State-space Equation

Discussion in 'Homework Help' started by czlee88, Mar 30, 2011.

  1. czlee88

    Thread Starter New Member

    Mar 30, 2011
    1
    0
    Hi, I'm new to state-space equation. Not sure how to solve problems 1.1 in my attachment.

    I had define
    input Vi(t) = VL+VR+VC
    output Vo(t)=1/C int(i) dt
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469

    Your starting equations are correct. The two needed state space equations are found from each of these. For a hint, consider that the state variables will be capacitor voltage Vc and series current i. So, how do you modify your equations so that you have proper state space formulation. The proper form will be the derivative of the state variable as a funtion of state variables and input signals.

    Hence, you should get functional forms as follows.

    di/dt=f(i,Vc, Vin)
    dVc/dt=f(i,Vc, Vin)

    Note that the i, Vc and Vin may or may not show up in these equations, but only these variables are allowed. Note that parameters, such as R, L and C are allowed in the equations.

    Then you need to find an equation for the output. Well, here you are all set because the output variable Vc is also a state variable. So you get Vc=Vc.

    Once you have the equations, you can put them in matrix form.
     
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