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Controller Design

  1. Oct 19, 2013 #1
    1. The problem statement, all variables and given/known data

    http://robotics.ucsd.edu/final_143b_13_version1.pdf [Broken]

    I am stuck on problem 1a. I understand all of the concepts I am just unsure of how to determine the best possible location to place the unknown zero.



    3. The attempt at a solution

    I know that the zero must be located to the left of z1 and to the right of the origin.
    From approximate design guides I have determined that wn=1.8/tr=10rad/s
    the damping ratio should be zeta>=.5 meaning theta>=30 degrees (from imaginary axis)
    I thought maybe there is a way of proving that this root locus plot forms a perfect circle in its rounded region(i am not sure of this but it looks like it from plotting it in matlab with axis equal). Since we know our damping and our frequency, we could determine the radius of the circle, and then find the ideal location to place za but that seems to be a bit stretched and unnecessary to obtain a solution,

    This was my final from last quarter by the way and it is our first homework assignment for the quarter.

    Any help would be great! Thanks
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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