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

Si consideri un sistema motore con solo controllo proporzionale che presenta un'elevata overshoot e oscillazione massima, riflessa nel segnale di errore e nella sua velocità di variazione.
Un segnale di errore positivo e un aumento della coppia positiva del motore inducono un significativo overshoot e oscillazioni dell'uscita a causa di una forza eccessiva e di una resistenza insufficiente.
Quando il segnale di errore e la coppia del motore sono negativi, l'accelerazione in uscita rallenta, causando una sottoelongazione.
Se, ancora, la coppia del motore è positiva, riduce l'undershoot causato dalla coppia negativa.
A questo punto, modificare il sistema e la sua funzione di trasferimento con il controller PD.
Il controllo PD riduce l'overshoot e l'undershoot regolando la coppia correttiva in base alla velocità di variazione del segnale di errore, agendo come un meccanismo anticipatore.
Il meccanismo di controllo PD utilizza la pendenza del segnale di errore per prevedere e correggere la direzione del sistema, frenando l'eccessivo overshoot. Influisce sull'errore di stato stazionario solo se l'errore fluttua nel tempo.

interpretazione del dominio del tempo del controllo pd

Time-Domain Interpretation of PD Control

Il controllo proporzionale-derivativo (PD), è un metodo di controllo ampiamente utilizzato in vari sistemi di ingegneria, per migliorare la stabilità e le prestazioni. In un sistema con solo controllo proporzionale, i problemi comuni includono un'elevata sovraelongazione massima e oscillazione, osservata sia nel segnale di errore che nella sua velocità di variazione. Questo comportamento, può essere suddiviso in tre fasi distinte: sovraelongazione iniziale, sottoelongazione successiva e stabilizzazione graduale.

Consideriamo l'esempio del controllo della coppia del motore. Inizialmente, un segnale di errore positivo genera una coppia positiva del motore in rapido aumento. Questo picco di coppia, porta a notevoli sovraelongazioni e oscillazioni dell'output, attribuite all'elevata forza e allo smorzamento insufficiente. L'output del sistema, supera il valore desiderato, riflettendo l'eccessiva correzione iniziale e la debole resistenza del controllo proporzionale.

Nella seconda fase, un segnale di errore negativo produce una coppia motore negativa, che decelera l'output, facendolo andare sotto il target. Questo undershoot, indica la tendenza del sistema a sovracompensare nella direzione opposta dopo il superamento iniziale. La riduzione della coppia in questa fase rallenta l'output, ma l'assenza di uno smorzamento adeguato, determina un comportamento oscillatorio.

Durante la fase finale, riappare la coppia positiva del motore, riducendo l'undershoot della fase precedente. Ogni oscillazione vede un'ampiezza di errore decrescente, stabilizzando progressivamente l'output del sistema. L'elevata correzione iniziale e la debole resistenza che hanno causato l'overshoot, sono controbilanciate da una maggiore resistenza e da una forza correttiva ridotta in questa fase. 
Il controllo PD, affronta efficacemente questi problemi introducendo aggiustamenti anticipatori basati sulla pendenza del segnale di errore. Questo meccanismo anticipatorio, consente al sistema di prevedere e correggere la sua direzione, mitigando l'eccessivo overshoot e riducendo l'ampiezza delle oscillazioni. Regolando la velocità di risposta del sistema, il controllo PD ottimizza la forza di correzione iniziale e aumenta la resistenza, generando overshoot e undershoot più piccoli. Di conseguenza, il sistema ottiene un output più stabile e controllato.

Interpretazione del Dominio del Tempo del controllo PD

Si consideri un sistema motore con solo controllo proporzionale che presenta un elevato overshoot e oscillazione massima, riflessa nel segnale di errore e nella sua velocità di ...

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Design of Control Systems

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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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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...

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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

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

PD Control Reduces Overshoot in Motor Torque

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