1

Fly-By-WireControl Augmentation

Anthony A. LambregtsFAA Chief Scientific and Technical Adviser for Flight Guidance and Control

Tony.Lambregts@FAA.gov

Tel 425-917-6581

SEA Control & Guidance Systems CommitteeLake Tahoe March 1-3, 2006

2

Overview

Motivation for Fly-By-Wire Design Top Level FBW Design Requirements

Time domain based Handling Qualities FBW design issues/choices

Algorithm types, design issues Observations

Proposed systematic Design Process Static Inversion of Short Period dynamics Stability Augmentation; Command Response Shaping, Hold Examples: PRC/PAH and FPARC/FPAH; relationships

Primary Flight Display & Controller requirements

Conclusions

3

Motivation for Fly-By-Wire Design

Costs Reduction common flight deck/ Handling Qualities / Type Rating

pilot training maintenance and spare parts weight reduction aerodynamic performance optimization (aft CG)

Flight safety improvements – Envelope Protection Customer Appeal

4

Top Level FBW Design Objectives

Suitable handling qualities - all control tasks simplify pilot's control task reduce workload consistent throughout the flight envelope avoid PIO

Flight envelope protection: prevent stall, overspeed, excessive bank angles and nz

not get in pilot’s way, or compromise airplane performance

5

FBW Control System Architecture

throttle

actuator

engine

e

airplane

TFlightControlComputer

display

Interface

actuatorS

stick

feel system

trimup

down

Sensor data

6

FBW Design Issues

Control algorithm choice (C*, C*U, etc.) & details handling qualities; PIO prevention certification: e.g. speed stability or equivalent safety envelope protection implementation

mode changes for up and away and takeoff / landing

display requirements

Column & Wheel versus Sidestick – sensitivity, authority

Passive versus Active feel system - implications

Actuator requirements bandwidth; central or remote loop closure

7

FBW Control Algorithm Choices

Simple electrical signaling only (no augmentation) example: Embraer 170

Classical Stability Augmentation pitch rate, angle of attack feedbacks simple command signal path

Non-classical Stability and Command Augmentation pitch attitude (), nz , flight path angle (FPA) feedbacks

suppression of phugoid multiple feed forward signal paths; pilot out of the loop “hold” function examples: Pitch Rate Cmd/ Att Hold; C* & C*U; FPA RC/Hold

8

Basic FBW System ExampleEmbraer RJ-170 / DO-728 concept

stick

e

Air Data

ActuatorActuatorElectronics

Pos sensor

ModularAvionics Units

Passive Feel

Default Gains

IRU

Airspeed Gain SchedAOA limiting

default

Autopilotservo

clutch

Autopilot cmds

9

Control Algorithm Response Types

• classical unaugmented airplanes are some timers referred to as “Alpha-Command response type”:• FBW control augmentation algorithms often classified by response type:

• Alpha-Command• pitch rate command• nz-command• FPA-rate command• other, e.g. Pitch Attitude or FPA proportional command

• response type classification is not very meaningful, since actual response and HQ depend very much on design details e.g.

• short term versus long term characteristics• pilot out of the loop chararacteristics• non-classical feedbacks, e.g. , Az,V, Ax, FPA…• feed forward paths and dynamic elements

Assuming thrust is controlled to maintain speed: then all these are variations on the same theme!

10

Response Types(Basic, without response shaping details)

KS e cmd

K

Kqq

KS

q

e cmdKP

S

KI

Proportional cmd without hold

KS

q

e cmd

K Kq

“Classical” SP augmentation

Pitch Rate cmd with pseudo Pitch Att Hold

11

Basic C* and C*U Control Algorithms

Fff1

KI

Sactuator

engine

compensationVc o

gK t

S

throttle

trimup

down

Boeing

+_ +_

V(nz pilot)attitude corrected

q

++_ +

stick

FFcomp

e

T

Airpl

+

+

12

C* and C*U Attributes

• inspired by C* handling qualities criterion??• C* HQ criterion was shown to be unreliable (AFFDL TR 70-74)

• design issues:• complexity, many sensors & customization features

• Az –feedback requires attitude compensation• flight condition tuning

• integral control of multiple feedbacks causes drift of control reference when pilot out of the loop – requires pilot tweaking

