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Homework Help: Control System Phase Lag

  1. Feb 6, 2017 #1
    1. The problem statement, all variables and given/known data
    A closed loop control system has three components, Controller, Process, and Measuring System. Each has it's own gain and phase angle. I understand how to find the total of the gain but I'm unsure as to how to find the total phase angle?

    2. Relevant equations
    Total Gain=

    3. The attempt at a solution
    Using this formula on the phase angle doesn't give a sensible answer. My instincts tell me that it is just straight addition? I know I've not got very far on this myself, just a nudge in the right direction would be hugely useful.

    Many thanks.
  2. jcsd
  3. Feb 6, 2017 #2


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    Every frequency corresponds to a complex number. That leads to a complex number for $$ \frac{A*B}{1+(A*B)*C} $$.
    The modulus of the complex number is the gain and the argument is the phase shift.
  4. Feb 9, 2017 #3

    rude man

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    You have
    A = |A|exp(jθA)
    B = |B|exp(jθB)
    C = |C|exp(jθC)
    then combine these in your formula to get the net θ.
    You do have to know how to manipulate complex numbers both in polar and rectangular form.[/SUB]
  5. Feb 9, 2017 #4


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    For real values of A,B and C the phase shift is (of course) zero - trivial, but unrealistic solution.
    Hence, all of these expressions must be considered to be frequency-dependent (complex expressions).
    For finding the total phase shift you have nothing to do than (a) to rewrite the transfer function and split it into a real and an imag. part, and (b) apply the definition for phase shift.
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