Name: transfer functions from signal-flow graphs
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 20 s
Channel: JoVE

La regla de Mason simplifica el cálculo de la función de transferencia a partir de gráficos de flujo de señal, evaluando varios elementos.
La ganancia de bucle se calcula trazando una ruta desde un nodo hasta sí mismo, tomando el producto de las ganancias de bifurcación.
La ganancia de la ruta de avance implica seguir una ruta desde el nodo de entrada hasta el de salida, calculando el producto de las ganancias.
Los bucles que no se tocan son bucles sin nodos comunes. La ganancia es el producto de las ganancias de estos bucles separados.
La función de transferencia se calcula a partir de estos elementos utilizando la regla de Mason.
Delta se deriva de series alternas de sumas de ganancias de bucle y ganancias de bucle no táctil tomadas dos o más a la vez. Delta_k se forma excluyendo las ganancias de bucle de Delta que se intersectan con la késima ruta de avance.
Para calcular la función de transferencia de un sistema, se identifican las ganancias del trayecto de avance y se evalúan las ganancias del bucle.
A continuación, se identifican los bucles que no se tocan y sus correspondientes ganancias.
Se calcula delta y Delta_k se evalúa eliminando las ganancias de bucle que se intersectan.
Finalmente, estos valores se sustituyen en la regla de Mason para producir la función de transferencia del sistema.

regla del masón

La regla de Mason es una herramienta poderosa en los sistemas de control y procesamiento de señales. Simplifica el cálculo de funciones de transferencia a partir de gráficos de flujo de señales. Este método aprovecha varios elementos, incluidas las ganancias de bucle, las ganancias de trayectoria directa y los bucles sin contacto, para determinar la función de transferencia de manera eficiente.
La ganancia del bucle se determina identificando y rastreando una ruta desde un nodo hasta sí mismo. Esto implica calcular el producto de las ganancias de las ramas a lo largo del bucle. La ganancia de cada bucle es crucial para los cálculos posteriores y contribuye al comportamiento general del sistema.
La ganancia de la ruta directa se calcula trazando una ruta desde el nodo de entrada hasta el nodo de salida. Al igual que la ganancia de bucle, implica el producto de las ganancias a lo largo de esta ruta. Las rutas directas representan la influencia directa de la entrada en la salida y son esenciales para determinar la función de transferencia.
Los bucles sin contacto son bucles en el gráfico de flujo de señales que no comparten ningún nodo común. La ganancia de los bucles sin contacto es el producto de las ganancias de los bucles individuales. Estos bucles sin contacto son importantes porque afectan el cálculo del determinante, Delta (Δ), utilizado en la regla de Mason.
Delta (Δ) se deriva de una serie alterna de sumas que involucran las ganancias de los bucles y las ganancias de los bucles que no se tocan, tomadas dos o más a la vez. Matemáticamente, se puede expresar como:
<img alt="Equation1" src="/files/ftp_upload/16108/16108_Equation_PT_001.svg" style="height: 50px;">
Δk es una versión modificada de Δ, que excluye las ganancias de bucle que se intersecan con la ruta de avance k-ésima. Esta exclusión es crucial para determinar con precisión la función de transferencia del sistema.
Para calcular la función de transferencia de un sistema utilizando la regla de Mason, se utilizan los siguientes pasos:
<ol style="padding-left: 35px; margin: 0;">
 <li>Identifique todas las ganancias de la ruta de avance (T_k) desde la entrada hasta la salida.</li>
 <li>Evalúe todas las ganancias de bucle (L_i) e identifique los bucles que no están en contacto.</li>
 <li>Calcule Δ sumando y restando los productos de las ganancias de bucle y las ganancias de bucle sin contacto como se describe.</li>
 <li>Para cada ruta de avance, calcule Δ_k excluyendo las ganancias de bucle que se cruzan.</li>
 <li>Sustituya estos valores en la regla de Mason, dada por:</li>
</ol>
<img alt="Equation2" src="/files/ftp_upload/16108/16108_Equation_PT_002.svg" style="height: 34px;">
A través de estos pasos, la regla de Mason proporciona un enfoque organizado y sistemático para derivar la función de transferencia de sistemas complejos, lo que la hace indispensable en la teoría de control y el procesamiento de señales.

Regla del masón

La regla de Mason simplifica el cálculo de la función de transferencia a partir de gráficos de flujo de señal, evaluando varios elementos.
La ganancia del bucle se calcula trazando una ruta ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Diagrams and Signal Flow Graphs

Diagramas y grafos de flujo de señales

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Mason&#39;s Rule

transfer functions from signal-flow graphs

Mason's rule helps students find transfer functions from signal-flow graphs in control systems and signal processing. It gives a clear path for solving graphs that can look complicated at first. The method uses loop gains, forward-path gains, and non-touching loops to organize the calculation.

A loop gain comes from tracing a path from a node back to the same node. The gain is the product of the branch gains along that loop. Each loop gain matters because it feeds into the later transfer-function steps and affects the behavior of the system.

A forward-path gain is found by tracing a path from the input node to the output node. It is also the product of the gains along that route. Forward paths show the direct effect of the input on the output, so they are essential for the final result.

Non-touching loops are loops that do not share any common nodes. Their combined gain is the product of the individual loop gains. These loop groups matter because they are used when building the determinant, Delta (&amp;#916;), in Mason's rule.

Delta is formed from an alternating series of sums and subtractions. It uses loop gains and the gains of non-touching loops taken two or more at a time. For each forward path, a modified value, Delta k, is also found. Delta k leaves out any loop gains that intersect with the kth forward path, which is needed for an accurate transfer function.

To use Mason's rule, first identify all forward-path gains, Tk, from input to output. Then evaluate all loop gains, Li, and find any non-touching loops. Next, calculate Delta, find each Delta k by removing intersecting loop gains, and substitute the values into Mason's rule. This gives a systematic way to determine the transfer function of complex systems in control theory and signal processing.

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Mason's rule helps students find transfer functions from signal-flow graphs in control systems and signal processing. It gives a clear path for solving graphs that can look complicated at first. The method uses loop gains, forward-path gains, and non-touching loops to organize the calculation. A loop gain comes from tracing a path from a node back to the same node. The gain is the product of the branch gains along that loop. Each loop gain matters because it feeds into the later...

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Learn how Mason's rule uses forward paths, loop gains, and non-touching loops to calculate transfer functions from signal-flow graphs in control systems.

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Transfer Functions from Signal-Flow Graphs

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