Robust Nonlinear Control of Aircrafts Using Neuro-adaptive ...nptel.ac.in/courses/101108047/module14/Lecture 38.pdf · Lecture – 38 Robust Nonlinear Control of Aircrafts Using Neuro-adaptive

Lecture – 38

Robust Nonlinear Control of Aircrafts Using Neuro-adaptive Augmented Dynamic Inversion

Dr. Radhakant PadhiAsst. Professor

Dept. of Aerospace EngineeringIndian Institute of Science - Bangalore

ADVANCED CONTROL SYSTEM DESIGN Dr. Radhakant Padhi, AE Dept., IISc-Bangalore

2

References

Radhakant Padhi, Narayan P. Rao, Siddharth Goyal and Abha Tripathi, “A Model-Following Neuro-Adaptive Approach for Robust Control of High Performance Aircrafts”, Automatic Control in Aerospace, Vol. 3, No. 1, May 2010.


3

Problem StatementPilot Commands:• Case -1: Longitudinal

(Roll Rate = 0, Normal Acceleration, Lateral Acceleration = 0, Total Velocity)

• Case -2: Lateral (Roll Rate, Height, Lateral Acceleration = 0, Total Velocity)

Turn Coordination: Lateral acceleration command is zero

Goal:• Airplane responds to the pilot commands “quickly” & “nicely”• The control design should have sufficient robustness for

parametric inaccuracies (mass, MI and aerodynamic coefficients)

Note: Essentially it is a Robust Tracking problem


4

Airplane Dynamics: Six Degree-of-Freedom ModelRef: Roskam J., Airplane Flight Dynamics and Automatic Controls, 1995

( ) ( )( ) ( )

( ) ( )

1 2 3 A 4 A

2 25 6 7

8 2 4 9

= c PQ+c L +c

= c

= c

T T

A T

A T A T

P QR c L N N

Q PR c P R c M M

R PQ c QR c L L c N N

+ + +

− − + +

− + + + +

( )

( )

( )

1 sin

1 sin cos

1 cos cos

X X

Y Y

Z Z

A T

A T

A T

U VR WQ g F Fm

V WP UR g F Fm

W UQ VP g F Fm

= − − Θ+ +

= − + Φ Θ+ +

= − + Φ Θ+ +

( )

= sin tan cos tan = cos sin = sin cos sec

P Q RQ R

Q R

Φ + Φ Θ+ Φ Θ

Θ Φ − Φ

Ψ Φ+ Φ Θ

= sin cos sin cos cosh U V WΘ− Θ Φ − Θ Φ

cos sin 0 cos 0 sin 1 0 0sin cos 0 0 1 0 0 cos sin

0 0 1 sin 0 cos 0 sin cos

E

E

E

x Uy Vz W

ψ ψ θ θψ ψ φ φ

θ θ φ φ

−⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥= −⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦


5

Aerodynamic Model (F-16)Ref: Eugene A. Morelli , American Control Conference Philadelphia, Pennsylvania June 1998

( , ) ( )

( , , ) ( ) ( )

( , , ) ( )

t q

t p r

t q

x x e x

y y a r y y

z z e z

C C C q

C C C p C r

C C C q

α δ α

β δ δ α α

α β δ α

= +

= + +

= +

( , ) ( ) ( ) ( , ) ( , )

( , ) ( ) ( )

( , ) ( ) ( ) ( , ) ( , ) ( )

t p r a r

t q ref

t p r a r ref

l l l l l a l r

m m e m z cg cg

n n n n n a n r y cg cg

C C C p C r C C

C C C q C x x

cC C C p C r C C C x xb

δ δ

δ δ

α β α α α β δ α β δ

α δ α

α β α α α β δ α β δ

= + + + +

= + + −

⎛ ⎞= + + + + + − ⎜ ⎟⎝ ⎠

/ 2 / 2 / 2T T Tp pb V q qc V r rb V= = =


6

Equations in Desired Form

( ) ( )V V V cX f X g X U= + ⎡ ⎤⎣ ⎦

( ) ( )R R R cX f X g X U= + ⎡ ⎤⎣ ⎦

[ ]TT E EX V P Q R X Y hα β Φ Θ Ψ

[ ]TVX U V W

[ ]TRX P Q R

[ ]TAX Φ Θ Ψ

[ ] [ ][ ]T Tc AER T a e rU U U Tδ δ δ

where


7

Definitions and GoalTotal Velocity:

Roll Rate (about x-axis):

Normal Acceleration:

Lateral Acceleration:

Goal:

P

where are pilot commands

( ) ( )( )/ 1/zz z An F m m F− = −

( ) ( )( )/ 1/yy y An F m m F=

P*, nz*, VT*

* * * *, , 0,z z y y T TP P n n n n V V→ → → = →

TV


8

Control Synthesis Procedure

Define new variables:

Key observation:

Known:

In Wind Axis Frame:

* *,y y y ya n V a n V− −

* *,z z z za n W a n W+ +

⇔( )* * TT

z y z yn n n n⎡ ⎤⎡ ⎤ →⎣ ⎦ ⎣ ⎦ ( )* * TT

z y z ya a a a⎡ ⎤⎡ ⎤ →⎣ ⎦ ⎣ ⎦

z z

y y

z n n c

y n n c

n f g U

n f g U

= +

= +T T

P P c

T V V c

P f g U

V f g U

= +

= +

0V W= =

wz wzwz n n cn f g U= +


9

Control Synthesis Procedure:LongitudinalDynamics:

Differentiate:

Case-1: (Longitudinal) Pilot commands:

• Roll Rate: • Normal Acceleration:• Lateral Acceleration:• Total Velocity:

cos cossin cos

z

y

a UQ VP ga UR WP g

= − + Φ Θ= − − Φ Θ

z z

y y

z a a c

y a a c

a f g U

a f g U

= +

= +

* 0P =*zn

* 0yn =

VT*


10

Control Synthesis Procedure:Longitudinal

Define (Errors):Fast Variables

Slow Variables

Design a controller such that:

*ˆ ( )T T TV V V⎡ ⎤−⎣ ⎦

( ) ( ) ( )* * *ˆ ˆ ˆ ˆTT

T z y z z y yX P a a P P a a a a⎡ ⎤⎡ ⎤ − − −⎣ ⎦ ⎣ ⎦

ˆ ˆ 0,T TX K X+ =

1 1 1, ,z yP n n

K diagτ τ τ

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

ˆ ˆ 0,TT V TV K V+ =

1T

T

VV

K diagτ

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠


11

Control Synthesis Procedure:Longitudinal

Calculate for every time

Calculate UT for every time

[ ]AERU tΔ

5 t⋅ Δ

[ ] 1AER U UU A b−=

[ ] 0 ,z z y

y

PT

U a n n

a

gA g K g g

g

⎡ ⎤⎢ ⎥

⎡ ⎤+⎢ ⎥ ⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦

[ ]*

*

*z

y

P

U z z a

y y a

P P fb K n n f

n n f

⎡ ⎤⎡ ⎤−⎢ ⎥⎢ ⎥− − ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥−⎣ ⎦ ⎢ ⎥⎣ ⎦

1

* *( ) ( )T T

T T T T

T V V

V V V AER T V T T

U d c

c f g U V K V V

−⎡ ⎤= − ⎣ ⎦

⎡ ⎤= + − + −⎣ ⎦


12

Control Synthesis Procedure:LateralCase-2: (Lateral) Pilot commands:

• Roll Rate: • Height:• Lateral Acceleration:• Total Velocity:

Generation of command:

• Define and aim for

• Solve for

*Θ

( )*h h h− ( )ˆ ˆ1/ 0hh hτ+ =

[ ] ( )( )* *sin cos sin cos cos 1/ 0hU V W h h hτΘ − Θ Φ − Θ Φ − + − =

*Θ Θ

*P*h

* 0yn =*VT


13

Control Synthesis Procedure:Lateral

Generation of command:

• Define and aim for

• Solve for

Control Computation:

• Define (Errors):

