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The Oxygen Exit concentration(O) and the Hydrocarbon Exit temperatures(H)
are the controlled variables.Figure1 also shows two controllers to maintain
O and H at their setpoints. Although, figure one does not show it nicely,
the two controllers correspond to two feedback loops.
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Loop 1: Maintains the Oxygen Exit Concentration at its setpoint by
manipulating the amount of air entering the system
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Loop 2: Maintains the Hydrocarbon Outlet Temperature at its setpoint
by controlling the fuel supply .
The purpose of the experiment is to design tune the PI
and PID controller in each loop using the Ziegler Nichols Tuning
Method. Alternatively loop2 should be tuned using the auotuning method.Note
that the second loop is also connected to a relay required in Autotuning.
EXPERIMENTAL PROCEDURE:
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The projects consists of three experiment (experiments 1-3). A lean outline
will be given in the following subsectios.
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Before you start, observe the initial values of the setpoints for the controlled
variable and familiarize yourself with the process in dynamic mode by manually
changing the values of the load variables and studying its effect on the
system.
EXPERIMENT 1: ZIEGLER NICHOLS
TUNING
Ziegler Nichols Tuning requires the experimental determination of the
Ultimate Gain. This can be accomplished by setting the controller to proportional
mode and increase the gain until the process falls into stable oscillations
of constant amplitude.A simple recipe you may adopt for this follows.
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Verify with the TA whether the Process Control Modules are installed on
your PC. To start the furnace model, first open the Mathlab application.
Use the Path browser in the file menu to change your working director to
pcm directory. Type ‘mainmenu’ in the command prompt and the click on ‘Furnace’
once. Then click on ‘Furnace with Control’ on the furnace menu.
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Make sure that both the feedback loops are in manual by setting the loop
switch blocks to the "off" position.
PHASE I. TUNING OF THE FIRST LOOP
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Change the setpoint of the controlled variable O to the value assigned
to your group in Table 2,by double clicking on the corresponding box.
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Double click on the concentration loop switch to change its status to ‘on’.
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To make the controller function as a proportional controller, double click
on the concentration PID controller box and set the integral and derivative
values to zero.
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Enter a value for ‘k’ and run the simulation. Observe the output. Keep
changing the value of ‘k’ until the closed loop system exhibits sustained
oscillations of constant amplitude. You may use the pointer checkbox and
position the pointer on the graph to check this. For more details on how
to vary ‘k’ refer Seborg2 .
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Use the rules for Ziegler Nichols tuning as given in the lecture
notes3 to design a PI and PID controller.
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Now enter the values of the calculated parameters for a PI control into
the concentration controller, set the derivative action to '0' and integral
action to '1' and run the simulation again. Note the amount of time it
takes for the oxygen Exit concentration to reach a new steady state.
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Repeat the same for PID controller and note the time it takes for O to
reach a new steady state.
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Calculate the Decay ratio and compare the response of a PID controller
with the PI controller.
PHASE II: TUNING OF THE SECOND LOOP
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Follow the same procedure as you did for Loop1.
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Remember to turn the Concentration loop switch to 'off' while you are tuning
Loop2. Alternatively the ultimate gain can be found using Autotuning. A
procedure for this is given below.
EXPERIMENT 2: AUTOTUNING
For tuning the loop 2 controller via autotuning turn off both the feedback
loops using the switch preceding the controller. Now set the switch which
follows the relay controller to ‘on’.
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The amplitude of input oscillation has been given to be 0.5.Run the simulation
to get oscillations of constant amplitude. Calculate Ku as:
Ku = 4 *d /P
* a
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Calculate Controller gain Kc as
= Ku cos (f) ,
integral time constant TI = a Td
where derivative time constant Td = tan(f)
* sqrt((4/a)+ tan(f))/
(2 *wc) and wc
= 2 P / P u as given in Doyle1
with a =4 and
f =
45.
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Compare these values of Kc with the values that you got by Ziegler Nichols
Tuning.
EXPERIMENT 3: ASSESSMENT OF THE
CONTROLLERS PERFORMANCE UNDER DISTURBANCES
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Enter the Hydrocarbon Outlet Temperature and the Oxygen exit concentrations
to the setpoints assignned to your group.
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Set the controller parameters using the proportional gain obtained from
Ziegler Nichols tuning rules. First switch both the integral and derivative
actions to off and disturb the system by changing the fuel gas purity to
the value assigned to your group in Table 1.
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Observe the response and calculate maximum deviation from setpoint.
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Repeat the above steps for PID controller where Integral and Derivative
action are both on.
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Compare both the responses in terms of dynamic characteristics.
Compile a detailed report of your Observations , calculations, outputs
on Experiments 1,2 and 3. Include your conclusions ,shortcomings and advantages
of your approach. Also include a comprehensive discussion of the observations
you make in testing your design, which entails a creative element beyond
the simple outline of Experiment 3. This report is due on
April
6, 2001.
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