Main

## Main.LectureNotes15 History

October 09, 2014, at 04:32 AM by 107.188.175.164 -
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!!!! Linear vs. Nonlinear Models
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!!!! Linear vs. Nonlinear Models: CSTR Case Study
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!!!! Linear vs. Nonlinear Models: Gravity Drained Tank Case Study
October 09, 2014, at 04:30 AM by 107.188.175.164 -

* %list list-page% [[Attach:CSTR_MATLAB.zip | CSTR Nonlinear vs. Linear MATLAB Solution]]

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October 06, 2014, at 05:58 PM by 107.188.175.164 -

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October 06, 2014, at 05:17 PM by 107.188.175.164 -
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* %list list-page% [[Attach:Lecture15_worksheet.pdf | Worksheet on Linearization Solution]]
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* %list list-page% [[Attach:Lecture15_worksheet_solution.pdf | Worksheet on Linearization Solution]]
October 06, 2014, at 05:17 PM by 107.188.175.164 -
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* %list list-page% [[Attach:Lecture15_notes.pdf | Lecture 15 Class Notes]]

* %list list-page% [[Attach:Lecture15_worksheet.pdf | Lecture 15 Worksheet on Linearization]]
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* %list list-page% [[Attach:Lecture15_notes.pdf | Linearization Notes]]

* %list list-page% [[Attach:Lecture15_worksheet.pdf | Worksheet on Linearization]]

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!!!! Homework

# Course reading for next class: 3.1-3.4 (PDC).
# Assignment due by the start of Lecture #16: [[Attach:sp9.pdf | SP9]]

Don't forget that the first part of each homework assignment is to write a sentence or two stating the purpose of the problem and what concept is reinforced.
October 05, 2013, at 01:41 PM by 69.169.131.210 -
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Half of the class derived a FOPDT model of the process using empirical fitting techniques.  The other half of the class used a material balance to obtain a model.  A comparison of the two models is shown below:
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We derived a FOPDT model of the process using empirical fitting techniques.  A first principles approach was also used to obtain a model from a material balance.  A comparison of the two models is shown below:
September 06, 2013, at 02:48 PM by 69.169.131.210 -

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* %list list-page% [[Attach:Lecture15_worksheet.pdf | Lecture 15 Worksheet on Linearization]]
!!! Lecture 15 - Linearization

Now that we've derived nonlinear models based on material and energy balances, we need to get them into a form for linear systems analysis.  We do this through a process called linearization.  In Lecture 15, we review the mathematics of how to linearize a nonlinear function.  We have a couple exercises to help practice the linearization process.

* %list list-page% [[Attach:Lecture15_notes.pdf | Lecture 15 Class Notes]]

!!!! Linear vs. Nonlinear Models

We previously ran through an example of a gravity drained tank.

Attach:tank2.png

'''Fig 1:''' Diagram of the Gravity Drained Tank

Attach:tank_percent_open.png

'''Fig 2:''' Sequence of Valve Movements to Test Models

Half of the class derived a FOPDT model of the process using empirical fitting techniques.  The other half of the class used a material balance to obtain a model.  A comparison of the two models is shown below:

Attach:tank_linear.png

'''Fig 3:''' Linear Model (FOPDT).  The linear response is easy to fit to the data but deviates, especially during the periods that are far from the steady state values.

Attach:tank_nonlinear.png

'''Fig 4:''' Nonlinear Model Based on a Material Balance.  The nonlinear response is valid over a wider range of operation.

!!!! Homework

# Course reading for next class: 3.1-3.4 (PDC).
# Assignment due by the start of Lecture #16: [[Attach:sp9.pdf | SP9]]

Don't forget that the first part of each homework assignment is to write a sentence or two stating the purpose of the problem and what concept is reinforced.