Project Report

Hovercraft

By

Hassan Abdulkareem

Jassim M. Alhor

Miguel A. Frontera

2

Table of Contents

Introduction …………………………………………………. 3

Abstract …………………………………………………. 4

Apparatus …………………………………………………. 5

Sensor Mechanism …………………………………………. 6

Time Response …………………………………………. 8

System Response …………………………………………. 9

Stability Analysis …………………………………………. 10

Control System …………………………………………. 11

Conclusion …………………………………………………. 15

Appendix A: Equation of Motion …………………………. 17

Appendix B: Budget …………………………………………. 19

Appendix C: Time Schedule …………………………. 20

Appendix D: Picture of the Hovercraft …………………. 21

Appendix E: Finding the Thrust …………………………. 22

Appendix F: Time Response Plot Data …………………. 23

Appendix G: MOSFET Specifications ……………………. 24

Appendix H: Computer Board Connector ……………………. 25

3

Introduction

We are designing a hovercraft that would maintain a certain altitude. Two

vertical poles are guiding the hovercraft when it’s in motion (see Figure 1). A battery

operated motor and propeller are providing the necessary power to left the hovercraft and

its load.

Manual control can be done by installing a variable resistor over the motor

power leads. The computer control system was done using I/O card.

Figure 1: Hovercraft

4

Abstract

Altitude of the Hovercraft was to be measured and controlled using a feed back

system. Feedback system was designed using a voltmeter and a resistor wire. As the

Hovercraft changes altitude, the internal resistance of the wire changes relatively. The

resistor wire was placed along one of the poles. A linear relationship between altitude and

the internal resistance was established as the guidance for the closed loop system. System

was constructed using wooden plate for the base, wooden poles, voltmeter, motor and

propeller, brass tubes as bearings, and wires. Parts were glued together (see Appendix D

for a picture of the hovercraft).

The system was designed for a one-semester project and is quite fragile. Some

reinforcement could be needed if the system was to last longer, including gluing some

stronger flat surface to the base of the system to avoid the misalignment of the poles

because of bending. Also, some reinforcement could be needed for the poles and some

springs could help avoid the hovercraft to hit the base to hard when the power is reduced

too sharply.

5

Apparatus

The following is a list of all of the part used to construct the hovercraft. The

actual project budget, $63.89, came under the initial estimate, $72.00. The cost of

each part is listed in Appendix B. The input/output computer card and board were not

included in the total budget because the University of Texas at San Antonio supplied

them. Minor supplies, such as glue and lubricant, were not included in the total

budget as well.

Table 1: Equipment List

Part Specifications

Motor Graupner “Speed 400”. Voltage 7.2. Produces

120W

Propeller SlimPROP “Super”. Size 9x5”

Resistor Wire 52cm long

Voltmeter RadioSHACK 22-410. 0-15V

Spinner C.G. 1”

Constant Current

Supply

LKG Industries M-W-122A

Electrical Wire 18 Gage

Brass Tube 7/16 round

Wood Sheet Size 0.25x6x36

Wood Sticks 52cm long

Hardwood Dowel Size 3/8x36

MOSFET Philips ECG2395 (See Appendix G)

Heat Sink 1.5”x1.0”x0.5”

Batteries Sanyo KR-600-AE. 8.4Volts

6

Sensor Mechanism

An altitude-sensing device is needed for this project. It was made from

resistor wire. The resistor wire was attached to the support stick. A voltmeter was be

used as a height gage. One voltmeter lead will be attached to one end of the resistor

wire, while the other lead will be attached to the hovercraft. The higher the

hovercraft goes, the higher the measured resistance will be (see Figure 2).

Figure 2: Sensor Mechanism

The following table is used to determine the location of the hovercraft. The

height in inches is given for selected voltage readouts. Other heights can easily be found

by interpolating between the given values.

Table 2: Voltage Across Variable Resistor

Voltage (V) 0.49 1.09 1.67 2.28 2.99

Height (in) 0 5 10 15 20

7

The following plot shows the relationship between the voltage measured across

the variable resistor and the height of the hovercraft.

Height vs. Voltage

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3 3.5

Voltage (V)

Hei

ght

By linearizing this relationship, we get the following equation describing the

voltage in terms of height.

