Researching Attitude-control Algorithm of Ejection Seats

based on Time-sharing Strategy

Minghuan Zhang

1

, Ming Wu

2

, Yu Su

1

and Cheng Zhang

1

1

School of Astronautics, Northwestern Polytechnical University, Xi’an, China

2

Aerospace Life-Support Industries, LTD, Xiangyang, China

Keywords: Ejection Seats, Attitude-control, Time-sharing Control, Minimum Safe Altitude, Optimization, Simulation.

Abstract: An attitude-control algorithm for ejection seats on “H” shaped motor is presented in this paper. The control

algorithm is based on time-sharing strategy, and the parameters in algorithm are optimized by using PSO

method. Through simulating under Matlab/Simulink in different ejection conditions, the infection of time-

sharing strategy in attitude-control is analyzed, and the minimum safe altitude is compared with K36D-

3.5A, ACES II and 120 ejection conditions in GJB 1800A-2007. The simulation results and analysis show

that this control algorithm on “H” shaped motor can improve escape performance at low-altitude and

adverse-attitude, thus proving the algorithm in this paper to be reliable and effective.

1 INTRODUCTION

Ejection seat is a key lifesaving appliance of modern

fighter in emergency (Wang, 2014), and its core

technology is attitude and trajectory control of the

seat after ejection. Most of ejection seats in service

at present are under the 3

rd

generation escape

system. To improve the pilot’s rescue, sequential

control technology (used in the 3

rd

generation) is

applied to make the seat for increasing the ejection

altitude (Miles, 2015 and Wang, 2014). Along with

high-tech of weapon, complexity of battlefield and

quicken of combat rhythm, pilot would be highly

possible to escape under low-altitude, adverse-

attitude conditions or at extremely high speed.

Therefore, it is imperative to achieve adaptive

control of ejection attitude. The 4

th

generation of

ejection seat is designed to solve the rescue problem

in low-altitude and adverse-attitude conditions

beyond the current generation, and its core is the

application of thrust vector continuous control

technology (Ma,2000 and Keller, 2008). By the fast

switching among thrust vector, the seat can gain

maximal lift as quick as possible. Thereby, the

safety is increased.

Technology on the 4

th

generation escape system

was start to study from 1970s, however, it has not

implemented for engineering application nowadays.

One of the main technical bottlenecks is the

application of thrust vector continuous control. U.S.

Air Force Research Lab proposed the structure of

the ejection seat under the 4

th

generation escape

system (Blairnald, 1998). The “H” shaped motor

installed on the seat so that the nozzles located at

four corners can obtain large moment arms for

attitude-control. It makes maintaining a constant

pressure become possible. (Feng, 2007) present a

safe altitude impact factor method under the 3

rd

generation. It analyzed infection of aircraft

parameters start from ejection to safe altitude.

Despite this work can improved escape performance

at medium-low-speed and lower-altitude somehow,

it only meet 44% of the minimum safe altitude in

GJB 1800-93. (Yuan, 2009) presents a nonlinear

inverse-dynamics method to design the control law

of the ejection seat under the 3

rd

generation. Results

under medium-low speed can be verified in 4

th

generation escape system, but the robustness of this

method need to be improved. Both of above two

methods are based on sequential control technology.

It can’t meet the requirement of the adaptive control

which is the symbol of the 4

th

generation.

We present a time-sharing attitude-control

algorithm based on thrust vector continuous control

technology. The parameters of controller is

optimized by Particle Swarm Optimization(PSO).

The experimental results and analysis show that this

algorithm can achieve fast robust attitude-control of

ejection seat. Moreoever, this strategy gives a new

262

Zhang, M., Wu, M., Su, Y. and Zhang, C.

Researching Attitude-control Algorithm of Ejection Seats based on Time-sharing Strategy.

DOI: 10.5220/0005975702620267

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 2, pages 262-267

ISBN: 978-989-758-198-4

Copyright

c

2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

solution of adaptive control under 4

th

generation

system.

