Derivative Controller (D-Controller)
With derivative action, the controller output is proportional to the rate of change of the measurement or error. The controller output is calculated by the rate of change of the deviation or error with time.
OD = - kD dEr / dt (3)
OD = output derivative controller
kD = derivative gain or action factor of the controller
dEr = deviation change over time sample dt
dt = time sample
The derivative or differential controller is never used alone. With sudden changes in the system the derivative controller will compensate the output fast. The long term effects the controller allow huge steady state errors.
A derivative controller will in general have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response.