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22. The Bode plots for a plant, G(s), used in a unity- feedback system are shown in Figure P10.7. Do the following: 20 log M Phase (degrees) a. Find the gain margin, phase margin, zero dB frequency, 180° frequency, and the closed-loop bandwidth. b. Use your results in Part a to estimate the damping ratio, percent overshoot, settling time, and peak time. 20 0 -20 -40 -60 -80 -100 10-1 -135 -180 -225 -270 10-1 10⁰ 10⁰ Frequency (rad/s) Frequency (rad/s) FIGURE P10.7 10¹ 10¹ 10² 10²

22. The Bode plots for a plant, G(s), used in a unity- feedback system are shown in Figure P10.7. Do the following: 20 log M Phase (degrees) a. Find the gain margin, phase margin, zero dB frequency, 180° frequency, and the closed-loop bandwidth. b. Use your results in Part a to estimate the damping ratio, percent overshoot, settling time, and peak time. 20 0 -20 -40 -60 -80 -100 10-1 -135 -180 -225 -270 10-1 10⁰ 10⁰ Frequency (rad/s) Frequency (rad/s) FIGURE P10.7 10¹ 10¹ 10² 10²

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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The Bode plots for a plant, \( G(s) \), used in a unity-feedback system are shown in Figure P10.7. Do the following: a. Find the gain margin, phase margin, zero dB frequency, 180° frequency, and the closed-loop bandwidth. b. Use your results in Part a to estimate the damping ratio, percent overshoot, settling time, and peak time. **Figure P10.7 Description:** - **Top Graph: Magnitude Plot** - The horizontal axis represents the Frequency in radians per second (\( \text{rad/s} \)) on a logarithmic scale ranging from \( 10^{-1} \) to \( 10^{2} \). - The vertical axis represents the magnitude in decibels (\( 20 \log M \)) ranging from -100 to 20. - The plot shows a decreasing trend as the frequency increases. - **Bottom Graph: Phase Plot** - The horizontal axis, also a logarithmic scale, represents the Frequency in \(\text{rad/s}\), identical to the top graph. - The vertical axis represents the Phase in degrees, ranging from -270 to -90. - The plot depicts a decreasing phase trend with increasing frequency.
Transcribed Image Text:The Bode plots for a plant, \( G(s) \), used in a unity-feedback system are shown in Figure P10.7. Do the following: a. Find the gain margin, phase margin, zero dB frequency, 180° frequency, and the closed-loop bandwidth. b. Use your results in Part a to estimate the damping ratio, percent overshoot, settling time, and peak time. **Figure P10.7 Description:** - **Top Graph: Magnitude Plot** - The horizontal axis represents the Frequency in radians per second (\( \text{rad/s} \)) on a logarithmic scale ranging from \( 10^{-1} \) to \( 10^{2} \). - The vertical axis represents the magnitude in decibels (\( 20 \log M \)) ranging from -100 to 20. - The plot shows a decreasing trend as the frequency increases. - **Bottom Graph: Phase Plot** - The horizontal axis, also a logarithmic scale, represents the Frequency in \(\text{rad/s}\), identical to the top graph. - The vertical axis represents the Phase in degrees, ranging from -270 to -90. - The plot depicts a decreasing phase trend with increasing frequency.
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