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
10
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
18
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
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