AeCo Flight Dynamics

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1Dr. M. Heller, R. Paul

AEROCONTROLS

Flight Dynamics I ETHZ Ed., WS 2012/13

Some Aspects of

Flight Dynamics and Flight Control

Unstable

ETHZ. Ed.; Status: October 2012

Ralph Paul

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AEROCONTROLS


Balanced/Harmonic Overall Design

Multi Object Optimization Performance, ....

Configuration/Payload/Stores/Propulsion

Physical/Technical Constraints

Stabilization Capability

Agility, Maneuverability

Trim ability, !

Integrative

Controller Design

Robust Control

Carefree Handling

Engine Control

Control Allocation

Flight Mechanics Requirements

Nz--Envelope

Control Potential w.r.t. all 3 Axis

Performance & Flying Qualities (MIL)

Aerodynamics

Basic/natural (In-)Stability SM

Aerodynamic Quality CL/CD, (CL)max

Control Effectiveness/Power

Flight Dynamics

Integrative Interactions

Embedding of Flight Dynamics into the Design Process

1 Overview: Flight Dynamics and Design

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Fundamental Design Objective of a Flight Dynamics/Controller Development

Provision of excellent Flying/Handling Qualities in order to exploit the Potential

of a configuration which is optimized w.r.t. other objecives like performance and

/or economy and/or stealth and/or passenger comfort, !

Flying & Handling Qualities

Controllability, Maneuverability, Agility

Disturbance Rejection: Gust Load & Pilot

Work Load reduction Care-Free-Handling

Reliability, Safety, Failure Scenarios & Fault Detection/

Analysis/Tolerance, Reversionary Modes Robustness Qualities

Design Problem:

In the Past: Natural (basic) Stability of the Aerodynamic Design Cm , Cn , ...

Today: Adequate Stabilization of the optimized (maybe unstable) Layout!

1 Fundamental Requirements

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Instability: Artificial Stabilization

Natural Stability

HT produces down force CL , CD

Worse flight performance

HT produces lift CL , CD

(CL)max , better flight performance

Zero moment Cm(L=0)

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Limitation of Stabilization

t

( )

TD

20

()max

M&

Tt

pitching moment

disturbance

maximum control moment

not stabilizable

control

moment

built up

dead time

stabilizable

()max

with control

activity

uncontrolled

Delays in the inner loop decisively limit the admissible, i.e. the controllable, instability!

2 Stabilization Capability

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Taileron/Flaperon Superposition of Long-/Lat-Demand

e.g. Stabilization demand via initial value disturbance or=1 and turbulence/gust-simulation according to MIL-Spec.

Trimming: trim trim (steady turn)

Maneuver Long/Lat:

Pitch acceleration qreq q e.g. qreq = 0.31/s2

Load factor nz n e.g. nz= 0 -2 g

Bank angle T45 T45 e.g. T45 < 1.9s

Stabilization (gusts)

Turbulence/cross windstab, stab

. .

Estimation of the Required Control Potential/Power:

, 2

lr +

=2

lr

=

2 Required Control Power

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Straight & Level Flight

le,ri[]

le,ri[]

Steady Turning Flight: nz = 2 g

Taileron/Flaperon Superposition of Long-/Lat-Demand

e.g. Stabilization demand via initial value disturbance or=1 and turbulence/gust-simulation according to MIL-Spec.

||||||||)||,|(|sup)( 45, stabTtrimstabnqtrimreqrl = &

Trimming: trim trim (steady turn)

Maneuver Long/Lat:

Pitch acceleration qreq q e.g. qreq = 0.31/s2

Load factor nz n e.g. nz= 0 -2 g

Bank angle T45 T45 e.g. T45 < 1.9s

Stabilization (gusts)

Turbulence/cross windstab, stab

. .

