- #1
How to Solve for s1 | Experts' Guide
- Context: Undergrad
- Thread starter shayaan_musta
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SUMMARY
The discussion centers on solving for s1 in the context of a second-order control system, specifically referencing the equation format s² + 2ξω_ns + ω_n². Participants highlight the importance of understanding dominant closed-loop poles, which are those near the origin. The problem is derived from "Modern Control Engineering 5th Edition by Katsuhiko Ogata," specifically from page 380, problem A-6-17. A key point of confusion arises regarding the integration of parameters β and x in the derivation process.
PREREQUISITES- Understanding of second-order control systems
- Familiarity with dominant closed-loop poles
- Knowledge of the standard form of control system equations
- Access to "Modern Control Engineering 5th Edition by Katsuhiko Ogata"
- Review the derivation of equations 6-32 and 6-33 from Ogata's textbook
- Study the concept of dominant poles in control theory
- Learn about the role of parameters like β in control system equations
- Explore practical examples of second-order system analysis
Students and professionals in control engineering, particularly those studying second-order systems and seeking to deepen their understanding of pole placement and system stability.
- #2
berkeman
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Can you say more about what part of the textbook derivation you are not following? Which step does not make sense? That would help us to guide you better.shayaan_musta said:
- #3
shayaan_musta
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It is from the book "Modern Control Engineering 5th Edition by Katsuhiko Ogata". Page no. 380 and problem no. A-6-17.
It is available in PDF.
It is available in PDF.
- #4
berkeman
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That's not what I was asking. I was asking you to go through the derivation for us step by step, up until the part that you are not understanding...shayaan_musta said:
- #5
shayaan_musta
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Ohhh sorry. My bad.
Actually, I am not getting the starting point. Because I don't know where does β go and from where does x come in equation (red box) because 6-32 and 6-33 are the sources of the equation (red box). Since, 6-32 and 6-33 has beta but the equation (red box) does not have beta. So I am not sure how to start derivation.
Actually, I am not getting the starting point. Because I don't know where does β go and from where does x come in equation (red box) because 6-32 and 6-33 are the sources of the equation (red box). Since, 6-32 and 6-33 has beta but the equation (red box) does not have beta. So I am not sure how to start derivation.
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