Helicopter mathematical models and control law development for

N88-16642 HELICOPTER

MATHEMATICAL FOR

Robert

T.

NASA

N.

MODELS

HANDLING

Chen,

J.

Ames

Research

U.S.

Army

Ames

Research

CONTROL

QUALITIES

Victor

B.

LAW

DEVELOPMENT

RESEARCH

Lebacqz,

Center, Mark

NASA

AND

and

Moffett

Edwin

Field,

W.

CA

hiken

94035

Tischler

Aeroflightdynamics Center,

Directorate

Moffett

Field,

CA

94035

SUMMARY

Progress

made

in joint

modeling,

design

parameter

identification

disciplines

is needed investigatins

permit

efficient for

acute

rotorcraft

for

and

generated expand

modeling

their

to modern

rotorcraft

flight

investigate

the

systems

combat

and paper via

for

time-domain describes contracts

range

design

along

laws

details

of

industry,

the

design

analysis

both

grants

the

Also with

that

rotorcraft

inhouse

of

used

digital

and

are

and

high-gain

in

flight

the

techniques, and

design

conducted

flight

applications

research

universities,

maneuvers

is a study

high-gain,

nonlinear models

frequency-domaln

are

reviewed

identification

for

to

classical

methodology

Parameter

the

linear

for

associated

rotorcraft.

generic

high-g

dynamic

rotorcraft

In

to

from

order in

addition,

to

flying

particularly

directions:

flight

ranginF

is

high

1-g

and

rotorcraft

research

from

control

developed

to

general

is reviewed.

approaches, results

two

flying

simulators,

research

The

interactive

conduct

of

complexity,

rotorcraft

these

to

in-flight

the

rotorcraft.

validity method

time-domain

control

for

flight-dynamics and

into

evaluation

requirements.

specific

of of

need

laws,

necessary

and

test

mathematical

utilization

A variety

approaches

flight The

their

rotorcraft

Research

tools

ground-based

mission

for

their

frequency

the

is pursued

paper.

analytical

compliance.

models

extend

systems.

both

of

concerning flight-control

in this

the

performing

demanding

nonlinear that

control

of

because

and

flight-dynamics models

using

specification

characteristics,

research

rotorcraft

is reviewed

means

qualities

for

to develop

qualities an

NASA/Army

methodologies

control

both are

other

frequency-

reviewed.

related

international

of to

The

efforts

collaborative

programs.

INTRODUCTION

This opment

of

qualities Research and

paper the

helicopter

research Center

parameter

provide

summarizes

using

(ARC}.

the math

models

both

the

The

identification

a capability

to

results

paper

of and

the

joint

also

the

and

discusses using

fidelity

837

NASA/Army

flight

ground-based

techniques

improve

the

the

laws

in-flight

the

flight of

control

efforts

test

data. models

of

at

state

These and

devel-

handling-

simulators

development

math

for

in the

Ames estimation

techniques

permit

an

efficient for

means

of

Efforts real-time

Army's

new

simpler laws

to

under

tion,

simulation

research

develop

a

evaluation

primarily

by

in

models

enhance

the

models

of

helicopter

flying

expressly

for of

UH-IH

developed

need

piloted

to

conduct

qualities

area.

military or

for

the

the

the

ground-based for

also

investigation

conduct

to

aerial

perform

NOE

combat.

In

research

use

1981,

on

the

computers.

these

Ames

analytical

ground

speed

To

stay

in addition

duction

of the

expanded number and

flight-dynamics

simulators

and

which

capacity,

within

level

of

of degrees fuel

at

typical

a reasonable

math that

of

models

time

the

were

had

Xerox

computational

freedom

the

fits

only

Sigma

cycle

were

also

used

as

and

To

provide

design

analyses

from to

or

for the

of

high-g

addi-

programs

using

mainly

a moderate

level

class

time,

of

the

digital

frequency

high-order

by

the

including models

ence of rotor bandwidth.

and

on

airframe

frequency

were other

used

an

of

control

in

the

of

the

investigation

and

models.

display

were

in

the

the

the

engine

level

control

of

system. for

the

used

to

exam-

operational of

turn.

This

coupling

turns

for

dynamics

888

new

that

flight

potential

of

the the

as and

of

linear

bene-

a new

models

were

procedure

was

simulates

analytical

characteristics

validity

analytical

model

single-rotor

extending

such

laws,

In particular,

a nonlinear

of

and

was

and

models

data

in

controls.

performance to

flight

intro-

{VMS)

for

with

simulation test

boundaries

effects

high-order

its

the

range

high-order

simulation

and

flight

moments

compatible

for

high-g

In addition

in the be

real-time

rotorcraft

the

to

the

models

and

near

of

With

included of freedom

Simulator

forces

a basis

from

direction

maneuvers

systems.

maneuvers,

expanded

the

the

Motion

flight-dynamics

Details

with

simulation

steep,

examine of

high-g

augmentation

helicopter

propulsion

linearization

uncoordinated,

significance

impact

nonlinear

permit

to systematically

the

validated

flight

nated

mis-

developed

dynamics.

Vertical

aerodynamic

expanded

characteristics

were

rigid-body

the

model.

for

integrating

developed

the the

also

of

generated

the to

full-flight-envelope

flight

They

were

simulation

systgem

helicopter

of

of of

in the

system

high-frequency,

envelopes.

6 DOF

dedicated

calculation

of

of

basic

machine

sophistication

control

aircraft/engine

the

the

7600

in the

sophistication

ine

to

a CDC

both

its

These

and

CH-47B

range of applicability of these simple models was somewhat limited. They at most the flapping-dynamics and the main rotor rotational-speed degrees

1982,

at

control

aircraft.

computational

(DOF),

the

directed

of

variable-stability

in-flight

for

airworthiness

were

helicopters

to and

support

and

Efforts

in

suitable

requirements

operations

VSTOLAND

to

model

use

conditions

the

flight-dynamics

qualities

terminal

capability

for

were

(NOE)

the

weather

the

handling

nap-of-the-Earth

math

helicopter

generic

helicopter

operations

night/adverse

Until for

to

the

of

civil

sions

test

motivated

doctrine for

display

two

1975

to determine

developing

the

in

simulation

standards

flight

compliance.

began

simulation

of

conducting

specification

a coordi-

procedure

was

in high-g

helciopters,

used

turns,

and

the

stability-and-controllinear the

rotor

model linear

and

flight

on helicopter

inflow

from

1-g

flight

model

was

also

dynamics.

investigation

of

to

These the

flight-control-system

influ-

Several

methods

have

been used

to design

handling-qualities investigations. were used in the design of control characteristics mission tasks. applied

helicopter

flight

control

laws

Early on, classical frequency-domaln laws to provide a variety of control

for

methods response

for experimental determination of their suitability for various Time-domain, linear quadratic regulator theory was subsequently

to the design

of a high

performance

stabliity-and-controi-augmentation

system for a hingeless rotor helicopter to be used for piloted evaiuatlon on a ground-based simulator. The linear quadratic regulator (LQR)-based, low-order compensation method developed at Stanford University was applied to the design of a hover hold system for the CH-47 research helicopter and was evaluated in flight on that aircraft. An optimal cooperatlve-control synthesis method developed originally for fixed-wing

aircraft

at Purdue

University

which

includes

an optimal

pilot

model

in the design procedure, was extended and applied to a CH-47 helicopter and was evaluated in a piloted ground-based simulation. In collaboration with industry, advanced control laws were developed for the Advanced Digital/Optical (ADOCS) demonstrator helicopter based on single-axis model-following cepts. A multivariable model-following control system was developed variable-stability

CH-47B

addition,

associated

problems

to enhance with

its in-flight

the design

and

simulation

Control System control confor the

capability.

implementation

In

of high-bandwidth

digital control systems for combat rotorcraft were investigated in order to reduce the cost and time involved in control system modifications or redesigns often required

during

the flight

It is essential analyses

test phase

of a development

that the mathematical

and syntheses

of flight

control

models

program.

for real time simulations

laws be evaluated

based

or for

on comparison

with

flight test data. To determine how well a simulation model represents the real rotorcraft, the trim characteristics and the response-time histories from flight tests must be compared with those predicted from the model. If the comparison between the test and the calculated data is clearly unacceptable, the correlation must

be improved.

This can be achieved

through

the use of parameter

identification

techniques. The development of parameter identification techniques suitable for rotorcraft application has also been an active area of research at ARC; these techniques have used both time- and frequency-domain approaches. In the following sections, the results of both the In-house research and the related efforts via contracts to industry, grants to universities, and international collaborative

programs

REAL-TIME

The development

are described.

FLIGHT

DYNAMICS

of rotorcraft

MATHEMATICAL

flight dynamics

MODELS

FOR ROTORCRAFT

math models

at ARC has been

prompted primarily by the need for real-time, piloted ground-based simulation. The complexity of a rotorcraft math model for real-time, pilOt-in-the-loop simulation depends

on the purpose

may be conveniently representing

for which the model

classified

the dynamics

using

is to be used.

the two major

of the rotorcraft

839

factors:

The math

model

(I) levels

complexity

of detail

and (2) levels of sophistication

in

in

calculating The

the

first

range

of

range

of

two

ware,

software,

and a

in

implies

simple

Models

lope.

such

However,

for

simulations The

dom.

