Application of QFT to the Problem of Failed In-Flight Controllers During ...

NASA-CR-202410

Application Controllers

of QFT During

to the Problem

Approach

and

Hwei-Lan Daniel

of Failed

Landing

In-Flight

of a B-720

Aircraft

Chou

J. Biezad

Cal Poly State University San Luis Obispo, CA 93407 Abstract Previous

studies

the use of throttles extremely using

control

characteristics

shown

by increasing

but improving

system

and landing

qualities

study.

were

by piloted

Throttle-Only

QFT

Quantitative

simulation

Cmu

Flight

Velocity-pitch

is

Control Theory

developed

Sideslip-roll pitch

rate (deg/sec)

coupling

Flight

flights.

controller

(deg)

designers

(deg)

response

augmented

aircraft

has

for

fidelity

the use of

an alternative Feedback

for better

The QFT technique insights

it provides

for a range

simulator

of

are

and

to specify

it shows within

handling

qualities

closed-loop

control why

design

and to increase

its design

a desired

control

Theory(QFT)

damping

7 was chosen

throughout

with a desired

not be achieved limits.

control

B720 flight

control

Throttles-Only

has found

flight

the Dutch-roll

bandwidth

characteristic,

the given

because

of the

process.

It allows

frequency

bandwidth

the desired

and damping performance

control

to

actuation

may and

rate

ratio

stick input(full

Kq

pitch

rate

KT

flight

path

K_

sideslip

deflection=]

feedback angle

angle

unit)

gain feedback

feedback

gain gain

in this paper

angle

feedback

functions

gain

a QFT augmented

throttle-only

flight

path controller for approach and landing is presented. Complete details of the aircraft model and justification for TOFC are not included, but the reader is reminded that "trimming" exist.

transfer

based improve

angle

G, 2t

thrust

good pilot ratings by increasing the bare and phugoid damping. The primary is to present

pitch angle thrust fibs)

bank

on a high

generally Dutch-roll

(deg)

frequency

NASA

on Quantitative

bank

K,

1 -2.

emergency

technique

0

damping

(TOFC)

aim of this study

@

_c

a simulation

for Boeing-720

and their analyses for a variety of aircraft in the literature 3-6. This controller was

of sideslip

natural

engine controllability

airplanes, available

path

(deg)

some

feasiblcrfor

flight

09 I

application,

by NASA

Control

angle

Z

angle

derivative

manipulations,

in providing

throttles

further

C113

throttle

useful

on a particular

obtained airframe

rate derivative

q "r

found

implemented

Feedback

+ 0; 2

multiengine aircraft in emergency situations with severe or complete flight control system failures. This paper focuses

for approach

Notation TOFC

for s 2 ÷ 2Cras

of gravity

Introduction Through

and

very difficult. The pitch controller of no or moderate turbulence. The

evaluated

form

center

The

band width

control

short

c.g.

been

bandwidth

of the augmented

IC,_I

using to an

roll controller performed well in conditions of no turbulence, but is sensitive to moderate turbulence. Handling

form of (s+a)

control

open-loop

the control

short

for a large

the Boeing 720, is investigated Theory. Results are compared in a previous

(a) to be

Flight

safe landing

unsatisfactory

substantially proved robust in conditions

have

control

for landing.

developed

corrected

Dryden

flight

to achieve

airplane, Feedback

augmented

damping,

especially

the throttles

jet transport Quantitative controller

for emergency

difficult,

only

by NASA

must

Augmented

summary procedure

be possible control

and

design

"controllability'" using

fashion. The full justification may be found in Reference

must

QFT is presented and step by step 8.

in a

Flighlpath Angle P r e f il t e r

loop

Pitch

Compensation

Rate

feedback y(deg)

,Ss(+ 1 units)

/

Full Deflection Symmetric Throttle

/ .,/

y(deg)

Figure 1. Flight Path Angle Control Block Diagram with Inner

Bank Angle Prefilter

Loop

Sideslip Angle Feedback

Compensation

_, (uniLs)

Loop Closed

,Oi.(deg)l

G,(d_t _,. ("=_

go (deg)

fi_(__+1 units)

_o (deg)

Figure 2. Bank Angle Control Block Diagram B-720 Linear Model

engines

The empirical transfer function developed is given in short form notation by

with Inner

p¢#ormance for the

Loop Closed

Specification

QFT allows designers to specify a desired clo_-d It,_p frequency response with an upper bound Bu, a lower bound

BL, and a tolerance _5B specified

performance. The maximum desired system damping. Severe band width attenuation occurs beyond frecl,uencies of 1 rad/sec. For this application his prevented the increase the closed-loop bandwidth beyond 1 rad/sec within the range of available thrust (see Ref. 6). Four configuration variations for the 13--720were considered as described in the Appendix. They are characterized in both the longitudinal and lateral axes by excessive resonance, low phase and gain margins, low crossover frequency, and large phase angle roll-off. QFT Controller Design To apply QFT, the aircraft model is rearranged in a unit feedback form as shown in Figures 1 and 2. The inner pitch rate and sideslip loops were closed using Kq=60 and KI3 = 4. which were the settings for the original simulation augmentation scheme.

