Can you imagine a water heater If you switch ON, It will heat the water and if you switch off the heat of the water will reduce gradually.
for example our aim is to control the temperature as constant so what will you do you will turn ON the heater when the temperature is lower than the set temperature and you will turn Off the heater if your temperature is more than the set temperature.
Derivative control means applying the heater voltage according to the error in temperature (set and actual temperature)
so that it can reach the set temperature quickly. consider a set temp of 80C
if actual temperature is 10 then more voltage on heater
if actual temperature is 78 then less voltage on heater terminals
It is ultimately to reduce the time to attain the resultant temperature
The problem in derivative control is it will take lot of time to settle in the set temperature as because of we are reducing the effect in nearer to set value. the integrator part will accumulate the settle time error and give its part on the output.
Integrator feedback accumulates small error over time to eliminate steady state error from a proportional feedback method. This is slow & steady but not sufficient if input changes quickly.
Derivative feedback amplifies small quick changes to anticipate required output. This gives faster response but also more jitter so gain must be balanced to conditions.