These

the

rigid-body

interaction is

and

The generic

no

can

are

most

involving

math

model and

Efforts

began

that

at

the

use

freedom

that

time

Sigma

cycle

time

model

was

rotor

rotational

(2)

tail

and

(6)

The ally

(on

of

the

order

rotor, control

The I-3) (3)

main

of

overall

rotor and

It

The

model summed

the

be

of

of

of

the

therefore, for

control,

free-

those

the

it

simula-

inclusion

required. along

the

two

generic

general

directions:

speed within

frequency

range

only

of

fuselage, elements forces,

rigid

the

I.

simulation model

(5)

blades

capacity,

typical

of and

the

6 DOF

the

rigid-

model,

of

which are:

is (I)

engine-dynamics-and-rpm

moments

with using

in

from

rotor

figure one

forces

essentially

the

the

dynamics

elements

Ti

of

computational

applicability

basic

for

simulators

reasonable

of

the

denoted and

and a

model

ground-based

flapping

to

The

azimuth,

84O

the

flight-dynamic

on

stay

in addition

the

investi-

regard

However,

feedback

flight

than

mode;

studies.

the

degrees

with

enve-

stall, and be included in

frequency

mode

investigations

(4)

about

higher

dynamic

simplified

model

assumes

of

are

inflow

of

flight

edges

rotorcraft and

and

stall.

Models

included

in figure

velocities,

the

the

of

linear

inflow,

or

of

to

rpm,

term

and

investigations

regions

much

pursued

To

arrangement

empennage,

of

a

freedom,

is shown

systems.

transfer

integrated

limited.

degrees

flapping

compressibility

specific

computational

ms),

of

levels

rotorcraft.

computers. 40

The

high-gain

been

specific

moderate

of

hard-

simula-

dynamics.

flapping-regressing

also

simulation

only

computer

rotor

lag, of

the

of

to develop

digital

necessarily

(refs.

to achieve another.

had

class

dynamics.

"ARMCOP"

1975

pilot-in-the-loop

second

rotorcraft.

differing

simulation

may

has

for

pilot-in-the-loop

Xerox

body

in

the

The

the

for

exploratory

of

Generic

exploratory

of

reflect

of

rotor

is

dynamics

development models

time.

simulation

exploration

generally

modes

in flight

of

cycle

for

limited

flap,

important

rigid-body

degrees

systems. frequency

simulation,

envelope

angles

for

characteristics

modes

included

the

the effects of compressibility, Also, nonlinear effects must

dynamic

models

used

involving

rotor

The

rotor

of

models

and small

within

include

the

models these

as

be

nature

modes

other

math

in generic studies must be included.

modes.

the

terms

real-time

flight

consideration

dynamic

with

in a

requirements

such

investigations

investigations

lag

with

the

for

in

permissible

aerodynamics

rotor

generally

tion of

the

a generic

whenever

model

in the

applications,

simplifications of

maximum

the

simplications

envelope, then even other nonlinearities the

the

validity

rotorcraft

representing

qualities

gated.

of

theory

especially

the

techniques.

specific

strip

with

handling

of

of

computation

dictate

list

on

aerodynamics of

sets

programming

I shows

Depending

moments,

digital

domain

together

completeness

use

validity

For

the

factors

Table tions.

and

the

interest

determines

These

forces

determines

applicability.

frequency factor

rotorcraft

factor

main

called main

rotor,

governor, I are

axis

and linear

required

sytem

moments

to

radi-

aerodynamics

as discussed earlier. primary Lock

design

number,

rotor

and

without

a general

curve

are

fit

for

it uses

a

large

model

inputs

from

has the

provides

addition,

curve

for

mechanical

expanded low

to

have

the

include

altitude,

flight

on

rotor

inflow

loads

for

tables

solve

for

attack,

the

and

inflow

effects

momentum

fluctuation the

and

inflow

For

theory

for

an

experimentally

by

vortex

represented

by

in

the

the

functions

simulator has

low

of

low-speed,

in the

form

as

of

angle

of

of the

derived

including and

hub

of

state,

downwash angle

of

a set

downwash

by

speed,

a uniform-plus-

given

and

been

of

vortex-ring

induced

are

effect

induced

value

The

a linear-

proximity,

steady

derived

In

and

effects

data

ground

accepts

analysis

assuming

are

heli-

inputs.

model

The

tunnel

flight

as

7).

uses ±15 °,

augmentation,

piloted

The

and

of

The

which

cyclic

permit

results of

2,

stability

aerodynamic

wind

shedding.

sideslip.

control

5).

6,

model

range

turbulence,

obtained

The

replacing

with

were

the

was

descending by

to

The

aerodynamic sideslip

the

teetering

dynamics. limits

figure

and

4,

(refs.

functions

caused

fluctuations

of

by using

as

steep

model

(refs.

some

of

stability

coefficients.

modeled

phasing

this

downwash

then

in and

a

blade

stall

or

atmospheric

flight

coefficients

were

effect

thrust

model

the

airspeed.

aerodynamic from

main

or

to

of

descending

attack

shown

to be

between

and

the

offset,

plane

fuselage

of

as

model,

operations

representation

slope

augmentation

model

steeply

first-harmonic

system,

made

tip-path

attack

angle

mixing

and

low-altitude

to

been

engine-out

of

contain

hinge

is assumed

the

The

angle

control

dynamic

improvements of

control

control

rotor

attack.

large

engine/governor

ized six-degree-of-freedom included. Some

of at

facilitates

a simplified

investigations

fit

tail

lift-curve

a nominal

a generalized pilot,

a

explicitly

restraint,

including

with

angles

over

simplified

The

without

modeled

representation

copter

and

and

of motion

flapping-hinge

coupling.

pitch

aerodynamics

and

namely:

pitch-flap

cyclic

empennage

a detailed

The flapping equations

parameters,

a

thrust-

magnitude

attack

of

and

airspeed. This

model

has

ground-simulator (ref.

8),

been

for

helicopter

terminal

area

simulate

other

(refs.

research

within

improvements

air

extensively

the

representation

tasks

and

combat The

model

model

in

I0),

for

operations

also

and

been

civil

modified

qualities and

through

the

and

for

(refs.

to expand

analyses

qualities

industry,

sought

design

handling

handling

proximity

details

9,

has

for

been

in ground

dynamics

(refs.

agencies, have

in experimental

helicopter

helicopters

government

namic

of

11-13).

specific

of of

used

investigations

and

in

the

grants

in

14-_6)

frequency

for

NOE

configured control

the

flight

university. the of

in

and/or

to

Continuing

areas

research

range

operations

of

in

NOE

aerodymission

applicability

of

the

model. A simpler model

for

tion

at

to be low

ARC

opponent

(ref.

relatively

speeds,

lers.

the

generic

The

aerodynamic

and model

9).

model

(called

(red)

helicopter

Because

simple. in

forward

uses

Even

of so,

flight,

quasi-static

representation,

but

"TMAN") in

was the

computer

developed

first

capacity

is capable

of

and

is easy

to fly

it also

stability uses

841

the

use

as

the

simulation

was

required

helicopter-air-combat limits,

it

linear

for

the

realistic with

and

complete

a

model

simula-

maneuvers simple

control

set

drivatives

nonlinear

at

hover,

of

controlfor

kinematic

its and

of

gravitational terms. Whenconfigured for the simulation of the red helicopter, it had the following specific characteristics: an attitude commandsystem for pitch and roll at hover and for low-speed flight; and an altitude-rate commandand a yawrate commandsystem in the vertical and directional axes, respectively. In forward flight, the pitch and roll axes were transformed into angular rate commandsystems while the directional axis provided an automatic-turn-coordination feature. The model is very easy to modify to achieve other desired stability-and-control response characteristics, and as such it was used extensively as both the blue and red helicopters in the subsequent helicopter air-combat simulations (ref. 17). In addition, it is currently being used in helicopter human-factors laboratory experiments and simulations.

Specific

Rotorcraft

Math Models

Several flight-dynamics models for specific rotorcraft have also been developed in-house or jointly with the manufacturers. Someof these were developed by modifying the generic ARMCOP model described earlier. Other models such as UH-IH, CH-47B, UH-60, AH-64A, and XV-15 were developed separately. These math models are briefly described below. UH-60 UH-60

ARMCOP-

Black

The

Hawk

helicopter

tor

investigations

and

a Navy-sponsored

Hawk

(ref.

of

20).

the

fuselage

The

Army

copter

and

Flight

following the ated

on

large

of

system other

the

show The

the

tics tems.

of

two

(fig.

7a)

(fig.

7b),

collective

was

was

aircraft the

configured

since rate

its limit

rotor

these

helicopter. the

rpm

allowable

the

of

for

the

842

generic

in flight

$3

of

control model

have

the

helicopter

which well

the

two

and

have

as

in

helicopter reference

actuator in

the

21 s.

sysARMCOP

dynamics

impact

(ref.

