I agree with Sachit Kadavil, type 1 system already have integrator which is essential for zero steady state error if the reference signal is constant or step, however for other reference signals or disturbances zero steady error cannot be achieved, because of internal model principle.
Desmond i fully agree with Prof. Michael well explained answer. why don't you try with disturbance observer to overcome the steady state error and also try with proper Pseudo filter when you add derivative function to improve/restore the phase margin and speed up the closed loop response.
No - not necessary: If there are no load disturbance then integrator is not necessary for type 1 system since the inherent integrator will track setpoint in a well tuned controller.
Yes-required: If there are disturbances then integral control is necessary for disturbance rejection.