In this screencast we will discuss the continuous cycling method which is also sometimes known
as the Ziegler-Nichols method. So this method is used in order to develop tuning parameters
for a process. Another important part about this methodology is that it is a closed loop
test, which many methodologies used for developing tuning parameters are open loop, where there
is no control being provided to the system, but in this case the system is being controlled
by a controller in this analysis. So in order to use this tuning parameter method we have
to get some understanding of the dynamic characteristic of how this control loop behaves, and the
way we do this is by using the following procedure. The first step of this is to shut off the
integral control, the i control, and the derivative control, the d control, and when you do that
it leaves a p only controller. Sometimes i control cannot be exactly shut off, but to
counteract the fact that you can't shut i control exactly off what you can do is select
a very high value of i such that the controller acts as a de facto p only controller. D is
generally easy to shut off. The second step is to put the controller in automatic, in
other words this is the part which gets us the closed loop. The third step is to alter
the controller gain, kc. Depending on the controller you have this could also be altering
the proportional band. Going to keep on altering your controller gain until the response that
is seen is undamped. So in other words we are in a state where the oscillations are
neither growing or receding. So what does this look like in terms of the response that
we would see. So here we'll do a sketch where our x-axis is time, and our y-axis is the
variable that we're interested in following. So if the system is perfectly undamped we
would see a response that looks something like this, where we could see consistent oscillations.
This would be our undamped response. However it is certainly possible that we could see
a response which instead of it being undamped we see something where we have growing oscillations.
So this is a system which is unstable, and obviously undesirable, and what this means
if you were to actually see this is that the assesment of the gain that you want
is too high. On the other hand is if what you are seeing are decaying oscillations,
something along these lines here, you have an underdamped system, but in terms of finding
the kc value you want this would mean the kc is too low. So what does this all mean
once we have actually found this value? What it means is that the gain that corresponds
to the undamped response is the ultimate gain, and the period of this response is the ultimate
period, and then from there what we can do is use the Ziegler-Nichols tuning parameters
in order to get an assessment. So this table on the bottom right, this represents the Ziegler-Nichols
tuning parameters. These tuning parameters were used in order to obtain aa undamped process
with a quarter decayed ratio. So if you recall, the decay ratio represents the relationship
between the second highest peak and the top peak. So therefore if I call this height here
B and this height here A the decay ratio, sometimes shortened as dr, can be defined
as B over A. So for Ziegler-Nichols it is designed such that this ratio will be approximately
point two five when you use these parameters for your process. So just recall from these parameters
that we have kcu, that is also known as the ultimate gain, and p sub u, which represents
the ultimate period. The transfer functions are known we can use direct substitution,
but when we do this the controller transfer function must be a p only controller. Why?
Because the continuous cycling method takes advantage of the fact that the controller
has been set to bp only, and then from that we can get the ultimate gain and ultimate
period using direct substitution, which will then allow us to substitute into the Ziegler-Nichols
table for whether its a p only controller, a p(i) controller, or a p(id) controller.
So the last question to ask is what problems can be confronted by using this methodology?
The first problem with using continuous cycling is that it pushes the process to its stability
limit, and this can be very problematic if you have unstable processes that are naturally
unstable, or processes which have safety issues. So in other words fears of things running
away, so you don't want to push a process to its stability limit, particularly if its
not going to be very easy to get it back to its stability limit, so that can be a potential
problems with using this method. The second is that it is a trial and error method, which means
that it can be time consuming, and this is particularly true for processes that are sluggish,
or take a long time to respond. So if the process takes five or ten seconds in order
to show how a change in the controller gain makes the process more stable or less stable,
or gets to the desired undamped, then it might not so bad. However if a time constant, this
is on the order of hours or days, then using this methodology can take a very, very long
time, and there are a host of other techniques that can be used which can be more time efficient.
A third problem is that the quarter decay ratio is unacceptable. So there are many control
loops where having a decay ratio of one fourth is much too high for our process, and it would
better if it were something much lower. In some cases we even want to eliminate the possibility
of oscillations. So therefore the quarter decay ratio is which is what Ziegler and Nichols
based their desired values, the parameters they used, based on their research back in
the nineteen forties, it could mean that it might not work well for the process you have
now. So therefore Ziegler-Nichols, or the continous cycle method is not the be all,
end all in terms of methods to fine tune parameters, but it is certainly one method that is used.
Important point to remember here is that these tuning parameters represent just a start.
So often times the values which the Ziegler-Nichols table presented may not be sufficient in terms
of conducting this analysis. It could represent a nice start, but you are going to have to
modify potentially the controller gain, or the integral time constant, or the derivative
time constant. So this is not just the final answer there are usually is a bit more secondary
tuning that is conducted afterwards.