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Consider the following block diagram. Use the Mason's rule to find the input out equation of this system. Explain which of the Mason's rule have you used and why? Show all the steps of the hand calculations and submit that in the dropbox. U(s) + + Σ 5 2 3 لا 1 4 1 S Σ + Y(s)

Consider the following block diagram. Use the Mason's rule to find the input out equation of this system. Explain which of the Mason's rule have you used and why? Show all the steps of the hand calculations and submit that in the dropbox. U(s) + + Σ 5 2 3 لا 1 4 1 S Σ + Y(s)

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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I believe I counted the forward paths and the loops correctly but my answer was incorrect. I would appreciate a break down. Thanks!

**Block Diagram Transcription and Explanation** The given block diagram represents a control system and you are required to use Mason's rule to derive the input-output equation. Here's a detailed description: **Diagram Components:** 1. The input is denoted by \( U(s) \). 2. The output is denoted by \( Y(s) \). 3. There are several integrators in the form of blocks marked with \(\frac{1}{s}\). 4. Summing junctions are indicated by the symbol \(\Sigma\). **Pathways:** - The input \( U(s) \) enters through a summing junction (leftmost \(\Sigma\)). - Multiple pathways link from the first summing junction: - Through a \(\frac{1}{s}\) block directly to the second summing junction (\( \Sigma \)) connected to the output \( Y(s) \). - Through a sequence of three \(\frac{1}{s}\) blocks in series before reaching the second summing junction. - Through feedback loops with gains of 2, 3, 4, and 5, returning to the input summing junction. **Feedback and Forward Paths:** - Feedback paths are highlighted in red with gains marked as 2, 3, 4, and 5. - Forward paths move the signal from left to right through integrators to the output. **Multiple Choice Options:** - \(\dddot{y} - 2\ddot{y} + 4\dot{y} + 2y - 5 = \ddot{u} + u\) - \(\dddot{y} - 7\ddot{y} - 4\dot{y} - 8y = \ddot{u} + u\) - \(\dddot{y} + 2\ddot{y} + 4\dot{y} + 2y + 5 = \ddot{u} + u\) - None of these answers - \(\dddot{y} + 3\ddot{y} + 4\dot{y} + 2y = \ddot{u} + u\) - \(\dddot{y} + 3\ddot{y} + 4\dot{y} - 3y = \ddot
Transcribed Image Text:**Block Diagram Transcription and Explanation** The given block diagram represents a control system and you are required to use Mason's rule to derive the input-output equation. Here's a detailed description: **Diagram Components:** 1. The input is denoted by \( U(s) \). 2. The output is denoted by \( Y(s) \). 3. There are several integrators in the form of blocks marked with \(\frac{1}{s}\). 4. Summing junctions are indicated by the symbol \(\Sigma\). **Pathways:** - The input \( U(s) \) enters through a summing junction (leftmost \(\Sigma\)). - Multiple pathways link from the first summing junction: - Through a \(\frac{1}{s}\) block directly to the second summing junction (\( \Sigma \)) connected to the output \( Y(s) \). - Through a sequence of three \(\frac{1}{s}\) blocks in series before reaching the second summing junction. - Through feedback loops with gains of 2, 3, 4, and 5, returning to the input summing junction. **Feedback and Forward Paths:** - Feedback paths are highlighted in red with gains marked as 2, 3, 4, and 5. - Forward paths move the signal from left to right through integrators to the output. **Multiple Choice Options:** - \(\dddot{y} - 2\ddot{y} + 4\dot{y} + 2y - 5 = \ddot{u} + u\) - \(\dddot{y} - 7\ddot{y} - 4\dot{y} - 8y = \ddot{u} + u\) - \(\dddot{y} + 2\ddot{y} + 4\dot{y} + 2y + 5 = \ddot{u} + u\) - None of these answers - \(\dddot{y} + 3\ddot{y} + 4\dot{y} + 2y = \ddot{u} + u\) - \(\dddot{y} + 3\ddot{y} + 4\dot{y} - 3y = \ddot
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