Fast Variables

Slow Variable

*Q

( )*Θ = Θ−Θ ( )ˆ ˆ1/ 0τΘΘ + Θ =

( ) ( )( )* *cos sin 1/ 0Q R τΘΦ − Φ −Θ + Θ−Θ =*Q Q

( ) ( ) ( )* * *ˆˆ ˆ ˆT T

T y y yX P Q a P P Q Q a a⎡ ⎤ ⎡ ⎤− − −⎣ ⎦⎣ ⎦*ˆ ( )T T TV V V⎡ ⎤−⎣ ⎦


14

Control Synthesis Procedure:Lateral

Design a controller such that

After some algebra, Finally:

1T

T

VV

K diagτ

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

ˆ ˆ 0T TX K X+ =1 1 1, ,

yP Q n

K diagτ τ τ

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

1[ ]TT

c U UU A b T−⎡ ⎤= ⎣ ⎦

( )(1/ )y y y

TT T T T

U P Q a n nA g g g gτ⎡ ⎤+⎢ ⎥⎣ ⎦

( ) ( ) ( )* * *y y

TT

U P Q a n yb f f f K P P Q Q f n⎡ ⎤⎡ ⎤− − − − −⎢ ⎥⎣ ⎦ ⎣ ⎦

ˆ ˆ 0TT V TV K V+ =


15

Control Synthesis Procedure:Combined Longitudinal & Lateral

Case-3: (Combined Longitudinal and Lateral) Pilot commands:

• Roll Rate (about velocity vector): • Normal Acceleration:• Lateral Acceleration:• Total Velocity:

Generation of command:• Define in the desired form as: where

and * ( tan / cos (cos tan sin ))( / )wzn TP

g g Vβ α β β β= − +

*P

* **

AP PP f g U= +

**(1/ cos (cos tan sin ))( sin (sin tan cos )

tan ( / ) ( / ) cos coswz

wP

n T T

f P R

f V g V

α β β β α β β β

β γ

= + − +

− + Φ

*wP

*zn* 0yn =*VT

*P


16

Control Synthesis Procedure:Combined Longitudinal & Lateral

Design a controller such that

After some algebra, Finally:

ˆ ˆ 0,TT V TV K V+ =ˆ ˆ 0T TX K X+ =

1[ ]TT

c U UU A b T−⎡ ⎤= ⎣ ⎦*z y z y

T TT T T T T T

U P a a n nPA g g g K g g g⎡ ⎤ ⎡ ⎤+ −⎣ ⎦ ⎣ ⎦

( ) ( ) ( )** *

z y z y

TT

U P a a n z n yPb f f f K P f f n f n⎡ ⎤⎡ ⎤− − − − −⎢ ⎥⎣ ⎦ ⎣ ⎦

1 1 1, ,z yP n n

K diagτ τ τ

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

1T

T

VV

K diagτ

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠


17

Alternative way to compute P* Command

Goal:DefineDesired error dynamics:

Substitute for and solve for

*Φ→Φ

( )*Φ Φ−Φ

( )1/ 0, 0τ τΦ ΦΦ + Φ = >

Φ *P P

( )* * *1sin tan cos tanP Q RτΦ

⎡ ⎤= Φ − Φ Θ+ Φ Θ+ Φ −Φ⎢ ⎥

⎣ ⎦

(Note: for longitudinal case)* 0Φ =


18

Results: Longitudinal(With φ∗ as a command)

Tracked Variables Control Variables

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

Φ (d

eg)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

n y(g)

0 20 40 60 800

1

2

3

Time (Sec)

n z(g)

0 20 40 60 80500

600

700

800

Time (Sec)

VT (f

t/s)

0 20 40 60 800

50

100

Time (Sec)

Thru

st (%

)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

Aile

ron

defle

ctio

n (d

eg)

0 20 40 60 80-4

-2

0

2

Time (Sec)

Ele

vato

r def

lect

ion

(deg

)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

Rud

der d

efle

ctio

n (d

eg)

New MethodExisting Method


19

P, Q, R Aerodynamic Variables

Results: Longitudinal(With φ* as a command)

0 10 20 30 40 50 60 70 80 90-1

0

1

Time (Sec)

P (d

eg/s

ec)

0 10 20 30 40 50 60 70 80 90-10

0

10

Time (Sec)

Q (d

eg/s

ec)

