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? 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

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.

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.

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:

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 :

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

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

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

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

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

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