# Standard First Order System

Definition 1: Standard 1st order system

The standard 1st order system has the Transfer Function $H(s)=sτ+1κ $ where $κ,τ>0$. $κ$ is called the

DC gainand $τ$ is called thetime constant.

Where does this come from?

It’s basically telling you that if you compute the transfer function of any first equation differential equation, you’ll be able to write it in this standard form.

- To convince yourself, look at the Linear Harmonic Oscillator example, or Cruise Control, which are both first-order systems