Find which graph goes to each pole **Root Locus Plot Analysis - Educational Exercise**1. **Consider the Root Locus plot shown below,** ![Root Locus](RootLocusDiagram) The plot presented is a Root Locus diagram illustrating the paths that poles of the closed-loop system will take in the s-plane as a system parameter is varied. The diagram shows: - A large circle intersecting the imaginary axis at \( \text{±j1} \) and the real axis between \( -0.5 \) and \( -3.5 \). - Key points marked as A, B, C, and D around the circle. **Figure 1. Root Locus for Question 1**2. **Match each step response below to its corresponding pole location (A, B, C, D) identified on the Root Locus plot in Figure 1.** The step response graph displayed below shows the system's response to a unit step input over time with amplitude on the y-axis and time (in seconds) on the x-axis. The initial overshoot and settling time are reflective of the damping and natural frequency characteristics of the system's poles. ![Step Response](StepResponseGraph) - **Axis Labels:** - Y-axis: Amplitude ranging from 0 to 1.4. - X-axis: Time (sec) ranging from 0 to 14. **Choose the pole location (A, B, C, or D) on the root locus plot (Figure 1) that corresponds to this step response:** _______________ **Instructions:**Look at the damping characteristics and settling time reflected in the step response and associate them with the likely characteristics of the poles in the root locus (damping ratio and natural frequency). An understanding of standard second-order system responses in relation to pole locations in the s-plane is necessary to determine the correct answer. ### Step Response Analysis#### Graph Descriptions:1. **First Graph: Step Response** - **x-axis**: Time (sec) ranging from 0 to 14. - **y-axis**: Amplitude ranging from 0 to 1.4. - **Description**: The response starts at amplitude 0, has a slight overshoot just above 1.2, then settles just below 1.2 and continues with a slight upward trend after about 5 seconds. **Question**: Choose the pole location (A, B, C, or D) on the root locus plot (fig. 1) that corresponds to this step response: ________________________ 2. **Second Graph: Step Response** - **x-axis**: Time (sec) ranging from 0 to 14. - **y-axis**: Amplitude ranging from 0 to 1.4. - **Description**: The response starts at amplitude 0, rises quickly to around 1.2 without overshoot, and stabilizes around 1.2 after approximately 2 seconds. **Question**: Choose the pole location (A, B, C, or D) on the root locus plot (fig. 1) that corresponds to this step response: ________________________3. **Third Graph: Step Response** - **x-axis**: Time (sec) ranging from 0 to 14. - **y-axis**: Amplitude ranging from 0 to 1. - **Description**: The response starts at amplitude 0 and smoothly increases, gradually approaching but not quite reaching 1 within the observed time range. **Question**: Choose the pole location (A, B, C, or D) on the root locus plot (fig. 1) that corresponds to this step response: ________________________These graphs represent different step responses of a control system. The task is to correlate these responses with specific pole locations on a root locus plot (referred to as fig. 1).

Answered: Find which graph goes to each pole

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Find which graph goes to each pole

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Power Measurement

According to Blondel's theorem, the total power is measured with one less number of wattmeters than the number of wires present in the system. So, a single-phase and two-wire system will require one wattmeter and a single-phase and the three-wire system will require two wattmeters, and a three-phase and the three-wire system will also require two wattmeters and a three-phase and the four-wire system will require three wattmeter devices. The wattmeter is a device that measures power using one voltage and one current input as shown in the above figure. Multiple current or voltage input pair cables are used by many power analyzers and digital storage oscilloscopes (DSOs) for measuring watts, in effect within a single instrument acting as multiple wattmeters. It is possible to measure three-phase and four-wire power with one correctly specified power analyzer.

Question

Find which graph goes to each pole

**Root Locus Plot Analysis - Educational Exercise**

1. **Consider the Root Locus plot shown below,**

![Root Locus](RootLocusDiagram)

The plot presented is a Root Locus diagram illustrating the paths that poles of the closed-loop system will take in the s-plane as a system parameter is varied. The diagram shows:

- A large circle intersecting the imaginary axis at \( \text{±j1} \) and the real axis between \( -0.5 \) and \( -3.5 \).
- Key points marked as A, B, C, and D around the circle.

**Figure 1. Root Locus for Question 1**

2. **Match each step response below to its corresponding pole location (A, B, C, D) identified on the Root Locus plot in Figure 1.**

The step response graph displayed below shows the system's response to a unit step input over time with amplitude on the y-axis and time (in seconds) on the x-axis. The initial overshoot and settling time are reflective of the damping and natural frequency characteristics of the system's poles.

![Step Response](StepResponseGraph)

- **Axis Labels:**
- Y-axis: Amplitude ranging from 0 to 1.4.
- X-axis: Time (sec) ranging from 0 to 14.

**Choose the pole location (A, B, C, or D) on the root locus plot (Figure 1) that corresponds to this step response:**
_______________

**Instructions:**
Look at the damping characteristics and settling time reflected in the step response and associate them with the likely characteristics of the poles in the root locus (damping ratio and natural frequency). An understanding of standard second-order system responses in relation to pole locations in the s-plane is necessary to determine the correct answer.

### Step Response Analysis

#### Graph Descriptions:
1. **First Graph: Step Response**
- **x-axis**: Time (sec) ranging from 0 to 14.
- **y-axis**: Amplitude ranging from 0 to 1.4.
- **Description**: The response starts at amplitude 0, has a slight overshoot just above 1.2, then settles just below 1.2 and continues with a slight upward trend after about 5 seconds.

**Question**: Choose the pole location (A, B, C, or D) on the root locus plot (fig. 1) that corresponds to this step response:
________________________

2. **Second Graph: Step Response**
- **x-axis**: Time (sec) ranging from 0 to 14.
- **y-axis**: Amplitude ranging from 0 to 1.4.
- **Description**: The response starts at amplitude 0, rises quickly to around 1.2 without overshoot, and stabilizes around 1.2 after approximately 2 seconds.

**Question**: Choose the pole location (A, B, C, or D) on the root locus plot (fig. 1) that corresponds to this step response:
________________________

3. **Third Graph: Step Response**
- **x-axis**: Time (sec) ranging from 0 to 14.
- **y-axis**: Amplitude ranging from 0 to 1.
- **Description**: The response starts at amplitude 0 and smoothly increases, gradually approaching but not quite reaching 1 within the observed time range.

**Question**: Choose the pole location (A, B, C, or D) on the root locus plot (fig. 1) that corresponds to this step response:
________________________

These graphs represent different step responses of a control system. The task is to correlate these responses with specific pole locations on a root locus plot (referred to as fig. 1).

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