 The integral term is given by

The integral term accelerates the movement of the process towards setpoint and eliminates the residual steady-state error that occurs with a pure proportional controller.However, since the integral term responds to accumulated errors from the past, it can cause the present value to overshoot the setpoint value (see the section on loop tuning).The derivative of the process error is calculated by determining the slope of the error over time and multiplying this rate of change by the derivative gain "K"d. The magnitude of the contribution of the derivative term to the overall control action is termed the derivative gain, "K"d.

The derivative term is given by

Derivative action predicts system behavior and thus improves settling time and stability of the system.