As I understand from theory that two integrators are required to provide zero velocity lag in a type 2 servo system. My question is how does 2 integerators help to nullify velocity errors. Less of maths with intuitive explanation will be useful
Integrators is just a fancy way of saying you want to check your results. A type 0 system simply does not check the result at all. A type 1 system is reading the position directly from the shaft for example. So if there would be any unknown load etc in the system then you could compensate for this position error.
Whatabout a type 2 system? Well since you can measure the position you can deduce what the position should be If you were moving at speed x. This system is supprise supprise an integrator, integrating velocity gives position. So a type 2 system just calculates where the position ought to be if velocity is what you think it should be versus where it is. It can then compensate for this error.