In

evalu-

characteris-

governor

strong

Heli-

helicopter

dynamic

resident

and a

first

6 from

the

model-

V/STOLAND

flight

of

research.

was as

UH-IH

model

program

models

3 through

engine

represen-

under

system

their

limits

BO-IO5

the

the

dynamic

BO-105's and

using

use

systems

In

a

a multivariable

helicopter

a

UH-60

and

of

the

rotor,

data,

research

19)

Sea

incorporate

(DFVLR),

NASA/Army

(ref. SH-60

tail

for

simulate

specifics

dynamics

joint

simula-

actuator.

to

characteristics

actuating to

a

the

piloted

the

canted

test

Figures

simple-engine

to simulate

two

is the

a

of

helicopters

pitch-bias

(MOU),

control

$3

the

of

for

using

modified

Establishment

using

of

Army

of

UH-60

part

developed

configured

and

As

used

implemented

performance

and

generic

dynamics

the Ames

and

the

been

at

systems

model

effects

Understanding

dynamics One

control

In addition,

has

for

simulation

landings

wind-tunnel

Research

MFCS,

BO-IO5

and

the

been

significantly

ARMCOP-

of

simulator

DFVLR

ARMCOP

these

the

actuators.

typical

generic

(MFCS)

in flight

the

$3

Aerospace

system

a ground-based

and

governor

has

systems

the

extensive

Memorandum

developing

differences

control

and

was

allow

shipboard

included

upon

BO-I05

German

Controls

control

process

of

stabilator,

to

model

control

model

based engine

This

flight

fuselage

and

the

18).

modified

simulation

horizontal

the UH-60 in ARMCOP.

was

modifications

ARMCOP

UH-IH/VSTOLAND U.S.

(ref.

advanced

aerodynamics,

tation of available

model

piloted

variable-incidence addition,

ARMCOP

21).

on

the

AI09 being

ARMCOP-

Under

configured

Efforts from

have

the

include model

to

been

AIO9K the

and

made

tests

part

(ref.

the

of

23).

conducted

with forces

a

full

160 knots.

quently, of

and

the

certain

requirements data

were

upon

input

and

(ref.

data

to

using

magnitude

and

UH-IH ically

rotor

the

use

uses

classical

tions

of

the

CH-47B real-time grams

for

use

Sigma

rotors

tail

the

the

uses

solutions in

externally

which

A model

dynamics

as

the

were

of

The

certain

of

the

OH-58D

and

and

moment

aircraft

model

was

nonlinear of

well

investigation

model

that

as

Subse-

24).

functions

small

conditions

force

of

of

to

problems

representation

terms

for

-40

(ref.

control

as

valid

simulator

System

aerody-

a function

of

trim

manufacturer. and

The

of

first-order as

range

aerodynamic

modeled

developed

equations and

a simulation

required

was

manufacturer.

directional

rotor,

the

this

fuselage, to

the

ground-based

developed

based

further

yaw-damping

relative

wind

by

it

total-force for

model.

suspended

rotor The

27)

and

and and

approach flapping

slung-load

for

moments

developed

simulation

a

simulator system

of

specif-

terminal-area

investigation

(ref.

representation

simple

model,

28).

for

of

The

similar

expressions

this

Vertol (ref. with

30).

model

to

the

that

of

contribu-

an

developed

in-flight

It

is

the

of motion.

time

DOF;

basis

has

for

This

of

been in

the

adapted

30

ARC msec.

tip-path

simulation

simulation

model

in

pro-

the

about

steady-state

for

use

nonlinear

implemented

cycle

option

29)

for

research

This

(ref.

rigid-body

includes

843

the

company

form

was

helicopter.

a digital

in six

equations

model

to support research

dynamics also

for

was

empennage.

Boeing

facility

and

and

uses

UNCLE

is operated

helicopter

augmentation

CH-47B

the

model

UH-IH

It has been used in simulations for the and guidance programs associated with an

simulations

simulation where

(ref.

forces

variable-stability

a

a Bell

stability

type,

Similar

ARC

of

investigations

V/STOLAND of

main-rotor

Model-

IX computer

model

plane

and

22)

simulation

Control

ARMCOP

ARC.

defined

the

data

efforts

AI09

terms.

values

form

is

requirements

a piloted

generate

ARMCOP

Army

for

degree-of-freedom

Bailey-Wheatley

model in

by

tasks (ref. 26). for the navigation

failures

piloted

using

simulation

The

known

of

a quasi-static,

the

RPM

the

the

the

at

inertial

a

test

Current

in

(ref.

airspeed

in

of

case,

an

Back-Up

to

off-line the

Model-

in flight

system

effects

AH-64

Italy.

VMS

model

flight

degree-of-freedom

supplied basis

the

display

allowed

ARMCOP

helicopter.

direction.

guidance and navigation development of software avionics

the

employed

effects

("UNCLE")

for

the

an by

control-sensitivity

as

this

and

and

for data

were

the

trajectory

model

moment

in

reference

reference

investigation In

supplied

include

and

was

25).

generated

a

the

conditions

used

a simulator

as

with

helicopter

six

the

AI09

inclusion

on

system of

particular

of

technique

for

modified

was

Apache

Italy,

Agusta

1986

for

gravitational

drivatives

model

of

SCAS

consisted

expressed

force

control

same

A similar

control

about

characteristics

helicopter

AH-64

its

flight

Aerodynamic

stability

spring

and

an

model

simulation

the

This

level

the

of

nonlinear

Army of

ARMCOP

digital

of

expansion

from

AI09

a piloted

are

airspeed.

perturbations as

of

U.S.

dynamics

the

AI09

initially

set

series

longitudinal

for

moments

the

flight

during

the

A model

and

a Taylor

of

model

between

the

investigation

The

namic

MOU

correlate

preparation

an

motion

of

to

development

AH-64A/OH-58Das

the

simulate

option,

of

the

of along

with

detailed slung-load equations of motion developed in-house (ref. 31}, will expedite research in areas related to sling-load operations. The CH-47Bmodel has been used in conjunction with flight research conducted on the CH-47Bresearch helicopter to develop a multivariable model-following control system (ref. 32) and to verify, in-flight, a control-system-design method using modern control theory (ref. 33). These research activities related to the control laws development are further discussed later in the paper. UH-60

(GENHEL)-

validation, from

a

ate

were

digital CDC

of

computer,

which

main

rotor

element

model

model,

for

speed Black

Hawk

from

lagging,

rather

than

the

has

CDC

been

drive

7600

computer

improved

train

modeling.

by

the

Black

basis trois

Hawk

accident

Other cific

Rotorcraft

rotorcraft

to NASA

the

than

as

from

In

35),

ref.

35

of

on

the

Also

for

VMS.

It

flight

and

available

real-time

at

ARC

simulation

flight

rules

models

described

flight

dynamics

extensive

in the

airworthiness

criteria

previously and

has

high-order

Traditionally,

(refs.

steady, 42,

qualities

the

43)

have

been

specifications

control-augmentation

41).

been

used

the

basis

(refs.

system

1-g for

44-47),

(SCAS)

for

of

the

to

be

stability design

rotorcraft.

844

of of

the

representaconduct

serves

as

speof

of

VTOL with

the

air-

instrument some

of

other

high-g

next.

DYNAMICS

as

motion

the

and

for

reference

control

analyses However,

small-disturbances flight

analyses, of

a

con-

several

phase

discussed

and

SH-3G (ref. 38), The XV-15 simula-

of

along

model

engine

a variety

investigations

airplane

flight

and

model,

in

FLIGHT

equations

rectilinear

development

investigation The

effects

PERTURBATION

standard

symmetrical,

(ref.

also

the

simulator

dynamic

SMALL

from

use

ground

covers

propulsion

are

during

utilized

it

also

in

the

small-angle in real time

diagram

to

in addition

such,

The as

is a blade

This improved highmodel has been used to

integrating

Models-

a block

of

a

well

It

area

tion

been

as

fidelity

in the

shows

interactions. simulation

investigations

developed

addition,

notably

SH-2F (ref. 37), one for for the XV-15 (ref. 40).

has

on

DOF.

and

a moder-

class

computer.

DOF

a math model for and a math model

model,

only

Sigma

a Sigma

rigid-body

model,

VMS).

acquired previously,

implementation

projects. They include one for RSRA (ref. 39),

craft,

was

had

Xerox

hub-rotational-speed

(ref.

benefits

models

for

six

Hawk

simulator

discussed

which the

machine

includes

and their real-time

Mathematical

math

Black

sideslip, and inflow, without using computer code was written to execute

simulation

to investigate potential (refs. 36, 70).

as

intended

ground-based

models

simulators (such

powerful

and

for

UH-60

other

force-and-moment

8 taken

tion of the simulation elements frequency, full flight-envelope,

was

mass,

(dedicated

Figure

ground

the

the

capability

more

total

considerably

use

on

program

for

all

Sikorsky

air

a

model

model

the full range of angles of attack, assumptions. From this model, the on

Army/NASA

Unlike

and

is a much

acquired

flapping,

joint

34).

expressly the

a

simulation

computational

GENHEL

of

(ref.