Mm

to obtain

robust

is also given to obtain a

Table l. QFT Performance

Specification

Freq.(r/s) Bu(d B) BL(dB)

0.1 17.0 16.8

0.3 17.0 -15.0

0.5 17.3 12.3

0.7 -I 6.0 4.6

1.0 -4.0 -12.4

2.0 20 7.1

3.0 - 13.0 -23.0

"'_R(dB)

0.2

2

5

8.4

8.4

9.1

15.0

specification

shown

The performance

in Table 1 are

the desired closed-loop responses for both the y - and _ loops. These two feedback loops are piloted open-loop systems. Additional specifications are ususallly given for piloted systems, such as a desired control bandwidth of 2 rad/sec. (see Ref. 9 for transport aircraft landing requirements) and a k/s slope near the crossover frequency. These added requirements promote good pilot handling qualities) °

Design

Constraints Four configurations

approach and landing summarized in Table 1 was used

were

as the nominal

Table

to study

confiuration

2. Flight

Weight fibs)

the

flight control Configuration

for control

Configurations (Gear

Conf

used

of B-720 throttle-only 2 and in the Appendix.

as

G r(d_)

A/S (Kts)

Flaps (%)

160

0 30

the Nichols

140,000

4,000

145

160,000

4,000

" 175

0

4,000

155

30

bounds

constraint

is a curve

tolerance system than

performance Chart

from Table

that shows

1 at each

guarantees

U contours

of the circle

of the

for each

for uncertainty

response will be

no less than

the damping

selected

for Minas

given

not

functions

can

be

reshape

consequently,

In this application, performance

due

more

specification

there is not enough compensation

will have

control

maximum

package

uncertainties,

some

in Figures

plant

limitation of them 3 and 4.

limits,

to provide

all the

of transfer

the uncertainty

template.

the designer

of handling

were

averaged.

loop

bends

Mode

Parameter

Gc.

Variation

Chart,

Lrer and

of the flight

path

functions

gain

be required'

from

raises

L_e_, the open-loop and bank

should

bends

forms

the

become

transfer

angle

function

and a pole

The compensation.selected

angle

feedback

functions loops,

'_'" _'6 _,." _ Ue_ L_. = 13, --e.

be kept on and above

the Bo(jcai), for each

to input

variations, These

frequency,

but

the quantity

of

variations

cot, on L_er and L_e_ to assure

performance. contour

L_e7 and

in order

application the controller outnumbering

L_e# must

to obtain

the additional poles).

robust

also not penetrate

the desired constraint

to be physically

to,

_ }' and 8 m

the transfer

to the right,

L_7=-er 13e" * GTe'.and

and

will

G ra,, and G ,0_ _ after reshaping,

respectively

where

transfer

the curve

to the left.

controller,

because

specifications.

parameter

4.33]

compensation

the Nichols

a zero

the curve

the

values

l I allows

and minimum

due to the software's

is required.

response

to meet

form

the

to be relaxed

and maximum

[_r%, and G/_,, e

The Qb"]"control

are listed

power

that is required

The minimum funclions,

compensation

to the engine

.93] (5.01)

Technique

the open-

curve,

restricted

4 Lateral

Poles/zeros/gain

wider

the more

3.651

.15] [24, .09 [.61,

Design

6 °/_m" On

constraints;

(5.02)

a

G _" and G ¢ the a_, pj_,

by the four configurations

variation,

1.07]

(z .03) J].0 , .20] [.29, 1.091(5.02)

Fil_re

expressed minimums and maximums. There are tradeoffs between plant parameter variations and performance. The the parameter

3.65]

.15] [.26,

.06 [.45,

=

Controller

variation

1) is:

of G_(_d_10 are:

(.98) [.60,

a.(d,_ max.

constraint.

parameter

configuration(config.

at high

frequency damping

transfer

Variation

(.98) [.81,

and max.

G_(d_._0

of M m,

the system's

For inner-loop

Parameter

.09 [.47,

=

Go(_J .8. (des) rain. =

Chart.

the U contour,

guaranteed

G#(_ei0 nominal ,0,. (dc_ and the rain.

frequency.

on the Nichols

the open-loop

1.57] (5.25)

3.01] .01] (5.19)

Mode

of the nominal

the

that has the magnitude

stretched

having

.111] [.441,

will be no greater

bound

are also shown

is a M-circle

frequencies._y

design

Satisfying

that the variation

is a performance

The U contour

penetrate

frequency.

(_R'

3.01]

r. 1'(dcg) _a,(dc_ are :

3. Longitudinal

The G #(dcD p,(4_J

on

]) ,s.

.01 (.28) [.46, 3.43] max. = (.58)[.45, 1.57] [.92, .14] (5.24)

Fil_ure

tolerance,

due to plant uncertainties

There

with part

the performance

specified

constraint response

_R.

Gr(dqO a,(_r,;

4,000

max.

[.624,

G_'(d_40 • .0053 (.162)[.35, e,,(_,) mm. = (.40)[.42, 1.48] [.66,

(MSL)

The

.01(.203)[.37, (.562)

Up)

confzguration(cunfig.

1=

and the rain. and

140,000

140,000

config.

design.

for B-720

Alt (Ft)

T,ne ,-,r(*_cs) oa,. (,_c_ of the nominal

damping. existed

realizable

the U In this

which

(zeros

not

required

Lateral Longitudinal

Flight

Path

Angle

Bank

Angle

Controller Transfer

Transfer Bo(]_),

and

Figure

function

U contour

5. Since

their

compensation contour then

contour.

G_am

Note

could

for example,

points

pulls

until

6(G_"

that

[_Y

Compensation satisfying

at any location

gain

the U

=16).

curve

81n

Pure

while

all the

curve

penetrate one zero

application,

the U contour. is physically

the compensator,

feedback

Chart.

G_ /3,, was not only

penetrated

loop,

bound,

hence

the system

The frequency function,

T r

the U contour.

G_: =