2 MATHEMATICAL MODEL OF

“H” SHAPED MOTOR

Fig.1 shows the “H” shaped motor installs at the

ejection seat back. The motor is equipped with four

fixed nozzle, which provide thrust for the ejection

seat. Under body axis system, the thrust of each

nozzle is shown as Eq.1 and Eq.2.

1,2,3,4i

refer to

the nozzle number as the Fig.1 shows.

11

1

11

sin cos

cos

( 1) sin sin

1,2

hix hi h h

hiy hi h

i

hiz hi h h

FF

FF

FF

i

(1)

22

2

22

sin cos

cos

( 1) sin sin

3,4

hix hi h h

hiy hi h

i

hiz hi h h

FF

FF

FF

i

(2)

And the moment of each can be describe as Eq.3

and Eq.4.

1

hix 1 1 h1 1 2

1 1 1 h2 1 1

1 1 1 1 1

( 1)

M ( 1) sin sin (L ) cos

2

( 1)

M sin cos L ( 1) sin sin

2

M sin cos ( ) cos

1,2

i

i

hi h h c hi h h

i

i

h y hi h h hi h h c

h z hi h h h c hi h c

F y F L

F F x

F L y F x

i

(3)

1

1

hix 2 2 2 2

2 2 h2 2 2

2 2 2

( 1)

M ( 1) sin sin cos

2

( 1)

M sin cos L ( 1) sin sin

2

M sin cos cos

3,4

i

i

hi h h c hi h h

i

i

hiy hi h h hi h h c

hiz hi h h c hi h c

F y F L

F F x

F y F x

i

(4)

Nozzle #1 and nozzle #2 have the same

installation angle direction, while nozzle #3 and

nozzle #4 have the same installation angle direction.

hi

and

hi

are shown in the Fig.1 b) and c), in which

i

refers to the nozzle number.

When all four nozzles work at the same time, the

total thrust and moment is shown as Eq.5 and Eq.6:

1 2 3 4

1 2 3 4

1 2 3 4

hx h x h x h x h x

hy h y h y h y h y

hz h z h z h z h z

F F F F F

F F F F F

F F F F F

(5)

c

O

cc

OZ

cc

OY

1h

L

2h

L

Nozzle #1 Nozzle #2

Nozzle #3 Nozzle #4

c

O

cc

OX

h

cc

OX

cc

OZ

c

O

h

a)Front View b)Side View c)Upper View

cc

OY

Figure 1: The structure of “H” shaped motor under body

axis system.

1 2 3 4

1 2 3 4

1 2 3 4

hx h x h x h x h x

hy h y h y h y h y

hz h z h z h z h z

M M M M M

M M M M M

M M M M M

(6)

The motion attitude equations of ejection seat are:

sin cos

( cos sin ) / cos

( cos sin )

yt zt

yt zt

xt yt zt

d

dt

d

dt

d

tg

dt

(7)

In above,

,,

refers to pitch, yaw and roll angle;

,,

xt yt zt

are palstances around three axes under

body axis system.

Attack and sideslip angle of ejection seat are

,

;

,,

xt yt zt

V V V

is three velocity components of

c

V

:

2 2 2

( / )

arcsin( / )

c xt yt zt

yt xt

zt c

V V V V

arctg V V

VV

(8)

3 ATTITUDE-CONTROL

ALGORITHM

To maintain internal pressure balance, “H” shaped

motor takes the control mode that each two nozzles

has dual thrust vector. Once installation angle

direction is set, it will not change through the all

procedure. Thus, interconnection of each attitude

angle between control moments is bad for the

control algorithm design. We take the time-sharing

control strategy. By optimizing installation angle

direction of each nozzle, we can achieve decoupling

of attitude-control moment.

3.1 Time-Sharing Control Algorithm

In time-sharing control strategy, “H” shaped motor

Researching Attitude-control Algorithm of Ejection Seats based on Time-sharing Strategy

263

has three modes (pitch, yaw and roll mode). The

thrust and moment of each is shown as Eq.9, Eq.10

and Eq.11.

