ENG3018: Control Engineering
MATLAB Practical 2
Christopher Edwards
This is an individual piece of work contributing 6% of the total assessment for the module Control
Engineering ENG3018. Once completed it needs to be electronically submitted via eBART.
Consider the feedback loop shown in Figure 1,
Figure 1: Block Diagram.
where the transfer functions are
G(s) = 10(s + 4)
s(s
2 + 4s + 5) and K(s) = (s + 1)
(s + 3) .
a) Find the closed loop transfer function T(s) between r and y in the feedback loop (a.k.a.
as the complementary sensitivity function) shown in Figure 1. Make use of the MATLAB
commands tf, poly, conv and feedback.
T(s) =
b) Determine the poles and zeros of T(s) of the feedback loop in Figure 1.
The poles are:
The zeros are:
c) The DC gain associated of T(s) is:
d) Determine the poles and zeros of the sensitivity function S(s) associated with the closed loop
system in Figure 1.
The poles are:
The zeros are:
1
e) Sketch the unit step response of T(s) using the axes given in Figure 2.
0 1 2 3 4 5 6 7 8 9 10
Time
0
0.2
0.4
0.6
0.8
1
1.2
Output
Figure 2: Unit step response
f) Sketch the response of the closed loop system y(t) in Figure 1 to a reference input r = sin(wt)
for w = 1.7 over the time interval [0, 10], sampled at intervals of 0.01, using the axes given in
Figure 3. Sketch the reference input r(t) on the same set of axes.
0 1 2 3 4 5 6 7 8 9 10
Time
-1.5
-1
-0.5
0
0.5
1
1.5
Output
Figure 3: Sinusoidal Response
g) Use the information obtained above to estimate the phase shift associated with T(s).
C Edwards
February 15, 2023