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Overshoot control.

  1. Mar 13, 2014 #1
    Hello,
    Suppose I have the following step response:
    ystep(t)=(kP/1+kP)(1-e(-t/τ))
    where k is constant and P is the plant.
    How may I determine the values of k for which there would be no overshoot?
     
    Last edited: Mar 13, 2014
  2. jcsd
  3. Mar 14, 2014 #2

    jim hardy

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    No takers yet ?

    Seems to me you'd have to plug in whatever f(t) describes P and find the damping.
     
  4. Mar 14, 2014 #3
    Here are the relevant functions:
    P(s)=s^2+a1*s+a0
    Y_step(s)=[kP(s)]/[1+kP(s)]
    Now, how exactly do I find the values of k which would prevent an overshoot?
     
  5. Mar 14, 2014 #4

    jim hardy

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    you're on the right track...

    Laplace Transfer function of plant then is P(s) = s2 + a1s +a0

    and when connected to feedback to close the loop takes that form KP/(1+KPh), h being feedback gain

    so you'll have to expand that by plugging in P(s) to get Laplace transform of the closed loop,

    and multiply that by a step, which in Laplace is 1/s,

    which will result in a pretty long fraction
    that'll have to be resolved by algebra

    but since this looks like a homework problem it'll be quite do-able, for textbooks are that way.

    Once the closed loop response is boiled down to a quadratic form it should be straightforward to extract damping.

    Now - it was 1965 when i took modern control theory course
    and my algebra has grown rusty, if you'll pardon a cheap excuse for not solving this and typing it out in latex.

    Above is the approach i'd have used in 1965. I remember struggling with the algebra of this type problems, and still dread them.
    Hopefully someone who's fresh will chime in now, i wanted to prime the pump for you. Could be they're teaching an easier method nowadays.
     
  6. Mar 14, 2014 #5
    This looks an awful lot like you're mixing up frequency- and time-domain expressions. I assume P is a (complex-valued) transfer function. How did you arrive at this expression?

    Are you sure you have the right P(s)? I ask because it's not a proper transfer function, i.e. it cannot represent any physically realizable system, which is a tad unusual in introductory control theory.
     
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