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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 -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 Kp at which the closed loop Find the gain margin of the system when the operating gain of the controller (ii) K, = 2. Use Fig. 2 to read the required values off the plot. Imaginary Axis

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 Kp at which the closed loop Find the gain margin of the system when the operating gain of the controller (ii) K, = 2. Use Fig. 2 to read the required values off the plot. Imaginary Axis

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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 -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 Kp at which the closed loop Find the gain margin of the system when the operating gain of the controller (ii) K, = 2. Use Fig. 2 to read the required values off the plot. 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 -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 Kp at which the closed loop Find the gain margin of the system when the operating gain of the controller (ii) K, = 2. Use Fig. 2 to read the required values off the plot. Imaginary Axis
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