<P> A drawback of proportional control is that it cannot eliminate the residual SP − PV error in processes with compensation e.g. temperature control, as it requires an error to generate a proportional output . To overcome this the PI controller was devised, which uses a proportional term (P) to remove the gross error, and an integral term (I) to eliminate the residual offset error by integrating the error over time to produce an "I" component for the controller output . </P> <P> In the proportional control algorithm, the controller output is proportional to the error signal, which is the difference between the setpoint and the process variable . In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain . </P> <P> This can be mathematically expressed as, </P> <Dl> <Dd> P o u t = K p e (t) + p 0 (\ displaystyle P_ (\ mathrm (out)) = K_ (p) \, (e (t) + p0)) </Dd> </Dl>

What is the difference between proportional band and gain