0 10 20 30 40 50 60 70 80 90-1

0

1

Time (Sec)

R (d

eg/s

ec)

0 20 40 60 80-2

0

2

4

6

Time (Sec)

α (d

eg)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

β (d

eg)

0 20 40 60 80100

200

300

400

Time(sec)

Dyn

amic

Pre

ssur

e (lb

/ft2 )

0 20 40 60 800.5

0.6

0.7

0.8

0.9

Time(sec)

M



20

Tracked variables

Results: Lateral(With P* as a command)

0 20 40 60-20

-10

0

10

20

Time (Sec)

P (d

eg/s

ec)

0 20 40 600.99

0.995

1

1.005

1.01x 104

Time (Sec)

Alt

(ft)

0 20 40 60-0.1

-0.05

0

0.05

0.1

Time (Sec)

n y(g)

0 20 40 60570

575

580

585

590

Time (Sec)

VT (f

t/s)

Control variables

0 20 40 600

20

40

60

80

Time (Sec)

Thru

st (%

)

0 20 40 60-4

-2

0

2

Time (Sec)

Aile

ron

defle

ctio

n (d

eg)

0 20 40 60-5

0

5

10

Time (Sec)

Ele

vato

r def

lect

ion

(deg

)

0 20 40 60-4

-2

0

2

4

Time (Sec)

Rud

der d

efle

ctio

n (d

eg)



21

Aerodynamic variables

Results: Lateral(With P* as a command)

0 10 20 30 40 50 60-20

0

20

Time (Sec)

P (d

eg/s

ec)

0 10 20 30 40 50 60-20

0

20

Time (Sec)

Q (d

eg/s

ec)

0 10 20 30 40 50 60-5

0

5

Time (Sec)

R (d

eg/s

ec)

0 20 40 600

5

10

Time (Sec)

α (d

eg)

0 20 40 60-0.2

0

0.2

0.4

0.6

Time (Sec)

β (d

eg)

0 20 40 60294

296

298

300

302

Time(sec)

Dyn

amic

Pre

ssur

e (lb

/ft2 )

0 20 40 600.536

0.538

0.54

0.542

0.544

Time(sec)

M


P, Q, R


22

Results: Combined Longitudinal and Lateral

Tracked Variables Control Variables

0 20 40 60

-10

0

10

Time (Sec)

Pw

(deg

/sec

)

0 20 40 60-0.1

-0.05

0

0.05

0.1

Time (Sec)

n y (g)

0 20 40 600

0.5

1

1.5

2

2.5

Time (Sec)

n z (g)

0 20 40 60570

575

580

585

590

Time (Sec)

VT (f

t/s)

0 20 40 600

20

40

60

Time (Sec)

Thru

st (%

)

0 20 40 60-1

-0.5

0

0.5

1

Time (Sec)

Aile

ron

(deg

)

0 20 40 60-2.2

-2

-1.8

-1.6

-1.4

Time (Sec)

Ele

vato

r (de

g)

0 20 40 60-0.6

-0.4

-0.2

0

0.2

Time (Sec)

Rud

der (

deg)


23

Summary: Nominal ControllerExisting Method:

Assumption:

More number of design parameters (11 & 12)

Works

New Method:

Assumption:

Less number of design parameters (5 & 7)

Works better...!• Lesser control magnitude• Smoother transient response• Better turn co-ordination

* * *

00

V W= =

Φ = Θ = Ψ =0V W= =

Neuro-Adaptive Control Designfor Enhanced Robustness

Indian Institute of Science, Bangalore


25

Objective:

To increase the robustness of the

“Nominal Controller” with respect to

parameter and/or modeling

uncertainties.


26

Robustness StudyParametric uncertainties was introduced in aero-coefficients and inertia parameters using Gaussian distribution around the nominal parameter values

Since no analytical method for analyzing robustness behavior is available, a stochastic approach has been followed in this paper as an alternative.

