State Space model
State Space model
(OP)
Hello,
I'm trying to obtain a state space model of a non-linear non-stationary circuit:
s*X(s) = A(s) * X(s) + B(s) * U(s)
(Laplace form)
Where X is the state vector and U the input.
There are plenty of examples out there, but all of these use the voltage and current as input and thus obtain a matrix A containing inductances and capacitances relating the states. However, in my case, I have to control stubs (thus the L's and C's) and use these as my inputs. However, when doing this I can no longer obtain a matrix A that does not already include the L's and C's.
Example:
Ground-----Stub1-----V1
|
transmission line
|
Ground-----Stub2-----V2
Does anybody have any idea or experience with this kind of problem?
Thank you.
I'm trying to obtain a state space model of a non-linear non-stationary circuit:
s*X(s) = A(s) * X(s) + B(s) * U(s)
(Laplace form)
Where X is the state vector and U the input.
There are plenty of examples out there, but all of these use the voltage and current as input and thus obtain a matrix A containing inductances and capacitances relating the states. However, in my case, I have to control stubs (thus the L's and C's) and use these as my inputs. However, when doing this I can no longer obtain a matrix A that does not already include the L's and C's.
Example:
Ground-----Stub1-----V1
|
transmission line
|
Ground-----Stub2-----V2
Does anybody have any idea or experience with this kind of problem?
Thank you.






RE: State Space model
RE: State Space model
Ytotal = Ystub + Yrest with Ystub = -j*Y0*cot(beta*l)
where beta is the lossless wave propagation constant. By choosing l appropriately we can change the behaviour of the stub.
Thanks for taking the time to read my question. Any suggestions are welcome!
RE: State Space model
Fyi
RE: State Space model
Thanks to both of you for your reply.
RE: State Space model
E*dx/dt = A*x + B*u, y = C*x + D*u
The L and C terms come out of the A and B matrices and end up in the E matrix. When using inductor currents and capacitor voltages as the states, you typically solve the circuit equations for [di/dt; dv/dt], which means you have to divide by L and C. You don't divide by them in descriptor form, you factor them out into another matrix E that is square and diagonal with the L and C terms on the diagonal. For example, in a circuit with one L and one C, the left side of the equation will be [L, 0; 0, C]*[di/dt; dv/dt]. You can change the E matrix while you run simulations at any given time step.
xnuke
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RE: State Space model
RE: State Space model
Btw, I'm a bit surprised that I had never heard of descriptor state space models before. I guess it can usually be reduced to the standard form, but still....Thanks for the tip!