Time-Domain Interpretation of PD Control

Consider a motor system with only proportional control that exhibits high maximum overshoot and oscillation, reflected in the error signal and its rate of change.

A positive error signal and rising positive motor torque induce significant output overshoot and oscillations due to excessive force and insufficient resistance.

When the error signal and motor torque are negative, output acceleration slows, causing undershoot.

If, again, the motor torque is positive, it reduces the undershoot caused by negative torque.

Now, modify the system and its transfer function with the PD controller.

PD control reduces overshoot and undershoot by adjusting corrective torque based on the error signal's rate of change, acting as an anticipatory mechanism.

The PD control mechanism uses the error signal's slope to predict and correct system direction, curbing excessive overshoot. It only impacts steady-state error if the error fluctuates over time.