If I have the following
circuit how would I go about representing it in state space form, specifically the non-linear devices diodes, BJTs, and LEDs? Would I be correct in focusing on the non-linear devices linear acting region? Or do I take their V I relationship and linearize it?Thanks ahead of time?
Hi there,
State Space does not really beg the question, "Do i linearize or do i not linearize", it's just another mathematical representation of a system, which can be linear or not linear in and of itself, and still have a state space representation. It's more about just getting a system into the right form, the way it exists as is. Yes, you may choose to linearize a non linear system, but that's a separate question apart from the representation itself. Of course a linear system will map more simply and will then lend itself to conventional techniques and if the system is non linear then you'll probably have to resort to numerical techniques.
For example take a diode, in linear form we may just write:
i=v/K1+K2
which is a linearized version, or we may write:
i=K1*(e^(v/K2)-1)
One is 'considered' linear and one is non linear. They are just different ways to represent the diode in mathematical form.
What is not clear in the drawing however, is where the light for the photo transistors is coming from. Is it coming from the ambient or from the LED's, or both? That would be something that would change the representation quite a bit, in fact completely, so that would have to be found out or else you'd have to consider all three ways unless there are other possibilities too and then you'd have to do those cases also.
What would probably help here is to do a couple much simpler systems maybe with one or two inputs and outputs first, then go from there. The linear cases are easier so that would be a good place to start