Hello again from KEB America. In a past video we talked about closed-loop
control. In this video we'll go into a little bit more detail on the PI
controller used in that closed-loop speed control.
How does a PI controller work in a VFD?
So you might remember from our past video, this is a basic block
diagram of closed-loop control. On the input side you have the command speed,
and on the output side you have the actual output to the motor.
The feedback includes the encoder feedback which can be an incremental
or resolver for example. And then you also have the motor model,
which is the drives electronic equivalent to the motor.
Both of these are fed to the speed control which is
the PI controller we'll talk about today. And then their current control,
which takes all of that feedback and calculates what the output to the motor
has to be.
The PI or proportional and integral controller is a commonly used
method in control systems to account for error between the command and actual
values. In a KEB Drive, this actual value can be from encoder feedback or using
our SCL control. The first step of the PI controller is to calculate the error at
a certain point in time. This is simply just the command speed minus the actual speed.
This error is then fed into the full PI control algorithm.
Now the PI controller can be broken up into its two respective parts.
the first half is the simpler of the two and is the proportional
The second and slightly more complex of the two
is the integral portion.
Now let's focus on the
proportional section in a little bit more detail. The first part of the
proportional is the bias. In a standard control system the bias will be simply
set to your desired output value on startup.
Thus with no error, your output value will be exactly equal to your command value.
The second portion begins with the KP or proportional controller gain.
This is a programmable value in the KEB Drive.
This is multiplied by your error term.
So a larger error has more effect on the output and importantly a larger
controller gain also has a larger effect on the control.
So with a higher gain
you'll more quickly adapt to error in the system.
Now we'll look at the slightly more complex integral portion of the control algorithm.
This still starts with your proportional control gain but then it's divided by
your integral time constant. This value is also programmable in the drive and
it's important to note that because you're dividing by that term, a smaller
value will have a harder effect on the control. It's also important to note that
these two values influence each other. So it may take some trial and error while
tuning your drive to get them just right.
These two values are then multiplied by
the integral sum of the error over time. The important part about this is that
because it's the entire sum of the air across the run of the system it's not
just the single air at a point in time.
So no matter what as long as there has
been error it'll be adjusting the control.
This is why the integral term is used to offset long term error in the system.
Next we'll see how the PI controller is implemented by looking at a graph of the
command and actual speed.
So in this graph you can see in pink the command
speed jumped immediately from zero to a thousand rpm and then stay constant.
However, due to real-world factors, such as a high inertia or current limits,
your orange actual speed won't be able to perfectly follow the command speed.
Thus an error is introduced.
So for instance at this point in time the error,
we'll call this time 5 seconds...
So at error at time 5, is roughly 500 rpm.
This error is then fed back into your
PI control algorithm and is multiplied by the proportional control factor
The integral control portion is a little bit more difficult to calculate
Because we can't simply just subtract the command speed versus the actual speed.
Instead, we must take the integral from time 0 to the current point in time of the control.
We can get a rough estimate of this by adding up the area between the command
and actual speeds in our graph.
Now for a rough estimate of this graph,
we can imagine this is time 2 and then at the very end when it crosses here is time 8.
Thus, we have a 6 second time here and then an error of a thousand. If we
roughly guess that it's half of a square, we get an error of 3000. We would
do the same thing up here to calculate the error. Your error would actually be
negative. So if we just roughly ballpark that this is say a quarter of the size
of that area, your error will equal to negative 750. So at this point in time
your error would be 300 minus 750 for your integral term. So with this graph
you can see how the error is roughly calculated and then fed back into your
PI control algorithm. The PI controller is a robust yet fast responding closed
loop system. This allows the drive - by only adjusting two parameters - to achieve
fast acting response to error between the command and actual speed, while also
adjusting for long term error in the system. This allows the drive to achieve
precise speed control of a motor.
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