proportionalderivative

Proportional-derivative control, commonly abbreviated as PD control, is a feedback control strategy that uses a weighted sum of the proportional and derivative of the error to compute the control signal. The control input is expressed as u(t) = Kp e(t) + Kd de(t)/dt, where e(t) = r(t) − y(t) is the error between the desired reference r(t) and the process output y(t). The proportional term provides immediate corrective action proportional to the current error, while the derivative term anticipates future error by reacting to the rate of change, improving damping and transient response.

PD control is valued for improving response speed and reducing overshoot without relying on integral action. However, it does not eliminate steady-state error by itself, which is why it is often used in conjunction with an integral term in a PID controller or in systems where the reference is changing rapidly and a fast, well-damped response is needed. The derivative action increases sensitivity to measurement noise, particularly at high frequencies, so practical implementations frequently include filtering of the derivative term. A common approach is to apply the derivative to the process variable rather than the error, reducing derivative kick when the reference changes.

Tuning PD parameters involves selecting Kp to balance responsiveness and stability, and Kd to provide damping. There are several methods, including manual tuning and frequency- or time-domain techniques; in many cases PD is derived from a broader PID design or from system identification followed by compensation design.

Applications of PD control appear in fast-acting robotics, CNC machine tools, servo and motion-control systems, and other domains requiring rapid, well-damped responses without integral action. It is typically used alone only when steady-state error is acceptable or when integral action is undesirable.