computers),

7600

UH-60

Aircraft

developed

level

part

blade-element

Sikorsky

which

As

the

modern

condition handling-

stability-andmilitary

rotorcraft are now being designed with a view toward expanding their roles in tactical missions such as combat rescue, antitank, and air-to-air operations that require high-g maneuvers that make frequent excursions to the limits of their maneuvering flight envelopes. Therefore, a new analytical framework is needed to permit a systematic examination of the flight dynamics and control characteristics of the basic aircraft and its SCASto ensure that the overall aircraft-SCAS system will perform satisfactorily, not only in operations near 1-g flight but also in high-g maneuvers. A fundamental characteristic associated with a rotorcraft with increasing load factor in high-g maneuvers is an increase in control effectiveness and damping, particularly in the pitch and roll axes. The extent of the increase depends, to a large measure, on the main rotor hub design. For a teetering-rotor helicopter, the control in pitch and roll is almost entirely through tilting the thrust vector of the main rotor; therefore, the increase in control effectiveness in these two axes is directly proportional to the load factor. At the other extreme, for a hingeless rotor the increase is much less because the direct hub moment, which produces most of the control power, is independent of the thrust level of the rotor system. The increase in the control effectiveness with the load factor has an obvious effect on the selection of the SCAS. Further, interaxis cross-coupling, such as pitch, roll, and yaw, that results from collective inputs and pitch-roll coupling which results from aircraft angular rates, also changes with load factor. The ramifications of these variations in stability-and-control characteristics for the handling qualities and the design of SCAsneeded to be considered. In addition to this extension of the linear model to high-g maneuvers, the frequency range of validity of the linear model must also be expanded for the design analysis of high-gain FCSsfor rotorcraft to meet the requirements for demanding mission tasks such as NOEflight and aerial combat. In the design analysis of such high-gain control systems, it is now essential that high-order dynamics of the system components be adequately modeled, in contrast to past practice in which only the lower-frequency, quasi-static, rigid-body flight dynamics were used in the design of low-gain FCSs. Recent flight investigations that used a variablestability CH-47Bresearch helicopter at ARCshowed that not only high-order elements such as rotor dynamics are required (refs. 48, 49, 32), but also other high-order effects such as dynamics of sensor filters, servo actuators, and data processing delays of the airborne computer must also be adequately modeled. Inclusion of the air-mass dynamics associated with a lifting rotor has also been shown in recent studies (refs. 49, 51) to be important in the design of highgain FCSs. The frequencies of the inflow dynamic modesare the sameorder of magnitude as those of the rotor blade flapping and lead-lag modes; therefore, the dynamic inflow has a significant influence on the aeromechanic stability of the rotor system. In the following sections, we will first discuss the linearization of the rotorcraft motion about a curved flightpath as a reference flight conditions, followed by a discussion of the high-order dynamics.

845

I

•

Linearization

of

Small-perturbation result

in a set

of

to operate

chosen

be a steady

to

motion

will

those

be

from

commonly

applied,

steady

Algorithms of

I) aircraft

2)

the

exists

been

these

(ref.

55).

of The

a study

several

results motions

for

helicopters,

single-rotor

flight

dynamics,

and

small-disturbance that

degraded

in steep,

and

turns

are

operations, to reduce

dynamic

computation

nated

turning

ordinated linear

magnitude aircraft table

decouple

1-g Once

about

the

bations inertial,

the

steep,

coupling

in

turn

has

is designed steady,

a

on

high-g

near

basis and

dynamic

and

lat-

turns,

significant

straight,

in operations

and

turns

longitudinal

the

normally

previously.

static

high-g

in coordinated,

of

from

of

levels

trim

level

and

governing

2)

influence of

that on

standard

level

I g becomes

direction

of

of

symmetric

flight

and

significantly

set

(ref.

positions of

trim

steep

for

a

in

general, for

an

general

uncoordinated

are

represented

extent

effi-

uncoordi-

and

steady,

the

steep

algorith_

permit

by

the

the in the

uncoordinated comparable

uncorecti-

ny (side force) at relationships shown

general, (to

to

algorithms

uncoordination

computation

the

56)

in a

turns

accelerometer signal closed-form kinematic

trim

rotorcraft

uncoordination,

extended

control

the

equations

the

was

uncoordinated

of the lateral gravity. The

simplify

and

2 gives

both

and

direction

turns

states

Table

asymmetric

and

coordinated

the

steady,

reference

equations operation

the the

motion

discussed the

these

which

turn

to

and

the

flight).

perturbation relate

the

greatly

perturbation

set

The

that

sideslip

and

flight.

including

and sign center of

thereby normal

by

maneuver.

flight.

strong

turns

such as in aerial combat, turns may intentionally be flown the turn radius. To investigate the extent to which the

for of

flight

of

as

are

computations

steep

In developing of

to

condition

first.

efficient

investigate

coordinated,

similar

operations

steady,

motion.

of

flight

established permit

is is

equations

perturbation

turns to

generally

equations,

be

will

flightpath

reference

influence

rotorcraft

SCAS

which

reference

the

that

of

the

direction

characteristics

expressly

cient

for

the

in coordinated

conducted in

equations

52-54)

to

I) that

an

flightpath

as

in coordinated

satisfactorily

turning

influenced

developed

that

performs

For some uncoordinated static

3)

curved

must

equations

the

equations

otherwise

(refs.

was

exists

a generic

Before

conditions

rotorcraft

eral-directional

43).

given

indicate

Turns

if

flight

positions

rotorcraft

algorithms,

characteristics

42,

flight

was

High-g

differential

1-g

refs.

control

Steady

small-perturbation

time-invariant

attention

in asymmetrical

Using

resultant

small-perturbation

special

about

However,

the

developed

and

About

differential

rectilinear

reference

have

associated

algorithms,

then

(e.g.,

states

motion

interpret.

linear

steady

employed

the

to

turn, of

of

Motion

time-varying

and

a set

obtained

most

equations

linear

difficult

Rotorcraft

time

rate

body-axis

are

from

and

of acceleration

motion

on

the

of

a steady

are

Euler

change

system,

aerodynamic

flight

of

and turn.

of 2)

by

and

then

This

Table

and

imposing

the

3 shows

846

two on

determined,

steps: the

the

a simpler

to

for

angular that

complete

terms form

small-

applying

of

the

equations

the

constraints

accounts aerodynamic

the

I) by

kinematic

roll-attitudes

development Also,

are

in

equations pitch-

coupling.

derivatives.

conditiolns obtained

the

pertur-

kinematic,

include the

that rates

a

complete

stability

and

control matrices in which the acceleration derivatives are neglected. The equations are given with respect to the general body-axis system and they are cast in the first-order, vector matrix format to which manyefficient software packages can be readily adapted. These equations were implemented in conjunction with the trim algorithms for generic uncoordinated, steep high-g turns in a variety of nonlinear simulation models (refs. I, 34, 40) to investigate a tilt-rotor aircraft and two single-rotor helicopters in various levels of uncoordinated, high-g turning maneuvers at low speeds. The results show I) that the aircraft trim attitudes in uncoordinated, high-g turns can be grossly altered from those for coordinated turns; and 2) that within the moderate range of uncoordinated flight (side-force ny up to ±O.1 g), the dynamic stability of the rotorcraft is relatively insensitive. However, the coupling between the longitudinaland lateral-directional motions is strong, and it becomessomewhatstronger as the sideslip increases (ref. 57). The results of a recent study conducted in a European laboratory (ref. 58) generally confirmed those of ARC. In particular, their results also indicate that in high-g turns, the coupling between the longitudinal and lateral-directional motions is strong. Consequently, the conventional short-period approximation and other approximations (ref. 59) suitable for rectilinear cruise flight become inadequate for predicting stability and response characteristics of the helicopter in high-g turns. As in the Amesstudies (refs. 55, 57), their results for turns also show that all the helicopter stability and control derivatives change with load factor (or bank angle). The variations in these derivatives are caused by aerodynamic, inertial, kinematic, and gravitational terms, but it is primarily the increased aerodynamic terms that have the most influence on the short-term dynamic modes.

Considerations for High-Order Dynamics The increasing use of highly augmenteddigital FCSs in modern military helicopters has prompted a recent examination at Amesof the influence of rotor dynamics and other high-order dynamics on control-system performance. In the past, industry has predicted stability augmentation gains that could not be achieved in flight (ref. 60, fig. 9). The operators of variable-stability research helicopters have also been aware of severe limitations in feedback gain settings when attempting to increase the bandwidth of FCSsneeded to assure good fidelity during in-flight simulations. Now, with an increasing emphasis on high-bandwidth mission tasks, such as NOEflight and aerial combat for military helicopters, coupled with the development of new rotor systems and the trend toward using superaugmented, high-gain, digital FCSs(refs. 19, 61, 62), there is a widespread need for improved understanding of these limitations. Therefore, a study was conducted at ARCto correlate theoretical predictions of feedback gain limits in the roll axis with experimental test data obtained from the variable-stability CH-47Bresearch helicopter. The feedback gains, the break frequency of the presampling sensor filter, and the computational frame time of the 847

flight

computer

theoretical

and

dynamics, usable

were

experimental

sensor

values

filter,

of

the

In addition in

the

design

dynamic same

order

motion.

A study inflow

hover.

Linearized

and

on

Fridovich

rated

in

68)

and

the

of

the

and

the

and

other

by

models

and

blade

number

(ref.

