Name: signal flow graph branch rules
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 16 s
Channel: JoVE

신호 흐름 그래프 대수에서 노드가 나타내는 변수의 값은 노드에 들어오는 모든 신호의 합과 같습니다. 그런 다음 이 값은 해당 노드를 떠나는 모든 분기를 통해 전송됩니다.
같은 방향의 병렬 분기는 원래 분기의 이득의 합계와 동일한 이득을 가진 단일 분기로 대체할 수 있습니다.
마찬가지로, 단방향 분기의 계단식 연결은 원래 분기 이득의 곱과 동일한 이득을 가진 단일 분기로 대체할 수 있습니다.
신호 흐름 그래프 또는 SFG의 피드백 시스템은 폐루프 전달 함수를 도출하는 데 사용할 수 있는 특정 대수 방정식을 따릅니다.
제어 시스템의 블록 다이어그램을 SFG 형식으로 변환할 수 있습니다. 여기에는 변수를 식별하고, 각 변수를 노드에 연결하고, 노드를 분기와 상호 연결하고, 각 분기에 적절한 이득을 레이블링하는 작업이 포함됩니다.
마지막으로, SFG는 일련의 대수 방정식으로 구성할 수도 있습니다. 이 프로세스에는 단계별 구성, 각 변수에 대한 노드 생성 및 방정식에 따라 상호 연결하는 작업이 포함됩니다.

sfg 대수학

<div>
 신호 흐름 그래프(SFG) 대수에서 노드가 나타내는 값은 해당 노드에 들어오는 모든 신호의 합에 의해 결정됩니다. 이 합산된 값은 노드를 떠나는 모든 분기를 통해 전송되므로 SFG는 제어 시스템을 시각화하고 분석하는 강력한 도구가 됩니다.
 
 SFG의 각 노드는 변수에 해당하며, 노드 간의 상호 작용은 연관된 이득이 있는 분기로 표현됩니다. 여러 분기가 노드로 이어지는 경우 해당 노드의 값은 모든 수신 분기의 신호 합계입니다. 그런 다음 발신 분기는 이 값을 해당 이득에 곱하여 후속 노드로 전송합니다.
 
 동일한 방향으로 신호를 전달하는 병렬 브랜치는 단일 브랜치로 통합될 수 있습니다. 이 새로운 브랜치의 이득은 원래 병렬 브랜치의 이득의 합입니다. 예를 들어, 이득이 G_1과 G_2인 두 브랜치가 병렬이면 이득이 G=G_1+G_2인 단일 브랜치로 대체할 수 있습니다.
 
 연쇄 분기 또는 직렬로 연결된 분기도 마찬가지로 단순화할 수 있습니다. 결과 분기의 이득은 원래 분기의 이득의 곱입니다. 예를 들어, 이득이 G_1과 G_2인 두 분기가 연쇄되면 이득이 G=G_1×G_2인 단일 분기로 대체할 수 있습니다.
 
 피드백 시스템에서는 특정 대수 방정식을 사용하여 폐루프 전달 함수를 도출합니다. 여기에는 피드백 루프를 인식하고 적절한 공식을 적용하여 시스템의 동작을 결정하는 것이 포함됩니다. 제어 시스템의 블록 다이어그램을 SFG로 변환하려면 다음 단계를 따르세요.
 
 <ol style="display: flex; flex-direction: column; gap: 10px;">
 <li>변수 식별: 시스템의 각 변수는 노드와 연결됩니다.
 </li>
 <li>상호 연결 노드: 변수 간의 관계를 나타내기 위해 노드 사이에 분기를 그려 신호 흐름의 방향이 정확하게 표현되도록 합니다.
 </li>
 <li>브랜치에 라벨을 지정합니다. 시스템의 해당 부분의 전달 함수를 반영하여 각 브랜치에 적절한 이득을 지정합니다.
 </li>
 </ol>

 SFG는 대수 방정식 집합에서도 파생될 수 있습니다. 이 프로세스에는 다음 단계가 포함됩니다.
 

 <ol style="display: flex; flex-direction: column; gap: 10px;">
 <li>방정식의 각 변수에 대한 노드를 식별하고 생성합니다.
</li>
<li>방정식으로 정의된 관계에 따라 노드를 연결하고, 이러한 관계를 나타내기 위해 분기를 사용합니다.
</li>
<li>방정식의 계수에 따라 분기에 이익을 할당합니다.
</li>
 </ol>
 SFG는 이러한 원리를 활용하여 복잡한 제어 시스템을 분석하고, 전달 함수의 도출을 용이하게 하며, 시스템 역학에 대한 이해를 높이는 다재다능하고 직관적인 방법을 제공합니다.
 
</div>

SFG 대수학

신호 흐름 그래프 대수에서 노드가 나타내는 변수의 값은 노드에 들어오는 모든 신호의 합과 같습니다. 이 값은 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Diagrams and Signal Flow Graphs

다이어그램 및 신호 흐름 그래프

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 sends its value to the next nodes, each outgoing branch carries that value multiplied by its own gain.

Parallel branches point in the same direction and can be combined into one branch. The gain of the new branch is the sum of the original gains, such as G1 + G2. Cascaded branches are connected in series and can also be simplified. In that case, the gain of the new branch is the product of the original gains, such as G1 × G2.

SFG algebra is also used in feedback systems to find the closed-loop transfer function. This requires identifying the feedback loop and applying the correct formula for the system. A block diagram can be converted into an SFG by identifying the variables, drawing the branches between them, and labeling each branch with the right gain. An SFG can also be built directly from algebraic equations by creating nodes for each variable, linking them by the equation relationships, and assigning branch gains from the coefficients.

Signal Flow Graph Branch Rules

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 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...

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 (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 signal flow graphs use nodes, branch gains, parallel and cascaded simplification, and feedback formulas to analyze control systems.

Signal Flow Graph Branch Rules | 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

Signal Flow Graph Branch Rules

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