# CHEE 319 Tutorial #8 â€“ Empirical Modelling

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CHEE319
Process Dynamics and Control
Winter 2010

Tutorial #6 - Feedback Control Optimization

Tuesday, March 30th, 2010
Work in groups of 3 or 4. Groups of 1, 2, or 5 will be docked 50%, 33% and 20%
respectively. Solutions will be due in the next tutorial on Tuesday April 6th.

In today’s tutorial we will design and implement a controller for the following process:

 1.66(8.0s  1)     13.28s  1.66
G( s)                      
(8.25s  1) 2
68.06s 2  16.5s  1
The zero in the numerator causes an initial inverse response. First we’ll simulate a step
response; open a new workspace in Simulink and create the transfer function above.
Connect a step input to it and send the output to a scope, as usual. Make the step time 10,
the final value 0.25, and the sample time 0.1. Change the total simulation time to 200
minutes by going to “Simulation  Simulation Parameters…” at the top of the screen,
then run the program. The output should initially go up for a brief period, then start to go
down and reach a negative steady-state. This initial inverse response acts in a way
similar to dead time, and when fitting an empirical model to this type of process we just
treat it as if it were.

1. Determine the first-order plus dead time model resulting from this step test (just
ignore the inverse response) using the 28%, 63% method from tutorial 5. Using
these parameters and the Ciancone correlations for tuning constants (step
response), get values for the controller gain Kc, and the integral time TI.
Remember to use the correlation for the PI Controller, not the PID Controller.

Now that we have our controller parameters, we need to add this controller to our
simulation. Add another transfer function block to your workspace with the values you
obtained from question 1 substituted into the following function. We’ll be using a PI
controller, the transfer function for which is:

    1  K cTI s  K c
 T s
Gc ( s)  K c 1    
    I      TI s
A feedback controller loop has the following form:
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D(s)          Gd
Final
Controller Element      Process
SP(s)                                       +
Gc           Gv        Gp                                    CV(s)
+                          F(s)        +
-           U(s)

Gs
M(s)
Sensor
We’re going to neglect final element and sensor dynamics, and we don’t have any
disturbances in our process (yet), so our simplified feedback algorithm is:

Controller           Process
SP(s)               Gc                  Gp                 CV(s)
+-

And this is pretty much exactly how your model should look on the Simulink workspace
when set up properly. The set point will be the same step input you used before, and the
output (CV) is the scope. Set up your scope to plot both CV and SP, so you can get a
better look at your controller’s performance. It should look like this:

2. Run your new simulation. Include the response plot with the controller
implemented in your assignment. Use a step of 1.0 at 10 minutes with 0.1 sample
time. About how long does it take (from when the step is implemented) for your
process to reach steady-state at the new set point?

page). From the “Math Operations” library add an “Abs” to calculate the absolute value
of your error. Add an “Integrator” from the “Continuous” library to sum the error, and
display it on a “Display” from the “Sinks” library.
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3. You are controlling the temperature of a reactor. The new set point value is the
highest temperature at which the process is stable, but also the most profitable.
i.  Optimize your PI controller response to the same unit step change by
manipulating the Kc value obtained from the Ciancone correlations.
controller response by manipulating the TI value.
Show the steps and thought process behind your optimization processes,
recording Kc, TI, and IAE for each step. Remember, as a chemical engineer, it is
your responsibility to meet the criteria outlined above as efficiently as possible.

a) What criteria did Ciancone and Marlin use to produce the
Ciancone correlations?
b) Why are the values from this original optimization inadequate for
c) What criteria did you use to optimize your control scheme?
d) What are your optimized controller gain, integral time, and IAE?
e) Include plots of the original Ciancone control scheme and your
two optimized control schemes. Which one would you institute
and why?

Lastly, we’ll add a disturbance to our model and see how the controller handles it. With
a disturbance, the feedback diagram looks like this:
D(s)             Gd

Controller             Process            +
SP(s)                 Gc                    Gp                         CV(s)
+                                             +
-

We’ll use a step input as our disturbance, and a simple first-order disturbance transfer
function:
1
Gd ( s) 
(5s  1)
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4. a) Run a process disturbance simulation with your original controller tuning
constants, a set point step change of zero (SP final value = 0), and a disturbance
step change of 0.25, sample time 0.1, and step time of 100. Include the response

b) Now reintroduce a set point change of size 1 at time 10 and keep your
disturbance of size 0.25 at time 60. Can your controller handle both set point
range?

c) If 25% disturbances were to be expected in your process, and you wanted to
avoid exceeding stable reaction conditions, how might you change your set point?
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