08 0.68 8.26 5.0 .025 11.6 0.68 9.08 .025 11.9 0.10 1.0 0.10 0.68 10.48 0.5 .02 12.0 0.70 16.00 .01 13.3 0.10 O. 1 A significant result lies in the fact that there appears to be a minimum value of J for the control authority level associated with the p control energy weighting of p = 1+5, rather than a monotonic reduction with increasing augmentation level (decreasing p). This would in fact be the case if the cost weighting r and the covariance matrix ~ remained constant for each case. However, to maintain a pilot control loop .
(~p) consistent with the optimal control pilot model for each solution,
r varies to obtain a TN ~.1 sec, and W is adjusted to maintain the
- appropriate noise to signal ratios. Finally, adding the motor noise v to M TABLE 3 Augmentation Gains with p p a(deg) e(deg/sec) e(deg) 5.0 - .14B .429 .OB7 °E -.032 .103 .020 of 1.0 -.20B .777 .211 °E -.042 .185 .050 of .5 -.130 .939 .245 °E - .190 .209 .057 of . 1 .236 1.21B .424 °E .043 .267 .101 of
EIGENYALUE LOCUS
1.
r,\ -30. -20.
-4. -3. -I.
-2. 1. 2.
REAL (0-) (l/sEC) --' Figure 2 w the pilot's input (in Eqn. 9) results in a sub-optimal pilot-model solution for up' Further, these effects appear to become significant at higher augmentation levels of authority.
As a result, for this chosen control law the optimization suggests a candidate design corresponding to a value of p near 1,0. We will evaluate this system further.
IV. CONTROL SYSTEMS EVALUATION In an attempt toevaluate results from the proposed methodology, two alternate augmentation synthesis methods are chosen for comparison with our simple output feedback control law. They are an optimal pitch-rate command augmentation system, and a linearized air-to-air combat mode augmentation, similar to the standard uir-to-air mode on the AFTI/F-16 aircraft [3J, A rate command control system is chosen because it is considered to be very effective in attitude tracking. Briefly, it consists of an augmentation system that is designed to minimize the error between the aircraft pitch rate and the pilot's stick input, which is taken as the commanded pitch rate from the pilot. The synthesis of the control- ler used here is summarized in the Appendix.
In addition, an augmentation system similar to the air-to-air standard normal mode present in the AFTI/F-16 aircraft is simplified and linearized about the steady state level flight condition of Table 1. This mode is also intended to provide precise tracking capabilities.
The characteristics of these two controllers are listed in Tables 4 and 5.
Table 4 Rate Command Control Law .
Veh.
Dynami cs X :: Ax + B uA
Contra 1 Law:
G x + G
= (\tick x u
- [EJ
uA = of A
* Gains .
u C! e e °stick 'VO .330 .942 .028 -.746 °E 'VO .073 .232 .007 -.187 of *A11 angles in degrees, u non-dimensiona1ized with U o Table 6 Performance Comparison CONFIGURATION Rr~s ERROR (deg) RMS STICK RATE (deg/sec) E: up Ca.nd. Des i gn .68 9.08 Rate Command .69 15.69 * Air-to-Air Mode .69 24.02 (1 b/ sec) *This system developed for pilot input in force.
Table 5 Air-to-Air Control Law
Veh. Dynamics: x = Ax + BU
A = L~ + Mx + NO st
"A= JOEl
Control Law:
LOF!
.
~ = F~ + Gx + HOst
O. .5076 2.336
M = [.0007
L = [l. .1056J
OoJ
O. o.
-1. O. O. O. O.
N F = 1. O.
=
-l.
[-.9308 J .24 O. o. O.
(Note: All angles O. O.
-l.
in degrees, stick input in pounds), O.
G = 7.66 H -2.685
=
[ O.
O. O. O·l
7.67 O. -3.066 O. O. o.
O. .24 The aircraft dynamics will now be compared in terms of tracking errors and stick rates, eigenvalues and eigenvectors, time responses, and predicted pilot rating.
Model based predictions of "mission performance" are shown in Table 6.
Although the higher stick rates of the two comparison systems may be reduced with higher stick gains, it might be at the expense of higher track'i ng errors. It woul d then seem fair to state that the candi date design exhibits equivalent predicted tracking performance scores.
The eigenvalues of the three systems are compared in Figure 3, along with the IIdescription" of the mode shape from the eigenvectors of the systems. All the systems exhibit a relatively fast pitch rate (§) pole, with the candidate system's eigenvalue near -16. (l/sec) while the others are at -18. and -35. (l/sec), respectively.