Pitch mode:

1 2 3 4

(1 )

,

22

0

h h h h h h

xy

KK

F F F F F F

MM

(9)

Yaw mode:

1 3 2 4

(1 )

,

22

0

h h h h h h

xz

KK

F F F F F F

MM

(10)

Roll mode:

1 4 2 3

(1 )

,

22

0

h h h h h h

yz

KK

F F F F F F

MM

(11)

h

F

is the total thrust of the “H” shape motor, which is

a constant value.

K

is the coefficient of each nozzle

in dual control mode. The trust of four nozzle is

determined totally by

h

F

and

K

.

We establish the inconsistent equations set on

Eq.6 and three control modes. And optimize the

installation angle of nozzles by finding optimal

solution of this set. This is also the procedure of

decoupling the control moment of three channels

(Pitch, Yaw and Roll). Due to the specialization of

inconsistent equations, coupling moments in three

control mode can be zero at the same time. But the

process of finding optimization ensures that residual

coupling moment is far miner than the main control

moment. Therefore, the residual coupling moment

can be taken as small perturbation.

3.2 Algorithm Design

Under the time-sharing control strategy, the time of

each channel is limited. The attitude-control is

further weakened by constraint of ejection altitude.

If control time is mainly spent on decoupling of

palstances, attitude-control period could be delayed.

If ignore the decoupling and concentrate on attitude-

control, the speed of attitude-control will be slow,

and even influence the stability of the system.

Finally, trajectory control will be affected.

To minimize the motion decoupling, we take a

switching strategy between coupling palstances and

attitude to achieve fast control of attitude.

3.2.1 Control Objective

Set

( , , , , , )

(refers to pitch, yaw, roll, pitch

palstance, yaw palstance and roll palstance) as

control variables, and its expectation is signed as

* * * * * *

( , , , , , )

. To maintain the stability of

system,

0/s

; To ensure that the seat

can get the maximum lift, the expectation of roll

is

*

0

and yaw is

0

by adjustment of

*

.

According to finding the optimization of

inconsistent equations, installation angle direction

of nozzle after decoupling is

12

40 , 58 ,

hh

12

72.5 , 7

hh

. When the pitch expectation is

*

38

, the lift can be maximum, and expectation

of control variable is :

* * * * * *

( , , , , , ) (38 ,0 ,0 ,0 / ,0 / ,0 / )sss

3.2.2 Transfer Function

To design the control system, the transfer function

between

K

and control variable:

3 3 4

2

42

3

2

42

3 3 4

2

42

3

()

()

()

()

()

()

()

()

s a s a a

K s s a s a

sb

K s s b s b

s b s b b

K s s b s b

sc

K s s

(12)

In above,

22

,ab

is static stability of related control

channel.

3 3 3

,,a b c

is the efficiency coefficient, which

refers to palstance increment of related control

channel when

K

increase.

44

,ab

is the palstance

increment of trajectory tangent line.

3.2.3 Linear Systems Control Design

Take pitch control channel as example, the system

block diagram is shown as Fig.2.

e

is the difference

of pitch expectation and actual value;

,,

P I D

K K K

refers to gain of proportion, integration

and differentiation in PID algorithm;

K

( thrust

partition coefficient of nozzles in pitch channel) can

be calculated by

,,

P I D

K K K

and current

e

.

In order to maintain the dynamic performance of

this control system,

,,

P I D

K K K

can be optimized

through PSO method.

e

P

K

I

K

s

D

Ks

k

()s

k

1

s

*

Figure 2: Control block diagram of pitch channel.

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

264

Velocity and position of particle in search space

can be described as:

1 1 1 2 2

11

( ) ( )

t t t t t t

t t t

v wv c r P a c r G a

a a v

(13)

In which,

a

is the particle position and

v

is velocity.

w

is inertia factor and

12

,cc

are acceleration

constants.

12

,rr

are random values between [0,1].

[ , , ]

t P I D

P K K K

is the optimal control parameter of

particle so far and

[ , , ]

t P I D

G K K K

is the whole

Particle Swarm’s best parameter so far.

