2.7 Signal-Flow Graph models (??????)

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2.7 Signal-Flow Graph models(??????)
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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Masons 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 Masons 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( ??????)

• 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 (??????)

• 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 Masons 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