Both the rate command and air-to-air systems have a real mode dominating angle of attack near -1. (l/sec), and the traditional phugoid pair near the origin dominating pitch and speed (or e and u). (The air-to-air mode also has three control system roots, one at -3.5 (l/sec) and two at -1. (l Isec. )) In definite contrast to these two systems, the candidate system has a single root at the origin associated with velocity perturbations u. Then a complex coupled mode is present near -.32:.. 4 j, that includes a significant amount of angle of attack a as well as attitude and velocity e and u. (the participation of this mode in the angle of attack will be clearly evident in the time histories shown later).
Clearly with a higher frequency and a significant a participation, this mode is not a conventional phugoid mode.
Now, consider the time responses to a step of one stick input unit, shown in Figures 4-8. The similarity between the rate command and air-to-air systems is evident, both clearly showing pitch rate command characteristics in the § and e responses, and nearly first order (a mode) response in angle of attack.
EIGENVALUE COMPARISON
~ COOPERATIVE CONTROL 3.
D RATE COMMAND
o AI R-AI R AFTI
2. IMAG COUPLED (jw) MODE (RAD/SEC) ~ .
.
e MODE
Ol MODE 0
FCS MODE (PLUS FCS) • .
·G8
5r-
-40. -30. -20.
-10. -3.
-4. -2.
U MODE (0") REAL (l/SEC) Figure 3
3.51 7 \
2.61 / \ Low AUTH.
0> Q) -0 1. 7 J -'" u co COMPARISON OF +-' +-' .::x:: '; .0.8 TIME RESPONSES - AOA Q) .- 0> C STEP INPUT .::x:: o.
HIGH AUTH.
Figure 4 -1.0 . 5 10 .
o.
. 50,..--------------, .8 .
0> .6 Q) 0> -0 Q) -0 s:::.
u -'" ctI PITCH~RATE U +-' ctI +-' .4 +-' .::x:: COMMAND +-' AFTI' AIR-AIR .::x:: 4- .25 4- Q) .- Q) 0> .2 .- c 0> .::x:: c .::x:: O.
-' \.!l 10 .
O. . 5 O.
Time (sees) O. 5. 10.
3.
Low AUTH.
COMPARISON OF TIME RESPONSES -- PITCH RATE .s::: U STEP INPUT +> HIGH AUTH, Figure 5 -1.
10.
5.
O.
.50 .8 ~------------~ ,6 u ~ OJ Vl ......
u PITCH-RATE COMMAND 0) OJ OJ Vl -c ......
.4 AFT!
AXR-AIR 0) OJ OJ -c +> .25 n:l a: OJ +> .s::: n:l u a: .2 +> .,...
.s::: e...
u +> .,...
e...
O.
N 10.
5.
O.
O.
10.
5.
Time (sec) O.
15·1
/
LOW AUTH,
12·1
0)
/
(jj -0 9.
COMPARISON OF Q) -0 ::l TIME RESPONSES -- ATTITUDE +l o~ +l +l c::( 6.
.£:: STEP INPUT U +l or- o...
3, Figure 6 f=·1 HiGH AUTH.
8.
4.
PITCH-RATE COMMAND 0) 6. AFTI AIR-AIR Q) ........
-0 0) Q) 3.
Q) -0 -0 :::l Q) +l -0 4.
:::l +l ...., +l c::( +l 2. ...., .£:: c::( U ...., .£:: 0... U 2.
+l 0...
1.
O.
N -' O. 5. 10.
O. 5. 10.
Time (sec)
LOW
AUTH.
1.5 ~"I.
-----.!-
t' -:: ,/
COMPARISON OF
1.0 ~ o HI GH AUTHORITY +> u
TIME RESPONSES -- ELEYATOR
Q) .- <t- Q) 0.5 o S- o STEP INPUT +> ttl > Q) o.
Figure 7 -0.5 O . 5. 10.
. 2 .4 O.
Ol Q)
--- Ol
Q) "0 "0 ~ ~ O.
-.2 +> u +> Q) u Q) COMMAND r- PITCH-RATE <t- .- Q) <t- AXR:"AIR
AFT!
Q) -,4 o s- -.4 s- 0 0 +> ttl +> > ttl Q) > ..- Q) l.W .- -,8 l.W -.6 -1.2 N N -.8 10.
O. 5.
5. 10.
Time (sec) LOW p:; /.
0) Q) COMPARISON OF -0
f="
HIGH AUTH, s::
IIME RESeQNSES -- ELAE
''- +' U Q) 4= Q) Cl STEP INPUT 0..
to r;:: .02 Figure 8 -.10 I , I O.
5. 10 .
. 2 .4 .1 .3 Ol Q)
--- Ol
-0 Q) -0 O.
s:: s:: .2 ''- 0 +' ''- u +' Q) u PITCH-RATE
AFT!
AIR-AIR
Q) 4= -.1 Q) 4= COMMAND Cl Q) .1 Cl 0..
to 0..
.- to LL.
.- LL.
