Lecture 6: Feedback Systems of Reactors

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Lecture 6 Feedback Systems of Reactors

• CE 498/698 and ERS 685
• Principles of Water Quality Modeling

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Feedback
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LINEAR ALGEBRAIC EQUATIONS
Matrix algebra
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Gauss-Jordan method
To compute the matrix inverse
Identity matrix
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Gauss-Jordan method
To compute the matrix inverse
1) Normalize
2) Elimination
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Gauss-Jordan method
1) Normalize
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Gauss-Jordan method
2) Elimination
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Gauss-Jordan method
2) Elimination
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Gauss-Jordan method
1) Normalization
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Gauss-Jordan method
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Gauss-Jordan method example
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Gauss-Jordan method example
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Gauss-Jordan method example
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Gauss-Jordan method example
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Gauss-Jordan method example
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Gauss-Jordan method

• Can also be used to solve for concentrations

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Excel - MINVERSE

• Enter your A matrix
• Block an area the same size
• Type MINVERSE(block location of Amatrix) and
  press CNTLSHIFTENTER

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We want to solve for C
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Homework Problem 6.2(a)

• Use both Gauss-Jordan method and Excel MINVERSE
  function

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C response W forcing functions A-1
parameters
response interactionsforcing functions
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Matrix Multiplication (Box 6.1)
columns in matrix 1 rows in matrix 2
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Terminology
SUPERDIAGONAL Effects of d/s loadings on u/s
reactors
DIAGONAL Effect of direct loading
SUBDIAGONAL Effects of u/s loadings on d/s
reactors
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Time-variable response for two reactors
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Time-variable response for two reactors
General solution if c1c10 at t 0
see formulason page 111