computer lab d

7/23/2019 Computer Lab D

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CHE 06405PROCESS DYNAMICS AND CONTROL

COMPUTER LAB D: Process dent i f i cat ion

Objec t ives :

Identify processes and process characteristics from output.

Fit a first order plus time delay model to data.

Par t : Identification by step response.

When looking a plot of a system and trying to match a transfer function, there are a number of important,quick, and easy questions you should start with:

o Is there a time delay? If so, how long is it?o Does the system oscillate?o Is the slope of the outputs response nonzero when it begins responding?o What is the minimum number of poles and zeros that must exist for this system?

Each of these questions gives you a specific attribute of the system and greatly speeds up the derivation ofan appropriate transfer function for the underlying system.

NOTE: Each of the following 6 graphs depicts the response of a system to aninput step of magnitude 1 at time = 2. Note that the initiation of the stepinput at t=2 is designed to help you see the initial dynamics more easily.

NOTE: In Part I, you are asked to estimate parameter values. You should doso by inspection only. For example, you do not need to find exact values fortime constants in higher order systems. At this point, you should be able todo this without spending much time.


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1.

Propose a transfer function for the system whose output is shown above. Include estimates for anyparameters that you can estimate. If you cannot estimate an actual value of a parameter, but can

discuss relative values (i.e. !> "), please include that information as well.

Note: It may help you to consider the following. (You do not need to actually answer thesequestions.)! Is there a time delay? If so, how long is it?! Does the system oscillate?! Is the slope of the outputs response nonzero when it begins responding?

0 2 4 6 8 10 12 14 16 18 20

0

0.5

1

1.5

time [unitless]

Input[unitless]

0 2 4 6 8 10 12 14 16 18 20

0

1

2

3

time [unitless]

Output[unitless]


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2.



If a first order system plus time delay were to be fit to this system, estimate the steady state gain

(K), time constant (") and time delay (

!

).

0 2 4 6 8 10 12 14 16 18 20 22 24

0

0.5

1

1.5

time [unitless]

Input[unitless]

0 2 4 6 8 10 12 14 16 18 20 22 240

1

2

3

4

5

time [unitless]

Output[unitless]


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3.





!

).

0 2 4 6 8 10

0

0.5

1

1.5

time [unitless]

Input[unitless]

0 2 4 6 8 10

0

1

2

3

time [unitless]

Output[unitless]


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4.




(K), time constant (") and time delay (!).

0 2 4 6 8 10 12 14 16 18 20

0

0.5

1

1.5

time [unitless]

Input[unitless]

0 2 4 6 8 10 12 14 16 18 20-1

0

1

2

time [unitless]

Output[unitless]


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5.




(K), time constant (") and time delay (!).

0 2 4 6 8 10 12 14 16 18 20

0

0.5

1

1.5

time [unitless]

Input[unitless]

0 2 4 6 8 10 12 14 16 18 20

0

1

2

3

time [unitless]

Output[unitless]


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6.





!

).

0 2 4 6 8 10 12 14 16 18 20

0

0.5

1

1.5

time [unitless]

Input[unitless]

0 2 4 6 8 10 12 14 16 18 20

0

1

2

3

time [unitless]

Output[unitless]


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Par t : Fit data to a First Order Plus Time Delay (FOPTD) model.Your boss asks you to model the liquid level dynamics in a tank. The company cannot afford anydisruptions in production, so you are unable to conduct any experiments with the tank, but your boss givesyou the operators log of liquid heights. Luckily for you, the operator recorded the tank level following thelast inflow increase. According to the operators log, the tank height was ~95ft before he increased theinflow from 50 gallons/minute to 55 gallons/minute.

Time[min]

Flow Ratein [gal/min]

TankHeight[ft]

0.5 50 95.1

1 50 95.8

1.5 50 93.4

2 55 94.7

2.5 55 97.0

4 55 95.2

5 55 93.9

6.9 55 95.9

7.6 55 98.7

9.6 55 95.8

11.7 55 100.0

13.5 55 98.9

15.2 55 102.0

16.8 55 103.1

16.9 55 103.2

19.5 55 103.7

22 55 106.4

25 55 107.2

28 55 108.631 55 108.9

34 55 108.3

37 55 109.6

40 55 110.1

44 55 110.0

47 55 110.3

50 55 111.6

52 55 109.4

55 55 110.2

57 55 112.6

60 55 110.5

Your boss suggests that you model the system as a first order plus time delay system so that you canimplement feedback control (you will learn more about this in a couple of weeks). In this situation, thetheoretical step response for times greater than the time delay (in terms of deviation variables) is:

)1()( /)( !"##$ #=

teyty (1)

where y#is the ultimate value of the response.


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Estimate K, the steady-state gain, from the ultimate value of the step-response data.

Note that you can rearrange equation (1) as follows:

!" /)( ##

$

$

=

# te

y

yy (2)

from which we can obtain:

!!

" t

y

yy#=

#

$

$ )ln( (3)

Transform the tank level data as indicated on the LHS of equation (3). BE CAREFUL WITHDEVIATION VARIABLES AND INPUT STEP TIME. Plot this versus time and find the equation

of the line that best fits the data. Use the equation of this line to find $and ". Then, use these values togenerate an equation for the predicted liquid level. Submit this plot with the equation of the line shownexplicitly on your graph.

NOTE: Noise in the data will affect the fit. Regions of data that are obviously noisy should be removedfrom the fit. Also, values of y that lead to undefined ln terms should be removed from the fit. Submit atable that includes the transformed data and highlights which points you used for your estimation.

Plot the data and the model on the same graph and submit that plot. Comment (briefly) on the fit.

computer lab d

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