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The integral term in a PID controller is crucial for eliminating steady-state error, which refers to the persistent difference between the desired setpoint and the process variable in a control system. It works by accumulating the error over time, meaning it takes into account the history of the error. As the integral of the error increases, the controller applies a corrective action proportionally to that accumulated error. This persistent action continues until the error is driven to zero, effectively ensuring that the output reaches and maintains the desired setpoint without continual offset.

Including an integral action adds a level of responsiveness not only to transient changes but ensures that any ongoing discrepancies are rectified, leading to improved accuracy in long-term operations. This is particularly valuable in systems where maintaining a precise setpoint is critical, such as in temperature control, flow rate adjustments, and other continuous processes.