Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive error signal generates a rapidly rising positive motor torque. This surge in torque leads to significant output overshoot and oscillations, attributed to the high force and insufficient damping. The system's output exceeds the desired value, reflecting the proportional control's excessive initial correction and weak resistance.
In the second phase, a negative error signal produces negative motor torque, which decelerates the output, causing it to undershoot the target. This undershoot indicates the system's tendency to overcompensate in the opposite direction after the initial overshoot. The torque reduction in this phase slows down the output, but the absence of adequate damping results in oscillatory behavior.
During the final phase, positive motor torque reappears, reducing the undershoot from the previous phase. Each oscillation sees a diminishing error amplitude, progressively stabilizing the system's output. The high initial correction and weak resistance that caused the overshoot are counterbalanced by increased resistance and reduced corrective force in this phase.
PD control effectively addresses these issues by introducing anticipatory adjustments based on the slope of the error signal. This anticipatory mechanism allows the system to predict and correct its direction, mitigating excessive overshoot and reducing the amplitude of oscillations. By adjusting the system's response rate, PD control fine-tunes the initial correction force and enhances resistance, leading to smaller overshoots and undershoots. Consequently, the system achieves a more stable and controlled output.
