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1st Order Nonlinear equation - Control

  1. Jul 11, 2008 #1
    Hello everybody,

    I've come cross the following first order nonlinear equation when trying to solve
    for the speed of an electrical motor at any given time t during motor start.

    y'=-(ay^2)+bx+c ; y(0)=0 ; a, b and c are constants; y=motor speed; x= time

    The Motor Starter uses a linear Torque control and the load exhibits a quadratic
    dependence of the motor speed. I am sure there is a possibility of solving this analitically.
    I've tried changing variables, reduction and using substitution with no success. Maybe I
    am missing something or haven't found the right substitution...Any ideas? I'll appreciate
    any help on this.

  2. jcsd
  3. Jul 11, 2008 #2

    Tom Mattson

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    Staff Emeritus
    Science Advisor
    Gold Member

    I plugged it into Maple, and there is indeed a closed form solution. But it's a complicated mess of Airy functions, so I don't think there's a "silver bullet" substitution that's going to make this nice for you.
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