The optimization flow chat of PSO algorithm in

pitch channel shows as follows:

Step 1 Initialize all the particle’s position and

velocity in swarm, and set optimum

control parameters

t

P

and

t

G

;

Step 2 Check whether the adaptive factor of

every particle is better than optimum

control parameter

t

P

, if yes, update the

t

P

to current particle adaptive factor;

Step 3 Check whether the adaptive factor of

every particle is better than optimum

control parameter

t

G

, if yes, update the

t

G

to current particle adaptive factor;

Step 4 Update particle’s position and velocity

use Eq.13;

Step 5 If the iterative step meet the max value

or the particle adaptive factor smaller

than lower limit, exit and get optimum

value. Otherwise, return to Step 2.

The parameters in PSO algorithm are as follows:

Inertia factor is

0.6w

;

Acceleration constants are

12

2cc

;

Iteration number is 100;

Particle number is 100;

Minimum particle adaptive factor is 0.1.

K

of each channel can be obtained:

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

P I D

P I D

P I D

P I D

P I D

P I D

de

K e K e dt K pitch

dt

de

K e K e dt K yaw

dt

de

K e K e dt K roll

dt

K

d

K K dt K pitch

dt

d

K K dt K ya

palstance

palstaw

dt

d

K K dt K roll

dt

nce

palstance

(14)

According to PSO results, gains of each control

channel are shown as Eq.15 and Fig.3.

1 2 3 4 5 6

1

2 3 4 5 6

1 2 3 4 5 6

6, 3

0.5 180 70

0.9 70 10

0.8 10 80

0.5 80 180

0, 10

0.8, 0.5, 0

P P P P P P

I

I I I I I

D D D D D D

K K K K K K

K

K K K K K

K K K K K K

(15)

3.2.4 Switching Control Strategy

Our switching control strategy of coupling

palstances and attitude is illustrated as Fig.4.

4 SIMULATION RESULTS AND

ITS ANALYSIS

Based on 120 ejection conditions which is regulated

by GJB 1800-2007 (General Specification for

Ejection Seat Type of Aircrew Emergency Escape

System), we experiment under Matlab/Simulink

simulation environment. And we verify the

performance of attitude-control algorithm by

minimum safe altitude and changing curve of

attitude angle after ejection.

We display simulation results under four type

conditions. The simulation time is 1.8s and the

simulation step is 0.001s. Fig.5 shows the changing

curves of attitude angle after ejection.

It is noted that all the angle and velocity here

refers to the angle and velocity of aircraft under

inertial frame. As simulation results, curves in red is

pitch, curves in blue is roll and curves in green is

roll.

Fig.5 a) and b) shows the simulation results of

large roll angle attitude.

0 10 20 30 40 50 60 70 80 90 100

0

0.5

1

1.5

2

2.5

3

3.5

Iteration Number

Gain

Figure 3: The optimization curve of PSO.

Researching Attitude-control Algorithm of Ejection Seats based on Time-sharing Strategy

265

abs(W_y)>200°/s

Yaw Palstance

Control

Theta>75° abs(Wx)>200°/s

Roll Palstance

Control

Pitch Control

abs(Gama)>160°且

Theta<30°

abs(Wx)>200°/s

Pitch Control

abs(Gama)>20° or

abs(W_x)>100°/s

abs(Wz)>100°/s

Pitch Palstance

Control

Roll Control

Pitch Control

Current State

6-DoF Model

Y

Y

Y

Y

Y

Y

Y

N

N

N

N

N

N

N

Roll Palstance

Control

Figure 4: Switching control strategy.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-200

-150

-100

-50

0

50

100

150

200

t(s)

Attitude Angle(°)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-40

-30

-20

-10

0

10

20

30

40

50

t(s)

Attitude Angle(°)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-80

-60

-40

-20

0

20

40

60

t(s)

Attitude Angle(°)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-200

-150

-100

-50

0

50

100

150

200

t(s)

Attitude Angle(°)

a)Large roll angle attitude:

velocity 0km/h, dive angle 0

0

,

sink-rate 0m/s, roll angle 180

0

b)Large roll angle attitude:

velocity 250km/h, dive angle 0

0

,

sink-rate 50m/s, roll angle 180

0

c)Large dive angle attitude:

velocity 0km/h, dive angle 60

0

,

sink-rate 0m/s, roll angle 0

0

d)Large dive angle attitude:

velocity 450km/h, dive angle 90

0

,

sink-rate 0m/s, roll angle 0

0

Attitude angle(

0

)

Attitude angle(

0

)

Attitude angle(

0

)

Attitude angle(

0

)

t(s) t(s) t(s) t(s)

Figure 5: Curves of attitude angle in adverse conditions.

