Excercise 4: Stability The Nyquist plot for some control system resembles the one shown in figure (a) below. A zoom of this plot, showing all important details around the critical point, is shown in figure (b). Assume that the open loop system is stable. 0.6 1000 (a) (b) 0.4 500 0.2 -0.2 -500 -0.4 -0.6 -1000 -100 -6 -4 Re L(iw) -2 -20 -80 -60 -40 Re L(iw) (a) Is the closed-loop system stable or unstable? (b) large value? What happens to the stability of the system as the gain goes from a very small to a very Im L(iw) Im L(iw) O

Question
Excercise 4: Stability The Nyquist plot for some control system resembles the one shown in figure (a)
below. A zoom of this plot, showing all important details around the critical point, is shown in figure
(b). Assume that the open loop system is stable.
0.6
1000
(a)
(b)
0.4
500
0.2
-0.2
-500
-0.4
-0.6
-1000
-100
-6
-4
Re L(iw)
-2
-20
-80
-60
-40
Re L(iw)
(a)
Is the closed-loop system stable or unstable?
(b)
large value?
What happens to the stability of the system as the gain goes from a very small to a very
Im L(iw)
Im L(iw)
O
Expand
Transcribed Image Text

Excercise 4: Stability The Nyquist plot for some control system resembles the one shown in figure (a) below. A zoom of this plot, showing all important details around the critical point, is shown in figure (b). Assume that the open loop system is stable. 0.6 1000 (a) (b) 0.4 500 0.2 -0.2 -500 -0.4 -0.6 -1000 -100 -6 -4 Re L(iw) -2 -20 -80 -60 -40 Re L(iw) (a) Is the closed-loop system stable or unstable? (b) large value? What happens to the stability of the system as the gain goes from a very small to a very Im L(iw) Im L(iw) O

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