1. You have a robot that travels 45 cm/s as it circles a track and crosses a single black line
each time. It has a sensor to detect the line, and it interrupts at a fixed rate to sample the
sensor (for black or white). You wish to measure the distance around the track.
a. Compute the minimum interrupt rate you will need to measure the distance with a
resolution of 0.5 cm or better.
b. Suppose your interrupt rate, however, is 50 Hz. What is your resolution?
c. At 50 Hz, suppose you are using an 8-bit counter. What is the longest track you will
be able to measure (without ambiguity)?
2. Fuzzy logic control systems.
You are to design a fuzzy logic motor controller. The diagram of the system is below:
The control inputs are S*, the desired motor speed in rpm, and S’, the current estimated motor
speed in rpm. The control output is U, the duty cycle of the PWM output in clock cycles.
Assume you choose a single crisp output, U, the change in duty cycle in clock cycles, U=U+ U.
(a) (5 pts) Define two reasonable crisp inputs that you could use for this system. Both will be 8-
bit values.
(b) (10 pts) Define six reasonable input fuzzy membership sets, three for each crisp input. Draw
two plots, one for each input showing how the membership sets might be allocated.
(c) (5 pts) Define three reasonable output fuzzy membership sets for the crisp output.
(d) (10 pts) Define the fuzzy rules that combine the fuzzy inputs to produce the fuzzy outputs.
Give your answer as a matrix, with fuzzy inputs for the row and column headings and fuzzy
output as the entries in the matrix.