automatic control of a jetpack - me461 presentation final

8/14/2019 Automatic Control of a Jetpack - ME461 Presentation Final

1/13

ME461 FALL 2008

AUTOMATIC CONTROL

JETPACK CONTROL

Team Space Cadets

Ryan Rudy

Sudeep Pillai

Vincent Wei Jie Lam

Wisit Jirattigalachote


2/13

Motivation & Control Problem

Motivation

Intriguing dynamics of a jetpack being propelled into the air

Very beneficial in firefighting and rescuing in tall buildings

Control Problem

Control the height of a person propelled by a jetpack in one

dimension (upwards)

Input would be the different thrust nozzle areas


3/13

Control Goals

Overall

Jetpack speed and acceleration less than 40m/s and 2grespectively

Attain vertical height of 300m within 30s

Fast response for smaller changes in height Account for disturbances

Closed Loop Control

Overshoot Less than 10% while ascending

Less than 1m while descending

Sufficiently small steady-state error (within 1%)


4/13

Free Body Analysis

Assumptions

Constant mass flow rate

Simplified fluid dynamics

Equation of motion

System Model

Fdrag

FthrustW = mg

+X

= ( ) ( ) + ( 101325 + 9.1) 2

=1

22

= ( ) ( ) + ( 101325 + 9.1)


5/13

Open Loop: Non-Linear Model

A x_dotx_dd x

ScopeProduct 1Product

Integrator 1

1

s

Integrator

1

s

Pe

384800Patm

101325

MVeng

Gain 1

9.1

300

Area

0.0058

Thrust Force

x^2

u2

K

0.13

Drag Force

multiply

g

9.8

const

1

Mass

200

M_dot(mass loss)

.1

Divide

Clock1

100

Mass Reduction


6/13

Linearization

Equation of motion linearized using a simplified Taylor

Series expansion

To simplify the model, the mass in the system will be

assumed constantover time The Linearized model at equilibrium is

The linearized transfer function is approximately:

= 0.000264 + 13.65 13.65 = 300 = = 0

=

13.65

2


7/13

Controller Derivation

-50

0

50

100

150

Magnitude(dB)

10-3

10-2

10-1

100

101

102

103-180

-90

0

90

Phase(deg)

Bode Diagram

Gm = -106 dB (at 0 rad/sec) , Pm = 0 deg (at 7.14 rad/sec)

Frequency (rad/sec)

-100

-50

0

50

100

Magnitude(dB)

10-3

10-2

10-1

100

101

102

103-180

-150

-120

Phase(deg)

Bode Diagram

Gm = -94.3 dB (at 0 rad/sec) , Pm = 60 deg (at 7.14 rad/sec)

Frequency (rad/sec)

Frequency Response of

G(j)/ [Green] and C(j) [Blue]

Frequency Response of

G(j)*C(j)

To achieve the control goals of overshoot 0.6 and > 60.


8/13

Controller Derivation

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4

Step Response

Time (sec)

Amplitude

0.1

1

10

100

Closed Loop step response for varying gains


9/13

Closed Loop: Non-Linear Model

_ _

_

K1

.1

Controller

13.93 s+8.423

s+8.423

_ _

Saturation

_

xx_dd x_dotA

x^2

u2

g

9.8

const

1

Product 1Product

Pe

384800Patm

101325

s

_

MVeng

300 K

0.13

Integrator 1

1

s

Integrator

1

s

Gain 1

9.1

Divide

_ _

multiply

g

9.8

const

1

Mass

200

M_dot

(mass loss)

.1

Divide

Clock1

0

_ _

_

Area

0.0058 _ _

Uniform Random

Number

Reference

_

_ _

_

_ _

_

_ _

_


10/13

0 20 40 60 80 1000

50

100

150

200

250

300

350

Time (s)

CurrentPosition(m

)

Jetpack response while attaining a height of 300m

Close Loop Response Curves Non-Linear

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8x 10

-3 Jetpack nozzle area change vs. time

Time (s)

NozzleArea(m2)


11/13

Simulation


12/13

Conclusion & Future Work

Conclusions

Successfully modeled a reasonably accurate non-linear

and linear systems for the Jetpack

Achieved all of our control goals

Future Work

Model the actuator with a low pass filter Consider the effects of additional mass


13/13

Questions?

automatic control of a jetpack - me461 presentation final

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