Type number of a transfer function?

Suppose a transfer function is G(s)= (s+4)/[(s+2)(s+3)] for example.

I have read that the number of integrators in G(s) defines its type number, but I have no idea what is meant by integrators here, so am confused about how to establish the type number of a given G(s).

I am just starting out on modelling/control so would appreciate it if you could explain in some detail or give examples.

Many thanks - Ian Hutcheson

What is an integrator. It is a function that if you input a step, the output will be an ever increasing ramp.

In the time domain, a one volt step input will cause a ramp rate of one volt per second for a unity gain integrator.

In the frequency domain, an input of a one volt sine wave at one radian per second will have an output of a one volt sine wave at one radian per second with a laging phase shift of 90 degrees for a unity gain integrator

A unitity gain integrator has the transfer function of

G(s) = 1/s.

Your transfer function has three poles and one zero so there are no integrators and it is a Type 0 transfer function.

A pure integrator is represented by 1/s.

This is only the start of this problem though. Just because the "transfer function" has s's in it, doesn't necessarily mean it is the proper function to be assessing the "number" of the system. Is the the function for the forward, open loop, or system? If 1/s is not recognized as an integrator, then it is unlikely that the proper "transfer function" is known either.

I'd suggest long hours with a good book. Internet searches could also find some good basic control theory.