# Constructing a block diagram from equations

$$$$X(s) = -A X(s) + Z(s) +B W(s)$$$$ $$$$W(s)= C X(s) -D W(s)$$$$ $$$$Y(s)= E W(s)$$$$

My question is would the system be closed loop block diagram?

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Commented Jan 11, 2023 at 18:33
• From each equation, could you draw a block diagram? If you can, then you should be able to connect the two block diagrams together to create a single large block diagram which will probably have three loops in it. It would be great if you can show the block diagram attempt you have made so far. Use the edit to add the details.
– AJN
Commented Jan 12, 2023 at 2:18

## 2 Answers

There is a formalism called the power bond graph method which allows you to assemble block diagrams knowing the transfer functions. The standard reference is Karnopp & Rosenberg, System Dynamics- A Unified Approach.

• Could you please explain how I can use this method for my system of equations? I don't have access to this reference. The input into the overall system is Z(s), and the output of the system is Y(s). I am struggling to create a block diagram, and thus overall transfer function for the system of equations. Commented Jan 11, 2023 at 21:56

And the closed-loop transfer function

$$Y\ =\ [U\ (I-F\ G)^{-1}\ F\ H]\ Z$$