Name: finding a transfer function from state space
Uploaded: 2024-11-21T14:54:05.000Z
Duration: 1 min 21 s
Channel: JoVE

La representación del espacio de estados también se puede convertir en una función de transferencia en el análisis de sistemas.
La transformación comienza con el estado dado y las ecuaciones de salida.
Aquí se aplica la transformada de Laplace, asumiendo cero condiciones iniciales. Esto transforma las ecuaciones del dominio del tiempo al dominio de la frecuencia.
La ecuación de estado se resuelve para X(s), donde I representa la matriz identidad. A continuación, esta solución se sustituye en la ecuación de salida.
La matriz resultante, conocida como matriz de función de transferencia, vincula el vector de salida con el vector de entrada.
Cuando estos vectores son escalares, se hace posible encontrar la función de transferencia final, completando así la transformación de la representación del espacio de estados a la función de transferencia.
Considere un sistema definido por matrices de diferentes dimensiones que forman las ecuaciones de estado y salida.
Si bien todos los demás términos de la ecuación de la función de transferencia ya están definidos, un término sigue siendo desconocido.
Para encontrar este término, se utilizan los valores conocidos de la matriz de la ecuación de estado. Además, se calcula lo inverso.
Tras la sustitución, la representación del espacio de estados se convierte en una función de transferencia.

espacio de estados a función de transferencia

State Space to Transfer Function

La conversión de una representación en el espacio de estados a una función de transferencia es un proceso fundamental en el análisis de sistemas. Proporciona un método para pasar de una descripción en el dominio temporal a una representación en el dominio de la frecuencia, lo cual es crucial para simplificar el análisis y el diseño de sistemas de control.
El proceso de transformación comienza con la representación en el espacio de estados, caracterizada por la ecuación de estado y la ecuación de salida. Estas ecuaciones se representan típicamente como:
<img alt="Equation1" src="/files/ftp_upload/16102/16102_PT_equation_001.svg" style="height: 14px;">
<img alt="Equation2" src="/files/ftp_upload/16102/16102_PT_equation_002.svg" style="height: 14px;">
Donde x(t) es el vector de estado, u(t) es el vector de entrada, y(t) es el vector de salida y A, B, C y D son matrices que definen la dinámica del sistema.
Para convertir estas ecuaciones al dominio de la frecuencia, se aplica la transformada de Laplace, suponiendo que las condiciones iniciales son cero. Luego, se resuelve la ecuación de estado para X(s).
Consideremos un sistema con matrices dadas A, B, C y D. El proceso de transformación implica calcular la inversa de (SI−A), sustituir los valores conocidos y simplificar la expresión para obtener la función de transferencia. Esta transformación es fundamental para analizar el comportamiento del sistema, diseñar controladores y comprender la respuesta de frecuencia del sistema.
En conclusión, convertir la representación del espacio de estados en una función de transferencia implica aplicar la transformada de Laplace, resolver la ecuación de estado en el dominio de la frecuencia y derivar la matriz de la función de transferencia, que se simplifica a una función de transferencia escalar para sistemas de entrada única, salida única (SISO).

Espacio de estados a función de transferencia

La representación del espacio de estados también se puede convertir en una función de transferencia en el análisis de sistemas.
La transformación comienza con el estado dado y la salida ...

Education

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JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Modeling in Time and Frequency Domain

Modelado en el dominio del tiempo y de la frecuencia

KEY TERMS AND CONCEPTS

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finding a transfer function from state space

Finding a transfer function from state-space form is a key step in system analysis. It changes a time-domain model into a frequency-domain form. That makes it easier to study and design control systems.

The process starts with the state-space equations. These include the state equation and the output equation. In these equations, x(t) is the state vector, u(t) is the input vector, y(t) is the output vector, and A, B, C, and D are the matrices that define the system dynamics.

Next, the Laplace transform is applied. This step assumes zero initial conditions. The state equation is then solved for X(s), the state vector in the Laplace domain.

For a system with known A, B, C, and D matrices, the next step is to calculate the inverse of (sI−A). The known values are substituted into the expression, and the result is simplified to obtain the transfer function. This result is especially useful for studying system behavior and frequency response.

The same method gives a transfer function matrix for multi-input, multi-output systems. For single-input, single-output, or SISO systems, that matrix reduces to a scalar transfer function. This conversion is an important tool for control design and system analysis.

Finding a Transfer Function from State Space

finding-a-transfer-function-from-state-space

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Finding a transfer function from state-space form is a key step in system analysis. It changes a time-domain model into a frequency-domain form. That makes it easier to study and design control systems. The process starts with the state-space equations. These include the state equation and the output equation. In these equations, x(t) is the state vector, u(t) is the input vector, y(t) is the output vector, and A, B, C, and D are the matrices that define the system dynamics. Next, the Laplace...

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Learn how state-space equations are converted into a transfer function using the Laplace transform, zero initial conditions, and the inverse of (sI−A).

Finding a Transfer Function from State Space | 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

Finding a Transfer Function from State Space

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