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!

Satellite Control System With Rate Feedback

  1. Apr 18, 2013 #1
    I'm trying to get the transfer function of this rigid control system that uses rate feedback to stabilize it. Using k=1 and kv=0
    Capture_zps6fbe8d62.png

    Attempt at a solution.
    When kv=0, the rate feedback is removed.
    In the block diagram, I moved the pickoff point and used the cascade rule to get [tex] 1/s^2 [/tex]
    and the transfer function for the top portion is [tex] H(s)=\frac{(1/s^2)k}{1+(1/s^2)k}=\frac{k}{s^2((k/s^2)+1)}[/tex]
    With the pickoff point moved you get [tex]\frac{1}{1/s}[/tex] at the bottom next to kv.
    This is where I'm stuck. How do I get the complete transfer function? I would like to put it in matlab.

    Thanks
     
  2. jcsd
  3. Apr 18, 2013 #2
    This looks like something you probably should have posted in the Homework section, just FYI.

    What transfer function is it you want? Is it θ(s)/θ_r(s)?
     
  4. Apr 18, 2013 #3
    Yes please.
     
  5. Apr 18, 2013 #4

    berkeman

    User Avatar

    Staff: Mentor

    (thread moved to HH)
     
  6. Apr 19, 2013 #5
    For K = 1, K_v = 0, you have a double integrator, 1/s^2, in a unity feedback configuration and the transfer function you posted, H(s), is the closed-loop transfer function θ(s)/θ_r(s) for this system.

    In case you're looking for θ(s)/θ_r(s) with K, K_v only known to be real, you could apply block simplification for the inner loop first, then the outer one using the rule for negative feedback loops. You already used this rule once in finding H(s).
     
  7. Apr 20, 2013 #6
    That's the only thing I'm not sure of...the block simplification. There's so many rules and I don't know which ones to apply here.
     
  8. Apr 21, 2013 #7
    This was the first link on Google for 'block simplification':
    http://www.msubbu.in/sp/ctrl/BD-Rules.htm

    Have a look at rule 1, 2 and 6. Try simplifying your block diagram to a single system using those rules and post here if you get stuck.
     
  9. Apr 21, 2013 #8
  10. Apr 21, 2013 #9
    Split up the summing junction and simplify the series inside the inner loop, rule 1 & 2:

    sys1.jpg

    Simplify the inner negative feedback loop, rule 6:

    sys2.jpg

    Do you understand those steps? How would you proceed?
     
  11. Apr 21, 2013 #10
    Understood. Proceed by using rule 2 again and that's it? Looks like I was over complicating things.

    Thanks
     
  12. Apr 21, 2013 #11
    Rule 2 to simplify the series inside the loop, but what about the loop itself?
     
  13. Apr 21, 2013 #12
    The output [itex]\theta[/itex] goes back into junction, which gives a transfer function of 1?
    We're looking for [itex]\frac{θ(s)}{θ_r(s)}[/itex] right?
     
  14. Apr 21, 2013 #13
    We want to simplify the block diagram so it looks like:

    θ_r -> box -> θ

    and nothing else. No loops!

    Have a look at the step I did using rule 6. Doesn't that look like something you could do again?
     
  15. Apr 21, 2013 #14
    Y=[itex]\frac{G1}{1+G1(1)}[/itex]= [itex]\frac{K}{s^2+s*K*K_v+K}[/itex]?
     
  16. Apr 22, 2013 #15
  17. Apr 22, 2013 #16
    Ok. Last Question. For K=1 and K_v=0, how do I use this transfer function in matlab to get the Root Locus or Bode plot?
     
  18. Apr 22, 2013 #17
    If you have the Control System Toolbox you could use its suite of commands, e.g.:
    tf
    bode
    rlocus

    and so on. Have a look at their help pages and that of the toolbox itself.

    If you don't have it, you could make your own functions to evaluate the transfer function for whatever range of parameters you're interested in and plot the results.
     
  19. Apr 22, 2013 #18

    jhae2.718

    User Avatar
    Gold Member

    There is an rlocus function in MATLAB that will plot the root locus plot of a given transfer function.
     
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: Satellite Control System With Rate Feedback
Loading...