Estimation of the Required Control Potential/Power:2

lr +

=

2

lr

=

2 Required Control Power

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Automatic Modes & Higher Functionalities: Autopilot

Conventional Control System (SAS) Integrated FCS

Pitch-/yaw damper

Attitude control (, ) trimmingcontrol support or coordination

Mechanical (or electr.) feed through

(mechanical backup/direct link

e.g. Tornado, Mirage)

Control of a flight state (, , nz ,...)

Full authority control system (Fly by Wire)

Highly control configured dynamic: CCV

Envelope protection "Care-free handling"

Absolutely safety critical "fail safe"

Goal: pilot relief, safety increase by standardization of procedures

Basic functionalities: attitude control, altitude control, auto-throttle, heading-hold

Higher functionalities: route-steering (navigation), automatic landing, h-/ -acquire, ...

3 Flight Control System Design

Primary Goals & Requirements: Basic CSAS

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Principle and Functionality CSAS (Fly-By-Wire)

Artificial stabilization (stability augmentation SAS)

Control behavior demand (control augmentation CAS)

defined aircraft response to a pilot command

Pilot flies aerodynamic configuration through the control system

CCV - Control Configured Vehicle with highly control configured dynamic

Idea: Control system compares current command input of the pilot with the measured (flight)

state (sensors) of the aircraft and performs correction by adequate computed control surface

deflection.

CSAS

ADS

y

stick

commandautopilot

trimming

demand

signal

required

control momentCSAS commanded

control deflaction

control tap

command

path

stabilization

limitation

control

distribution

actua-

tors

aircraftD

Path

M

sensor

signal


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Purpose and Goals: Stability Augmentation System (C)SAS

Modification of the Eigen Modes, i.e. SP/DR frequency &

damping , 0, Lat evt. also the eigenvectors, Roll timeconstant TR, !. How? Of Course by feedback!

Knowledge of basic Root Loci of the aircraft is important!

Improvement of the transition behavior (i.e. step response)

Handling Quality Requirements have to be met

How? Command Augmentation & (Pre-)Filtering.

Disturbance rejection/supression (gusts, turbulence, !)

Standardization/simplification of the aircraft behavior

Pilot feels unified flying qualities over a wide range

of the envelope (different flight conditions)

Compensation/Coordination basis for autopilots

M+

Mq

+

td

q& td

q &

Z

M

Z

Control Path

Pitch Axis

q

K

Kq


2

2=opt

j

optqK ,

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Example Pitch Axis: Rate Command/Attitude Hold System (RC/AH)Stick released:

return to neutral

Pilot commands with the stick the

pitch rate qc (rate command)

Release of the stick forces pitch rate

q = 0 and thereby hold of the pitch angle (Attitude Hold)

no trim button necessary!

Insures a simple

trajectory control!

Integral q-feed back:

q = qC especially q = 0 for

stick neutral q hold

phugoid damping

feed back optional

q&

+

+

+

+

q

C

y +

+

KIqz

qC

+

aircraftfilter

proportional-/integralq- feed back

td

c-demand

q

filter


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CAREFREE- Properties

Angle of attack: Limitation of and dependent on flight state

Load factor limit: Limitation of nz and nz dependent on flight state

Actions: Limits of the demand signal (limiter)

Limits of the demand rate (rate limiter)

Minimization of the overshoot (e.g. nl-feed back)

Fading of the lateral control command (pedals, SPILS)

.

.

g-Compensation (Long)

Independent from the position and from the direction of the earth acceleration, a

conventional flight behavior despite a q-feed back should be insured.

Limiter

Rate-Limiter

ss1

nonlinear feed back

Knl

Actions:

qc-demand dependent from flight attitude/-path

direction cosine (a, ) on (Lead by deviation of the direction cosines)


X

Z

q = 0

g

g

Inverted Flight

q > 0

V0mg

L

mg Lgr


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Basic Control System of the Lateral Motion (Demands/Goals/Problems)

Weakly damped Dutch Roll leads to heavy coupling in (,)

Artificial damping of the yaw movement

Artificial decoupling of roll and yaw axis

Roll subsidence mode, primary degree of freedom (p)

Artificial damping of the roll mode (roll damper)

Spiral mode, primary degree of freedom ( )

Command of a required pilot behavior spi = 0 (attitude control)

Steady state decoupling

Turning coordination and turning compensation, e.g. -demand AS is finished!

