Proportional control, Integral control

broccoli

I want to know the proper nomenclature about control theory.

Problem is below.

" There is the system, which is controlled by P control or I control (anything is Ok.) where a is proportional gain and b is integral gain. When proportional gain, a is slightly changed, system output is big different. "

What is the proper nomenclature or name?
Which book is helpful for studying?