Editing Proportional–integral–derivative controller (section)

===Integral===
An '''integral''' term increases action in relation not only to the error but also the time for which it has persisted. So, if the applied force is not enough to bring the error to zero, this force will be increased as time passes. A pure "I" controller could bring the error to zero, but it would be both weakly reacting at the start (because the action would be small at the beginning, depending on time to become significant) and more aggressive at the end (the action increases as long as the error is positive, even if the error is near zero).

Applying too much integral when the error is small and decreasing will lead to overshoot. After overshooting, if the controller were to apply a large correction in the opposite direction and repeatedly overshoot the desired position, the output would [[oscillate]] around the setpoint in either a constant, growing, or decaying [[sinusoid]]. If the amplitude of the oscillations increases with time, the system is unstable. If it decreases, the system is stable. If the oscillations remain at a constant magnitude, the system is [[marginal stability|marginally stable]].