I just started reading state space representation from book by (Norman s.)
and in this book all examples of state space representation are either of series RLC with voltage source as an input or parllel RLC with current source as an input.
But
How to represent a state space model for a parallel RLC circuit with voltage source as an input ?
I tried but in this case
1.I confused about what should be order of system (because here different system variable as an output give different order of differential equation )
2.how many minimum system variables require to write the state equations?
Or
3.its state representation is not possible ?
Best Answer
There are several possible state variable presentations for the same circuit, but I guess you want state variables which are measurable quantities of the circuit. In that case you should use inductor currents and capacitor voltages as the state variables.
Capacitors have stale law dUc/dt = I/C where Uc is the cumulated voltage over the capacitor and I is the charging current. Inductors have dI/dt = U/L where I is the cumulated current through the inductor and U is the voltage over the inductor.
The series RLC circuit:
You can write the wanted equations with these laws. Express the voltage over the inductor with your V(t), I, R and Uc. Divide it by L and there's your expression for dI/dt, the right side of the first state equation.
The second state equation is simply (as already written) dUc/dt = I/C.
Circuit analysis programs which do transient analysis generate the equations automatically and solve them numerically. You must enter the initial values of the state variables i.e. inductor currents and capacitor voltages or let them be zero.