Root locus for a closed-loop system with L(s)=(1)/(s(s+4)(s+6)) is shown below.
From the values shown in the figure, compute the following.
a) Range of K for which the closed-loop system is stable.
b) Range of K for which the closed-loop step response will not have any overshoot. Note that when all poles are real, the step response has no overshoot.
c) Smallest possible peak time of the system. Note that peak time is the smallest when omega _(d) is the largest.
1
is shown below.
Root Locus
15
0.81
0.7
0.56
0.38
0.2
0.89
System: sys Gain: 239 Pole: -0.00417 + 4.89i Damping: 0.000854 Overshoot (%): 99.7 Frequency (rad/s): 4.89
10
0.95
0.988 Imaginary Axis (seconds1) 20 0:988
10
System: sys Gain: 16.9 Pole: -1.57 Damping: 1 Overshoot (%): 0 Frequency (rad/s): 1.57
0.95
-10
0.89
0.81
0.7
0.56
0.2
-25
-20
-15
-10 -5 Real Axis (seconds1)
10
From the values shown in the figure, compute the following
(e Range of K for which the closed-loop system is stable. b) Range of K for which the closed-loop step response will not have any overshoot.
Note that when all poles are real, the step response has no overshoot.
c) Smallest possible peak time of the system. Note that peak time is the smallest
when wa is the largest.