Main

## Main.LectureNotes6 History

September 19, 2014, at 01:34 PM by 107.188.175.164 -
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September 19, 2014, at 01:33 PM by 107.188.175.164 -
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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:
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:
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At the end of class we ran through an example of a gravity drained tank.
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One example of comparing linear and nonlinear models is with the following gravity drained tank application.

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!!!! Homework

# Course reading for next class: Chapter 7-9 (PPC).
# Assignment due by the start of Lecture #7: [[Attach:sp3.pdf | SP3]]

* %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.
September 06, 2013, at 02:46 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 fit used a material balance to obtain a model.  A comparison of the two models is shown below:
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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:
'''Fig 1:''' Diagram of the Gravity Drained Tank
'''Fig 2:''' Sequence of Valve Movements to Test Models
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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.
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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.

Attach:tank_percent_open.png
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Attach:tank.png
to:
Attach:tank2.png

!!!! 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.
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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.
!!! 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]]

* %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.