Name: pd control reduces overshoot in motor torque
Uploaded: 2024-11-21T14:54:16.000Z
Duration: 1 min 7 s
Channel: JoVE

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&#39;s rate of change, acting as an anticipatory mechanism.
The PD control mechanism uses the error signal&#39;s slope to predict and correct system direction, curbing excessive overshoot. It only impacts steady-state error if the error fluctuates over time.

time-domain interpretation of pd control

Time-Domain Interpretation of PD Control

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&#39;s output exceeds the desired value, reflecting the proportional control&#39;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&#39;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&#39;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&#39;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.

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

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pd control reduces overshoot in motor torque

PD control helps reduce overshoot and oscillation in motor torque systems. Proportional control uses the size of the error signal to set the correction. When the response is too large or too small, the output can move away from the target and then swing back.

With proportional control alone, the system often goes through three stages. First, a positive error signal creates a rapidly rising positive motor torque. That strong push can cause a large overshoot because the system has high force but not enough damping, which is the resistance that helps slow motion.

Next, the error signal turns negative. This produces negative motor torque, which slows the output and can make it undershoot the target. The system then overcorrects in the opposite direction, and the lack of damping keeps the motion oscillating.

In the final stage, positive motor torque appears again and reduces the undershoot. Each new swing becomes smaller as the error amplitude drops and the output settles closer to the desired value. PD control improves this behavior by adding an anticipatory adjustment based on the slope, or rate of change, of the error signal. That extra correction helps predict the direction of the error, lowers overshoot and undershoot, and makes the output more stable.

PD Control Reduces Overshoot in Motor Torque

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key terms and concepts

Learn how PD control uses the error signal and its slope to reduce overshoot, undershoot, and oscillation in motor torque systems.

PD Control Reduces Overshoot in Motor Torque | JoVE K12

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PD Control Reduces Overshoot in Motor Torque

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