5. A root locus plot of a transfer function is given below. Determine the transfer function from the root locus plot. Imaginary Axis (seconds) 1.5 1 0.5 -0.5 -1 -1.5 -2.5 -2 Root Locus -1.5 Real Axis (seconds ¹) -0.5 0.5

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### Root Locus Plot of a Transfer Function

**Problem Statement:**
A root locus plot of a transfer function is given. Determine the transfer function from the root locus plot.

**Description of the Root Locus Plot:**

- **Axes:**
  - **X-axis (Real Axis):** Labeled as "Real Axis (seconds⁻¹)" with a range from -3 to 0.5.
  - **Y-axis (Imaginary Axis):** Labeled as "Imaginary Axis (seconds⁻¹)" with a range from -1.5 to 1.5.

- **Plot Features:**
  - The plot shows trajectories of system poles as the feedback gain, typically denoted as \( K \), is varied.
  - There are four main markers on the plot:
    - Two poles, marked with an "X" at approximately (-1.5, 1) and (-1.5, -1).
    - Two zeros, marked with an "O" at approximately (0, 1) and (0, -1).

- **Curves on the Plot:**
  - The curves start at the poles (X) and move towards the zeros (O).
  - One green curve moves upwards from the pole at (-1.5, 1) towards (0, 1).
  - One red curve moves downwards from the pole at (-1.5, -1) towards (0, -1).
  - A blue curve moves from near the real axis on the right (close to 0) away from (-1.5, -1).
  
This root locus plot illustrates the stability and response characteristics of the control system as the gain varies. Determining the exact transfer function would involve additional information and analysis based on this graphical representation.
Transcribed Image Text:### Root Locus Plot of a Transfer Function **Problem Statement:** A root locus plot of a transfer function is given. Determine the transfer function from the root locus plot. **Description of the Root Locus Plot:** - **Axes:** - **X-axis (Real Axis):** Labeled as "Real Axis (seconds⁻¹)" with a range from -3 to 0.5. - **Y-axis (Imaginary Axis):** Labeled as "Imaginary Axis (seconds⁻¹)" with a range from -1.5 to 1.5. - **Plot Features:** - The plot shows trajectories of system poles as the feedback gain, typically denoted as \( K \), is varied. - There are four main markers on the plot: - Two poles, marked with an "X" at approximately (-1.5, 1) and (-1.5, -1). - Two zeros, marked with an "O" at approximately (0, 1) and (0, -1). - **Curves on the Plot:** - The curves start at the poles (X) and move towards the zeros (O). - One green curve moves upwards from the pole at (-1.5, 1) towards (0, 1). - One red curve moves downwards from the pole at (-1.5, -1) towards (0, -1). - A blue curve moves from near the real axis on the right (close to 0) away from (-1.5, -1). This root locus plot illustrates the stability and response characteristics of the control system as the gain varies. Determining the exact transfer function would involve additional information and analysis based on this graphical representation.
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