Consider the following Nyquist plot from which one may note down the details in the table below (NOTE: the magnitude values are in absolute, NOT in dB): ↑ Im (4) 0.5 # -135⁰ ون =1 Frequency Magnitude, Phase |L| Angle, ZL (w) 1 1 -135° -180° 1.5 Re (L) 0.5 With the above information, fill out the following sentences! 1) The gain crossover frequency is 1 ← 45 0 margin is 180-135 = 45 2) The phase crossover frequency 1.5 is ← margin is 20 log10 0.5 dB rad/sec, and the phase rad/sec, and the gain
Consider the following Nyquist plot from which one may note down the details in the table below (NOTE: the magnitude values are in absolute, NOT in dB): ↑ Im (4) 0.5 # -135⁰ ون =1 Frequency Magnitude, Phase |L| Angle, ZL (w) 1 1 -135° -180° 1.5 Re (L) 0.5 With the above information, fill out the following sentences! 1) The gain crossover frequency is 1 ← 45 0 margin is 180-135 = 45 2) The phase crossover frequency 1.5 is ← margin is 20 log10 0.5 dB rad/sec, and the phase rad/sec, and the gain
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![### Nyquist Plot Analysis
Consider the following Nyquist plot, which provides details summarized in the table below. **Note:** The magnitude values are in absolute terms, not in decibels (dB).
#### Diagram Description:
The Nyquist plot is a complex plane diagram with the Real part \( \text{Re}(L) \) on the x-axis and the Imaginary part \( \text{Im}(L) \) on the y-axis. The plot includes the following key features:
- A curve passing through the point where the real part is \(-1\).
- A marked point at frequency \(\omega = 1\) with a phase angle of \(-135^\circ\).
- A marked point at frequency \(\omega = 1.5\) with a phase angle of \(-180^\circ\).
#### Table of Values:
| Frequency (\(\omega\)) | Magnitude (\(|L|\)) | Phase Angle (\(\angle L\)) |
|------------------------|---------------------|----------------------------|
| 1 | 1 | \(-135^\circ\) |
| 1.5 | 0.5 | \(-180^\circ\) |
### Calculations:
Using the information provided:
1. **Gain Crossover Frequency:**
- The gain crossover frequency is \( 1 \) rad/sec.
- The phase margin is calculated as:
\[
180^\circ - 135^\circ = 45^\circ
\]
2. **Phase Crossover Frequency:**
- The phase crossover frequency is \( 1.5 \) rad/sec.
- The gain margin is given by:
\[
\text{Gain margin} = 20 \log_{10}(0.5) \, \text{dB}
\]
This analysis helps evaluate system stability margins, providing insights into the control system's robustness.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93e18a88-13ba-47d2-8c84-ec9d29397d2a%2Fc59f3674-002b-43f9-bda0-deece1054e5d%2Fsq5zyvl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Nyquist Plot Analysis
Consider the following Nyquist plot, which provides details summarized in the table below. **Note:** The magnitude values are in absolute terms, not in decibels (dB).
#### Diagram Description:
The Nyquist plot is a complex plane diagram with the Real part \( \text{Re}(L) \) on the x-axis and the Imaginary part \( \text{Im}(L) \) on the y-axis. The plot includes the following key features:
- A curve passing through the point where the real part is \(-1\).
- A marked point at frequency \(\omega = 1\) with a phase angle of \(-135^\circ\).
- A marked point at frequency \(\omega = 1.5\) with a phase angle of \(-180^\circ\).
#### Table of Values:
| Frequency (\(\omega\)) | Magnitude (\(|L|\)) | Phase Angle (\(\angle L\)) |
|------------------------|---------------------|----------------------------|
| 1 | 1 | \(-135^\circ\) |
| 1.5 | 0.5 | \(-180^\circ\) |
### Calculations:
Using the information provided:
1. **Gain Crossover Frequency:**
- The gain crossover frequency is \( 1 \) rad/sec.
- The phase margin is calculated as:
\[
180^\circ - 135^\circ = 45^\circ
\]
2. **Phase Crossover Frequency:**
- The phase crossover frequency is \( 1.5 \) rad/sec.
- The gain margin is given by:
\[
\text{Gain margin} = 20 \log_{10}(0.5) \, \text{dB}
\]
This analysis helps evaluate system stability margins, providing insights into the control system's robustness.
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