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2.7 Signal-Flow Graph models （信号流图模型） Why SFG? Block Diagrams are adequate for representation, but cumbersome. SFG provides the relation between system variables without requiring any reduction procedure.

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What is SFGM? Definition: A signal-flow graph is a diagram consisting of nodes that are connected by several directed branches and is a graph representation of a set of linear relation. Only valid for linear system

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Basic elements of SFG Branch: A unidirectional path segment Nodes: The input and output points or junctions Path: A branch or a continuous sequence of branches that can be traversed from one node to anther node.

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Continued Loop: A closed path that originates and terminates on the same node, and along the path no node is met twice. Non-touching loops: If two loops do not have a common node. Touching loops: Two touching loops share one or more common nodes.

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Mason’s gain formula The linear dependence (Gain) T i j between input variable x i and output variable x j is given by the following formula:

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Transfer function The Mason gain formula can be used to obtain the transfer function between input variable R(s) and output variable Y(s) as :

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Application of Mason’s formula Examples: refer to (P69-71) Other examples: refer to (2-26,27,28,29)

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2.8 Simulation Computer analysis of control systems Simulation of systems using MATLAB Refer to (P71-73) Refer to (P80-94) Self-learning after class

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Sequential design example ( 循序渐进示例 ） Refer to P23-24 and P94-97 Pay attention to model simplification Ignoring the section with small time-constant

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2.9 supplement ( 补充几个概念） Extraneous input: Closed-loop transfer function Closed-loop error TF Closed-loop disturbance TF Open-loop TF Reference input and Disturbance input

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Summary DE model and its solution TF model and system response Block diagram and its reduction SFG models and Mason’s formula Simulation using MATLAB

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Assignment Review Ch2 (P66-97) E2.19 E2.22 E2.23 E2.26 E2.29 P2.32

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