How to Solve for s1 | Experts' Guide

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Discussion Overview

The discussion revolves around solving for a specific variable, s1, in the context of control systems, particularly focusing on the derivation from a textbook problem related to second-order systems. Participants are seeking clarification on the derivation process and the role of certain parameters in the equations presented.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant requests assistance in finding s1 from an equation presented in a red box, referencing dominant closed loop poles and the standard form of a second-order system.
  • Another participant asks for clarification on which part of the textbook derivation is unclear, suggesting that understanding the specific step could facilitate better guidance.
  • A participant identifies the source of the problem as being from "Modern Control Engineering" by Katsuhiko Ogata, specifically page 380 and problem A-6-17.
  • One participant expresses confusion regarding the starting point of the derivation, particularly the absence of the parameter beta in the equation while it appears in the referenced equations (6-32 and 6-33).

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing different levels of understanding regarding the derivation process and the role of specific parameters in the equations.

Contextual Notes

Participants have not fully articulated the assumptions underlying their questions, and there is a lack of clarity regarding the definitions and roles of certain variables in the equations referenced.

shayaan_musta
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Hello experts,

I have attached two images below. Kindly tell me how to find s1 (the equation in red box)?

Dominant closed loops poles:
Those poles which lie near to the origin.

The standard form of second order system:
s2+2ξωns+ωn2
 

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shayaan_musta said:
Hello experts,

I have attached two images below. Kindly tell me how to find s1 (the equation in red box)?

Dominant closed loops poles:
Those poles which lie near to the origin.

The standard form of second order system:
s2+2ξωns+ωn2
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. :smile:
 
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.
 
shayaan_musta said:
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.
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...
 
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.
 

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