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5- For the control system shown in Fig. 4, determine the steady state error for step input to 5, and for ramp with slope 10. (1,3,6] R(s) k s² + 5s +6 1 (s+1) C(s)

5- For the control system shown in Fig. 4, determine the steady state error for step input to 5, and for ramp with slope 10. (1,3,6] R(s) k s² + 5s +6 1 (s+1) C(s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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STEADY STATE ERROR (NEED A NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE)

### Control System Steady State Error Analysis **Problem Statement:** For the control system shown in Figure 4, determine the steady-state error for a step input of 5 and for a ramp input with a slope of 10. **System Description:** The control system contains the following components: 1. A summing junction, taking \( R(s) \) as the input and producing the error signal. 2. A transfer function, \( \frac{k}{s^2 + 5s + 6} \), representing the system dynamics. 3. A feedback loop with a transfer function \( \frac{1}{s + 1} \). **Figure 4:** - **Input Signal \( R(s) \):** This is the initial input into the system. - **Summing Junction:** This component adds the input signal \( R(s) \) and subtracts the feedback signal. - **System Block:** Consists of the transfer function \( \frac{k}{s^2 + 5s + 6} \). - **Output Signal \( C(s) \):** The output of the system before being fed back. - **Feedback Loop:** The output passes through the transfer function \( \frac{1}{s + 1} \) and is fed back into the summing junction. **Objective:** - To calculate the steady-state error for a step input of magnitude 5. - To calculate the steady-state error for a ramp input with a slope of 10. --- To solve these problems, students will need to use concepts from control system theory such as steady-state error calculations, transfer function manipulation, and sensitivity functions. Detailed steps and assumptions must be provided to arrive at the solution for each type of input. Reminder for Students: - Review the final value theorem and apply it appropriately for both step and ramp inputs. - Recall that steady-state error can be different for various types of inputs, depending on the type and order of the system.
Transcribed Image Text:### Control System Steady State Error Analysis **Problem Statement:** For the control system shown in Figure 4, determine the steady-state error for a step input of 5 and for a ramp input with a slope of 10. **System Description:** The control system contains the following components: 1. A summing junction, taking \( R(s) \) as the input and producing the error signal. 2. A transfer function, \( \frac{k}{s^2 + 5s + 6} \), representing the system dynamics. 3. A feedback loop with a transfer function \( \frac{1}{s + 1} \). **Figure 4:** - **Input Signal \( R(s) \):** This is the initial input into the system. - **Summing Junction:** This component adds the input signal \( R(s) \) and subtracts the feedback signal. - **System Block:** Consists of the transfer function \( \frac{k}{s^2 + 5s + 6} \). - **Output Signal \( C(s) \):** The output of the system before being fed back. - **Feedback Loop:** The output passes through the transfer function \( \frac{1}{s + 1} \) and is fed back into the summing junction. **Objective:** - To calculate the steady-state error for a step input of magnitude 5. - To calculate the steady-state error for a ramp input with a slope of 10. --- To solve these problems, students will need to use concepts from control system theory such as steady-state error calculations, transfer function manipulation, and sensitivity functions. Detailed steps and assumptions must be provided to arrive at the solution for each type of input. Reminder for Students: - Review the final value theorem and apply it appropriately for both step and ramp inputs. - Recall that steady-state error can be different for various types of inputs, depending on the type and order of the system.
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