-.2 O.
v..
'"
-.3
I I
-.1 j
O. . 5 10 .
,
I
O.
5. 10.
Time (sec) In constrast, we see that the candidate design exhibits charac- teristics similar to a lightly damped attitude command system in that the attitude response tends to a steady state value. Also note the oscillatory response in angle of attack. as mentioned in discussing the presence of a coupled (u, e, a) mode.
In this regard they nre neither like the AFT! air-to-air mode discussed here, nor the decoupled pitch pointing mode [3J that decouples attitude response from flight path response - but rather somewhere between these modes.
It is significant that in further application of this methodology, by allowing only pitch-rate and angle of attack feedback (instead of
a, 8, and e as in the above cases), the resulting pilot-optimal control
laws were similar to the rate-command systems presented here. In this
case (a and 8 feedback only) the 8 mode, referring to Figure 3, remained
near -16. (l/sec), but the angle of attack was dominated by a single pole at -0.6 (l/sec), and two phugoid roots appeared near the origin.
Therefore, these eigenvalue locations are very near those in the rate command and AFTI air-to-air systems (still referring to Fig. 3).
Likewise the time responses were similar to these two "rate-command" systems. Additionally, even with feedback of attitude angle not included. the tracking error only increased to 0.69 degrees while the stick rate increased slightly also to 9.4 deg./sec. (referring to Table 6). Therefore, it would appear that in the absence of attitude-angle for feedback, the optimum system dynamics for attitude tracking are like K/s, agreeing with well known results. However, if attitude feedback is allowed, significantly different dynamics are optimum for this pitch tracking task, but with only slightly improved track'ing errors, however.
Another closed-loop analysis method, the Neal-Smith criterion?
has been proposed to obtain pilot-rating predictions from frequency response characteristics of the pilot-aircraft system in pitch tracking tasks [llJ. In their work, Neal and Smith hypothesized that "pilot ratin9 is correlated with the pilot's compensation required to achieve good 'low frequency performance (good tracking) and the pilot/vehicle oscil'iation that resulted", In recent studies by Bacon and Schmidt [lOJ, the same approach was considered but with the use of the opti- mal control pilot model instead of a describing function modeling approach. Using this technique, a relationship was established between predicted pilot rating, pilot phase (lead or lag) compensation, and the resonance peak of the closed,-loop system transfer function, or It-I .
c max Based on the above, we compare the three configurations of inter- est in our research in terms of the Neal-Smith parameters, and results are given in Figure 9. Here, the levels of handling qualities are defined by __ CANDIDATE DES. <p=l.)
• . RATE COMMAND lag
Lead • AFTI AIR-AIR
_ 6 CO a
-
x ro _E4 u LEVEL 3 ~ 0'.:> + ..
LEVE l 2 LEV EL 1
o~----~~--------~------~--------~~---------------------- __ --~~_
-20 o 20 40 60 80 -40 100 Pi lot Compensation (deg) Figure 9 Neal-Smith Analysis Results Level = 1.0 3.5 Cooper-Harper Scale, good Level 2 = 3.5 6.5 Cooper-Harper Scale, fair Level 3 = 6.5 10.0 Cooper-Harper Scale, poor From Figure 9, all the confi9urations fall within the bounds of Level and therefore they are predicted to attain good handling qualities characteristics according to the Neal-Smith criterion.
V. SUMMARY Analytical evaluations have shown a favorable comparison between the simple augmentation system obtained and systems obtained using two alternate methods. The same level of tracking perfonnance is predicted for all the controllers, which are also predicted to be acceptable to the pilot in the task considered. It was noted that the augmented vehicle dynamics are Significantly different, showing the presence of nonconventional modes. This leads one to conjecture about the poten- tial of significantly different dynamics in future vehicle designs.
Finally, we note that the procedure resulted in a system that, at least for low frequencies, behaved like a pure gain plant (or 8(S)/ 8 (S) = K) while the other design approaches (and the proposed st method without 8 feedback) tended to lead to plant characteristics more like K/S. Which are ultimately optimum in the variety of tasks over the flight envelope for future vehicles are yet to be determined.
APPENDIX The equations of motion of the aircraft in state variable form were given for the flight condition of interest as (A.l) with -T ' x = [u, a. e,s] , Assuming the stick input to be proportional to commanded pitch rate, yields !:. •
o = e
st c The corrmanded signal is modeled then as a first order Markov process • 1 u -8 =--8 +l; (A.2) P - st 's st with: 's = .2 sec time constant related to the pilot dynamics l; = Gaussian random variable with zero mean and intensity a~ Augmenting (A.l) with (A.2), yields u + -* The optimal u is chosen such that the following index of per- formance is mi nimi zed " 1 (T .. 2 T J = E{llm ~ [(e-e ) + ~ F~ dt} c T-+<Xl 1 Jo F = fI sf a scalar I' Accord; ng to 1; nea r optimal control theory we have -* 1 T ,-~ "I (A. 4) u = - -f [B 0] pi; = [K l
[U;J
where P is the solution of the algebraic Riccati equation where Using (A.4) the augmented dynamics have the form or ACKNOWLEDGMENT This work was supported by the NASA Dryden Fl ight Research Facility, Ames Research Center under grant number NAG-4-l. This suppot't is gratefully apprec"iated.