-4 -2 0

-2

2

j [1/s]

[1/s]

Dutch Roll

Spiral Mode

Roll Sub. Mode


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Decoupling of Roll an Yaw Movement

Command decoupling:

Stick commands roll around

velocity vector V0 with

, constant!

Steady decoupling:

Coordinated turn with 0 (stick)or angle of sideslip with 0 (pedals)

Dynamic decoupling (| / |):Angle of sideslip disturbance does not induce

a large bank angle and vice versa!

Longitudinal and lateral decoupling

always if 0 and 0, inertial coupling

Coordinated use of all 3 ruddersrequired, compensation paths!

Roll around velocity vector Constancy of angle of attack and sideslip

Roll around body fixed x-axis Transformation from angle of attack to angle

of sideslip

V0

q

pa

x

r

p

inertial coupling pitch up (bar-bell model)

sincos

tansin,cos:0

rpp

p

rprpp

a

aa

+=

===


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Primary feed back gains:

Allegation of stability characteristics"

K - basically frequency of the dutch roll

Kr - basically damping of the durch roll

Kp - roll time constant TR

Remaining feed back coefficients

Degrees of freedom for decoupling:

especially feed back for reduction of the roll-yaw coupling

Illustration: Lead through proper

aileron deflection at a disturbance in

permitted prohibited

-8 -4 -2 0

-2

2

6

-6 [1/s]

Dutch Roll

max)( RT min)( DST

Roll Mode

|/|dr < 5 ... 7

Spiral Mode

2/2DRFeed Back Path

+p

+r

r

p


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arctan

+c

c -limiterdead zone

P

I

Command Filter

Control Law:

-

--

a

a

w

lat. dynamics + actuators

+ sensors

p

r

trim values(=: 0)

r

f

r

f

ua

y

y

commandfilter

c (=0)

c

e

KII

Hfeed forward

KSASbasic controller

+= eKrHyKu ISASa

g

V&arctan

C&

r

roll stick

roll stick

Multivariable state controller:

output feed back: y ua

Optional: Stick or turn rate input

Integral , feed backfor disturbance compensation

Feed forward control H


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Demand: Dynamic decoupling: First choice"

Eigen Structure Placement (ESP) (e.g.: A320 lat, ...)

Due to the existence of multiple control variables, besides the

eigen values also the eigen vectors can be placed partially.

Lateral motion:

Placement of the eigen values of dutch roll, roll and

spiral mode, as well as partially of their eigen vectors:

Roll-yaw coupling |/|dr 0 Spiral- & roll mode with 0

vd

e N1

eN2 x

y

z

NullraumNi

vi

Projection of theeigen vectors zero space

Eigen Vector Placement Lat

Modell jMa = 0.5

rollmode

spiralmode

Modell iMa = 0.2

d =-0.3 s-1

T =3.33 sd

0vd =

d =-2.0 s-1

T =0.5 sd

0vd =

Modell kMa = 0.9

dutchroll

0d =1.3 s-1

d =0.89

0

0vd =

= x

pr

0 = to zero specified eigen vector component

x unlimited component=~

~

e

i

g

e

n

v

e

c

t

o

r

pole Placement

KSASBasic Controller

Dimensioning of the Feed Back Path

)()()()()(0 1

)(

1

1

0

)(0

1tdecetdeet

t n

i

Tii

ti

n

ii

tt

tt ii uDuBwvCvCuDuBVVCxVVCy +

+=++=

=

=

Solution of the state equations:


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Steady decoupling by feed forward control H

Inversion of the nominal steady process dynamics

Command Decoupling:

Definition of alternate rudders", which only act onthe desired rotational axis plus g-compensation,

demand values, ...

