Name: cruise control and aircraft system models
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 22 s
Channel: JoVE

El control de crucero en los automóviles, un sistema de múltiples entradas, se ajusta a la preferencia de velocidad del conductor y compensa las perturbaciones cuesta arriba.
El diagrama de bloques para este sistema incluye la velocidad deseada y la perturbación como entradas.
Cuando se anula la perturbación, el diagrama de bloques se simplifica a una función de transferencia específica. Cuando se anula la señal de entrada primaria, el diagrama de bloques produce otra función de transferencia.
La respuesta global del sistema es la suma de las respuestas debidas a la perturbación y a las señales de entrada.
Un avión es un sistema multivariable con múltiples entradas y salidas, como los controles de vuelo y el movimiento del avión.
Los diagramas de bloques pueden ilustrar cada entrada y salida, mientras que una versión simplificada emplea vectores para representar múltiples entradas y salidas.
Estos sistemas también se pueden representar mediante retroalimentación, donde las relaciones entre las diferentes partes del sistema se expresan en forma de matriz.
Al resolver estas ecuaciones, la matriz de transferencia de bucle cerrado proporciona la relación final entre la salida y la entrada.
Considere matrices específicas para las funciones de transferencia. Tras la sustitución, se puede calcular la matriz de funciones de transferencia de circuito cerrado.

sistema multientrada y multivariable

Multi-input and Multi-variable systems

Los sistemas de control de crucero de los automóviles están diseñados como sistemas de múltiples entradas para mantener la velocidad deseada por el conductor y compensar las perturbaciones externas, como los cambios en el terreno. El diagrama de bloques de un sistema de control de crucero generalmente incluye dos entradas principales: la velocidad deseada establecida por el conductor y cualquier perturbación externa, como la inclinación de la carretera. Al ajustar el acelerador del motor, el sistema mantiene la velocidad del vehículo lo más cerca posible del valor deseado.
En ausencia de perturbaciones, el diagrama de bloques del sistema de control de crucero se puede simplificar a una función de transferencia específica. Esta función de transferencia representa la relación entre la entrada de velocidad deseada y la velocidad real del vehículo.
<img alt="Equation1" src="/files/ftp_upload/16107/16107_PT_equation_001.svg" style="height: 36px;">
donde T_d(s) es la función de transferencia de la velocidad deseada R(s) a la velocidad real Y(s).
Por el contrario, cuando se anula la señal de entrada principal (la velocidad deseada), el diagrama de bloques se simplifica a otra función de transferencia, que representa únicamente la respuesta del sistema a perturbaciones externas.
<img alt="Equation2" src="/files/ftp_upload/16107/16107_PT_equation_002.svg" style="height: 52px;">
donde T_u(s) es la función de transferencia de la perturbación D(s) a la velocidad real Y(s).
La respuesta general del sistema de control de crucero es la superposición de las respuestas tanto a la velocidad deseada como a las perturbaciones de entrada. Esto se puede representar matemáticamente como:
<img alt="Equation3" src="/files/ftp_upload/16107/16107_PT_equation_003.svg" style="height: 30px;">
Este principio de superposición ilustra cómo el sistema se ajusta para mantener la velocidad deseada mientras contrarresta las perturbaciones.
En un sistema más complejo, como un avión, se deben considerar múltiples entradas y salidas. Las entradas pueden incluir señales de control del piloto, como ajustes de alerones, timón y elevador, mientras que las salidas son las respuestas de la aeronave, como cambios en el balanceo, cabeceo y guiñada. La complejidad de un sistema de este tipo requiere el uso de vectores y matrices para representar las múltiples entradas y salidas de manera sucinta.
Los diagramas de bloques de sistemas multivariables, como los aviones, se pueden simplificar mediante representaciones vectoriales. Las entradas y salidas se expresan como vectores y sus relaciones se capturan en una matriz de transferencia. Los bucles de retroalimentación de estos sistemas también se pueden describir mediante ecuaciones matriciales, lo que permite una representación integral de la dinámica del sistema.

