
Example 4.36
An overdamped second-order system is subject to proportional control as shown in Figure 4.96.
A sensor is present in the feedback loop.
Baseline values of the system and sensor parameters are
K
p
¼ 15, t
1
¼ 3s, t
2
¼ 15 s, K
T
¼ 0:1, t
T
¼ 0:25 s
(a) Create a model ‘‘sys’’ for the open-loop system with K
C
¼1.
(b) Use the control system toolbox to draw a Bode plot of the open-loop system.
(c) Determine the stability margins of the control system and the critical gain K
cr
.
(d) Find v
0
, the frequency of oscillations for the marginally stable system.
(e) Check the results for K
cr
using a root-locus plot and the characteristic equation.
(f) Plot step responses ...