Lock

linear

dynamic

mode.

duced

the

by

also the

shows

that

destabilized

dynamic

inflow,

acceleration

response

becomes

pronounced

more

Pitt

rotor-body

of the

flapping

inflow

to an as

were

flapping

abrupt

in a input

either

the

motion

along initial

the

in

the

thrust

coefficient

effects

the

of

67),

were

Carpenter

incorpoin

a good

in

by

variations

thrust

correlation

transient and helicopter.

frequency The

in destabilizing

the

inflow

the

mode

in

pitch. or

of

helicopter

overshoot

collective

of

developed

role

with

on

are

rotorcraft

the

In addition,

key

63-67)

modes

modes;

of

for

significant

lead-lag

(ref.

large

also

modes

Peters

mode,

the

the

one

a

flapping

limit

and

models,

plays

rotor

(refs.

investigate

analysis, and the variable-stability

inflow

be

dynamic

in

compared

49).

linear CH-47B

results

and

can

flapping

vertical

the

severely

research

changes to

excellent

gains.

inflow

blade

Ames

dynamic

was obtained between the results responses measured in-flight on analysis

rotor

can

dynamics

the

showed

that

delays

Recent of

significant

flapping two

indicate

inflow

at

which

feedback

rotorcraft.

conducted

of

10),

processing

frequencies

produce

therefore

results,

roll-attitude

for

those can

versions

(ref.

{fig.

dynamics,

the

rotor-blade

simplified

coefficient

as

inflow was

dynamic

FCSs that

magnitude

dynamic

and

flapping

shown

The

digital-data

roll-rate rotor

varied.

correlation

and

high-gain

has

of

therefore,

to

of

inflow

systematically

the

This blade

the

intro-

vertical overshoot

Lock

number

is

reduced. The system

influence

of

the

design

for

a helicopter

(ref.

69)

under

Curtiss attitude

feedback

gain

ics

Beyond

the

system

dynamics

and

is

lightly

damped

fuel-control dynamic

rotor/airframe icists that

have are

flight-test modifications propulsion the ref.

airframe

can

lag

degrees

the

of

when

opposite

approach. design

a helicopter

dynamics

the at

in the

rather

freedom.

An

rotor

the

levels

design

of

and

effect and

are

within

the

drive the

a

can

of

70).

848

the

surface

program,

Therefore,

both

system.

result,

it

fuel

train

bandwidth

the

propul-

flight

dynam-

have

of

the

engine

a sophisticated for

the

later

to

dynamproblems

ground-

costly

compatible system

flight

interface

in the

important

engine

helicopter

Helicopter

control

rate

verifica-

systems

requiring is

that

the

helicopter

dynamic

sophistication the

but

dynamics,

use model

by

showed

experimental

inflow

on

rotor

control

stage

He

of

manufacturers

As

analytically

flight. coupling,

development

problems.

hover

rudimentary

the

automatic-control-

body-flap

which engine

a

the

by

a profound

designing

in the

to rectify

dynamics

with

on

investigated

near

by

helicopter modes

freedom

been

for

caused

have The

dynamic

anticipated

system

grant

Traditionally,

dynamics

phases

recently

effects

in conjunction

of

primarily

the

also

torsional

used

not

by

qualities.

system.

model

has

limited

high-order

handling

degrees

a NASA-ARC

feedback gain is limited tion is needed.

sion

lead-lag

or

add-on

model

the

with

those

of

FCS

(see

and

the

FLIGHTCONTROL LAWSDEVELOPMENT

A variety of methods have been used to design rotorcraft flight control laws for handling qualities investigations. They range from classical frequency-domain design methods to modern time-domain control methodology. Classical frequencydomain methods were first used in the design of control laws to provide a wide spectrum of control response characteristics for experimental determination of their suitability for various mission tasks. These designs were performed mostly in the continuous (or analog) s-domain. To expose potential problems associated with digital implementation, especially for high bandwidth digital control systems, an extensive case study based on the ADOCS was conducted in a discrete z-domain and w-domain. Modern methods for time-domain control law design were subsequently employed in several case studies. Lienar quadratic regulator theory was applied to the design of a high-performance SCASfor a hingeless rotor helicopter for piloted evaluation on a ground-based simulator. An LQR-based, low-order compensator method was applied to the design of a hover hold system for the CH-47 research helicopter as part of the collaborative efforts with Stanford University. An optimal cooperative controllaw-synthesis method, which includes an optimal pilot model in the design procedure, was modified and applied to a tandem-rotor helicopter and was evaluated in a piloted ground-based simulation. A multivariable MFCSwas developed for the variablestability CH-47Bresearch helicopter to enhance its in-flight simulation capability. Generic Control Laws for Various Types of ResponseCharacteristics Generic FCSswhich can be configured to provide a variety of helicopter response characteristics including rate and attitude were implemented in the basic ARMCOP model (ref. I) and the ARMCOP/UH-60 model (ref. 18) for handling qualities research. The general form of the SCASthat was incorporated in the ARMCOP model employs a complete state feedback as well as a control mixing structure that facilitates implementation of control crossfeed, with control quickening from each of the four cockpit control inputs. Also, the augmentation-system gains may be programmed as functions of flight parameters, such as airspeed (fig. 2). This constant-galn configuration was subsequently modified (ref. 20) to include dynamic compensation elements in order to represent the SH-6OBfor the handlibng qualities investigation of its shipboard operations. A more complicated implementation of the generic FCSwas incorporated in the ARMCOP/UH-60 for the development of the Army's ADOCS. As part of the ADOCS program, control laws suitable for an attack helicopter mission were synthesized, evaluated in piloted simulations of both visual (ref. 71) and instrument flights (ref. 72) under various meteorological conditions, and implemented in a UH-60 demonstrator helicopter. Figure 11 presents a block diagram of the FCSdesign for the ADOCS program. The primary flight control system (PFCS) shown in the figure was designed to yield satisfactory unaugmentedflight by providing feed-forward command

849

augmentation

and

stabilization tion

feedback

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of

of

system

to

designs

method

was

knowledge

determining

models,

develop

process

test

CCS

helicopter

indicate

and

for

IDENTIFICATION

motion

from of

Two

a CH-47

frequency-domain

identification

simulation

While of

of

Parameter

rotorcraft

of

is derived

more

difficult

is a

equations

application

frequency-domain

simulation

criteria),

identification set

system

dynamics.

PARAMETER

eters

augmentation modified

flight

classical

design

the was

method

methods)

piloted

with

with

design

classical

fixed-base

favorably

favorably

This

case

record, modes,

responses,

short

param-

if

can the

and the

with

Early efforts were madeby the Army and NASAin the development of advanced time-domain techniques for rotorcraft state estimation and parameter identification (refs. 83, 84), in attempts to overcome someof the difficulties described previously. Considerable efforts were subsequently devoted to the development of frequency-domain techniques (refs. 85-87), thereby providing a better perspective from which to assess the two approaches, and leading toward the development of a unified time- and frequency-domain parameter identification methodology for rotorcraft in the future. Time-Domain Parameter Identification First applications of time-domain (digital) parameter identification techniques to rotorcraft by NASAand the Army at Langley and elsewhere employed a measurement error method--Newton Raphson(ref. 88) and a simpler advanced method using the Extended Kalman Filter algorithm (refs. 89, 90). Typical procedures of using these two parameter identification methods are shown schematically in figure 23 (ref. 91). Both methods include the initial step of using a digital filter to process the raw flight data to reduce the data noise content. Applications have been made to the identification of quasi-static, rigid-body stability-and-control derivatives of single-rotor helicopters and a tandem-rotor helicopter. Both methods give a gross underestimation of primary derivatives such as roll, pitch, and yaw damping; it is not uncommonfor positive values of the damping derivatives to be identified using the quasi-static rigid-body model. If the lower-order model is used, large fitting errors in someresponse variables (e.g., vertical acceleration) are also apparent (fig. 24). The then-available identification software and the lack of measurementsof the rotor blade motion have limited those applications to the identification of only the rigid-body quasi-static stability-and-control derivatives without considering the effects of rotor dynamics and other high-order effects discussed in the earlier sections. In addition to adequate modeling of the vehicle/rotor system, two other areas must be addressed to accurately identify the stability-and-control parameters: (I) instrumentation and measurementdata analysis and (2) test input design. A joint Army/NASAprogram involving both Amesand Langley was therefore initiated in 1976 with the aim of developing a comprehensive advanced technique for rotorcraft state estimation and parameter identification, which addressed all aspects of problems peculiar to rotorcraft. The techniques developed by a contractor (ref. 84) are illustrated in figure 25. Applications of someof these techniques have been made to the Rotor System Research Aircraft (refs. 92, 93) and to the Pumahelicopter (ref. 94) under a NASA/UK(Royal Aircraft Establish) collaboration. As part of an ongoing US/GermanMOUon helicopter flight control, an extensive joint study is being conducted to analyze the XV-15 database using both time domain and frequency domain techniques. The objectives of this study are to gain a better appreciation for the relative strengths and weaknessesof those two different approaches and to develop improved methods of identification for rotorcraft. The time domain approach used by the DFVLRof the Federal Republic of Germany(FRG)

855

(refs.

95,

analysis eter

96)

is shown

blocks

shown

identification

tional

in

figure

the

The

with

this

26.

figure

described

algorithms.

conjunction

in

in

are

25,

domain

effort

shown

in figure extraction

27.

lateral-stick are

shown

ure

28(c).

in

figure

condition

so

likely

smooth (3)

input

that

the

stay

the

and

format: These

can

These

used

nonparametric

obtained

from

discrepancies

in

characteristics plots

with

ric

models

and

for

the may

assumed that

terms.

