# Control Systems Engineering - Signal Flow Graphs

• GreenPrint
In summary, the conversation discusses the difficulties of transitioning from state space representation to signal flow graph representation. The main question is whether or not it is allowed to draw transistors in both directions between nodes representing equal variables. It is clarified that for the signal flow graph, the output can directly be the sx1 node without the need for an arrow.
GreenPrint
Hi,

I seem to be having some issues going from state space representation of a system to signal flow graph representation. My troubles seem to be, if I have something like this

$\frac{d}{dt}x_{1}(t) = v_{1}(t)$

In state space representation I list functions to which the derivatives are as a function of the state space variables.

In signal flow graph model of a system am I allowed to draw transistors from one node to another node by multiplication of one in either direction?

I don't if I'm explaining this well, but if I have a node for $sx_{1}(t)$ and a node for $v_{1}(t)$ am I able to to draw the transistor arrow from the nodes in either direction since they are equal to each other? That is a arrow coming out of the node that represents $sx_{1}(t)$ and going into $v_{1}(t)$ or the arrow coming out of the node representing $v_{1}(t)$ and into the node representing $sx_{1}(t)$. Mathematically I don't see why the direction of the arrows from the nodes can be reversed as needed since they have a one-to-one equivalency. I just want to make sure. If I'm not able to do this and I'm not sure I can solve this problem I'm trying to solve.

Thanks for any help.

your output doesn't always have to be equal to 1 state variable
ex.

$\dot{X}$=AX+BU
Y=CX+Du

A=[0 4
7 -2]

B=[1
3]

if you want y to equal $\dot{X1}$, you can say
C=[0 4]
D=[1]

Does that make sense?

So that means for the signal flow graph that your output can directly be that sx1 node. You don't need to draw an arrow, that node can simply be sx1 and v1

Last edited:

## 1. What is a signal flow graph?

A signal flow graph is a graphical representation of a control system that shows the flow of signals through the system. It consists of nodes, which represent system components, and directed edges, which represent the flow of signals between the nodes.

## 2. How are signal flow graphs useful in control systems engineering?

Signal flow graphs are useful in control systems engineering because they provide a visual representation of the system, making it easier to analyze and understand the behavior of the system. They also allow for the application of mathematical techniques, such as Mason's gain formula, to analyze the system's stability and performance.

## 3. How do you construct a signal flow graph?

To construct a signal flow graph, first identify the components of the control system and assign them as nodes on the graph. Then, draw directed edges to represent the flow of signals between the nodes. Finally, label the edges with appropriate transfer functions or gains.

## 4. What are some advantages of using signal flow graphs?

Some advantages of using signal flow graphs include their ability to simplify complex systems, provide a visual representation of the system, and aid in the analysis and design of control systems. They also allow for the identification of feedback loops and can easily be converted into mathematical equations for analysis.

## 5. Can signal flow graphs be used for both continuous and discrete systems?

Yes, signal flow graphs can be used for both continuous and discrete systems. For continuous systems, the transfer functions on the edges are represented by Laplace transforms, while for discrete systems, they are represented by z-transforms. The same principles of signal flow graphs apply to both types of systems.

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