REFERENCES 1. Schmidt, O.K., "Optimal Flight Control Synthesis via Pilot Modeling", AIAA Journal of Guidance and Control, July-August 1979.
2. Schmidt, O.K., and Innocenti, M., "pilot-Optimal Mu1tivariable Control Synthesis by Output Feedbackll, NASA CR-16312. July 1981.
Also submitted to the AIAA Journal of Guidance, Control and Dynami cs.
3. Anderson, D.C., Smith, K.L., and Watson, J.H., "AFTljF-16 Advanced Multimode Flight Control System Development Concepts and Oesign," AIAA paper 82-1571, presented at the 1982 Guidance and Control Conf., San Diego, CA, Aug., 1982.
4. Innocenti, M., "Cooperative Pilot-Optimal Augmentation System Synthesis for Complex Flight Vehicles", Ph.D. Thesis, Purdue University, West Lafayette, Indiana, December 1982.
5. Kleinman, O.R., Baron, S., and Levison, W.H., "An Optimal Control r~odel of Human Response", Parts I and II, Automatica, Vol. 6, pp. 357-383, 1970.
6. Schmidt, O.K., "~1ultivariable Closed Loop Control Analysis and Synthesis for Complex Flight Systems II , AGARD Flight Mechanics Panel Symposium on Combat Aircraft Manueverability, Florence, Italy. October 1981.
7. Hess, R.A., "Prediction of Pilot Opinion Ratings Using an Optimal Pilot Model ", Human Factors, 1977.
8. Schmi dt, D. K .• liOn the Use of the OCM's Quadrati c Objecti ve Function as a Pilot Rating r4etric", 17th Annual Conference on Manual Control, Los Angeles, CA., June 1981.
9. Prasad, S,N., "Design of Pilot-Optimal Control Systems for Air- to-Air Tracking", M.S. Thesis, Purdue University, West Lafayette, IN., 1980.
10. Bacon, B.J., and Schmidt, O.K., "A Modern Approach to Pilot/Vehicle Analysis and the Neal-Smith Criteria", AIAA Paper 82-1357, 9th Atmospheric Flight IvJechanics Conference, San Diego, CA., August 1982.
11. Neal, T.P., and Smith, R.E., "An In-Flight Investigation to Develop ll Control System Design Criteria for Figher Airplanes , AFFDL-TR- 70-74, Vol. I, 1970.
1.
Report No. 2. Government Accession No. 3. Recipient's Catalog No.
NASA CR-170411
I
4. Title and Subtitle 5. Report Date January 1984 Optimal Cc)operative Control Synthesis Applied to a 6. Performing Organization Code Control-Configured Aircraft 7. A.uthor(s) 8. Performing Organization Report No.
D. K. Schmidt and M. Innocenti 10. Work Unit No.
Performing Organization Name and Address 9.
and Astronautics School of Aeronautics 11. Contract or Grant No.
Purdue University NAG4-1 W. Laf ayet.te, Indiana 47907 13. Type of Report and Per i od Covered 12. Sponsoring Agency Name and Address .- Topical Contractor Report National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, D.C. 20546 RTOP 505-36-21 15. Supplementary Notes NASA Technical Monitor: Donald T. Berry, Ames Research Center, Dryden Fli ght Research Facility, E:dwards, CA 93523.
16. Abstract A multi variable control augmentation synthesis method is presented that is intended to enable the designer to directly optimize pilot opinion rating of the augmented system. The approach i.nvolves the simultaneous solution for the augmentation and predicted pilot's compensation via control techniques. In this paper, the methodology is applied to optimal the control law synthesis for a vehicle similar to the AFTI-F-16 control- configured aircraft. The resulting dynamics, eKpressed in terms of eigen- structure and time/frequency responses, are presented with analytical predictions of closed-loop tracking performance, pilot compensation, and other predictors of pilot acc)eptance.
.
17. Key Words (Suggested by Author(s)) 18. Distribution Statement Optimal control Unclassified-Unlimited Pilot in the loop Flying qualities STAR category 08 Price' Security Classif. (of this report) 20. Security Classi!. (of this page) 21. No. of Pages 19. 22.
Unclassified 33 A03 Unclassified "'For sale by the National Technical Information Service, Springfield, Virginia 22161.