Welding, to the best of my knowledge, is a process of current - no current - current ...

Why not reset the integrator at the no current intervals? That way there will be no long term drift

Excellent Suggestion, Why did this not strike my head. Thank you very much Erik. You are right erik, welding is a process with intermittent current flows, The current flows only during weld stage and doesn't flow during squeeze, hold and off stages thus there is sufficient time to reset the integrator. And if I am getting it right the resetting of integrator has to be done by discharging the capacitor that is put in between output and input to op-Amp [ Along feedback path ].

Thanks & Regards,
Prahlad Purohit