Project Report
Hovercraft
By Hassan Abdulkareem Jassim M. Alhor Miguel A. Frontera
Table of Contents
Introduction
…………………………………………………. …………………………… …………………….
3
Abstract
…………………………………………………. ………………………………………………….
4
Apparatus
………………………………………………….
5
Sensor Mechanism
…………………………………………. ………………………… ……………….
6
Time Response
…………………………………………. ………………………… ……………….
8
System Response
…………………………………………. ………………………… ……………….
9
Stability Analysis
…………………………………………. ………………………… ……………….
10
Control System
…………………………………………. …………………………… …………….
11
…………………………………………………. ………………………… ……………………….
15
Conclusion
Appendix A: Equation of Motion
………………………….. …………………………
17
Appendix B: Budget …………………………………………. ………………………………………….
19
Appendix C: Time Schedule
20
………………………….
Appendix D: Picture of the Hovercraft Appendix E: Finding the Thrust
………………….
21
………………………….. …………………………
22
Appendix F: Time Response Plot Data
………………….
Appendix G: MOSFET Specifications
……………………. 24
Appendix H: Computer Board Connector
……………………. 25
2
23
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
3
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.
4
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
Motor
Specifications
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
LKG Industries M-W-122A
Supply 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
5
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
6
The following plot shows the relationship between the voltage measured across the variable resistor and the height of the hovercraft.
Height vs. Voltage 25
20
15 t h g i e 10 H
5
0 0
0.5
1
1.5
2
2.5
3
3.5
Voltage (V)
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.
7
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)] / [s 2(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/b 2 + e-bt ] Where
b: coefficient of friction T: thrust g: gravity constant t: time
8
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 9 8 7 6 e s 5 n o p s e 4 R
0.23 Thrust 0.25 Thrust 0.27 Thrust
3 2 1 0 0.0
0.4
0.8
1.2
Time
9
1.6
2.0
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.
10
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
11
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.
12
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
13
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.
14
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
15
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.
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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)] / [s 2+sb)]
∴Y(s)
= [g(T-1) – sy(0)(1-s) + sy’(0)] / [s 2(s+b)]
17
Laplace
Transfer Function: Y(s) = g(T-1) / [s 2(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)/b 2 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/b 2 + e-bt ]
Nomenclature: b = coefficient of friction T = thrust g = gravity constant t = time m = mass v = velocity F = Force
18
Time Response
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
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63.89
Appendix C Time Schedule
9/20 – 10/4
10/5 – 10/19
Conception Buying Parts Building Testing Computer Control Finalizing Report
20
10/20 – 11/4
11/5 – 12/10
Appendix D Picture of the Hovercraft
21
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 0.30 0.28 t s 0.25 u r h T
0.23 0.20 4
4.2
4.4
4.6
Voltage (V)
22
4.8
5
Appendix F Time Response Data
Assumptions: Friction Coefficient b = 1
Equation: y(t) = g(T-1) [ t/b – 1/b 2 + 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
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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
24
Appendix H Computer Board Connector
6024E I/O Connector
25
