Main

Lecture Notes 15

Main.LectureNotes15 History

Hide minor edits - Show changes to output

October 08, 2014, at 10:32 PM by 107.188.175.164 -
Changed lines 15-16 from:
!!!! Linear vs. Nonlinear Models
to:
!!!! Linear vs. Nonlinear Models: CSTR Case Study
Changed line 23 from:
----
to:
!!!! Linear vs. Nonlinear Models: Gravity Drained Tank Case Study
October 08, 2014, at 10:30 PM by 107.188.175.164 -
Added lines 16-23:

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

(:html:)
<iframe width="560" height="315" src="//www.youtube.com/embed/RqbnfjOF5tU?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)

----
October 06, 2014, at 11:58 AM by 107.188.175.164 -
Added lines 10-13:

(:html:)
<iframe width="560" height="315" src="//www.youtube.com/embed/EJxGZKWnuxQ?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
October 06, 2014, at 11:17 AM by 107.188.175.164 -
Changed line 9 from:
* %list list-page% [[Attach:Lecture15_worksheet.pdf | Worksheet on Linearization Solution]]
to:
* %list list-page% [[Attach:Lecture15_worksheet_solution.pdf | Worksheet on Linearization Solution]]
October 06, 2014, at 11:17 AM by 107.188.175.164 -
Changed lines 5-7 from:
* %list list-page% [[Attach:Lecture15_notes.pdf | Lecture 15 Class Notes]]

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

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

* %list list-page% [[Attach:Lecture15_worksheet.pdf | Worksheet on Linearization Solution
]]
Deleted lines 29-35:

!!!! 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 07:41 AM by 69.169.131.210 -
Changed line 21 from:
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:
to:
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 08:48 AM by 69.169.131.210 -
Added lines 37-55:

----

(:html:)
 <div id="disqus_thread"></div>
    <script type="text/javascript">
        /* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */
        var disqus_shortname = 'apmonitor'; // required: replace example with your forum shortname

        /* * * DON'T EDIT BELOW THIS LINE * * */
        (function() {
            var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
            dsq.src = 'http://' + disqus_shortname + '.disqus.com/embed.js';
            (document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);
        })();
    </script>
    <noscript>Please enable JavaScript to view the <a href="http://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>
    <a href="http://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>
(:htmlend:)
Added lines 6-7:

* %list list-page% [[Attach:Lecture15_worksheet.pdf | Lecture 15 Worksheet on Linearization]]
Added lines 1-34:
!!! 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.