• integral control of Az and results in Phugoid damping, speed divergence – requires tight thrust control - Authrottle preferred• C*U airspeed feedback “restores” classical phugoid, static speed & stick force stability : “more classical” response

• autothrottle ON: U (airspeed)feedback degrades control • if reference speed commands differ, control divergences

θ

13

C* and C*U Responses

14

• C* algorithm: • No Static Stability: Fstick /knot = 0• without thrust control, speed diverges monotonically – resulting in stall for low speed conditions: need speed envelope protection

• display of flight path acceleration helps in setting thrust • with closed loop thrust-speed control (manual or automatic) effect of speed dynamics on the pitch Attitude/FPA control is eliminated, yielding lower pilot workload and tighter FPA tracking• pilot’s task reduces to maneuver control only

• C*U algorithm:

• classical response with undamped phugoid requires pilot to stay in the loop to suppress phugoid and provide continuous compensatory tracking • same result can be achieved in a simpler way: using classical stability augmentation only

C* and C*U Additional Comments

15

C* Morphed into FPA rate cmd/hold

• responses identical to original C*, if gains are equivalent• fewer, simpler sensors• no pilot-out-of-the-loop control reference drift• still need extensive flight condition tuning• missing: integral control of -error

actu

engine

throttle

q

e

TAirplane

Kq

KFF

K

stick

γ

cmdγ

γK

+

Prefilter

KI

S_+ +_+_

16

Control Algorithm DesignConsiderations

What response characteristics are desirable? Classical Short Period augmentation only?

If yes, achievable HQ improvements limited! SP + Phugoid augmentation? Other? Which one, why?

Sensor requirements? Algorithm complexity,

Analyzability of “Higher order” design Applicability of classical Handling Qualities criteria use of “Equivalent Lower Order Systems”: problematic

Achieving good Handling Qualities still very difficult !

17

Handling Qualities

Definition: The conglomerate of characteristics and features that facilitate the execution of a specific flight control task; includes display and feel system!

• good HQ requires design attributes appropriate to control task (e.g. pitch attitude, FPA, or altitude control)

• each task has a finite time allotment or expectation for its completion (bandwidth requirement)

• direct control of “slow variables” requires special design attributes (e.g.FPA response augmentation & display)

• desired HQ and control harmony achieved when the pilot can execute the task without undue stress and high concentration effort, e.g. using interim innerloop(s) & control targets

18

Unaugmented SP Pitch Dynamics

q

2

t

qe

+++

1

1

2Se

Cm

Cm

yyI

cSq ..

qCm

+-

S

1

S

1

2SPSPSP

2

2SP2θ

ωSω2ζS

ω

S

K

eδ

θ .1Sτ

2=

VT*(CL)1g

g*CL =

2*(W/Sw)g**VT*CL

V-const:

19

FBW Control – Time Domain Response Attributes for good HQ

Harmonious response:1. Coordinated start-up2. Correct sensitivity (K )3. Low SS response lag 4. Minimal overshoot,5. Good Damping6. Short settling time

1

Time

Task VariableResponse

Input stick

KS

stick

2

3

46

5

Stick

20

Design Methodology- An Update -

Desired: • systematic/reliable process, producing desired results:• generalized/reusable design – minimal application & Flt Condition adaptation

Approach: Step 1: Stability Augmentation using Static Inversion

eliminates flight condition dependencies, gain schedules defines basic SP innerloop characteristics: ,

Step 2: Add Integral Feedback loop “retrims” airplane - eliminates SS command response droop

Step 3: Add Command Augmentation Feed Forward Paths shapes response to pilot control inputs, as desired provides “Hold” function for pilot established command

21

S

1

S

11S

1

2θτ +++

+

q_

Cm e

Cm

q

)(SGact -

I YYcS.

ec

Unaugmented Aircraft SP modelCmq

+--

Ce

m

1

Cmq

Cm

ec

SP model inversion

Outerloopcmd

q

+--

K q

K

New SPdesign

cS

I yy.

q

q_

Step 1: Static Inversion Based Stability Augmentation

22

Step 2: Add Integral ControlConcatenate the State Feedbacks

Airplane Dynamics reduced to series of integrators - feedback serves as new - feedback for S.P.

augmentation Integral feedback control eliminates SS response droop dropping loop gains by factor 4 for each state assures all

poles placed on real axes (>1); Alternatively, pole placement directly yields gains

S

1

S

1+-

+-+- S

K IqKK

cmd

Stripped SP

dynamics

New SP dynamics

1SK/1SKK/1SKKK/1

1

KKKSKKSKS

KKK

θ

θ

I2

θI3

qθIqθIqθ2

q3

qθI

cmd

23

0.382)(S1S2.618)(S

1

14S4SS

1

θ

θ23

cmd

Short Period dependency on and and q eliminated!