Since

extracted,

for

effects. inputs

The

tion

was

transfer

for

of

the

transfer

transfer

extracted

time-domain

function

identification

helicopter.

1983

open-loop

and

of

completed

dynamics

of

The

trim dynamics forms

frequency based

on

range. the

responses

between

in Bode-plot

vs.

frequency

has

been

selected

(fig.

27).

assumed.

As

directly

expose

limitations functions

with and

modal

frequency-response

The

results

are

paramet-

frequency

the the

studies

equivalent-system

carefully

with

those

and

control-system-design

includes

such,

testing.

compared

the

are

and

presented

lower-order be

driven

fig-

identifica-

wave

response

selected

frequency-response

to avoid

methods

important

is an

are

coupling

flight-test-control

characteristics. procedure

single-rotor The

in

behaved;

desired

is

XV-15

used.

the

output

identified

after

can

which are

response

Identification in

in

is completed

matrix

are

aircraft

well

function.

given

models

a BelI-214-ST

research

the

procedure

and

transfer

the

Multiinput/multioutput a

the

to

transfer-function-based

specifications

the

model.

be

Approximate fitting

extracting

initiated

document

also

of

Frequency-Domain

and

can

by

useful

input

simulations

models.

the

the

shown

about

methods

structure

models

aircraft,

tandem-rotor

results

and

86}

for

of

handling-qualities-compliance

obtained

frequency-domain

tilt-rotor

model

85,

concatenated,

tests

inputs

the

are

the

be

order

verify

to

or

in

inputs

response

are

frequency results

(refs.

typical,

flight

input

employs

no

nonreal-time

the

approach

design

paramcomputa-

Army

frequency-domain

over

output

since FCS

simulator

fitting

Finally, to

and

qualities

overparameterized suitable

for

also

this

the

the

and

U.S.

ARC

symmetric

constant

analytical

are

handling

of

the

functions

high-resolution

identification

real-time

(2)

at

rate

excessive

spectral

ARC

to

not

identification

nonparametric directly

roll

is roughly

range;

the

hover

suited

is generally

phase

the

well

are

the

Two

computer-generated,

motions

data

in detailed

frequency-sweep

than

linear

The

and

using

corresponding

resulting

extract

developed

during

form

estimation

by

verification.

wave

analysis,

to

are

be

the

the

pairs.

magnitude

the

aircraft

spectral

output

the

rather

autospectrum

results

they

model

(I)

so

z-transform

input

generated

for

with

within

regular,

input

For Chirp

are

is especially

because:

to

and

the

28(a)

and

Identification

approach

completed

state

different

employed

Parameter

data

sweeps

the

analysis

next.

inputs

Pilot-generated,

procedure

are

step

frequency

frequency-sweep tion

Flight

and

to

approach

frequency-domain-identification

model

compatibility

although

is discussed

Frequency-Domain The

data

similar

figure

frequency

MOU

The

results the in the

856

has

been

helicopter, are

XV-151986. XV-15

briefly The The

from

applied

to an

and

NASA/Army

the

described

objectives tests

CH-47B

below.

frequency-domain

flight

XV-15

were for

identificato

identify

several

operating conditions including hover, to compare response characteristics for identifying problem develop system detail

a validated

transfer-function

model

studies. The results for hovering in references 86 and 85.

the aircraft and simulation areas in the math modeling,

description

flight

for future

and cruise

flight

and to

use in controlare reported

Figure 29 shows an example of a comparison of the frequency responses, extracted from flight and simulator data, of the open-loop roll rate response lateral

control

input in hovering

flight.

The correlation

to

of the VMS simulation

the flight data which indicates

is quite good for the frequency range from 1.0 to 10.0 rad/sec, that the roll-response control effectiveness is accurately mod-

eled.

considerable

However,

low-frequency-magnitude the damping ratio tion model (i.e., dentally, during

these

response.

of the unstable more unstable),

low-frequency

the pilot's

Subsequent

discrepancies

analysis

The low-frequency

in the math

phase

model

comparison

and

for the

suggests

that

roll mode is slightly overestimated by the simulawhereas the natural frequency is accurate. Inci-

errors

qualitative

are apparent

in

in the simulation

evaluation

of the real-time

model

were also

reported

on the simulator. math model

indicated

problems

in the

representation of rotor flapping for large lateral-velocity changes (such as the case of the low frequency range of the roll response). There is also strong sensitivity of the numerically linearized transfer functions to the size of perturbation. Corrections to the math modeling in these two areas were included later in the nonreal-time XV-15 simulation. The comparison between the current nonreal-time model,

real-time

significant

model,

improvements

and the flight achieved

data

during

is shown

in figure

29, and indicates

the

the last 3 years.

Having completed the extraction of the frequency responses, the next step is to fit the frequency response with a transfer-function model. A standard fourth-order model with an effective time-delay term was chosen (ref. 86) as the structure of the model for identification of its attendant parameters. Figure 30 shows a fit of the magnitude and phase of the identified transfer function. The predictive capability of the transfer-function model is illustrated in figure 31, which shows the rollrate response of the open-loop aircraft to a step aileron input. When the identified transfer function is driven with the same input, the response coplotted in the dashed curve is obtained, which shows the model and flight data responses generally compare

very

well, and thus provides

Demonstration

a validation

of Frequency-Sweep

Testing

for the identified

Technique

Using

a Bell

model. 214-ST

Helicop:

ter- Research supporting the development of the LHX-handling-qualities specification ADS-33 (ref. 97), which is an updated version of MIL-H-8501A, indicates the need for frequency-domain

descriptions

to adequately

characterize

the transient

angular-

response dynamics of highly augmented combat rotorcraft. The proposed LHX criteria for short-term angular response are given in terms of two frequency-domain parameters--bandwidth (mBW) and phase delay directly from frequency response plots

(Tp). These quantities are determined of the on-axis angular responses to control

inputs, such as was generated from the XV-15 (fig. 29). A key concern in incorporating such descriptions in a specification is the practical problem of extracting frequency

responses

from flight

data

for compliance

857

testing.

To

address

this

frequency-sweep hours)

was

(fig. (90

32).

the

each

frequency

shown

for

the

hover

over

compliance

ducted

to

flight

domain

of

craft

to

the

(ref.

for

The

correlation

response

frequency

study

of

and

(ref.

fied

49).

the

to

therefore

flight the

to

the

for

each

cyclic

the

axis.

As

stick

spectral

and

of

conditions.

accurate

and

Model

identification vertical work

required

analyses

These

an

is

estimate

is

specifi-

were

models

con-

accurately

validate

the

linearized

in Hover-

The

same

of

dynamics was

developed

to

the of

two

the

identify

from

all

data

the

frequency-

aircraft

CH-47B

the

was

also

research

helicopter

analytical

a means

models.

These responses in figure

frequency vertical

range

the

air-

vertical

modeling

efforts

the As

of

acceleration

corresponds

fits

range

of

0.1

to

for

the

frequency

than

the

(ref.

the

compare identified

applicability, owing

to

capability

in collective

favorably

expected,

models the

with are

identiquasi-

flapping

and

caused

and

by

inflow varia-

a fourth-order

model,

instead

it proved

range;

of

0.1

first-order

the

to

20

model

models

as

to

fit

rad/sec

to match

(fig.

characteristic

completely

high-order

858

of

input those

plotted

first-order

fails the

the

34).

All

predicted

in

49).

predictive

input

of

to

parametric

classical

higher-order phase

of

the

frequency

the

around analytical

fit

effects

fre-

extracted

the

series

a fitst-

3 rad/sec

a nonminimum

in

the

at

was

effects

entire

low

The peak

quasi-static

causes

exhibit

to

possible

first-order over

a

order

the

This

a step

of

model

for

identify

input.

resonant

efforts,

fifth

includes

to

predicted

to

models.

testing

35.

modeling

accurately

efforts

responses

previously

to account

the

is a

other

at

modeling

For

employed

first

model

used

model

to

to

from

first-order

there

as

analytical

34.

models

for

the

lead

were

to collective

that

frequency-response

the

better

responses

the

the

of

higher-order

As

The

in figure fit

phase

was

pitch

acceleration

indicates

fourth-order

limited

analytical

shown

flight

Additional

cruise

frequency-

helicopters.

collective

ranging

The

rpm).

shown

difficult

applied

on

fifth-order

rotor

are

34)

models,

vertical

of

longitudinal

behavior

Dynamics

this

those

vertical

Based

and

(the

in

model

the

plots.

model,

dynamics

the

of

in

a substantial

frequency

static

of

the

both

rad/sec),

and

the

identification

to

obtained.

models

in the of

with

(fig.

transfer-function

as

used

inputs

response

rad/sec

was

(0.2-10.0

in hover

at

An

flight

helicopter

using

Excellent

33.

