Problem 1. Hand sketch the asymptotes for the Bode magnitude and phase plots for each of the
following open-loop transfer functions. Then verify your plot using bode command in MATLAB.
Please submit both hand-sketched plots along with the MATLAB plots:
5 + 1 s
10 + 1
s(s + 1)(s + 100)
L(s) = −s
(s + 1)(s − 1)
L(s) = 1 − s
s(s + 1)
L(s) = 4
2 + 1
2 + 1)
10 (s + 1)2
10 + 1
L(s) = e
s(s + 1)
L(s) = 10(s + 1)
2 + 20s + 100)
L(s) = 1 + 0.5s
Problem 2. Effect of Additional Zero on the 2nd-Order Time and Frequency Responses:
Consider the following 2nd-order loop transfer function with a zero at s = −z:
z + 1
2 + s + 1
We want to see how both the time response and the frequency response of the system would change
as the location of the zero varries relative to the location of the poles in the 2nd-order system. For
z = 0.01, 0.1, 1, 10, 100, use step, stepinfo, bode, and getPeakGain functions in MATLAB to:
(a) Plot step reponses of the system for the different values of z, all on the same figure.
(b) Find the maximum percentage overshoot for the different values of z.
(c) Plot the frequency response of the system (both magnitude and phase) for the different values of z,
all on the same figures (i.e., one figure for all magnitude responses and one for all phase responses)
(d) Find the resonant peak in the frequency response for different values of z.
(e) Please discuss how the varying zero location is impacting your time and frequency response.
Please submit both your MATLAB code along with the plots and the tables of percentage overshoot
and resonant peak values.
Problem 3. Effect of Additional Pole on the 2nd-Order Time and Frequency Responses:
Consider the following loop transfer function:
L(s) = 1
p + 1
2 + s + 1)
These homework problems are compiled using the different textbooks listed on the course syllab