Consider the electrical circuit shown:
Let the state variables be x1(t)=Vc(t), x2(t)=iL(t), and x3(t)=Vc(t); output is Vo(t). Write the state-space equations in matrix form and find the transfer function, T(s)=Vo(s)/Vi(s).
KCL and KVL
The Attempt at a Solution
Differential Equations for State Variables:
Now this is the part that I am stuck at. I know that I have to solve for X1', X2', and X3' in terms of the state variables and inputs only. However, I can't seem to reduce the equations enough to get it into this format.
Basically, I am trying to solve for i2, i5, and V2 in terms of i4, V1, Vo, and Vi only (the state variables and inputs). Once I have these equations, I can easily put them into matrix form and solve using MATLAB. I solved a problem earlier that was exactly the same, only the first capacitor was replaced with an inductor. So, I think it is the capacitor that is giving me problems.
A few equations that I found:
Thanks for the help!
I looked over the problem again, and it seems that I can't solve for i3 without it containing a V2 or an i2. Is there any way to solve for i3 with a combination of only i4, V1, Vo, and Vi? Once I find this, I will be able to solve the problem.
Last edited by a moderator: