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3. A unit-step torque (i.e. T(t) = Uatep(t) N-m) is applied to the rotational dynamic system shown below. The resulting angular velocity is provided in the graph. a. Provide an estimate for the transfer function relating the angular displacement to the applied torque. b. Find the parameters, J, and D, for the system T(t) 0(t) J

3. A unit-step torque (i.e. T(t) = Uatep(t) N-m) is applied to the rotational dynamic system shown below. The resulting angular velocity is provided in the graph. a. Provide an estimate for the transfer function relating the angular displacement to the applied torque. b. Find the parameters, J, and D, for the system T(t) 0(t) J

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Step Response Analysis This graph illustrates the step response of a system, showing how the output, denoted as \(\omega(t)\) in radians per second, changes over time \(t\) in seconds. #### Key Details: - **Horizontal Axis (t, [sec])**: Represents time in seconds. - **Vertical Axis (\(\omega(t)\), [rad/s])**: Represents the system's output in radians per second. - **Response Curve**: The blue curve depicts how the system's output responds to a step input over time. - **Final Value**: The output approaches a steady-state value of approximately 125 rad/s. - **Rise Time (Tr)**: Marked on the graph as 0.20 seconds, indicating the time taken for the output to rise from 0 to its steady-state value. This step response graph is commonly used in control systems to analyze the stability and performance of a system after a disturbance. The quick rise to its final value suggests a fast system response with minimal overshoot.
Transcribed Image Text:### Step Response Analysis This graph illustrates the step response of a system, showing how the output, denoted as \(\omega(t)\) in radians per second, changes over time \(t\) in seconds. #### Key Details: - **Horizontal Axis (t, [sec])**: Represents time in seconds. - **Vertical Axis (\(\omega(t)\), [rad/s])**: Represents the system's output in radians per second. - **Response Curve**: The blue curve depicts how the system's output responds to a step input over time. - **Final Value**: The output approaches a steady-state value of approximately 125 rad/s. - **Rise Time (Tr)**: Marked on the graph as 0.20 seconds, indicating the time taken for the output to rise from 0 to its steady-state value. This step response graph is commonly used in control systems to analyze the stability and performance of a system after a disturbance. The quick rise to its final value suggests a fast system response with minimal overshoot.
**Rotational Dynamics Problem** 3. A unit-step torque (i.e. \( T(t) = u_{\text{step}}(t) \, \text{N-m} \)) is applied to the rotational dynamic system shown below. The resulting angular velocity is provided in the graph. a. Provide an estimate for the transfer function relating the angular displacement to the applied torque. b. Find the parameters \( J \), and \( D \), for the system. **Diagram Explanation** - The diagram depicts a rotational dynamic system where a torque \( T(t) \) is applied. The system consists of a block labeled \( J \), representing the moment of inertia, connected to a damping element \( D \). - \( \theta(t) \) represents the angular displacement resulting from the applied torque. - The damping element \( D \) is shown connected to the system, indicating the resistive force acting against the rotation. This setup typically models how the angular displacement and velocity respond over time to the applied torque. Further analysis of the system's response can reveal the system's transfer function and key parameters such as the moment of inertia \( J \) and damping coefficient \( D \).
Transcribed Image Text:**Rotational Dynamics Problem** 3. A unit-step torque (i.e. \( T(t) = u_{\text{step}}(t) \, \text{N-m} \)) is applied to the rotational dynamic system shown below. The resulting angular velocity is provided in the graph. a. Provide an estimate for the transfer function relating the angular displacement to the applied torque. b. Find the parameters \( J \), and \( D \), for the system. **Diagram Explanation** - The diagram depicts a rotational dynamic system where a torque \( T(t) \) is applied. The system consists of a block labeled \( J \), representing the moment of inertia, connected to a damping element \( D \). - \( \theta(t) \) represents the angular displacement resulting from the applied torque. - The damping element \( D \) is shown connected to the system, indicating the resistive force acting against the rotation. This setup typically models how the angular displacement and velocity respond over time to the applied torque. Further analysis of the system's response can reveal the system's transfer function and key parameters such as the moment of inertia \( J \) and damping coefficient \( D \).
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