In this screencast we will discuss the differences between interacting and non-interacting processes.
Recall in a process from a control standpoint what we are interested in finding is how an
input, x, influences an output, y. However, the relationship between the input variable
x and the output variable y may not be direct, in other words it may not happen with just
one material or one energy balance. In fact there could be a number of intermediate variables
which allows for a relationship between the input x and the output y. For a non-interacting
system the input is directly related to an intermediate variable, which can be related
to one or more other intermediate variables in perfect succession until it reaches the
output variable y. This is generally seen for systems in pure series. For an interacting
system, what happens here is the fact that although there are intermediate variables
present, whats happening is the fact that there is some variable on the left or in the
beginning is a function of a variable that comes afterwards. So for example, if the variable
B were a function of A, that would indicate and interaction between all the variables.
The two most common ways that we see interacting variables are for recycle streams, systems
where recycling is occurring, a common occurrence in chemical engineering processes, and for
the sake of a control course, any feedback control scheme has some interaction
because you are using the variable at the very end to the measurement of the measurement
of the controlled variable, you are using that variable in the beginning to conduct
analysis because you are trying to find the error between that value and the set point.
To show an example of interacting and non-interacting systems we are going to look at some tanks
in series. We'll develop a model of three tanks in series. The transfer function we're
interested in is how the exiting temperature, T3, is going to be influenced by a change
in the inlet temperature, T(naught). So therefore the transfer function of interest here is
T3 over T(naught). Obviously the temperature of T3 is not immediately related to T(naught).
The temperature of T3 will be based on the temperature that comes out of the second tank,
T2. If we assume the fact the tank is well mixed, then the temperature of the fluid exiting
the tank will be the same as the fluid tank temperature. However T2, the new input variable,
is also not related to the inlet temperature. We can get those connected by the temperature
exiting the first tank. And again if we assume a well mixed tank, the exiting temperature
coming out of T2 will also be equal to the temperature of the fluid in the second tank.
We can finally connect that value to the input T(naught) via the first tank, where similarly
we have the fact that the outlet of the first tank is equal to the fluid temperature inside
the first tank. So we see here is that by changing T(naught), which if we look at our
above case will be x, we have changed what the temperature inside the first tank will
be. That will change whats going on coming out of the first tank, which will be T1, variable
A, which will then affect the second tank and the outlet temperature T2, which will
then affect the temperature T3. But note this goes in a direct fashion. T(naught) influences
T1, which influences T2, which influences T3. For an example of interacting, we can
take a look at the same non-interacting system that we just developed. However, by making
one modification to our diagram here, we can change our system from being non-interacting
to interacting. As an example, and to be consistant with what we discuss for interacting processes
above, what could happen is the fact that the fluid in the second tank could be recycled back
to the first tank. So what this means is that the inlet temperature, T(naught), affects
T1, but T1 is influenced not only by just T(naught), but is also influenced by the change in the
temperature in the second tank, which in turn is influenced by the temperature coming out
of the first tank, hence the interaction. So therefore this provides an example of an
interacting system. In controlled processes we will always deal with interacting processes.
As you would probably hazard to guess, the mathematical analysis of these equations is
a little more challenging because of the more coupling nature, the interacting nature between
these. So hopefully through this screencast you have seen and appreciated the difference
between interacting and non-interacting systems.