3. ( Consider again the system in Fig. 1. The plant transfer function in the frequency domain is 100 G(jw) = (jw +2)(jw + 4)(jw + 10) Fig. 2 shows a Nyquist contour for G(jw). Nyquist Diagram 1.5 0.5 -0.5 -1.5 -1.5 -0.5 0.5 1.5 Real Axis Figure 2: Nyquist Contour (i) system becomes marginally stable and the practical range of safe operating gains for the proportional controller. Apply the Nyquist criterion to find the gain K, at which the closed loop Find the gain margin of the system when the operating gain of the controller (ii) Kp = 2. Use Fig. 2 to read the required values off the plot. Imaginary Axis

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3.
Consider again the system in Fig. 1. The plant transfer function
in the frequency domain is
100
G(jw):
(jw +2)(jw + 4)(jw + 10)
Fig. 2 shows a Nyquist contour for G(jw).
Nyquist Diagram
1.5
0.5
-0.5
-1.5
-0.5
0.5
1.5
Real Axis
Figure 2: Nyquist Contour
(i)
system becomes marginally stable and the practical range of safe operating gains for
the proportional controller.
Apply the Nyquist criterion to find the gain K, at which the closed loop
(ii)
K, = 2. Use Fig. 2 to read the required values off the plot.
Find the gain margin of the system when the operating gain of the controller
Imaginary Axis
Transcribed Image Text:3. Consider again the system in Fig. 1. The plant transfer function in the frequency domain is 100 G(jw): (jw +2)(jw + 4)(jw + 10) Fig. 2 shows a Nyquist contour for G(jw). Nyquist Diagram 1.5 0.5 -0.5 -1.5 -0.5 0.5 1.5 Real Axis Figure 2: Nyquist Contour (i) system becomes marginally stable and the practical range of safe operating gains for the proportional controller. Apply the Nyquist criterion to find the gain K, at which the closed loop (ii) K, = 2. Use Fig. 2 to read the required values off the plot. Find the gain margin of the system when the operating gain of the controller Imaginary Axis
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