Due to the time-sharing strategy, the system is in

pitch control channel from 0-0.35s in Fig.5 a). Since

the initial aerodynamic-force is too low to take into

consideration, the roll angle has not changed in this

period; The roll angle is close to the control target

38°around 0.35s, so we switch the system to roll

control channel. During the period of 0.35-1.2s the

system is under roll control channel, pitch angle has

drifted in some extend due to the increase of

aerodynamic-force and infection of coupling

palstances. The system enters stability augmentation

control condition after 1.2s; Roll and pitch angle are

around the control target during 1.2-1.8s. In the

whole process, the velocity of ejection seat is quite

small, therefore the infection of aerodynamic

moment from sideslip-angle is not big and the

control period is quite short.

Similarly in Fig.5 b), during the time period 0-

0.4s and 0.4-1s, roll angle control and pitch angle

control has been affected due to the switching

strategy. In addition, the pitch and roll channel

realize fast attitude stable.

Fig.5 c) and d) shows the simulation results of

large dive angle attitude. The system can achieve

fast stable of pitch attitude within 0.5s. Because “H”

shaped motor has symmetric control moment in

pitch channel and coupling moment of roll and yaw

is negligible, the change of roll and sideslip-angle is

too small to affect dynamic performance of the

system.

From simulation results, this time-sharing

strategy can achieve fast, effective and stable control

of ejection seat attitude.

We compare our results with the minimum safe

altitude requirement of ACES II, K36D-3.5A in

adverse conditions (Barnette, 1998) in Tab.1. The

minimum safe altitude is

12

min(0, )h h h

,

1

h

is the

altitude when ejection and

2

h

is the lowest altitude of

movement curve.

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

266

Table 1: Comparison of minimum safe altitude.

No.

Aircraft Attitude

Velocity

(KEAS)

Minimum Safe Altitude(ft)

Dive Angle(

0

)

Roll Angle(

0

)

ACES II

K36D-3.5A

Our Results

1

0

60

120

0

0

0

2

0

180

150

150

96

91

3

0

1

0

150

116

137

66

4

60

0

200

335

288

259

5

30

0

450

497

518

454

6

60

60

200

361

299

331

7

45

180

250

467

323

353

Notes: 1. The current sink-rate of aircraft is 10,000ft/min;

2. KEAS (Knots Equivalent Air Speed) is 1knot=1.85km/h.

In the first 5 states in Tab.1, our minimum safe

altitudes are all lower than that in ACES II and

K36D-3.5A; And the following two are better than

ACES II.

GJB 1800-2007 regulates 120 conditions, 88 of

which is low speed and 32 is high speed. By

experimental comparison, our algorithm can meet

the 67 conditions in low speed, about 76%. In high

speed, 24 conditions can meet the requirement,

about 75%. Based on ejection seat with “H” shape

motor, our algorithm can effectively increase the

ejection altitude and therefore improve the

occupant’s rescue.

5 CONCLUSIONS

This paper proposes an attitude-control algorithm for

ejection seats based on time-sharing control strategy.

The parameters of controller are optimized by

applying PSO method. Simulation results show that

our algorithm can meet the requirement of 75%

conditions in GJB 1800-2007, which included low-

altitude, adverse-attitude and some of the high speed

conditions. Based on continuous thrust vector

control framework, our approach is designed totally

under 4th generation escape system. Experiment and

its analysis verify that our approach can feasibly and

effectively achieve adaptive control.

ACKNOWLEDGEMENTS

This work is supported by the National Natural

Science Foundation of China (No.61502391), the

China Space Foundation (No.N2015KC0121).

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