Name: mason’s rule in signal flow graphs
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 18 s
Channel: JoVE

信号流图可作为表示控制系统的方框图的替代方法。它由代表系统的支路和代表信号的节点组成。
信号流的方向由箭头指示，传递函数写在箭头旁边。
信号流图中的每个信号会对其流入的信号进行求和，这与框图不同，在框图中负号与求和点相关联。
将方框图转换为信号流图时，首先为系统绘制信号节点。
随后，节点通过代表系统的分支相互连接。
考虑一个具有多个反馈回路的框图。该过程首先创建信号节点，这些节点相互连接以表示信号的流向，每个节点由其特定的传递函数来标识。
在得到的信号流图中，方框图中求和点处的负号对应为负的传递函数。
最后一步通过消除只有一个流入和流出的信号来简化图形，从而得到更简洁的表示。

信号流图

Signal Flow Graphs

信号流图提供了一种简化且直观的方法来表示控制系统，为传统框图提供了另一种选择。这些图使用分支来表示系统，使用节点来表示信号，有效地说明了系统内的关系和相互作用。

在信号流图中，分支表示系统的传递函数，而节点表示信号。信号流的方向用箭头表示，相应的传递函数写在每个箭头旁边。与框图不同，框图中的求和结点包含负号以表示减法，而信号流图将这些负号直接合并到传递函数中。

将框图转换为信号流图的第一步是识别系统信号。然后，这些信号被表示为信号流图中的节点。识别并绘制系统中每个信号的第一个节点是这一转换过程中的关键。然后，用表示系统传递函数的分支将这些节点连接起来，确保准确描绘信号流的方向。

例如，在具有多个反馈回路的框图中:
<ol style=" padding-left: 35px; margin: 0;">
 <li>首先为反馈回路中的每个信号建立节点。</li>
 <li>用表示传递函数及其方向的分支将节点链接起来。框图中求和结点处的负号被纳入信号流图中的传递函数中。</li>
</ol>

将框图转换为信号流图的最后一步是简化图。简化是通过消除只有一个传入分支和一个传出分支的中间信号来实现的，从而降低图的复杂性并使其更易于分析。

一旦建立了信号流图，就可以应用梅森公式计算系统的传递函数。这涉及:
<ol style="padding-left: 35px; margin: 0;">
 <li>确定从输入到输出节点的所有可能的前向路径并计算它们的增益。</li>
 <li>识别所有环路及其增益，并确定哪些环路是非接触的。</li>
 <li>使用交替的环路增益和非接触环路增益之和来计算 Δ。Δ_k 通过排除与第 k 个前向路径相交的环路增益计算。</li>
 <li>将这些值代入梅森公式即可获得传递函数。</li>
</ol>

通过将框图转换为信号流图，可以更有效地分析控制系统，利用梅森公式提供的系统方法来确定传递函数。

信号流图可作为表示控制系统的方框图的替代方法。它由代表系统的支路和节点组成，……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Diagrams and Signal Flow Graphs

图表与信号流图

KEY TERMS AND CONCEPTS

关键术语与概念

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 into the transfer functions on the branches. This makes the graph a compact picture of how signals move through the system.

To convert a block diagram into a signal-flow graph, the first step is to identify the system signals. Each signal becomes a node. Then the nodes are connected with branches that represent the transfer functions and the correct direction of flow. When the block diagram has feedback loops, the same method is used. The negative signs from the summing junctions are included in the transfer functions.

The final step is to simplify the graph. Intermediate signals with only one incoming branch and one outgoing branch can be removed. This reduces the number of nodes and makes the graph easier to analyze. Once the signal-flow graph is ready, Mason’s rule can be used to find the system transfer function.

Using Mason’s rule starts with finding every forward path from input to output and calculating each path gain. Next, all loops are identified, along with their gains, and the non-touching loops are noted. Then Δ is calculated from an alternating series of loop gains and non-touching loop gains. Δk is found by leaving out any loop gains that touch the kth forward path. Substituting these values into Mason’s rule gives the transfer function for the control system.

Mason’s Rule in Signal Flow Graphs

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signal flow graphs

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key terms and concepts

Learn how signal-flow graphs represent control systems, convert from block diagrams, and use Mason’s rule to find transfer functions.

Mason’s Rule in Signal Flow Graphs | JoVE K12

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electrical engineering

Mason’s Rule in Signal Flow Graphs

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