In this screencast we will analyze each of the individual blocks that are present in
a generic feedback-only control loop. In order to motivate this what we are going to
do is we are going to focus on an example where we have a heat exchanger presented where
we are trying to warm a cold process fluid by the use of steam. So in this case the controlled
variable of interest here is the temperature of the fluid exiting the heat exchanger, and
we are trying to control that by manipulating the flow rate of steam. So a nice way to start
the development of this block diagram is to actually start at the end, which is the fact
that the variable that we are interested in here is the temperature of the exiting fluid.
So thats the variable that we are going to want out of our feedback control loop because
that is our controlled variable, but what we now want to do is follow the process by
which the controls work. So if we look at our diagram, we start here at the warmer fluid,
we see the fact that the first thing that the temperature will see is the temperature
sensor. So we will draw the block diagram as such, and this is the block for the sensor
and the transmitter block. I will talk in more detail about this in just a minute. So
what is coming into this block would be, again, the actual fluid temperature, but what the senor/transmitter
is going to do is its going to do two things. The sensor, the first part, is going to sense
the temperature, so therefore lets assume that this fluid was fifty degrees Celsius.
The sensor is going to say OK this is going to do the measurement that says this is fifty
degrees Celsius. However, we are not done yet because the controller does not read in
temperature units, mainly because controllers could be used for flow rates, composition,
pressures, etc. So it takes in a signal of some sort. What type of signal is dependent
on the type of control scheme you have, so for the sake of our discussion here we are
going to say an electrical signal, which can be represented as milliamps. Additionally
this signal can also be represented as percent transmitter output. So a point to note here
is the fact that in order for a controller to operate, a controller takes in not the value
of the actual temperature, what it is interested in is the difference between the actual temperature
and the desired temperature. By convention, the set point, AKA the desired temperature,
is the positive value, and then you take away the value of the actual temperature, the measured
temperature. But and important point here is our subtractor has to be like versus like,
so therefore it has to come in here is a signal, either in milliamps or percent transmitter
output. However, what comes in here is the actual steady state temperature, so therefore
we need a relationship to relate the actual desired sep point temperature, and the appropriate
signal that goes to the controller. So this is abbreviated as KM, I'll explain more about
the actual blocks again in just a minute or two. So what then happens is we go from this
signal, this is now this difference represents in milliamps, or percent transmitter output,
the error between the set point and the actual value. If we follow our diagram here, the
value of the sensor through this dashed line gets sent to our controller, which is represented
as Gc. So Gc will take in that error in percent transmitter output, and will output a signal,
usually in percent controller output, basically saying this is how active the controller should
be. If we then follow the signal there, the controller then sets its signal to the valve,
which is represented by Gv. What will come out of the valve transfer function in this
case will be the flow rate of steam. But in all situation what will typically come out
of the valve transfer function is the value of the manipulated variable, which in almost
all cases is the flow rate. So therefore, this will be in some flow rate unit. So what
then happens is the last part of this connection by changing the flow rate of steam, it is
going to cause my fluid to warm, so I need a relationship between those two. That would
represent the process, in other words the heat exchanger. So this process block here
would represent the energy balance on the heat exchanger, which relates how much a change
in the steam flow rate will affect the temperature of the outlet process fluid, and it will also
give an idea of not only gain, so for example a change in one CCM of steam causes a two
degree Celsius change in the fluid temperature, but also some time dynamics, understanding
of how we get there, will it happen instantaneously or will it happen over some set period of
time. So thats the information we can get from the process transfer function. A note
here about why this is a generic feedback only control loop is the fact that in this
analysis we are assuming that there is just one transfer function that relates the two
variables. In some cases this may not be the case, so the process block area may be a bit
more convoluted. Additionally this block diagram does not take into account the potential of
disturbances, which we'll deal with in other screencasts. So now that we have discussed
this what we are now going to do is discuss each of the blocks present in our block diagram
analysis. So we'll start by looking at Gm. So Gm represents the transfer function for
the sensor transmitter. Because the fact that sensors generally act very quickly, this is often
times is a zeroth order transfer function. In other words, it is just a gain represented
here as KM. Occasionally the sensor will have first order time dynamics which would be of
the form KM over tau(m) s plus one. So you may be looking at this came KM and saying,
well we've already defined the variable KM in our block diagram, so we have the KM here,
and the KM present in this block diagram here. This is not an accident.These KMs will always
be the same. To figure out why lets think about a hypothetical here where the outlet
fluid temperature is the set point. So therefore, in a case where the outlet fluid temperature is
equal to the set point, that would mean that our error would be zero. In order for error
to be zero, that would have to mean that the two milliamp signals coming in would have to be identical.
So if I am starting with the same value coming into that block, in order to get the same
value coming out of those respective blocks, the KM block and the GM block, it would have
to mean the fact that the gains of the two would have to be identical. So therefore the
gain for the sensor/transmitter transfer function must be exactly equivalent to the one that
is handling the set point temperature. And again, this doesn't matter what type of variable
it is. The next transfer function here that we see is Gc, that is the controller transfer
function, and its transfer function is dependent on what type of controller you have, whether
it be PPI, PID, PD, etc. Virtually all controllers must have a gain. An additional note here is
the fact that Kc being greater zero, or Kc being less than zero does have some significance.
So when Kc is greater than zero it is known as a reverse acting controller. When Kc is
less than zero that is known as a direct acting controller. You can get some more information
about reverse versus direct acting controllers using other screencasts. Moving along to the next
block, which is Gv, that is the valve transfer function. Valve transfer functions are typically
similar to sensors, zeroth of first order transfer functions. So here we would have
either Kv or Kv over tau(v) s plus one, and again the determination about whether or not
it would be necessary to include theses time constants from both the sensor, the valve,
and the process which I will describe later, is how quickly it takes for changes to be made.
In most situations the sensor/transmitter dynamics can be neglected because they are
much faster than the valve and or the process. In some cases the valve can be ignored, usually
in cases where the dynamics are much faster than the process transfer function. The gains
of the valve transfer function are explicitly based on the fail-safe status of the valve.
So here, when Kv is greater than zero, this will be a whats known as a fail-closed valve.
In other words when the power goes out the valve will be fully closed as a safety criteria,
and Kv is less than zero will represent the opposite, a fail-open valve. Finally Gp, the
last transfer function block represents the process. For an example as simple as the one
we have here where there is only one process transfer block. This will represent usually one material
or energy balance. However, more complicated systems may have more material and or energy
balances. And the transfer function here will be dictated by the balances. So depending
on if there are things in series or what not, for the majority of the time these transfer
functions, particularly for a generic system, will be either first order or a first order
plus dead time, but this is dictated by the balances. Process gain Kp is dictated by the
specific process. So in some cases the gain will be positive, so an increase in the manipulated
variable will cause an increase in the controlled variable, very similar to the example we have
here where if I increase the steam flow rate I am going to increase the temperature of
the process fluid. However if this were cooling water instead of steam, an increase in cooling
water would cause a decrease in the temperature of the other process steam, which would cause
a negative gain. So in this screencast we went through the generic block diagram for
a feedback control loop, and went into some detail regarding what these blocks contain.