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2.7 Signal-Flow Graph models （信号流图模型）

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. What is SFGM?.

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2.7 Signal-Flow Graph models （信号流图模型）

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  1. 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.

  2. 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

  3. 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.

  4. 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.

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

  6. 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 :

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

  8. 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

  9. 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

  10. 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

  11. 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

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

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