mdts 5705 : controldynlab.mpe.nus.edu.sg/mpelsb/mdts/control 1n v2.pdf · mdts 5705 : control...

G. Leng, MDTS, NUS

MDTS 5705 : ControlLecture 1 : Missile control configurations

G. Leng, MDTS, NUS

References

• G. M.. Siouris, “Missile Guidance and Control Systems”,

Springer-Verlag, 2004

• B. Stevens. "Aircraft Control & Simulation", J. Wiley,

1992.

• D. McRuer, I. Askenas & D. Graham, "Aircraft Dynamics

and Automatic Control“, Princeton University Press, 1973

G. Leng, MDTS, NUS

Training Programme

1 : Missile control configurations

or making sense of the aerodynamics for flight control

2 : Missile dynamics and control models

or when to simplify, when to stop and how to simulate

3: Designing the flight control system

or defining the control limits of the missile

G. Leng, MDTS, NUS

1.1.1 : A first step is to define a convenient axis system or

reference frame fixed to the missile.

Question : Why fixed to the missile ?

1.1 : Axes System

G. Leng, MDTS, NUS

x

z

1.1.2 : Body axes

yy

The convention for flight dynamics is :

I) The positive x axis points towards the nose

II) The positive y axis points to the right

III) The positive z axis points downwards.

Note that this is a right handed

coordinate system.

Question : Where should the

origin be placed ?

G. Leng, MDTS, NUS

1.1.3. The set of axes as defined in 1.1.2 is called the body axes. It is fixed to the missile and translates and rotates with it.

Question : Implications for equations of motion ?

G. Leng, MDTS, NUS

1.1.4 : Aerodynamics axes

Question : Why do the axes point

this way ?

x

z

y

y

Typically, aerodynamicists and structural engineers use different

conventions for their axis systems creating unnecessary

confusion

G. Leng, MDTS, NUS

1.1.5. Using the body axes, the missile's velocity V is written

as V = {u, v, w} where

u, v, w

are the velocity components in the X,Y,and Z axes direction.

G. Leng, MDTS, NUS

x

z

Figure 1.1.1 : Velocity components

y

v

w

u

V

G. Leng, MDTS, NUS

1.1.6. Similarly we denote the missile's rotation with an

angular velocity vector = {p, q, r } where p, q, r, are the

roll (wings up/down)

pitch (nose up/down)

yaw (nose right/left)

rotational rates.

G. Leng, MDTS, NUS

x

z

Figure 1.1.2 : Angular velocity components

yp roll rate

r yaw rate

q pitch rate

G. Leng, MDTS, NUS

1.2 : Aerodynamic Forces and Moments

1.2.1. Aerodynamic forces and moments on the missile depend

on the orientation of the missile with respect to the flight

trajectory

1.2.2. This orientation is specified by the two important angles

: angle of attack

: sideslip angle

G. Leng, MDTS, NUS

v

u

w

Figure 1.2.1 : AOA & sideslip angle definition 1

V

G. Leng, MDTS, NUS

v

u

w

Figure 1.2.1 : AOA & sideslip angle – definition 2

V

s

Question : Can you spot the difference ?

G. Leng, MDTS, NUS

Example : Aerodynamic database

How does the aerodynamics vary for a real missile ?

G. Leng, MDTS, NUS

Example – CZ variation

G. Leng, MDTS, NUS

Example - Cm variation

Question : Why must Cm vary this way with AOA ?

AOA

Cm

e

trim pt

G. Leng, MDTS, NUS

How does one “control” a missile ?

Maverick

Sidewinder

Control

surfaces

Control

surfaces

G. Leng, MDTS, NUS

Missile aerodynamic control surfaces

servo motor

control

surface

hinge

line

G. Leng, MDTS, NUS

• Deflection of control surfaces changes aerodynamic forces acting on the surface

• Changes in forces generate moments about the cg which roll, pitch and yaw the missile

• How well does this work ?

• Can you estimate the aerodynamic control forces on a missile ?

Basic aerodynamic control technique

G. Leng, MDTS, NUS

Ex : Control force estimation

• AIM 9 @ Mach 2.5

• Triangular fin

• Area = ½ x 0.3 x 0.3

= 0.045 m2

Force =

=

=

G. Leng, MDTS, NUS

Examples of missile control surfaces

• Foldable fins

• Tube launched weapons

G. Leng, MDTS, NUS

Examples of missile control surfaces

• Lattice control surface

• AA-12 Adder

G. Leng, MDTS, NUS

Performance implications 1

Tail control missile

Lw

W Lt

So what’s the problem ?

G. Leng, MDTS, NUS

Non–minimum phase response

time

commanded

latax

actual latax

Initial response heads off in the wrong direction

G. Leng, MDTS, NUS

Performance implications 2

Canard control missile

Lw

W

Lc

Comments ?

G. Leng, MDTS, NUS

Ex : Comment on the control configuration of this missile

G. Leng, MDTS, NUS

Multi-control surfaces - Rafael Python 4

G. Leng, MDTS, NUS

G. Leng, MDTS, NUS

1.3 Missile control methods - examples

ailerons

rudder

elevator

Where are the control surfaces ?

G. Leng, MDTS, NUS

1.3.1 Cartesian control for homing

• Separate sets of control surfaces

for pitch (up/down) and yaw

(left/right)

• Guidance generates required

latax for pitch and yaw planes

• Pitch and yaw controls can act

simultaneouslytarget

G. Leng, MDTS, NUS

Missile control methods - example

Moving wings serve as both

ailerons and elevators

Fixed tail surfaces

Question : What can of control

method was employed ?

G. Leng, MDTS, NUS

1.3.2 Polar control for homing

• Guidance generates

roll command and

required pitch latax

(twist & steer)

• Needs roll angle

reference

• How fast is the

missile response ?

target

target

G. Leng, MDTS, NUS

1.3.3 Skid to turn for mid-course

• Turn executed by

“skidding” the missile

• Hence missile is not

aligned with velocity

vector during turn

• Typically used for fast

turn response

• May lead to large AOA &

sideslip – problems ?

G. Leng, MDTS, NUS

1.3.4 Bank to turn for mid course

• Missile rolls to vector lift

• Missile is aligned with velocity vector during turn

• Small AOA & sideslip

• Why bank to turn ?