Polar Plots Problem 3 Frequency Response Analysis | Summary and Q&A

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August 4, 2023
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Ekeeda
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Polar Plots Problem 3 Frequency Response Analysis

TL;DR

Learn how to sketch the polar plot of a system with the given open loop transfer function.

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Key Insights

  • 🐻‍❄️ The polar plot helps in visualizing the frequency response of a system.
  • 🤣 The magnitude decreases as the frequency increases, indicating a high-frequency roll-off.
  • 🛀 The phase angle shows the phase shift introduced by the system at different frequencies.
  • 🐻‍❄️ The polar plot is useful in analyzing system stability and designing control systems.
  • 💁 The polar plot provides valuable information about system behavior without complex calculations.
  • 😥 The points on the plot can be used to determine system stability margins.
  • 🐻‍❄️ The angle of the polar plot indicates the phase shift, while the distance from the origin represents the magnitude.

Questions & Answers

Q: What is the first step to sketch the polar plot of a system?

The first step is to replace the variable "s" with "j omega" in the transfer function equation.

Q: How do we calculate the magnitude and phase angle of gj omega?

The magnitude is given by 1 / (1 + omega^2), while the phase angle is -2 * tan inverse of omega.

Q: How do we plot the magnitude and phase angle on polar coordinates?

The magnitude is represented by concentric circles, and the phase angle is represented by radial lines.

Q: How do we obtain the polar plot from the plotted points?

The plotted points are connected to form a curve, which represents the polar plot of the system.

Summary & Key Takeaways

  • The video explains the steps to sketch the polar plot of a system with the given open loop transfer function.

  • The first step is to replace the variable "s" with "j omega" in the transfer function equation.

  • Then, the magnitude and phase angle of gj omega are calculated for various values of omega, and plotted on polar coordinates to obtain the polar plot.

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