Lecture Notes 6
Main.LectureNotes6 History
Hide minor edits - Show changes to output
Deleted lines 40-58:
----
(: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 = 'https://' + 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="https://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>
<a href="https://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>
(:htmlend:)
Added lines 16-19:
(:html:)
<iframe width="560" height="315" src="//www.youtube.com/embed/ELEUFKzwUj0?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
<iframe width="560" height="315" src="//www.youtube.com/embed/ELEUFKzwUj0?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
Deleted lines 22-25:
(:html:)
<iframe width="560" height="315" src="//www.youtube.com/embed/ELEUFKzwUj0?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
Changed lines 3-6 from:
A
to:
The Gain (K_p), Time Constant (tau_p), and Dead-time (theta_p) can be graphically extracted from a step test when fitting to a First Order Plus Dead Time (FOPDT) model. There are many situations when it is not possible or doesn't make sense to generate a complete step test or there are other model forms that better describe the system.
An FOPDT model can be obtained by fitting the model to data. This allows other forms of step testing such as:
An FOPDT model can be obtained by fitting the model to data. This allows other forms of step testing such as:
Changed lines 18-22 from:
to:
One example of comparing linear and nonlinear models is with the following gravity drained tank application.
(:html:)
<iframe width="560" height="315" src="//www.youtube.com/embed/ELEUFKzwUj0?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
(:html:)
<iframe width="560" height="315" src="//www.youtube.com/embed/ELEUFKzwUj0?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
Deleted lines 36-46:
!!!! Homework
# Course reading for next class: Chapter 7-9 (PPC).
# Assignment due by the start of Lecture #7: [[Attach:sp3.pdf | SP3]]
You'll use your answers from Q3.1 and Q3.2 on SP3. I've included the answers to Q3.1 and Q3.2 for your reference.
* %list list-page% [[Attach:Q5.1_Q5.2_notes.pdf | SP3 Homework Notes]]
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.
Added lines 48-66:
----
(: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 = 'https://' + 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="https://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>
<a href="https://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>
(:htmlend:)
Changed line 28 from:
Half of the class derived a FOPDT model of the process using empirical fitting techniques. The other half of the class fit used a material balance to obtain a model. A comparison of the two models is shown below:
to:
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:
Added lines 22-23:
'''Fig 1:''' Diagram of the Gravity Drained Tank
Added lines 26-27:
'''Fig 2:''' Sequence of Valve Movements to Test Models
Changed lines 32-33 from:
The linear response is easy to fit to the data but deviates, especially during the periods that are far from the steady state values.
to:
'''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.
Changed line 36 from:
The nonlinear response is valid over a wider range of operation.
to:
'''Fig 4:''' Nonlinear Model Based on a Material Balance. The nonlinear response is valid over a wider range of operation.
Added lines 15-30:
!!!! Linear vs. Nonlinear Models
At the end of class we ran through an example of a gravity drained tank.
Attach:tank.png
Half of the class derived a FOPDT model of the process using empirical fitting techniques. The other half of the class fit used a material balance to obtain a model. A comparison of the two models is shown below:
Attach:tank_linear.png
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
The nonlinear response is valid over a wider range of operation.
Changed line 12 from:
In practice, smart-stepping or PRBS signals for identification of models for multivariable control. For tuning of PID controllers a step, doublet, or pulse test is often preferred.
to:
In practice, smart-stepping or PRBS signals are used for identification of models for multivariable control. For tuning of PID controllers a step, doublet, or pulse test is often preferred.
Added lines 1-25:
!!! Lecture 6 - Fitting models to data
In Lecture 4 we reviewed how to extract the Gain, Time Constant, and Dead-time from a step test. There are many situations when it is not possible or doesn't make sense to generate a complete step test.
A FOPDT model can be obtained by fitting the model to data. This allows other forms of step testing such as:
* Pulse: step up followed by step back to original value
* Doublet: two pulses in opposite directions
* Pseudo-Random Binary Sequence (PRBS): steps of varying frequency and magnitude
* Smart-stepping: optimize steps to extract the most information while keeping the process within bounds
In practice, smart-stepping or PRBS signals for identification of models for multivariable control. For tuning of PID controllers a step, doublet, or pulse test is often preferred.
* %list list-page% [[Attach:Lecture6_notes.pdf | Lecture 6 Class Notes]]
!!!! Homework
# Course reading for next class: Chapter 7-9 (PPC).
# Assignment due by the start of Lecture #7: [[Attach:sp3.pdf | SP3]]
You'll use your answers from Q3.1 and Q3.2 on SP3. I've included the answers to Q3.1 and Q3.2 for your reference.
* %list list-page% [[Attach:Q5.1_Q5.2_notes.pdf | SP3 Homework Notes]]
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.
In Lecture 4 we reviewed how to extract the Gain, Time Constant, and Dead-time from a step test. There are many situations when it is not possible or doesn't make sense to generate a complete step test.
A FOPDT model can be obtained by fitting the model to data. This allows other forms of step testing such as:
* Pulse: step up followed by step back to original value
* Doublet: two pulses in opposite directions
* Pseudo-Random Binary Sequence (PRBS): steps of varying frequency and magnitude
* Smart-stepping: optimize steps to extract the most information while keeping the process within bounds
In practice, smart-stepping or PRBS signals for identification of models for multivariable control. For tuning of PID controllers a step, doublet, or pulse test is often preferred.
* %list list-page% [[Attach:Lecture6_notes.pdf | Lecture 6 Class Notes]]
!!!! Homework
# Course reading for next class: Chapter 7-9 (PPC).
# Assignment due by the start of Lecture #7: [[Attach:sp3.pdf | SP3]]
You'll use your answers from Q3.1 and Q3.2 on SP3. I've included the answers to Q3.1 and Q3.2 for your reference.
* %list list-page% [[Attach:Q5.1_Q5.2_notes.pdf | SP3 Homework Notes]]
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.