Gaussian Distribution

Perturbed CoefficientUnperturbed

Coefficient


27

Longitudinal Mode

0

y

Pilot Commands given: ; 2 ;

( and being maintained at zero);

Limits Imposed on the steady state error:: 3 ; n : 0.05 ; 1%; 15%

T T z

y

T z

V V n g

n

g V n

φ

φ

∗ ∗

∗ ∗

= =

± ± = ± = ±


28

Lateral Mode

0 0

y

Pilot Commands Given: 40 ; ; ; 0

Limits Imposed on the steady state error:h: 1%; n : 0.05 ; 1%; 10%

T T y

T

V V h h n

g V

φ

φ

∗ ∗ ∗ ∗= − = = =

± ± = ± = ±


29

Longitudinal Maneuver (Failure)

0 20 40 60 800

2

4

6

Time (Sec)

n z(g)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

n y(g)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

Φ (d

eg)

0 20 40 60 80400

600

800

1000

1200

1400

Time (Sec)

VT (f

t/s)


30

Longitudinal Maneuver (Failure)

0 20 40 60 800

20

40

60

80

100

Time (Sec)

Thru

st (%

)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

Aile

ron

defle

ctio

n (d

eg)

0 20 40 60 80-2.2

-2

-1.8

-1.6

-1.4

Tim e (S e c )

Ele

vato

r def

lect

ion

(deg

)

0 20 40 60 80-1

-0.5

0

0.5

1

Time (Sec)

Rud

der

defle

ctio

n (d

eg)


31

Lateral Maneuver (Failure)

0 10 20 30-50

0

50

Time (Sec)

Φ (d

eg)

0 10 20 300.99

0.995

1

1.005

1.01x 104

Time (Sec)

Alt

(ft)

0 10 20 30-0.8

-0.6

-0.4

-0.2

0

0.2

Time (Sec)

n y(g)

0 10 20 30570

575

580

585

590

Time (Sec)

VT (f

t/s)


32

Lateral Maneuver (Failure)

0 10 20 305

10

15

20

25

Time (Sec)

Thru

st (%

)

0 10 20 30-10

-5

0

5

Time (Sec)

Aile

ron

defle

ctio

n (d

eg)

0 10 20 30-2.5

-2

-1.5

-1

Time (Sec)

Ele

vato

r de

flect

ion

(deg

)

0 10 20 30-20

0

20

40

60

Time (Sec)

Rud

der

defle

ctio

n (d

eg)


33

Robustness in Longitudinal Mode

76%78%96%98%100%100%% Success

10%5%10%5%10%5%Mass and Inertia coefficient

5%5%2%2%1%1%Aerodynamic coefficient


34

Robustness in Lateral Mode

86%95%100%100%100%100%% Success

10%5%10%5%10%5%Mass and Inertia coefficient

5%5%2%2%1%1%Aerodynamic coefficient


35

Neuro-Adaptive Design

Problem: • The DI design sensitive to modeling

parameter inaccuracies

Solution: • Enhance Robustness by augmenting the DI

with “Neuro-Adaptive Design”

The adaptive design should preferably be compatible with “any” nominal controller


36

Desired output dynamics:

Output Robustness:Robustness of Inner Loop

Actual output dynamics:

as soon as possibledY Y→Objective:

( ) ( ) ( )d dY YY f X G X U d X= + +


37

Strategy:

aY

Y dYstateDesiredstateActual

stateeApproximat

N-A for Robustness of Output Dynamics

Dynamics of auxiliary output:

( ) ˆ( ) ( ) ( )d da Y Y a aY f X G X U d X K Y Y= + + + −

NN Approx.


38

Steps for assuring a dY Y→

0d dE KE+ = ( )d a dE Y Y−Enforce the error dynamics

After carrying out the necessary algebra

In case of control affine system

The control is given by

( , ) ( , , , ) a d df X U h X X X U=

( ) [ ( )] ( , , , )d a df X g X U h X X X U+ =

1[ ( )] { ( , , , ) ( )}d a dU g X h X X X U f X−= −


39

Steps for assuring

The error in the output is defined as

Ideal neural network is given by:

where is the weight matrix and is the radial basis function

aY Y→

( )a aE Y Y− ( )a i aiie y y−

( ) ( )Ti i i id X W Xϕ ε= +

iW ( )i Xϕ


40

Function Learning:

Define error

Output dynamics

)(ii aia yye −Δ

( ) ( ) ( )ˆ( ) ( ) ( )

i i i

i i i i i

Y Y i

a Y Y i a a

y f X g X U d X

y f X g X U d X k e

= + +

= + + +

ˆ( ) ( )

( )i i i

i i

a i i a a

Ti i i a a

e d X d X k e

W X k eε

= − −

= Φ + −

( ) ( )Ti i i id X W Xϕ ε= +

From universal function approximation property

ˆ ˆ( ) ( )Ti i id X W Xϕ=

Error dynamics


41

Lyapunov Stability Analysis

1 2

ˆ( )

ˆ( )

i i

i i i

i i i ai

Ti a i a i i i

T Ta i i i i a a i i i

Ti a i i i i a i i a i

L e p e W W

e p W X k e W W

W e p X W e p k e p

γ

ε γ

γ ε−

= +

⎡ ⎤= Φ + − −⎣ ⎦⎡ ⎤= Φ − + −⎢ ⎥⎣ ⎦

Lyapunov Function Candidate:

Derivative of Lyapunov Function:

Weight Update Rule:0


42

This condition leads to

whenever

Using the Lyapunov stability theory, we conclude that the trajectory of and are pulled towards the origin.

Hence, the output dynamics is “Practically Stable”!

/i ia i ae kε>

iaaiiai pekpeLiii

2−= ε

iae iW~

Lyapunov Stability Analysis


43

Problem Specific equations

Output vector in longitudinal mode:

Output vector in lateral mode:

T

z y TY P a a V⎡ ⎤⎣ ⎦

T

y TY P Q a V⎡ ⎤⎣ ⎦


44

Basis Function

where mean values chosen were:

22 2 11 122 2 22 231 2( )

TY YY Y Y Y aa a

X e e eiσσ σ

ϕ

⎛ ⎞⎛ ⎞ ⎛ ⎞ −− − ⎜ ⎟⎜ ⎟ ⎜ ⎟ −− − ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎡ ⎤⎢ ⎥⎢ ⎥= ⎣ ⎦

1 2 30.1, 1, 10σ σ σ= = =


45

Design parameters selected (Longitudinal mode)

The learning rates and the scalar values:

The constants selected are:0.0001, 0.05, 0.001, 0.005p n n Vz y T

p p p p= = = =

60P n n Vz y Tγ γ γ γ== = =

[ ][ ]5 5 5 4

0.05 0.05 0.05 1a

K diag

K diag

=

=


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Design parameters selected (Lateral mode)

The learning rates and the scalar values:

The constants selected are:

60; 40P n n Vz y Tγ γ γ γ== = =

0.0001, 0.05p q n Vy Tp p p p= = = =

[ ][ ]5 4 4 4

0.05 0.8 0.05 0.05a

K diag

K diag

=

=


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Outputs in Longitudinal Mode


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Controls in Longitudinal Mode


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Outputs in Lateral Mode


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Controls in Lateral Mode


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Robustness Enhancement:Longitudinal Mode


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Robustness Enhancement:Lateral Mode


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SummaryNominal control design has been carried out using “dynamic inversion” (the new method shows remarkable improvement in performance!)

The nominal design has been augmented with “neuro-adaptive design” for improvement in robustness.

Simulation Results• Tracking performance is very good

• Enhancement of robustness is substantial


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ReferencesRadhakant Padhi, Narayan P. Rao, Siddharth Goyal and Abha Tripathi, “A Model-Following Neuro-Adaptive Approach for Robust Control of High Performance Aircrafts”, Automatic Control in Aerospace, Vol. 3, No. 1, May 2010.Radhakant Padhi and S. N. Balakrishnan, “Implementation of Pilot Commands in Aircraft Control: A New Dynamic Inversion Approach”, AIAA Conference on Guidance Navigation and Control, 2003, Austin, TX, USA. Radhakant Padhi, Nishant Unnikrishnan and S. N. Balakrishnan, “Model Following Neuro-Adaptive Control Design for Non-square, Non-affine Nonlinear Systems”, IET Control Theory and Applications, Vol. 1 (6), Nov 2007, pp.1650-1661.


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