V = 0.126H + 0.49

Where V: Voltage in (V)

H: Height in (in)

This equation was used in the control diagram to convert the desired height

into voltage. This step allows for a direct comparison between the voltage readout

across the variable resistor and the desired height.

8

Time Response

The time response was found with the following assumptions:

• No air drag

• Gravity = constant

• Weight is constant (neglecting the weight of the wire)

• Ground effect is constant

• Vo = yo = 0

• Thrust is formulated as a multiple of weight and treated the two as step

function

The time response expressed in the Laplace domain is (see Appendix A for the

complete derivation):

Y(s) = [g(T-1) – sy(0)(1-s) + sy’(0)] / [s2(s+b)]

By assuming the initial conditions as zero, the time response can be expressed as

follows:

y(t) = g(T-1) [ t/b – 1/b2 + e-bt ]

Where b: coefficient of friction

T: thrust

g: gravity constant

t: time

9

System Response

In order to calculate the system response, the thrust of the motor had to be

calculated. Then, the time response equation can be solved.

The trust was found by keep the hovercraft at a certain altitude and taking voltage

measurements. These voltage measurements were taken across the motor. By repeating

this process using different weights, a plot of the voltage vs. thrust was found (see

Appendix E). The voltage range was from 4.2 to 5.0 volts. The thrust range was from

0.226 to 0.290 N.

Assuming a friction factor b of 1, the following plot was generated for different

thrust values (see Appendix F for the table of data used to generate the plot).

Response vs . Time

0

1

2

3

4

5

6

7

8

9

0.0 0.4 0.8 1.2 1.6 2.0

Time

Res

pons

e 0.23 Thrust0.25 Thrust0.27 Thrust

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Stability Analysis

The stability of the system was determined using the Routh-Hurwitz method. A

MathLAB code was developed to analyze the system and predict its behavior (see Figure

3). By varying the thrust of the motor, the roots for the characteristics equation were

found.

Figure 3: MathLAB Code

The following plot shows the behavior of the system. For a stable system, the

solutions with negative real part are considered.

11

Control System

After setting the desired height for the hovercraft to reach, the motor starts

with full power. Then, the controller adjusts the power to the motor by a MOSFET to

increase or decrease the power going to the motor (see Figure 4). The terminals of

the variable resistor are connected to the computer card to provide the necessary

height information for the controller. Once the desired height is reached, the

controller holds the hovercraft for the desired period of time.

Figure 4: Control System

The nomenclature for the above figure is as follows:

H: Desired Altitude

K2: Gain

V: Voltage necessary to maintain a given height

Km: Motor Gain

MC/s: Motor Dynamics

1/s(s+B): Dynamics of System

K1: Sensor

12

The following, Figure 5, is the circuit diagram for the hovercraft, power

supply, and the input/output card (see Appendix H for pin configuration).

Figure 5: Circuit Diagram

The MOSFET control was also a problem. Not only maximum current and

voltage needed to be checked before using a MOSFET or another; maximum power also

needed to be taken in account as the used motor was actually producing up to 80 watts of

power. These was initially overlooked the team and many MOSFETS were burned before

getting the right one. At the end the MOSFET used was capable of handling 150 Watts

and even then the high current drawn by the motor caused the MOSFET to heat up

rapidly and a fan had to be used to cool it.

13

LABview, a control program, was used to construct the control algorithm for the

system. Two methods of control were developed: position control and velocity control.

The velocity control algorithm did not work as well as the position control. Some

spikes of +- .01 volts were observed coming from the sensor into the LABview

algorithm. Because of the design of the algorithm this spikes were amplified to up to +-.1

volts into the gate of the MOSFET controlling the motor voltage. This resulted in spikes

of more than +- 1 volt to the motor voltage. This change of almost two volts created a

change in motor rpm of about 1000 making the system totally unstable. Increasing the

delaying time for sampling seemed to improve the stability of the system. It was

suggested that an averaging algorithm could be setup to smooth these spikes and improve

the response of the system.

Position control, on the other hand, relies only on one parameter to determine the

current height of the hovercraft (see Figure 6). By comparing the voltage readout across

the variable resistor to the current readout, the voltage to the MOSFET gate was

determined. By changing the voltage across the gate, the power to the motor was

changed accordingly.

