Finding s1 from dominant closed loop poles

  • Level: Undergrad 
  • Thread starter shayaan_musta
  • Start date
4 replies · 2K views · last reply
shayaan_musta
Messages
208
Reaction score
2
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
 
Attachments
  • Textbook page showing Figure 6-90, a unity-feedback block diagram with a summing junction, a block G_c(s), and a plant 1/(s(s+1)(s+5)), followed by the lag-lead compensator solution with the equations for G_c(s), K_c = 50 sec^-1, and the pole-zero cancellation condition.
    page1.PNG
    22.1 KB · Views: 518
  • Textbook page, page 381, showing the magnitude and angle conditions for dominant closed-loop poles, with s1 = -x + j√3x highlighted in a red box and the solved values β = 16.025 and x = 1.9054.
    page2.PNG
    22.9 KB · Views: 550

Discussion

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.
 

Similar threads

How to model the behavior of a closed loop position system?
  • pit34
  • · Replies 9 ·
  • Electrical Engineering
Replies
9
Undergrad Cavitation in a closed loop pumping system
  • Aptx4869
  • · Replies 9 ·
  • Mechanics
Replies
9