Riccati-Design (LQR)

with proper choice of weightingsatisfying decoupling reachable

Nonlinear Dynamic Inversion (partial)

Negative feed back of the inner coupling terms(nonlinear), e.g. inertial coupling, adaptation of

stability characteristics by pole placement

Hfeed forward

11

1mod

])([

)]0([

=

+=

aaT BCKBAC

GH

c

c

v

v

X

Z

g

g

X

Z

mg

r = 0

g

g

A


Turn (Knife Edge Flight)

about g-compensation in lat.

r > 0

mg

Further Design Aspects for the Lateral Motion Control Systems


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Initial point: existence of a control design

Validation of the design necessary

Proof of concept (requirements, stability, certification)

Problem: Multiple uncertainties (partly unknown),

model deviations or neglected dynamics,

e.g. CG-position, ADS, aerodynamics, masses, ...

Worst case combination of various influence

parameter must be tolerated robust stability/quality

Linear analysis: Evaluation of sufficient stability reserves (robustness) and performance

Nonlinear analysis: complex mathematical implementation of all (sub-)systems and

effects (aerodynamics/engine, actuators, sensors, discrete controller, ...)

Non real time simulation: influence of nonlinear effects, limit cycles, limitations

Manned real time simulation: special maneuver, pilot evaluation, critical corners

Proof of sufficient stability- and handling-qualities

Evaluation of the Control Design (Assessment)


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Robustness & Stability Reserves ?

Sideslip angle nonlinearities: Design with

= 0 Behavior & stabilization for 0?

High angle of attack area:

Departure (=Spin) threat rudder power

fading out of the pedal commando 0

Carefree qualities Limitation of:

Roll rate & acceleration

Angle of sideslip & increment Roll priority: At fast roll will be faded out

in favor of the roll rate pa

unstable

typical Cn -nonlinearity

Cn

stable

0

neutral

unstable

&


tT

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FCS Rig Tests contain

Integration sensor- and actuator LRIs with the FCCs

System tests (air data system, fuel/store system,

autopilot, flight control system)

End-to-end tests and closed loop tests with

aircraft model and pilot

Contribution to Certification

Proof of all FCS flight safety

aspects for the approved flight

envelope (e.g. validation fault tree)

Contribution to Qualification

Proof of compliance of the requirements

from the system specification

Test and Certification of the Complete System with the Rig


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Parameter excitation

+ Gain scheduling hidden gains

Integrator wind up"

Transonic pitch-up

Local instabilities

Rate/deflection limitations

PIO (own discipline, Gibson Spider)

CG-movement & areas

ADS-systems, sensors, tolerances

Nonlinear aerodynamics &

engine characterisitics and, and, and ...

Discretization hybrid systems

Implementation (nonlinear)

Error analysis & propagation

Failure safety

Reconfiguration, fallback solution

Aeroelastic & structural coupling

Moding & cross-fade

Software design

+ safety critical

+ real time validated

Certification & Proof

AS is

ENLIGHTNED!

Design & Analysis for 99% Linear. But The World is Nonlinear


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Recommended Literature

x

y

z

V0

Flight Dynamics Part I: Aircraft Stability and Control

[1] DiStefano, J.J.: Feedback and Control Systems (2/ed);

Schaums Outline Series, McGraw-Hill Inc.,1990.

[2] Brockhaus, R.: Flugregelung. Springer Verlag, Berlin 1994.

(German Language!)

[3] Steven, Lewis: Aircraft Control and Simulation. John Wiley & Sons, Inc., New York 1992.

[4] McRuer: Aircraft Dynamics & Automatic Control. Princeton University Press, 1973.

[5] Etkin, B. & Reid L.D.: Dynamics of Flight - Stability and Control, 3rd Edition,

John Wiley & Sons, New York, NY, 1995

[6] Fllinger, O.: Regelungstechnik. 8. Auflage, Hthig Verlag, Heidelberg 1994.

(Good German Feedback Control Textbook)

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AeCo Flight Dynamics