Control Allocation What, why, and how? Ola Hrkegrd Aircraft - - PDF document

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Control Allocation

What, why, and how? Ola Härkegård

Aircraft maneuvering

• Pitc

h

• Roll
• Yaw
• (S peed)

3 DOF 3 DOF T he pilot controls

2

T raditional configuration

Canard wings

Modern configuration

Rudder T railing edge flaps L eading edge flaps

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Control allocation

How do we distribute the c

• ntrol action

among a redundant set of actuators? How do we distribute the c

• ntrol action

among a redundant set of actuators?

• Modular control design

( )

u , x f x =

• (

) ( )

u , x m , x f ~ ≈

• Aircraft dynamics:

( )

v , x f ~ =

dim ≈10 dim 3

• 1. Design v=k(x,r) for closed loop

performance.

• 1. Design v=k(x,r) for closed loop

performance.

• 2. S olve m(x,u) ≈ Bu=v for u.

4 u x

Controller overview

Control alloc. S tate feedback v

r

Pre- filter

Why is modularity good?

• Not all c
• ntrol designs methods handle

redundancy.

• S eparate control alloc

ation simplifies actuator c

• nstraint handling.
• If an ac

tuator fails, only c

• ntrol

reallocation is needed.

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Practical considerations

... while solving Bu=v:

• u is c
• nstrained in

position and in rate.

• Minimum-phase

response.

• Want to minimize

– drag – radar signature – structural load

• We are in a hurry!

(50-100 Hz)

u u u ≤ ≤

• T he ac

tuators have limited bandwidth.

• Ac

tuators should not c

• unteract

eachother.

S olutions

• Optimization based approac

hes

• Direct control alloc

ation

• Daisy chaining

u u u v Bu ≤ ≤ =

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Daisy chaining

• 1. Use elevators

until they saturate.

• 2. Use T VC for

additional c

• ntrol.

Direct control allocation

u v=Bu v

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( )

u u u v Bu u f min

u

≤ ≤ =

Optimization based CA

• How do we c

hoose f(u)?

• Can we solve the problem in real time?

Pseudo-inverse

v Bu u min

2 u

=

T he optimal solution to is given by

( )

v B v BB B u

† 1 T T

= =

−

Extension:

( )

2 p u

u u W min −

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( ) ( ) ( )

t v h t u =

Half-time summary

S o far, static CA: S ame relative control distribution regardless of situation:

• maneuvering (transient)
• trimmed flight (steady state)

Dynamic control allocation

• Explicit filtering:

v

1

u

2

u

LP HP How c an we impose

u u u v Bu ≤ ≤ =

? Incorporate filtering into an

• ptimization framework.

Incorporate filtering into an

• ptimization framework.

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Main idea

• S tability?
• Control distribution?

u u u v Bu ≤ ≤ =

( ) ( ) ( ) ( ) ( ) ( )

2 2 2 2 2 s 1 ) t ( u

1 t u t u W t u t u W min − − + −

( ) ( ) ( )

• +

− =

2 2 0 t

u t u W

T he non-saturated case

( ) ( ) ( ) ( ) ( ) ( )

v Bu 1 t u t u W t u t u W min

2 2 2 2 2 s 1 ) t ( u

= − − + −

is solved by

( ) ( ) ( ) ( )

t Gv 1 t Fu t Eu t u

s

+ − + =

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Is v→u stable?

T hm: If W1 is non-singular then all eigenvalues of F satisfy

( )

1 F < λ ≤

• Asymptotically stable.
• Not oscillatory.

S teady state distribution?

us c an be computed from

( )

v Bu u u W min

s p s us

= −

( )

s t

u t u lim =

∞ →

v Bus =

T hm: If us satisfies then

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Design example

• Mach 0.5, 1000 m
• Pitc

hing only

– canards – elevons – T VC

• T rimmed flight: elevons only
• Canards: high frequencies
• T VC: midrange frequenc

ies

Parameters

• Design variables:

v 2 . 20 / 1 us           − =           = 1 . 1 1 W

1

          = 2 10 1 W

2

[ ]u

87 . 2 . 20 . 8 Bu v − − = =

• Dynamics:

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Frequency distribution

10

• 2

10

• 1

10 10 1 10 2 10

• 4

10

• 3

10

• 2

10

• 1

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Frequency (rad/sec) Control effort distribution

—Canards —Elevons —T VC

2 4 6 8

• 5

5 time [s] u [deg]

Aircraft response

2 4 6 8

• 5

5 10 15 20 25 q [deg/s] time [s] q r —Canards —Elevons —T VC

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Computing the solution

( )

u u u v Bu u u W min

2 u

≤ ≤ = −

( ) 2

a

v Bu W min arg u − ∈

Can this problem be solved in real-time? Not acc

• rding to the litterature.

Problem specific info

• S imple inequality bounds.
• From t-1:

– u – ac tive constraints

• Convergence in one sample not

necessary. T rim existing methods! T rim existing methods!

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S ummary

• Dynamic

control allocation - a new conc ept.

• Need for efficient solvers.
• New field ⇒ lot’s to do!