Example: K q= 4, K = 1, K I = .25

Step 3: Command Response Augmentation

To create classical transfer function

add forward loop integrator to realize K/S-like response

add 2nd order numerator, cancel one of denominator poles

Result:

stickθ/δ

1})S(1/K)SK(1/K)SKK{(1/K

1)SKS(K

S

K

δ

θ

I2

θI3

qθI

FFI2

FFPstick

stick

Step 2 cont’d :Pitch Rate Command / Attitude Hold

Algorithm (PRCAH)

2_

24

Step 3 cont’d :PRCAH Algorithm Implementation

controls (CAP)

controls SS -response lag (Drop Back),

relative to : actuator effect not considered (design to be minor)

FFPK 0t

FFIK

S

KK Istick

FFII KK /1

++-S

1 cmd

Augmented SP dynamics

22

2

2 SPSP

SP

SS

IKstickK

FFIK

FFPK

+ +stick S

1

2SPθq

SPSPq

ω.KK

ω2ζK

25

Step 3 cont’d :PRCAH Feed Forward Gains Determination

NumeratorTherefore KFFP = n1.n2 ; KFFP = n1 + n2

-Response lag determined by KFFI and KI : select , then: select KFFP to cancel “slowest” denominator pole,

associated with KI integral control feedback loop

Special Case 1: Design denominator to include pole with desired final ; Select and to cancel remaining poles: -response reduces to first order!

IFFI KK /1

FFIK FFPK

1.11 212 SSSKSK nnKKIFFP

26

Special Case 2: Design system to have the “ideal”

Classical SP form and response characteristics n , SP , SP :

This requires n1 = n and n2 = d

n fulfills the role of , but is not affected by flight condition

final algorithm is generalized, no Flt Cond dependencies, assuming constant is desired

Flt Cond adaptations handled in Static Inversion Module

1)S1}(τ)Sω/(2)S{(1/ω

1)S1)(τS(τ

S

K

1})S/ω(2ζ)S{(1/ω

1)S(τ

S

K

δ

θ

dSPSP22

SP

n2n1stick

SPSP22

SP

nstick

stick

Step 3 cont’d :PRCAH Feed Forward Gains Determination

2θτ

270 5 10 15 20 25

0

1

2

3

4

5

6

Time ~sec

Pitc

h R

ate,

Pic

h A

ttitu

de,

Thet

a C

md

~deg

.sec

, deg

Pitch Rate Cmd /Pich Att Hold Agorithm responsesKq = 4, Ktheta = 1, Ki = .25, Kffi = 3.5, Kffp = 2.309

Tautheta = .5 sec, no actuator dynamics

Pitch RatePitch AttitudePich Att Cmd

PRCAH Algorithm: Example Response 1

CAP = 2.309 (g/VT)

280 5 10 15 20 25

-1

0

1

2

3

4

5

6

Time ~sec

Pitc

h R

ate,

Pitc

h A

ttitu

de, P

ich

Att

Cm

d ~

deg/

sec,

deg

Pitch Rate Cmd / Pitch Att Hold Algorithm responsesKq = 4, Ktheta = 1, Ki = .25, Kffi = 5, Kffp = 6.236

Tautheta = -1, no actuator dynamics

Pitch RatePitch AttitudePitch Att Cmd

PRCAH Algorithm: Example Response 2

CAP = 6.236 (g/VT)

29

PRCAH AlgorithmFrequency Response

-200

-150

-100

-50

0

50

Pitch Rate cmd/Att Hold algorithm Kq=4, Ktheta=1, Ki=.25, Kstick =.1rad/sec/full stick

Frequency response Theta/stick ~rad/full stick

Mag

nitu

de

(dB

)

10-2

10-1

100

101

102

103

-360

-315

-270

-225

-180

-135

-90

-45

Pha

se (

de

g)

Frequency (rad/sec)

