Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Routh stability test question.

  1. Dec 20, 2006 #1
    to find values of k for which the system is stable.


    first (1+k)must be >0 and 2K must be >0 then i construct routh array
    to get 3k-1/2k as a coefficent of s^2 and
    (3k-1)/2k *(1+k) - 4k as a coefficent of s .
    then k must be>1/3 and K>2.15 and K>-0.154 then k must be >2.15 ????
    is this right or there is something wrong??
  2. jcsd
  3. Dec 21, 2006 #2
    the idea is right but your numbers are wrong . it will be k > 1 .
  4. Dec 24, 2006 #3


    User Avatar

    For the line [tex]s^1[/tex] I got
    [tex]-\frac{1}{3} < k < 1[/tex]
    And for the line [tex]s^2[/tex]
    [tex]\frac{1}{3} < k [/tex]
    So, you should have
    [tex]\frac{1}{3} < k < 1[/tex]
  5. Dec 25, 2006 #4
    how did you get that for s^1 k<1
    the coeff is (3k+1)(k-1)(2k) so K must be >1 not <1 !!!!!!
    i just want to know how did you get this as i substituted by a value greater than 1 and found system to be unstable.is there anything wrong with my rules or numbers???
  6. Dec 25, 2006 #5


    User Avatar

    I did the calculations wrong. The coeff for s is [tex](3k-1)(1+k) - 8k^2 = -5k^2 + 2k -1[/tex], whose roots are complex. Since the higher power of k has a negative coeff, the parabola has the concavity down. For all values of k the polynomial has negative value.
    Your system is unstable for every k.
  7. Dec 25, 2006 #6
    i am really too confused everytime i solve this problem i get different solution !!!!!!!!!!!!! i solved now and got the same result as yours.

    but plz tell me if the coeff of s^1 is(3k+1)(k-1) then how to get the range????
  8. Dec 26, 2006 #7
    i think you reached this for S^1 :

    [ (3k-1)(1+k)-8k^2 ] / 3k-1 > 0

    you cant multiply by 3k-1 , so :

    (1+k) - (8k^2 / 3k-1) > 0

    simplify to get : 5k^2 - 2K +1 < 0

    and since your first condition from S^3 is K>0 , then :

    system is unstable for all values of k ..
  9. Dec 28, 2006 #8
    ha, my control systems prof basically said routh hurwitz was BS and skipped it. Can't help ya here.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook