Lecture 10 ME 176 Reduction Of Multiple Su
22
ME 176 Control Systems Engineering Department of Mechanical Engineering Reduction of Multiple Subsystems
-
Upload
leonidesdeocampo -
Category
Documents
-
view
1.479 -
download
5
Transcript of Lecture 10 ME 176 Reduction Of Multiple Su
ME 176Control Systems Engineering
Department of
Mechanical Engineering
Reduction of Multiple Subsystems
Signal Flow Graphs: Elements:
Branches = SystemsNodes = SignalsArrow = Direction of signal flow
Transfer function written adjacent to line.
Department of
Mechanical Engineering
Branches
Nodes
Signal Flow Graphs: Each signal is sum of signals
flowing into that node.
Department of
Mechanical Engineering
Signal Flow Graphs: Cascade Form Represent Singals as Nodes Interconnect the nodes with system branches
Department of
Mechanical Engineering
Signal Flow Graphs: Parallel Form
Department of
Mechanical Engineering
Signal Flow Graphs: Feeddback Form
Department of
Mechanical Engineering
Signal Flow Graphs:
Department of
Mechanical Engineering
Signal Flow Graphs:
Department of
Mechanical Engineering
Signal Flow Graphs:
Department of
Mechanical Engineering
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.
Department of
Mechanical Engineering
Mason's Rule: Definition
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..
Department of
Mechanical Engineering
Mason's Rule: Definition
Nontouching Loops:
Loops that do not have any nodes in common
Department of
Mechanical Engineering
Mason's Rule: Definition
Nontouching-loop Gain:
The product of loop gains from nontouchingloops taken two, three, four, or more at atime.
Department of
Mechanical Engineering
Mason's Rule:
Department of
Mechanical Engineering
Mason's Rule: Example Step 1 : Identify the forwardpath gains:
Department of
Mechanical Engineering
Mason's Rule: Example Step 2 : Identify the loop gains:
Department of
Mechanical Engineering
Mason's Rule: Example Step 3 : Identify the loop gains (2 @ a time):
Department of
Mechanical Engineering
Mason's Rule: Example Step 4 : Identify the loop gains (3 @ a time):
Department of
Mechanical Engineering
Mason's Rule: Example Step 5 : Using Mason's rule - evaluate for :
Department of
Mechanical Engineering
Mason's Rule: Example Step 5 : Using Mason's rule - evaluate for :
Department of
Mechanical Engineering
Mason's Rule: Example Step 5 : Using Mason's rule - evaluate for :
Department of
Mechanical Engineering
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.
Department of
Mechanical Engineering