No Actuator

No Actuator

Attuator =1024/(S2+64S+1024)

Tautheta=-1

Tautheta=1

Tautheta=0

Tautheta=-1

Tautheta=0

Tautheta=1

30

PRCAH AlgorithmComments

• may be selected for the specific task, e.g. • for -control 0; for FPA control < 0

• Algorithm Feedback gains may be selected to support Autopilot outerloop modes• Feed Forward gains can compensate to a large extend to provide desired augmented manual responses• Not clear how to interpret CAP criteria, since ~ the same response characteristics can be achieved with different sets of feedback & feedforward gains, yielding different values for CAP, compare slide 27: CAP =2.309 (g/VT) and slide 31: CAP =1.73(g/VT)

• here CAP = (g/VT).KFFP.KI.K.Kq

31

0 5 10 15 20 25-1

0

1

2

3

4

5

6

Pitch Rate Cmd / Pitch Att Hold Control AlgorithmKq = 3, Ktheta = 1, Ki = .333, Kffi = 2.5, Kffp = 1.73

Tautheta = .5, No actuator dynamics

Time ~sec

Pitc

h R

ate

, P

ich

Att

itu

de,

Pit

ch A

tt c

md

~d

ed/s

ec,

deg

Pitch RatePich AttitudePich Att cmd

CAP = 1.73 (g/VT)

32

Flight Path Angle Rate Command / Hold (FPARCH) Algorithm

Direct FPA rate command and Hold control strategy is very attractive:

eliminates need for using iterative -control to satisfy higher order objective: reduces work pilot workload FPA will be maintained without pilot tweaking, regardless of speed & configuration changes, turbulence and windshear

facilitates altitude crossing at designated waypoints,

continuous descent procedures, final approach tracking HUD compatible

needs suitable display

33

FPA Rate Command / FPA HoldAlgorithm- System 1

++-S

1 cmd

Augmented SP dynamics

22

2

2 SPSP

SP

SS

IKstickK

FFIK

FFPK

+ +stick S

1

1

1

2S

K

-

FPA ()

αLCV .g.

)/.(2τ

.2θT

SW

, continuously computed on board

2SPθq

SPSPq

ω.KK

ω2ζK

34

FPA Rate Command / FPA HoldAlgorithm – System 1

IθqIγθqθθqq2

IθqFFI2

FFPstick

stick KKKSKKKK1)S)(τKKSKS(S

KK1)KSKS(K

S

K

δ

γ

2

Make , then transfer function becomes

, where is identical to TF on slide 23 !

Conclusion: FPARCH and PRCH algorithmscan provide identical and responses!

2θγ τK

1)S1}(τ)S(1/K)SK(1/K)SKK{(1/K

1)SKS(K

S

K

δ

γ

2θI2

Iθ3

Iθq

FFI2

FFPstick

stick

stick

stick

35

FPA Rate Command / FPA HoldAlgorithm – System 1

and in the numerator of can be

selected to satisfy two conditions: the desired response lag:

Thus, cancellation of one of the poles in the denominator;

Best strategy: cancel pole associated with

Example (next slide): and KFFI = 5

Then , and

Scheduling KFFI and KFFP with eliminates

response variability due to

FFIθIγ K)τ(1/Kτ2

stickδ

γFFIK FFPK

γθIFFI τ)τ(1/KK2

12 nFFIn τKτ 2ττ

21 θn 6.0.ττK

21 nnFFP

2θτ1τγ

2θτ

2θτ

36

0 5 10 15 20 250

1

2

3

4

5

6

FPA RAte Cmd /FPA Hold algorithm responsesKq = 4, Ktheta = 1, Ki = .25, Kffi = 5, Kffp = 6, Kstick = 5 deg/sec/full stick

Time ~sec

FP

A C

md,

FP

A,

Pic

h A

ttitu

de ~

deg

Pich AttitudeFPA FPA cmd

FPA Rate Command / FPA HoldAlgorithm-System1

Note: polecancelled

2

CAP = 6.0 (g/VT)

37

FPA Rate Command / FPA HoldAlgorithm-System1

-250

-200

-150

-100

-50

0

50

FPARCH algorithm Freq response FPA/dStick ~radians/unit Kq=4, Ktheta=1, Ki=.25, Kffi= 5, Kffp=6, Kstick=.1 rad/unit

