EE 5351
UMD
Spring, 2015
HW – 3: 30 Points (No Formal Report is Necessary)
1. Use difference equations in a Math program to model the solution to the following initial value
problem of a second order differential equation:
X’’ + 2X’ + 5X = 60; X(0) = 8 , X’(0) = 0
a. Plot the solution at an appropriate time step
b. Solve the equation by hand or using math software, plot the solution and compare with
the difference equation plot from a.
2. A 4-wheeled, 4 wheel drive, robotic platform weighs 10 kg, including its battery. It has 10 cm
diameter wheels, must achieve a top speed of 6 m/sec and accelerate from zero to top speed in
5 seconds while on a 10% grade.
a. Calculate the total motive force required to achieve this specification.
b. Calculate the Torque in N-m for each motor.
c. Calculate the Power in watts for each drive motor at top speed.
3.
S.Norr
A robotic platform weighs 15 kg without motors or battery. It has three wheels, two drive
wheels and a trailing castor. The design goals are that the robot achieves a top speed of 3 m/s,
and can accelerate from zero to top speed in 3 seconds. It must also climb a 20% grade. A
choice of wheel diameter is available: 5 cm or 8 cm. System voltage is desired to be 24 or 48
volts, and minimum usage time is 4 hours.
a. Perform calculations to determine a proper size for the two drive motors. (See “Drive
Motors” on the course webpage)
b. Shop around the ‘net for actual suitable 24 DC permanent magnet motors and gear
ratios.
c. Take the full-load amp data for your motors and identify batteries for the platform and a
4 hour run-time..
d. Sum the weight of the motors and batteries and add them to the mass of the platform.
e. Repeat part a) to see if new motors would be required. If so, repeat the process until
you reach equilibrium.
f. Report the total cost of the motors and batteries at 24 Volts. Make a reasonable effort
to identify a 48 volt motor/battery combination with similar performance and compare
its cost against the 24 volt system.