Download - Lecture 10 ME 176 Reduction Of Multiple Su

ME 176Control Systems Engineering

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Mechanical Engineering

Reduction of Multiple Subsystems

Signal Flow Graphs: Elements:

Branches = SystemsNodes = SignalsArrow = Direction of signal flow

Transfer function written adjacent to line.

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Branches

Nodes

Signal Flow Graphs: Each signal is sum of signals

flowing into that node.

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Signal Flow Graphs: Cascade Form Represent Singals as Nodes Interconnect the nodes with system branches

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Signal Flow Graphs: Parallel Form

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Signal Flow Graphs: Feeddback Form

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Signal Flow Graphs:

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Mason's Rule: Definition

Loop Gain:

The product of branch gains found bytraversing a path that starts at a node andends at the same node, following the directionof the signal flow, without passing through thenode more than once.

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Forward Path Gain:

The product of gains found by traversinga path from the input node to the outputnode of the signal-flow graph in thedirection of signal flow..

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Nontouching Loops:

Loops that do not have any nodes in common

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Nontouching-loop Gain:

The product of loop gains from nontouchingloops taken two, three, four, or more at atime.

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Mason's Rule:

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Mason's Rule: Example Step 1 : Identify the forwardpath gains:

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Mason's Rule: Example Step 2 : Identify the loop gains:

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Mason's Rule: Example Step 3 : Identify the loop gains (2 @ a time):

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Mason's Rule: Example Step 4 : Identify the loop gains (3 @ a time):

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Mason's Rule: Example Step 5 : Using Mason's rule - evaluate for :

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Laboratory : Material for the laboratory sessions that come after this lecture can be viewed from the class site at: http://sites.google.com/a/vinta.com/me-176/

Please make sure to read the directions at the bottom of the page for instructions on how to submit the laboratory working sessions.

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