EE 5351
UMD
Spring, 2014
HW – 4: 30 Points (No Formal Report is Necessary)
1.
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 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.
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!
2. Analyze a series RLC circuit that is in the DC Steady State with the following parameters:
Vs = 12 V, L = 250 mH, C = 0.1 uF, R = 1 K
a. Write the KVL loop equation around this series circuit and arrange it into a second-order
differential equation for Vc, the capacitor voltage.
b. Solve the equation for a step change in input from 12 volts to -8 volts at time=0
c. Transform the differential equation into a set of first order State Space equations, x’=Ax
+ Bu, realizing that capacitor current is inductor current in the series circuit and that the
current is therefore C*Vc’. The output, y will be Vc.
d. Model the State Space using difference equations in a math program of your choice.
Run an iterative solution of the state space for a step change condition
e. Plot the exact solution from b) and d) and compare them.
3. Take a color digital image of some object (yes, beer is an object). Perform the following:
a. Import the image into MATLAB or Scilab or any other appropriate software.
b. Perform a grayscale transformation using 256 levels of gray.
c. Perform a binary threshold filtering of the image, using a true/false threshold that will
still maintain a good likeness of the original image.
d. Perform an edge-detection processing of the image.
S.Norr