what is a first order system and what physical phenomena give rise to first order system(It's transfer function)?

WHAT IS A FIRST-ORDER SYSTEM?

A first-order system is one whose output, y(t), is modeled by a first order,linear differential equation

 






Define,

 

𝜏_p is known as the time constant of the process

and KP is called the steady state gain or static gain or simply the gain of the process.

From eqn, it is easily found that the transfer function of a firstorder process is given by;

A first-order process with a transfer function given by above eqn. is also known as: first-order lag, linear lag, exponential transfer lag.

If on the other hand, a0 = 0, then from eqn. we take

which gives a transfer function

In such case the process is called purely capacitive or pure integrator

where f(t) is the input (forcing function). If a0 # 0, then above eqation yields,