# Control Systems, State space to Transfer Function

• k87
In summary, The conversation is about converting a dynamics system from a state space representation to a transfer function. The participants are at the stage of solving for the transfer function and are seeking help with the next step. They have a pictorial representation and corresponding transfer functions, but are unsure how to obtain the numerators.
k87
Hi guys,

Need a little help with an example my tutor and I are trying to work through.

We're converting a dynamics system from a state space representation to a transfer function.

This is where we are at so far...

[s^2 + (C/Mb)S + (K1/Mb), -((C)S + K1)/Mb; -((C)S + K1)/Mw, S^2 + (C/Mw)S + (K1+K2)/Mw] [X3;X4] = [0; k2/mW]*Zr(.)

Zr(.) being the differential of Zr which in this case is velocity.

We have what we think is the next step but I'm still not entirely certain so would appreciate some help

This is it in pictoral form and the corresponding transfer functions, I don't understand how to get the numerators though

## 1. What is a control system?

A control system is a system that manages, commands, directs, or regulates the behavior of other systems or processes. It uses feedback mechanisms to maintain its desired output or performance, and can be found in various applications such as industrial, mechanical, and electrical systems.

## 2. What is state space representation in control systems?

State space representation is a mathematical model used to describe the behavior of a control system. It involves representing the system's inputs, outputs, and internal states as a set of first-order differential equations, which can then be solved to obtain the system's response. This representation is often used for complex systems with multiple inputs and outputs.

## 3. What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a control system. It is a ratio of the output of the system to the input, and is often expressed in terms of complex variables. The transfer function can be used to analyze the stability and performance of a system, and it is an essential tool in control system design.

## 4. How do you convert from state space to transfer function?

To convert from state space to transfer function, you need to first obtain the state space representation of the system. Then, you can use various methods such as the Laplace transform or diagonalization to solve the state space equations and obtain the transfer function. The transfer function can also be obtained directly from the state space matrices using the Cayley-Hamilton theorem.

## 5. What are the advantages of using state space representation over transfer function?

State space representation allows for a more comprehensive description of a system, as it can handle multiple inputs and outputs and is not limited to linear systems. It also provides a more intuitive understanding of the system's behavior and allows for easier analysis and design. Additionally, state space representation can be used for both continuous and discrete-time systems, whereas transfer function is only applicable to continuous-time systems.

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