Derivative (D) Control is a control method in which the controller output is proportional to the rate of change of the error with time. It is expressed as
u(t) = Kd de(t)/dt, where u(t) is the controller output, e(t) is the error, and Kd is the derivative gain. By responding to how quickly the error is changing, derivative control anticipates the future trend of the system, helping reduce overshoot, oscillations, and improve transient response. However, because differentiation amplifies high-frequency noise, pure derivative control is rarely used alone and is commonly combined with proportional and integral actions in a PID controller.
Derivative (D) Control Simulation
Explore how a derivative controller responds to the rate of change
of the error signal.
u(t) = Kd × de(t)/dt
● Error e(t)
● D-Control Output u(t)
Current Error e(t)
0.00
Rate of Error de/dt
0.00
D-Control Output u(t)
0.00
What to observe:
The blue curve represents the error signal e(t). The red curve
represents the derivative controller output. When the error changes
rapidly, de/dt becomes large and the controller produces a stronger
output. When the error is temporarily constant, the derivative
output approaches zero. Increase Kd to amplify the
derivative response. Increasing measurement noise demonstrates why
derivative control can be sensitive to high-frequency noise.