# Order of a system

I can find it when the transfer function is written in standard form but I don't know how to find it if it is written differently. For example $$G(s)=\dfrac{1}{s(s+1)^3}$$, is this order three or four?

• PLEASE DON'T SHOUT IN YOUR QUESTION TITLE. It will get you extra attention but not the sort you want. Hit the edit link below your question to fix it. – Transistor Apr 9 '20 at 18:48

## 1 Answer

There are two (between others) characteristics that define the transfer function of the system and moreover the system itself.

• Order $$\ \rightarrow$$ Defined by the maximum power of the laplace variable $$\ s$$ in the denominator
• Type $$\ \ \rightarrow$$ Defined by the number of poles at the origin (only) of the transfer function. Poles of a system are the roots of the denominator of the transfer function.

In this particular example, by working out easily the math of the denominator, you will find out that the order of the system is: $$\ 4$$. For some extra tiny analysis, you can see that this system is of type $$\ 1$$. You can also find relevant information at this page by using matlab to find out the order of your system. However, I encourage you at least in the beggining to find it out by yourself:

https://www.mathworks.com/help/control/ref/order.html

Although I answered your question, I advise you to first do your own search and try to figure out the solution to your problem on your own before posting here since this was a pretty simple question and could be answered easily by doing a quick google search.

• +1 for the last paragraph – OpticalResonator Apr 10 '20 at 11:17