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

 

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

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.