Figure 6: LABview Position Control Algorithm

14

By experiment, the voltage to maintain a certain height was found to be 2.37V.

Figure 7 illustrates the interface of the position control algorithm. Changing the height

triggers the control algorithm to reach the given height.

Figure 7: Interface of Position Control Algorithm

The LABview position control algorithm allowed the hovercraft to get to a certain

height with accuracy within a half an inch. The hovercraft reached this position within a

reasonable period of time, ranging from two seconds for small changes to about five for

large displacements.

15

Conclusion

As the project is concluded, some details deserve to be noted about this project.

The LABview position control algorithm allowed the hovercraft to get to a certain

height with accuracy within a half an inch. The hovercraft reached this position within a

reasonable period of time, ranging from two seconds for small changes to about five for

large displacements.

The LABview velocity control algorithm however did not work as well as the

position control. Some spikes of +- .01 volts were observed coming from the sensor into

the LABview algorithm. Because of the design of the algorithm this spikes were

amplified to up to +-.1 volts into the gate of the MOSFET controlling the motor voltage.

This resulted in spikes of more than +- 1 volt to the motor voltage. This change of almost

two volts created a change in motor rpm of about 1000 making the system totally

unstable. Increasing the delaying time for sampling seemed to improve the stability of the

system. It was suggested that an averaging algorithm could be setup to smooth these

spikes and improve the response of the system.

The motor performed flawlessly but the power source (batteries) was quite

problematic, as recharging was constantly needed. A power supply would be much more

reliable and usable for long studies of the stability of this system. The motor had been

tested to draw an average of 8.47 amps at 8.4 volts that was achievable by many modern

power supplies; the problem arose at "spool up" time. When the motor was started from

zero angular velocity it needed higher amperage to get to normal operational speed; this

resulted in a spike of high current that caused the power supplies to shut down to avoid

damage for over-current. The motor was later tested to calculate the size of these high

current spikes and they were found to be in the order of 14 to 15 amps when the motor

was fed with an 8.4 volts battery. It was difficult to calculate the exact size of the spikes

because of the equipment used, the brevity of their existence and because they were

changing, as the motor was getting hot and the battery discharged. The solution to this

16

problem is to use a power supply that can deliver more than 15 amps under normal

operation or a 10-amp power supply with no surge protection. The brevity of the spikes

should not cause the power supply to fail.

The MOSFET control was also a problem. Not only maximum current and

voltage needed to be checked before using a MOSFET or another; maximum power also

needed to be taken in account as the used motor was actually producing up to 80 watts of

power. These was initially overlooked the team and many MOSFETS were burned before

getting the right one. At the end the MOSFET used was capable of handling 150 Watts

and even then the high current drawn by the motor caused the MOSFET to heat up

rapidly and a fan had to be used to cool it.

The system was designed for a one-semester project and is quite fragile. Some

reinforcement could be needed if the system was to last longer, including gluing some

stronger flat surface to the base of the system to avoid the misalignment of the poles

because of bending. Also, some reinforcement could be needed for the poles and some

springs could help avoid the hovercraft to hit the base to hard when the power is reduced

too sharply.

All in all, it was interesting to find out how practically any system could be

controlled through a computer using a relatively easy to use program. The major

difficulties in this project came from parts not belonging to the proper design of the

system, but other parts such as the use of the MOSFETs and power supplies. Much

knowledge was gained about computer control algorithms, systems stability and of

course, troubleshooting of prototypes. It was an interesting and valuable hands-on

experience.

17

Appendix A

Equation of Motion

Assumptions:

• No air drag

• Gravity = constant

• Weight is constant (neglecting the weight of the wire)

• Ground effect is constant

• Vo = yo = 0

• Thrust is formulated as a multiple of weight and treated the two as step

function

Laplace Derivation:

ΣF = ma = Tmg – mg – bv

d2y/dt2 = g(T-1) u(t) – bdy/dt

s2Y(s) – sy(0) – y’(0) = g(T-1)/s – b[sY(s) – y(0)]

s2Y(s) + bsY(s) + y(0) – sy(0) – y’(0) = g(T-1)/s

Y(s)[s2+sb] + y(0)[1-s] – y’(0) = g(T-1)/s

Y(s) = [g(T-1)/s – sy(0)(1-s) + y’(0)] / [s2+sb)]

