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How to solve this nonlinear output regulation problem

  1. Jun 29, 2011 #1
    Hello, everyone

    There is a control theory problem that i would like to ask for help here.

    Suppose a very simple nonlinear system as follows

    x' = u
    y = (2-cosx)*(2-cosx)

    how to find a control law u that makes the output y can track a constant asymptotically,
    of course the x should be stable too.

    best wishes
     
  2. jcsd
  3. Jun 30, 2011 #2

    Mark44

    Staff: Mentor

    Here's what I would do.
    Starting with your 2nd equation, expand the right side.
    y = 4 - 4cosx + cos2x

    This equation is quadratic in cosx. Use the quadratic formula to solve for cosx, and then use trig to solve for x.
    Take the derivative to get u.
     
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