Mag

nitu

de

(dB

)

10-2

10-1

100

101

102

103

-450

-405

-360

-315

-270

-225

-180

-135

-90

Pha

se (

de

g)

Frequency (rad/sec)

No Actuator

No Actuator

102464SS

1024:Actuator

2

Gain Margin ~27 db (factor ~22.5)

38

5 10 15 20 25 30 35

-1

0

1

2

3

4

Full Airplane Simulation with FPARCH algorithm step dStick=10%, Kstick=.0641 rad/sec/unit stick

Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft, Tauthetatwo=2 secKq=4,Ktheta=1, Ki=.25, Kffi=5, Kffp=6

Time ~seconds

FPA ~deg

FPAcmd ~deg

delta Pitch Att ~deg

delta-Trust/10000~lbs

Elevator ~deg

VE-error ~kn

FPA Rate Command / FPA HoldAlgorithm-System1

39

5 10 15 20 25 30 35-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Full Airplane Simulation with FPARCH algorithmTwin Jet, Weight 120,000 lbs, Ve=350 kn, Alt=25,000ft,

step dStick=10%, Kstick=.04475 rad/sec/unit stickKq=4, Ktheta=1,Ki=.25, Kffi=4.47, Kffp=4.411, Tauthetatwo=1.47 sec

Time ~seconds

FPA ~deg

FPAcmd ~deg

delta Pitch Att ~deg

delta-Trust/10000~lbs

Elevator ~deg

VE-error ~kn

5 10 15 20 25 30 35-4

-2

0

2

4

6

8

Full Airplane Sim FPARCH AlgorithmTwin jet Weight=100,000 lbs, Flaps Down, Gear down, Alt=10000 ft, Ve=127kn

step dStick=10%, Kstick=.1066 rad/sec/unit stick Kq=4, Ktheta=1, Ki=.25, Kffi=5.08, Kffp=6.243, Tauthetatwo=2.08 sec

Time ~seconds

FPA ~deg

FPAcmd ~deg

delta Pitch Att ~deg

delta-Trust/10000~lbs

Elevator ~deg

VE-error ~kn

FPA Rate Command / FPA HoldAlgorithm-System1

40

++-S

1 cmd

Augmented SP dynamics

22

2

2 SPSP

SP

SS

IKstickK

FFIK

FFPK

+ +stick S

1

1

1

2S

K

-

FPA ()

1)S(1/K)SK(1/K)SKK(1/K

1)SKS(K

S

K

δ

γ

I2

Iθ3

Iθq

FFI2

FFPstick

stick

Selecting 2 K

results in

Conclusion: response no longer a function of 2

FPA Rate Command/FPA HoldAlgorithm-system 2

41

FPA Rate Command/FPA HoldAlgorithm-System2

For System 2, only K needs to be adjusted for to maintain invariable response

KFFI and KFFP can be selected to cancel two poles, making the / cmd transfer function

first order (in this simplified SP approximation analysis)

2θτ

42

0 5 10 15 20 25-1

0

1

2

3

4

5

6

Timw ~sec

FP

A C

ms,

FP

A,

Pitc

h A

ttitu

de ~

deg,

Pitc

h R

ate

~de

g/se

c FPA Rate Cmd / FPA Hold algorithm responses (System 2)Kq = 4, Ktheta = 1, Ki = .25, Kffi = 3, Kffp = 1, Kstick = 5 deg/sec/full stick

Pitch AttitudeFPA FPA cmdPitch Rate

FPA Rate Command/FPA HoldAlgorithm-System2

/ cmd TFReduced toFirst Order

43

FPA Rate Command/FPA HoldDisplay Requirement

FPA must be displayed to allow pilot to close loop

on FPA FPA response delay cannot be reduced enough to

make display of “raw FPA” adequate A quicker responding display symbol is needed:

cmd developed in algorithm meets the need

display as a separate symbol blend with actual : CmdFPA

1Sγτ

SγτFPAFPA Quickened

If pilot closes loop on quickened he cannot induce PIO !!

44

Controller Authority &Sensitivity Scheduling

Airplane manuever authority (nz) is proportional to

Controller dead zones and command discontinuities must be avoided; maneuver command limit must

occur at controller displacement limit be matched to airplane maneuver authority

Controller sensitivity around neutral must be suitable

and sensitivity variation must be minimal

2

2

stallV

V

These requirements are difficult to reconcile with passive feel system, but its advantage is simplicity

45

Controller Authority & Sensitivity(Fixed Displacement)

.5 1

Nz - cmd

-.5-1

stick

2.5

0

2.0

1.5

-.5

Vmin = 1.07 Vstall

Ve =1.41 Vstall

Ve 1.58 Vstall

Authoritylimit

46

Final Algorithm & control System Implementation Details

• “Front-end” sensitivity scheduling:• need to assure pilot cannot command more than the airplane maneuver limits, to prevent stall and excessive nz

• “Tail-end” control surface command processing:• need to include software cmd rate and position limits, that correspond to actuator performance capability

• prevent command wind-up• minimize delay on control command reversal

• Assuming control surfaces are dimensioned correctly, then pilot + control algorithm should always operate within airplane performance capability and limits:

• Minimizes PIO susceptibility

47

Optimal Pilot Gain and Phase Compensation

• Optimal pilot phase compensation is assumed to be zero• Optimal pilot gain definition: Maximum gain the pilot can use in a continuous compensatory control tracking task, to get to his desired target as quick as possible, but without overshoot• Example:

• previous FPARCH algorithm (system 1)

5 10 15 20 25 30 35-4

-2

0

2

4

6

8

Time ~seconds

Full Airplane Simulation with FPARCH algorithm Twin jet 120,000 lbs, Ve=200kn, Alt=10,000 ft

closed loop response with pilot model Kp =4.7 units dStick/rad FPA-error Kq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tauthetatwo=2 sec

FPAcmd ~deg

FPA ~deg

Pitch Att ~deg

Elevator ~deg

FPA loop closureStep FPA tracking error=.1 rad

dStick

48

Loop Closure Options and Effects

5 10 15 20 25 30 35

-4

-2

0

2

4

6

8

Full Airplane Simulation with FPARCAH algorithm Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft

closed loop response with pilot model Kp=8 units dSick/rad FPAerrorKq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tauthetatwo=2 sec

Time ~seconds

FPAcmd ~deg

FPA ~deg

Pitch Att ~deg

Elevator ~deg

FPAcmd loop closureStep FPA tracking error=.1rad

dStick

5 10 15 20 25 30 35

-4

-2

0

2

4

6

8

Time ~seconds

Full Airplane Simulation wirh FPARCH algorithm Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft

closed loop response with pilot model Kp=8 units dStick/rad FPAerrorKq=4, Ktheta=1, Ki=.25 Kffi= 5, Kffp=6, Tauthetatwo=2

FPAcmd ~deg

FPA ~deg

Pitch Att ~deg

Elevator ~deg

FPAquickened loop closureStep FPA tracking error=.1 rad

dStick

49

PIO SusceptibilityGraceful stability Degradation

(No cliffs, No actuator rate & position limiting)

5 10 15 20 25 30 35-6

-4

-2

0

2

4

6

8

Time ~seconds

Full Airplane simulation with FPARCH algorithm Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft

closed loop response with pilot gain Kp=15 units dStick/rad FPAerrorKq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tautheta2=2 sec

FPAcmd ~deg

FPA ~deg

Pitch Att ~deg

Elevator ~deg

Pitch Attitude loop closure

dStick ~units

5 10 15 20 25 30 35-8

-6

-4

-2

0

2

4

6

8

10

12

Full Airplane Simulation with FPARCH algorithmTwin jet Weight =120,000 lbs, Ve=200kn, Alt=10,000 ft

clossed loop response with pilot gain Kp=15 units dStick/rad FPAerrorKq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tauthetatwo=2 sec

Time ~seconds

FPAcmd ~deg

FPA ~deg

dPitch Att ~deg

Elevator ~deg

FPA loop closureStep FPA tracking error=.1 rad

dStick

50

Conclusions

Existing FBW control algorithms and design methodologies are complex, difficult to understand & analyze A new, simpler, more systematic methodology was discussed, consisting of three major design phases

static SP Airplane model inversion synthesis if new SP innerloop dynamics command response augmentation to satisfy HQ

Result: a generalized, flight condition independent design PRCAH and FPARCH algorithms can be designed to produce identical responses and HQ FPARCH algorithm requires display of quickened FPA