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Non-Linear Control System and Motor synchronization

  1. Feb 6, 2008 #1
    I am currently trying to design a system that will sychronize two propellor motors, and I must design using the following equation:
    w'*I + (w^2*r^2*p*S*C_d)/(2) = T_t + T_ss
    w' = Angular acceleration
    I = moment of inertia
    w = angular velocity
    r = radius of blade
    p = air density
    S =Surface Area
    C_d = Drag coeeficient
    T_t = transient torque
    T_ss = Steady state torque

    The problem is this is a non-linear system, and I do not know how to 'linearize' the system to use general linear control system theory. Any help would be greatly appreciated. Thanks.
  2. jcsd
  3. Feb 6, 2008 #2
    this is just a shot in the dark, but can you break the problem up into 2 linear models? Will that help at all?
  4. Feb 6, 2008 #3
    what do you mean by two linear models?
  5. Feb 6, 2008 #4
    sorry, probably worded that wrong.

    Is there anyway to break the problem up into pieces? Other than that, I don't have much to offer, sorry.
  6. Feb 7, 2008 #5
    For linearization, follow the procedure in http://en.wikipedia.org/wiki/Jacobian

    and evaluate at the operating point that you want. It will clear out the nonlinear terms in the Jacobian and give you a linear system at that point in the form of [tex]\dot{x} = Ax + Bu[/tex]
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