Sistema multientrada y multivariable

El control de crucero en los automóviles, un sistema de múltiples entradas, se ajusta a la preferencia de velocidad del conductor y compensa las perturbaciones cuesta arriba.
El diagrama de bloques para ...

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

cruise control and aircraft system models

Cruise control systems show how a control system can handle more than one input. In a car, the driver sets a desired speed, and the system also responds to outside disturbances such as changes in road slope. The throttle is adjusted so the vehicle speed stays as close as possible to the target value.

When the disturbance is ignored, the cruise control block diagram can be reduced to a transfer function. This transfer function describes how the desired speed input, R(s), affects the actual speed output, Y(s). When the desired speed signal is set to zero, the diagram can be reduced in a different way. That case gives the transfer function for the disturbance input, D(s), to the vehicle speed, Y(s).

The full system response comes from adding these two responses together. This is the principle of superposition. It shows how the cruise control system works to track the driver’s setting while also reducing the effect of disturbances.

More complex systems, such as airplanes, have multiple inputs and outputs. The pilot may change the aileron, rudder, and elevator, and the aircraft responds with roll, pitch, and yaw. Because there are several signals on both sides, vectors and matrices are used to write the system in a compact form.

In these multi-variable systems, inputs and outputs are grouped into vectors. Their relationships are described with a transfer matrix. Feedback loops can also be written with matrix equations. This gives a complete way to represent how the system behaves.

Cruise Control and Aircraft System Models

cruise-control-and-aircraft-system-models

elements of block diagrams

Block Diagrams in Control Systems

Block diagrams show the input-output relationships in a system. They help students see how one signal affects another. A heating system is a simple example. The set temperature turns the furnace on, and the room warms to the desired level. Block diagrams can model both linear and nonlinear systems. Linear systems often use Laplace transform variables. Nonlinear systems are usually described with time domain variables. This makes block diagrams useful for many kinds of control problems. A...

relation between mathematical equations and block diagrams

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

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...

block diagram reduction

Simplifying Control System Block Diagrams

Simplifying control system block diagrams helps make a system easier to analyze. The goal is to reduce several connected blocks to one block so the transfer function can be found more easily. This process keeps the system behavior the same while making the diagram simpler to work with. A branch point is the place where one signal splits into multiple paths. To simplify the diagram, the branch point can be moved to a new location. The new position must preserve the mathematical relationship...

multi-input and multi-variable systems

Cruise control systems show how a control system can handle more than one input. In a car, the driver sets a desired speed, and the system also responds to outside disturbances such as changes in road slope. The throttle is adjusted so the vehicle speed stays as close as possible to the target value. When the disturbance is ignored, the cruise control block diagram can be reduced to a transfer function. This transfer function describes how the desired speed input, R(s), affects the actual...

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...

signal flow graphs

Mason’s Rule in Signal Flow Graphs

Signal-flow graphs are a clear way to represent control systems. They offer an alternative to traditional block diagrams. In these graphs, branches stand for systems and nodes stand for signals. Arrows show the direction of signal flow, and the transfer function is written next to each arrow. Signal-flow graphs also handle subtraction in a different way from block diagrams. In a block diagram, summing junctions often use negative signs. In a signal-flow graph, those negative signs are built...

sfg algebra

Signal Flow Graph Branch Rules

Signal flow graph (SFG) branch rules show how signals move through a control system. Each node in an SFG stands for a variable. The value at a node is the sum of all signals entering it. That summed value then travels through every branch leaving the node. Branches connect the nodes and show the relationship between variables. Each branch has a gain, which tells how strongly the signal is passed along. When several branches enter the same node, their signals are added together. When one node...

key terms and concepts

Learn how cruise control uses multiple inputs, transfer functions, and superposition, and how airplanes use vectors and matrices to model roll, pitch, and yaw.

Cruise Control and Aircraft System Models | 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

Cruise Control and Aircraft System Models

Description

Transcript

Tags