(6

using

50).

quency

be

analyzed

in figure

Vertical

objective

Frequency-sweep

tion

was

performed

then

single-rotor

identification

in hover.

dynamics

for

program

were

axes

of

BelI-214-ST

were

attitude

response

practicality

tests

all

readily

step

CH-47B

that

for

the

instrumented

previously.

pitch

function

with

demonstration

an

data

range

are

concept

procedure

applied

frequency

transfer

Identification

of

condition

large-amplitude

frequency-response

The

achieved

parameters

identify

the

flight-test using

described

response

a broad

cation

predict

was

associated

step-input

axis.

procedure

extracted

a 1985

and

control

responses

the

achieved

17

technique,

Frequency-sweep for

concerns

in October

identification

example,

other

testing

conducted

knots)

domain

and

of

effects

identified generated

the

with

because

predict of

models, from

analytical

together

models, to

the

were

inflow

of

the

model.

flight the

data

Some as

limited

overshoot

and

the

the

flapping

of

the

dynamics. does the

The fourth-order first-order model

model provides for the initial

a much better transient.

CONCLUDING

This ing

paper

has

rotorcraft

parameter tion

handling the

pilot

research

a

for

required

rotorcraft

characteristics, that have been are

currently

of

required

is probably

acute

dynamic results

for

implications

in performing

made

research

a variety

of

mission.

Although

all

of

way

to

design

than

concern-

require

aimed

at

integrated

aircraft,

atten-

the

approach

need

complexity,

controls,

the

assisting to

is particu-

high-order

requirements. Accordingly, basis for combined research

dynamics,

and

experimentally

concepts this

of

all

and

mathematical

integrate

research

methodologies,

disciplines

dynamic

classes

their

NASA/Army

analytically

and demanding mission reviewed here form the

under

joint

control

exploring

for

because

in

flight

interactive

a basis

capability

REMARKS

progress

modeling,

These

to provide

qualities

the

which

the

identification.

in order

larly

reviewed

flight-dynamics

predictive

and

the efforts

identification

methodologies. The here. led

need

for

As was

to a capability

disk ate

and

more

for

which

the

types

require

simplicity

for

greater

high-g tion the

of

To

design

and

must

It

their

is also must

The of

model-following

models

that

are

dynamics

have

of

showed

that

details

an

and

existing

that

the

into

paper

are

the

joint

work

explicitly

to

and that

higher

important,

achievable

do

reviewed early

been

process,

suited for

here

the

developed

control

terms,

in the

aerodynamic

frequencies the

been

rotorcraft practices

has

in

account

control

system

859

the

that

and

models

the

be

improved

performance

design for

and the

remains

of

influlower-

order

regardless modern the has

itself

of

control high-

utilized

control

control

as

developed

higher

demonstrated

implementation

sufficiently

data

the

selection

for

for

design

flight

process,

accurate

identifica-

procedures

these

of

adequate

paper

parameter using

rotor

missions

effects

must

in

dynamics;

rotorcraft

the

has

appropri-

retaining

importance

(inflow)

digital-control-system not

for

to assessing

design

to achieve system

overlooked

extended important

described

basis

demonstrated also

been

frequency-domain

rational

for

have

while the

models

full-flight-envelope

modeling the

for

experiments

accurate

excellently

a

dynamics

work

higher-order

the

providing

historically

current

the

be

the

modes

reviewed

initially

must

Further, the

more

particular,

this

from

accurate

Equally

review

of

system

performance. that

for

and

flight

rotor

purposes.

work

simulation

models

include

elastic

envelope;

basis

In

or

the

modes, These

but

to

of

real-time

flapping

to date,

lag

importance

be accounted

origin.

as

integrated

in

clear

such

most

on

models.

performance

flight

standard.

dynamics

applications gain,

be

blade

considered

the

the

from

research

element

simulation

the

forms

discussed

ence of these order models.

dynamics

and

the

rigid

blade

freedom

of

ascertain

verification NASA

including using

missions

regions

techniques

is apparent

paper,

pilot-aircraft of

maneuvering

tools.

in the

of

more

degrees

over

integration

recently

additional

at

this

reviewed

system adds

designs;

the

implementation digital far

design

less

than

was

predicted.

Therefore,

inevitably

pointed

frequency

ranges

effects,

and,

oriented

in

The

among be

the

craft.

be

The the

combat

need

and for

and

modeling

limiting shown,

a

perform modeling integrate past

and

closer

control,

design

for

that

and

in

the

methodologies

the

with

past

10 yr

accurate

a variety

research

a

has

As

the

has

over

of

become

all

procedures

technologies

that

of of

of

higher

interactive increasingly

higher previous

capable have

work

of been

dealing initiated

10 years.

86O

with in

the

be

considered

integrated

and

envelope

in this

techniques is

these

stems

stability/control

control,

goal

may

improvements

must

include

and

hence

rotor-

air-to-air

requisite

presented

The

and the

as

is

interaction

rotorcraft

such

bandwidth

knowledge

of

elements

harmonic

elements.

the

the

elements

controls

more

systems,

missions

achieve

high

and

and

details of

interactive such

existing these

actual

details

To

control,

transfer,

extension of

of

dynamics gains

rotorcraft

rotorcraft

process;

review

the

to the

flight.

state

flight higher

to the

variety

design

of

coupled

demanding

rotor

even

dynamics coupling

on

energy

rotorcraft

require

closely

control

integration

the

conducted

explicitly paper,

nap-of-the-Earth

cueing.

and

models

this

various

emphasis

considerable the

the more

rotor-rpm

and

in

maneuverability,

flight/propulsion augmentation,

work

dealing

research

this

automated

in agility

for

of

concepts

becoming

increasing

and

in the

NASA/Army

controls

to

need

the

direction.

to examining

said

from

the

capable

demonstrated

this

current

oriented

to and

as

in general,

to

new

joint

paper

is

required

provide problems, research

has to

systematic and of

to

the

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tan

_I

nz +

cos

0

cos

_ +

tan

_z(sln

cos

L + Iyz(q

2

6 cos

O sin

¢ -

8(cos

a cos

0 cos

B sin

O

+ cos

sin

6 cos

0

cos

¢)

= 0

sin

_

sln

9)

= 0

B cos

e

sin

@)

= 0

@ +

a cos

-

r 2)

+

Ixzpq

-

Ixyr

p +

(ly

-

Iz)qr

_

lyzp

q +

(i z

_

Ix)r

p _

Ixzq

r

(i x

_

Iy)pq

M +

Ixz(r2

-

p2)

+

ixyqr

N +

Ixy(p2

-

q2)

+

iyzr

+

= 0

p

= 0

-

0

-tan-1 ) =

-+ tan-Z

-

L

cos

y

+

j

right

n 2

m

turn;

n 2

"b

n 2

'4" n 2

y

z

x Kinematic

q -

- left

turn

relationships

_ sin2@z{

-

(sin

y sin

8 + ny

cotan2@l

) 2

±

_sin

q

+ _z

tan

p!

B.

m

-

y

sin

B +

ny

tan

8

(sin2y

q

a

-

r w sin

r

= pt

sin

a

+

r t

e

=

¢

= tan-Z(q/r)

Euler

Straight

n

equations

-

sin

0

cotan

'1z/2_ ¢z)J

-

n

0

+

cos

cos

0

cos

@ -

0

0

sin

_

-

0

L "

M -

N -

0

p-q-r-O

sin a(sin

+ Z

relationships

{cos

n;

Flight

ny

,,, sin -z

+

COS

X

0

cos28

(-p/_)

Uncoordinated

Kinematic

-

_

cos

Steady-state

1 sinZ_ z

cos

p = p t

Steady

2 -

?ny

sin I cos 8

sin -z

cotan2_z)

y

8)

+ sin

a[cosZB

- ny

C08

[_2z_'

870

-

sin2y

+

n

(2

sin

B sin

y,

A STEADY,

TABLE

3.- SMALL-PERTURBATION EQUATIONS FLIGHT (ACCELERATION x =

Xu -

- -

zu + .........

iI

Xw

r

....

qo

I0

" qo

Xq

r

-

Fx

+

(6u,

6w,

_

(A6 e,

6q,

60;

6v,

6p,

6¢,

TURNING

6r) T

Gu

I t

wo

.........

-8

cos

A6 c,

_6 a, a6p) T

I I

_o

_.........

, Zq + u o L .........

zw

_

OF MOTION OF AIRCRAFT FROM STEADY DERIVATIVES NEGLECTED)

xv

Xp

+ r o

, -g cos i .........

¢o

sin

%1

II

.......

I..... zv -

Zp -

Po

0

tI

T ......... t "g

v o

Xr

+ VO

I ....... sin

¢o

cos

%

t

zr

{..... I

I x.._z

mp mu

.

mw

mq

0

Iy

2po

+

mr

2re

(I x -r°

(I x

Iz) -Po

I

r i

F "' ..... Yu " .... ttU .... 0 .... n_

re

.... O

r l

l r

....

, _

' L

Yw + ....

J'

Po

.......... Yq

' L ......... +

I'

_'q

r ,

......... Sir ¢o tan

L

....

L

.........

I J

nl

tlPo

i -g sin ' ..............

¢o

c2r°

It

0

00

*.............. I _o sec 0 o

-

sin

t3Po

tlro

-

t -T O cos 0o i I ......................

r .......

