Cohen Coon Tuning (Process Reaction Curve) Video Lecture - Electrical Engineering (EE)

In this screencast we will take a look at how we can use process data in order to develop
an appropriate selection of tuning parameters
for process that is desired to be controlled.
So here we are given information about a test
that was done where the controller output was
decreased from 57 to 54 percent CO instantaneously,
and as a result of changing that controller
output you are causing a change in your output
variable. In this case the temperature of
a process fluid in a heat exchanger. Based
on this information from this test how can
we develop appropriate parameters for PI control
using the Cohen Coon Tuning methadology. So
Cohen-Coon is one of many types of tuning
parameter correlations that is based on open
loop testing, and an open loop test is what we
have just described earlier which is basically
the controller being on manual and an adjustment
being made to that controller. Because if
you think about how the controller works is
the controller sends its signal to the valve,
so therefore by adjusting the controller output
you are adjusting the openess of the valve.
Whether or not it is opening or closing when
you go from 57 to 54 percent is a function
of whether or not the valve fails open or
fails closed. So an important point to remember
here is just because you are decreasing controller
output does not mean that you are closing
your valve more and decreasing the amount
of your manipulated variable. So many of these
open loop tests what the goal is is to find a
transfer function that can take into account
the affects of the valve, the sensor, and
the process, which is what the open loop test
accomplishes. So in many cases, depending
on your tuning parameter methodology, they
are going to require you to turn this transfer
function into a particular form, whether it
be first-order, first-order plus dead time,
second-order plus dead time, second-order
integrating process, etc. For the sake of
the one that we are doing here for Cohen-Coon,
and one of the more common techniques is we are
looking at trying to make this process a first-order
plus dead time process. So an important point
to remember with the first-order plus dead time
process is that the corresponding transfer
function is k e to the negative theta s over
tau s plus one, and if you look at the Cohen-Coon
tuning parameter table, what you'll notice is
that the kc values contain tau, theta, and
k, all the three parameters that we get from
this mode, and for the tau(i) and tau(d) what
you'll notice is they contain just theta and
tau, also the two parameters we get here.
So what we now need to do is develop a transfer
function from our data that can be turned
into a first-order plus dead time process.
So because of the fact that we have made a
step change in the controller output this
method is often known as the step test method.
Another name for this is the process reaction
curve method. The reason why its called the
process reaction curve method is because the
figure that we shows how the process reaction
change in the controller, hence this is the
process reaction curve. So there are a whole
host of different ways in order to find the
three relative FOPDT parameters, the gain,
the dead time, and the time constant. Some
methods are more graphical in nature, and
some methods focus more on the time where
the process has gone a certain percentage
of the way from going from its starting point
to its finishing point. So in this case we
are going to use a more graphical approach,
so what we are going to do here is attempt
to connect the data points, and what we're
going to take advantage of here is we first have to find the inflection point,
and here we'll just estimate the inflection
point as somewhere around here. The next step
is we have to develop a tangent line that
runs through the inflection point, and then
what we do is take a look at where the process
crosses the initial value and the final value.
So, if look at this it crosses the initial
value at approximately t equals five minutes,
so therefore this value represents theta in
the transfer function for the FOPTD. And then
we look at where it crosses here, we'll say
that this is nine, and this value represents
the magnitude of tau minus theta. So therefore
since theta is five that means that tau is
going to be four. So we have theta and we
have tau. The gain we find by the definition
of change output over change in input, and if
you recall what happened here is we had a
change in input from 57 to 54, so therefore
the change in our input value went down
down by negative three, as we look here
our process started at 55, but ended at 53.2,
so therefore the gain is negative 1.8 over
negative 3, which is just 0.6. So with all
this information we have developed our FOPTD
here as the gain 0.6 e to the 5s, the dead
time, over 4s plus 1, where tau is 4. So we
were looking to try to develop the tuning
parameters for a PI controller. Kc will be
about 1.34 percent controller output per percent
transmitter output. So when we put this all
together we end up with a tau(i) of 4.96 minutes.
The reason why its minutes is because the
graph that we had before had its units in
minutes if our analysis of tau and theta were
done in minutes. So before we wrap up this screencast
we'll talk briefly about some of the disadvantages
of the process reaction curve. The first is
disturbances are problematic. The reason why
is the fact that we are attempting to make
a step change in the controller output, and
see how the process responds. However, if
there are any disturbances that affect the
data it is going to impact whats happening
because the transfer we're trying to find,
which is the multiplication of the process,
the sensor/transmitter,and the valve, will
get a bit lost and muddled by the presence
of the disturbance. Additionally the second
issue is the fact that the calibration of
the controller is important, and this is because
we have to ensure the fact that the change
in percent controller output is consistent,
other wise this could become potentially dependent
on whether or not you did an increase or a
decrease, or where this increase or decrease
occurred. Another potential issue is the fact
that if any of these things are significantly
non-linear, and somewhat related is the fact
that if the process doesn't represent a first-order
plus dead time. So if any of these issues
happen that can influence the accuracy of
the results that you get. And fourth and finally
this method does not really work very well
for an unstable process because there is no
controls, and therefore if there is no control
this process will just continue acting unstable,
so therefore this to be aware of the fact
that this method is not the only method, for
example zegore-nickols analysis involves continuous
cycling, there are a host of other methods
which use other methodologies in order to
determine the two parameters. So in this screencast
we showed how we could use process data from
an open loop system, however there is no control
being put upon it in order to develop appropriate
tuning parameters. And again, these tuning
parameters serve only as a beginning as you
go into the complete research of this or the
complete experimentation of this, fine tuning
is most likely going to be necessary. These
tuning parameters represent a nice start.