1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bode plot and stability margins

  1. Nov 14, 2015 #1

    Maylis

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    upload_2015-11-14_17-45-51.png

    2. Relevant equations


    3. The attempt at a solution
    Hello, In part (b), I found ##k_{cu} = 0.5##. I found in part (d) a controller gain of ##k_{c} = -0.3## yielded a diverging output. Here are the bode plots for parts (a),(c), and (d). I don't understand how I should use the "stability margins" which are the dots on the plots for part (e) in order to determine ##k_{cu}## without ziegler-nichols tuning.
    upload_2015-11-14_17-46-59.png
     
  2. jcsd
  3. Nov 15, 2015 #2

    LvW

    User Avatar

    Maylis - at first, are you familiar with the definition of stabiliy margins (phase resp. gain margin) ?
     
  4. Nov 15, 2015 #3

    Maylis

    User Avatar
    Gold Member

    I know the gain margin is the inverse of the amplitude ratio at the crossover frequency (the frequency at which ##\phi = -180^{o}##), ##GM = 1/AR_{co}## and the phase margin is the phase angle at which ##g_{c}g_{p} = 1##. ##PM = \phi_{pm} + 180^{o}##

    Admittedly I hadn't read this section in my textbook prior to posting this question, so I see I can use those dots to identify my crossover frequency and gain margins.

    I think it doesn't make any sense to use the bode plot of ##g_{cu}*g_{p}## to find ##k_{cu}##, I should use the bode plot of ##g_{p}## and use those stability margins to determine ##k_{cu}##? And compare with what I determined it to be by playing with simulink to be ##k_{cu} = 0.5##

    Here is a bode plot for just the transfer function ##g_{p}##
    upload_2015-11-15_19-49-23.png
    The phase margin is -31.8 degrees at 0.777 rad/s, and the gain margin is -6.21 dB at 0.633 rad/s. With this information, I'm not sure how to determine what ##k_{cu}## should be.
     
    Last edited: Nov 15, 2015
  5. Nov 16, 2015 #4

    LvW

    User Avatar

    If you reduce the gain the cross-over frequency will be shifted to smaller values (the phase response remains the same).
    And - as a consequence - the phase margin will increase. I think, that`s what the green curve in the first diagram shows.
     
  6. Nov 17, 2015 #5

    Maylis

    User Avatar
    Gold Member

    How can I use this information to find ##k_{cu}##?
     
  7. Nov 17, 2015 #6

    Maylis

    User Avatar
    Gold Member

    Never mind, you just find the value that will give zero phase and gain margin
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Bode plot and stability margins
  1. Bode Plot Plotting (Replies: 1)

  2. Bode Plot (Replies: 5)

  3. Bode Plot (Replies: 4)

Loading...