0ol

Yv

' Yp + i .......

t'v

I'

_'P +

r --,

0

we

txqo " l

--

-

_. v

0

, , XSc

X6e --'1-

, #

-

z6 e f z6 c I --J--L-.J--I , m6c

m6e --

0

Xi

YI ;

"_"

T "

m6a

! , m6P

,

--

0

I

_-

Y6e

jI y6c

_

1 _ 0

' i

, ng e

!I

' J

T

,

I-

,

n6 c ,

i -

,0_ EOOR

;_ Y6p

_

L .

_ 0

' !

i

I"

n6 a

_ 0

,

, n6p_

u,

v,

w;

p,

q,

r;

6e,

6c'

_a'

_p

= TY I

I

xz Ni

IxI

z

-

I 2 XZ

Lt

+

LI

+

I

I

I I ni

I x

tl

m

•

I:z(l

z I

2 xz

I xz -

I

-I

X z

12 xz

+

I X Z

I

Ix -

-

12 XZ

I},)

I

x -

X z

12 xz

;

t_

-

I ,

nv r

"

0

k--

Y6 a

_1_ 0

-

Zl

! t£

0

_,r

ZSp

,

0

-L

Ni

m

z(z - _y)+ IX_ _ IxI

-

871

I xz 1

• I

I -I X _

ue

t2-oq

-, ........ , cos 0 0 tan

-

,

Mi :i

I! -

0

-_- ; z_ --_

Yi

"

' ........

where

xi

Yr , ........

I _

t3q o

O0

%

1--r--T'O

G m

-

z8 a

I t

ie

cos

-sin

, x8 ,

xsa

-r

¢o

L .........

_! P -

I w

, 8 cos I .........

r ....... _

L .......

!i

I z)

Y

0

I -- --I......

' ..............

.

q

I..... I 0

, ,

.... 0 nt w

i......... , 0

¢o

r , I ,

t'W

......... cos

I

Y .... 0

#

0

mv

z XZ

QUALi't_

tlq°

_o

PILOT-_STABILIT COMMAND / STATE__J VECTOR1

Y

AND CONTROL AUG

t

MAIN ROTOR FLAPPING DYNAMICS

RIGGING, AND CONTROL PHASING I1 GEARING,

TAIL ROTOR F LAPPING EQS. STATE VECTOR

WIND AND TURB.

H

H

AND MOMENTS FORCES

H

AND MOMENTS FORCES _DEG OF FREEDOM RIGID BODY EQNS. OF MOTION

HORIZ. STAB. FORCES

TIVE WIND RELA-

VECTOR STATE

VERT FIN FORCES

FUSELAGE FORCES AND MOMENTS

ROTOR

rpm

COMMAND

GOVERr_

/

ROTOR___ r_ _

Figure

_I

NOR

I.-

Block

diagram

showing

DYNAMICS ENGINE

principal model.

872

elements

I

of

single

ROT. DEG OF ROTOR FREEDOM

rotor

_1_

ROTOR rpm

helicopter

+_Xo 6ap_

_ap --[_

"p-f_ 6p,,_,_

,,. p-IN-" [O,.ECT,O._. _e

_. _ _ ) L,_'_C

j_CONTROL CYCL.C _.C'_CO_ TR OC CO. "2S. "O_

.o._,TOO,..,c_c.,cco.T.O.-""o :2o'_,c"_,_s "''COLLECTIVE

'°,-E_+

CONTROL

=

GEARING

.,oo,.o

_

_ep--__

CROSS-FEED FEED FORWARD

AIRCRAFT

E.x

,_XoXo

AND GAINS

Figure

II

2.-

FEEDBACK

Structure

GAINS

of

873

control

X = (u, w, o, 0, v, p, ¢, r) T

system

model.

LVDT'S

I

t

(2 PLCS) "_i

SERIES SERVOS

t

(PITCH(2 AND PLCS)ROLL)

SAFETY STICK

I

1

I

j_J

CONTROL STOPS

RESEARCH STICK FORCE ,' SENSOR

PITCH PARALLEL SERVO

ROLL DISCONNECT LINK

PITCH DISCONNECT LINK

ROLL SAFETY BUNGEE ROLL PARALLEL SERVO RESEARCH MAGNETIC BRAKE (PITCH)

Figure

3.-

UH-IH

PITCH AND ROLL ;ITION SENSORS

V/STOLAND

control

PITCH SAFETY BUNGEE

RESEARCH MAGNETIC BRAKE (ROLL)

(PITCH

system

BUNGEES AND ROLL)

longitudinal

874

and

lateral

cyclic

controls.

PILOT'S

INPUT

(S c AND Sp ONLY)

COMMANDEE MODEL

SERIES

SERVO

_CONTROL

CONTROL FOLLOWINGIINPUTS SYSTEM

v_ ±/

2 + 105.6S + 5685.01

J PARALLEL

Figure

4.-

+

POSITION RATE AND' F LIMITS

Simulated

SERVO

UH-IH

V/STOLAND

875

actuating

system.

TO BASE HELICOPTER

BASIC CONTROL SYSTEM

SWASH PLATE

co., .OO o.sT .

SAFETY-PI

LOT

FORCE

1

SUPERVISORY SYSTEM

r

ENGAGE DISENGAGE FLY-BY-WIRE CONTROL SYSTEM

I .I

] CONTROLS SIMULATION-PI

I

LOT

LIMITER

CONTROL FORCE SIMULATION

POTENTIOMETER

Figure

5.-

B0-I05

$3

876

control

system.

I

COMMANDED CONTROL

MODEL FOLLOWING CONTROL SYSTEM

TO BASE HELICOPTER

ACTUATORS 2526.6 INPUTS

_ I S2 + 95.5S + 2526,6

POSITION LIMITS RATE AND

._

=1

Figure

6.-

Simulated

B0-I05

$3

actuator

dynamics.

THROTTLE

(MAIN

AND TAIL

(ON/OFF) QE°

REQUIRED) ROTOR TORQUE

1 1 + Tts

' GOVERNORI

"1

G (s)

| ENGINE I KE

550 wf

! (a)

_C

QR

AW.

GOVERNOR G(rlS

+ 1)(rys

+ 1) ENGINEKE 1 + rES

rlS

i

(b)

Figure

7.-

RPM

governor.

(a)

877

Generic.

(b)

Simulated.

_o

PILOT INPUT

CONTROL

STANDARD ATMOSPHERE

CONTROL MIXING

SYSTEM MODULES

1

RIGID

AMBIENT CONDITIONS

SERVOS

,

BODY

POSITIONS, VELOCITIES, AND ACCELERATIONS

_,

FUEL CONTROL

l t,

MAIN ROTOR

TAIL ROTOR i

ENGINE

CLUTCH

•--_

GEARBOX |=m,

,

i

i

i

FUSELAGE

•-I"

i

VERTICAL TAIL

STABI LATOR i

SUM FC RCES AND

MOMENTS

I

EQUATIONS OF MOTION i

r

SENSORS

,]"

Figure

8.-

GenHel

simulation

878

elements.

4_

23

m

Q ud m2 u. ug kn-r 0

CH-53

v- 1 Q.

S-61 CH-46 0 THEORY CH-53 Figure

9.- Analytical

and flight

FLIGHT TEST

test gain limits ref. 60).

879

for pitch

rate feedback

(from

ANALYTICAL

PREDICTION

CH47B

FLIGHT

TEST RESULTS

Kp = ROLL RATE FEEDBACK GAI N, deg/deg/Nc

25

K¢ = ROLL GAIN,

ATTITUDE deg/deg

FEEDBACK

4 Kp = 0.7

0.3

K¢=0

2

_" = -o.o45

2O

= 8 rad/sec

15

_'= 0.5_ Kp = 0.2 K¢ = 1.0

_- = 0.05

"o

E

_o = 4.2 radlsec 10

Figure

I0.-

Comparison

of

calculated

and CH-47B limits.

88O

flight

test

results

concerning

galn

BUCS

_

_z__L 7_2/7_777/7 -/7/7// S-/7/7/7777/f_

E"n-_:

-3002co180 -400 10

.1

100

FR EQU ENCY, rad/sec

Figure

33.-

Identified

pitch

898

response,

9/6LO N.

FLIGHT DATA ..........

4O

1ST ORDER MODEL 4TH ORDER MODEL

"o

b =_ 20 N

, ,--%,,'T, ." ;':" " "_- .....

0

I

I

I

I

I

I

III

I

I

I

I

I

I

I1

1

I

150 -

..l.,j.,Oo

• -o

•

"o

b

,,,,

0"

...........

N ¢l

-150

I

I

I

I

I

.1

Figure

i

I I I

I

|

1.0 FREQUENCY,

34.- Transfer-function

models

f

I

I

1 I

f I

I

I

30

10 rad/sec

fit to flight-extracted CH-47B.

Bode plots

of the

42FLIGHT DATA rad/sec

0-

.............

1ST-ORDER

0.1 to

3.0

1ST-ORDER

0.1 to 20.0

4TH-ORDER

0.1 to 20.0

4_

m" z O

36-

o. ¢/) gJ m N34IB

......... 32 .... 3O 0

Figure

A .,

,,,,,

X_t.M

'rwv _vv,'w",,,v _,

35.-

_JVI=..6/

v', _,

"" v,"

1

I

i

i

!

I

I

I

i

!

2

4

6

8

10 TIME, sec

12

14

16

18

20

Comparison

of predicted

responses

899

of identified

models

with

flight

data.