Name: spring-mass-damper laplace block diagram
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 20 s
Channel: JoVE

Considere la ecuación diferencial de segundo orden de un sistema resorte-masa-amortiguador. El sistema se transforma en el dominio de Laplace bajo cero condiciones iniciales.
A continuación, la ecuación se reorganiza para aislar la salida, que puede interpretarse como señales que entran en bloques con funciones de transferencia específicas.
La salida se obtiene integrando dos veces o multiplicando posteriormente.
Para simplificar, las señales del lado derecho están conectadas, lo que lleva a la representación final del diagrama de bloques del sistema.
Se puede lograr una mayor simplificación factorizando el término del bucle de retroalimentación interno, lo que da como resultado un diagrama de bloques alternativo.
El modelo de diagrama de bloques también puede incorporar variables internas que representan la aceleración y la velocidad.
Como 1/s corresponde a la integración en el dominio de Laplace, la aceleración se integra inicialmente para obtener la velocidad, y posteriormente, la velocidad se integra para producir la señal de desplazamiento.
La función de transferencia del sistema se encuentra moviendo el bloque en las señales de entrada y retroalimentación al lado derecho del comparador y simplificando el bucle de retroalimentación interno. La ecuación resultante es la función de transferencia del sistema.

relación entre ecuaciones matemáticas y diagramas de bloques

Relation between Mathematical Equations and Block Diagrams

En un sistema de muelle-masa-amortiguador, la ecuación diferencial de segundo orden describe el comportamiento dinámico del sistema. Cuando se transforma al dominio de Laplace en condiciones iniciales cero, esta ecuación se puede analizar y manipular de manera efectiva. La transformación al dominio de Laplace convierte las ecuaciones diferenciales en ecuaciones algebraicas, lo que simplifica el proceso de aislar la salida.

<img alt="Equation1" src="/files/ftp_upload/16105/16105_PT_Equation_001.svg" style="height: 36px;">

La aplicación de la transformada de Laplace a la ecuación diferencial estándar del sistema muelle-masa-amortiguador da como resultado lo siguiente:

<img alt="Equation2" src="/files/ftp_upload/16105/16105_PT_Equation_002.svg" style="height: 24px;">

Al construir el diagrama de bloques, las señales del lado derecho se pueden conectar para simplificar la representación. El diagrama de bloques se puede refinar aún más para incorporar variables internas como la aceleración y la velocidad. Dado que 1/s corresponde a la integración en el dominio de Laplace, la señal de aceleración se integra para obtener la velocidad y la velocidad se integra para obtener la señal de desplazamiento.

La simplificación del diagrama de bloques implica factorizar términos del bucle de retroalimentación interno. Este proceso conduce a un diagrama de bloques alternativo que representa visualmente las relaciones entre aceleración, velocidad y desplazamiento.

Para obtener la función de transferencia del sistema, el bloque que representa las señales de entrada y retroalimentación se desplaza al lado derecho del comparador y se simplifica el bucle de retroalimentación interno. La ecuación resultante proporciona la función de transferencia:

<img alt="Equation3" src="/files/ftp_upload/16105/16105_PT_Equation_003.svg" style="height: 38px;">

<img alt="Equation4" src="/files/ftp_upload/16105/16105_PT_Equation_004.svg" style="height: 120px;">

Esta función de transferencia es esencial para analizar el comportamiento del sistema, predecir su respuesta a diversas entradas y diseñar estrategias de control para lograr las características de rendimiento deseadas.

Relación entre ecuaciones matemáticas y diagramas de bloques

Considere la ecuación diferencial de segundo orden de un sistema resorte-masa-amortiguador. El sistema se transforma en el dominio Laplace bajo cero ...

relation-between-mathematical-equations-and-block-diagrams

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spring-mass-damper laplace block diagram

A spring-mass-damper system can be written as a second-order differential equation. This equation describes how the system changes over time. When the equation is transformed into the Laplace domain with zero initial conditions, it becomes easier to analyze and rearrange.

The Laplace transform changes a differential equation into an algebraic equation. That makes it simpler to isolate the output. For the standard spring-mass-damper model, the transformed equation gives the output in a form that can be used directly for block diagram construction.

The block diagram is built by connecting the signals on the right-hand side of the equation. It can also include internal variables such as acceleration and velocity. In the Laplace domain, 1/s means integration. So acceleration is integrated to get velocity, and velocity is integrated to get displacement.

The diagram can be simplified by factoring terms from the internal feedback loop. This creates another block diagram that shows the links between acceleration, velocity, and displacement more clearly. To find the transfer function, the block for the input and feedback signals is moved to the right side of the comparator, and the internal feedback loop is reduced. The final transfer function helps describe system behavior, predict the response to inputs, and support control design.

Spring-Mass-Damper Laplace Block Diagram

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A spring-mass-damper system can be written as a second-order differential equation. This equation describes how the system changes over time. When the equation is transformed into the Laplace domain with zero initial conditions, it becomes easier to analyze and rearrange. The Laplace transform changes a differential equation into an algebraic equation. That makes it simpler to isolate the output. For the standard spring-mass-damper model, the transformed equation gives the output in a form...

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Spring-Mass-Damper Laplace Block Diagram

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