Modeling Basics: 2. Incidence Graphs
By Peter Woolf ([email protected])University of Michigan
Michigan Chemical Process Dynamics and Controls Open Textbook
version 1.0
Creative commons
Scenario
After creating a detailed verbal description of your process, you want to map out and interpret how the key variables influence each other.
Scenario
Variables that might be of interest:
Temperature
Level
Pressure
Flow
Valve status
v4
v2 v3
v6
v1
v5
T1
L1
P1
F1
v1
Scenario
Variables that might be of interest:
Temperature
Level
Pressure
Flow
Valve status
P1
P3P2
T1
T2
T3
T4
L1
L2
v4
v2 v3
v1
v5
F3F2
F1
F4
F5
T1
L1
P1
F1
v1
v6
L1
L2
v4
v2 v3
v1
v5
F3F2
F1
F4
F5
v6
What kind of stable and direct relationships can we identify?
Flow type relationships:Opening v2 increases F2Opening v3 increases F3Opening v4 increases F4
Level relationships:Increasing F2 decreases L1Increasing F3 decreases L1
Question: Why or why notOpening v2 decreases L1?
Although true, the effect is indirect. The effect on L1 is directly caused by F2 and F3, and indirectly by v2 and v3.
Incidence Diagrams• Diagramatic and analytic tool to
describe direct, monotonic, and causal relationships between variables.
x
X
y
y
X
y
x y
“Increasing x causes y to increase”
“Increasing x causes y to decrease”
L1
L2
v4
v2 v3 F3F2
F1
F4
F5
Flow type relationships:Opening v2 increases F2Opening v3 increases F3Opening v4 increases F4
Level relationships:Increasing F2 decreases L1Increasing F3 decreases L1
v2 F2
v3
v4 F4
L1F3
If gravity fed, may have a feedback effect on L1 on the flow..Increasing L1 increases F2Increasing L1 increases F3
T1
Control system may regulate the column temperature with reflux..T1 opens (increases) v2Increasing F2 decreases T1
T1
Control actionPhysical response
L1
L2
v4
v2 v3 F3F2
F1
F4
F5
T1
v2 F2
v3
v4 F4
L1F3
T1
Interpreting an incidence diagram• Break a system into independent or semi-independent parts• Detect consistent chains of effectse.g. if I could force L1 to increase, what would be the effect?
L1
L2
v4
v2 v3 F3F2
F1
F4
F5
T1
v2 F2
v3
v4 F4
L1F3
T1
e.g. if I could force L1 to increase, what would be the effect?
Identify all paths from and to the variable
L1
L2
v4
v2 v3 F3F2
F1
F4
F5
T1
v2 F2
v3
v4 F4
L1F3
T1
e.g. if I could force L1 to increase, what would be the effect?
Identify all paths from and to the variable(1) L1-> F2 -| L1(2) L1 -> F3 -| L1(3) L1 -> F2 -| T1 ->v2->F2 -|L1
{+, +, -}{+, +, -}
{+, +, -,-,-,+}
Inconsistent path: system will resist change
Consistent path: system will reenforce change
Side effect: forcing L1 to increase will cool the column causing v2 to close, decreasing F2, and increasing L1.
Focal adhesion signal transduction pathay in human cellsfromhttp://www.wikipathways.org/images/5/54/Hs_Focal_adhesion_KEGG.svg
A second ChemE exampleIncidence diagram showing the interaction of you reactor conditions on profitability.
Based on this graph alone, changing what variables will consistently increase profitability?
Options:
Purification efficiency -> profitability {+,+}
Consistent effect on profit:• Purification efficiency
Consistent effect on profit:• Purification efficiency• Mixing speed
{+,+,+}
{+,-,+,+}
{+,+,-,+,+}
{+,-,-,-}
Options:Mixing speed ->purification efficiency -> profitability
Mixing speed -| culture density-| purification efficiency -> profitability
Mixing speed -> final broth pH -| culture density-| purification efficiency -> profitability
Mixing speed -| culture density -> fermentation temp -> mixing speed
Consistent effecton profit:• Purification efficiency• Mixing speed
Inconsistent:• culture density
{+,-,-}
{+,+,+,+,+}
{+,+,+,-}
{+,+,+,+,-}
Options:Culture density -| purification efficiency -> profitability
culture density-> fermentation temperature ->mixing speed -> purification eff -> profitability
culture density-> fermentation temperature ->mixing speed -| culture density
culture density-> fermentation temperature ->mixing speed -> pH -| culture density
Check the rest!
Consistent effect on profit
Inconsistent effect on profit
Note! This does not mean that these are the only ways to increase the profitability of the plant, but instead these are the only consistent ways to increase profit according to this diagram.
Consistent vs. inconsistent networks
• Whole networks can be consistent or inconsistent. Consistent networks have the advantage that they can be collapsed into a single conceptual unit
a b c d e f a f
a b c d e f
ghi
a f
From http://controls.engin.umich.edu/wiki/images/6/61/ConsistentGraphs.doc
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