∴Y(s) = [g(T-1) – sy(0)(1-s) + sy’(0)] / [s2(s+b)] Laplace

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Transfer Function:

Y(s) = g(T-1) / [s2(s+b)]

g(T-1) / [s2(s+b)] = A/s2 + B/s + C/(s+b)

where

A = g(T-1)/b

B = -g(T-1)/b2

C = g(T-1)

Y(s) = g(T-1)/bs2 – g(T-1)/b2s + g(T-1)/(s+b)

∴ y(t) = g(T-1) [ t/b – 1/b2 + e-bt ] Time Response

Nomenclature:

b = coefficient of friction

T = thrust

g = gravity constant

t = time

m = mass

v = velocity

F = Force

19

Appendix B

Budget

The speed controller, batteries, transmitter and receiver were not included in the

total budget because they are used temporarily. A computer-controlled system will

replace these parts in the second phase of this project. Minor supplies, such as glue and

lubricant, were not included in the total budget as well.

Part Cost

Motor 10.00

Propeller 5.00

Voltmeter 14.00

Constant Current Supply 19.99

Electrical Wire 3.00

Brass Tube 1.75

Wood Sheet 4.00

Wood Sticks 1.50

Hardwood Dowel 1.50

MOSFET 5.70

Heat Sink 0.50

Batteries Temporarily

Total 63.89

20

Appendix C

Time Schedule

9/20 – 10/4 10/5 – 10/19 10/20 – 11/4 11/5 – 12/10

Conception

Buying Parts

Building

Testing

Computer Control

Finalizing Report

21

Appendix D

Picture of the Hovercraft

22

Appendix E

Finding the Thrust

The trust was found by keep the hovercraft at a certain altitude and taking voltage

measurements. These voltage measurements were taken across the motor. By repeating

this process using different weights, a plot of the voltage vs. thrust was found.

Experimental Data:

Hovercraft height = 5in from the ground

Mass of hovercraft = 226g

Thrust = Mass x Gravity

Voltage vs. Thrust

0.20

0.23

0.25

0.28

0.30

4 4.2 4.4 4.6 4.8 5

Voltage (V)

Thr

ust

23

Appendix F

Time Response Data

Assumptions:

Friction Coefficient b = 1

Equation:

y(t) = g(T-1) [ t/b – 1/b2 + e-bt ]

Thrust Time Response Thrust Time Response Thrust Time Response

0.23 0.0 0.00 0.25 0.0 0.00 0.27 0.0 0.00 0.1 0.04 0.1 0.04 0.1 0.03 0.2 0.14 0.2 0.14 0.2 0.13 0.3 0.31 0.3 0.30 0.3 0.29 0.4 0.53 0.4 0.52 0.4 0.50 0.5 0.80 0.5 0.78 0.5 0.76 0.6 1.12 0.6 1.09 0.6 1.07 0.7 1.48 0.7 1.45 0.7 1.41 0.8 1.88 0.8 1.83 0.8 1.79 0.9 2.32 0.9 2.26 0.9 2.20 1.0 2.78 1.0 2.71 1.0 2.63 1.1 3.27 1.1 3.18 1.1 3.10 1.2 3.79 1.2 3.69 1.2 3.59 1.3 4.32 1.3 4.21 1.3 4.10 1.4 4.88 1.4 4.76 1.4 4.63 1.5 5.46 1.5 5.32 1.5 5.18 1.6 6.06 1.6 5.90 1.6 5.74 1.7 6.67 1.7 6.49 1.7 6.32 1.8 7.29 1.8 7.10 1.8 6.91 1.9 7.93 1.9 7.72 1.9 7.52 2.0 8.58 2.0 8.35 2.0 8.13

24

Appendix G

MOSFET Specifications

Model Number: Philips ECG2395

Power: 150W

Current: 50A

BVDSS: 60V

BVGSS: 30V

GFS: 17min.

RDS ON: .028ohm

Toff: 170nS

Tf: 120nS

MOSFET Diagram

25

Appendix H

Computer Board Connector

6024E I/O Connector