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So we have a basic difference between analogue and digital controllers.
We shall refer to analogue controllers as "classical" controllers.
What are these basic differences? One of these differences relates to the types
of signals. the signals in used in the analogue control
systems are analogue. While signals in digital control signals are
discrete. Discrete refers to the fact that the signal
has specific levels. We can think of having discrete levels as
having a staircase; you can only place objects on the steps, not between steps.
If we had a staircase with 100 steps, and we wanted to place a ball on it, we can only
place the ball on one of the steps. While analogue signals can take on any of
an infinite number of values. The number of bits used in the digital control
system decides the number of available levels. With 8 bits, we can use any of 256 levels.
With 10 bits, we can use any of 1024 levels. So assuming the original analogue signal varies
between 0 and 10 V, and it was represented using 8 bits, then each level will span 10
V divided by 256, which is approximately around 40 mV.
The fact that the number of levels that can be represented is restricted, leads to an
error called "quantisation error". This occurs due to the fact that the original
signals has to be rounded up or down to the nearest level.
So this is the first of the main differences between the two types of control systems.
The next difference is caused by the fact that the digital control system will sample the inputs
at regular intervals. This leads to the signal being "continuous"
in the analogue control system and sampled in the digital control system.
So in an analogue control system we know the value of the signal at every instant in time.
In a digital controller, we "see" the signal at interval of time, T only.
The sample and hold process is applied to the original signal.
this means that only samples of the signal are stored inside the controller.
Whenever a time interval of T elapses, a sample of the input is acquired.
so, why did we need to move from analogue controllers to digital controllers?
(it is worth remembering that we move from analogue to discrete signals, and then we
move from discrete to digital). (signals inside the microcontroller or the
PC are stored as digital signals, such as 8 bits or 10 bits).
A signal is thus changed from analogue to a discrete signal, having a finite number
of levels. The signal is then converted from discrete
to a digital representation. The analogue to digital converter does this
conversion in one step; but it is useful to remember that the process involves the two
stages described above. The signal is stored as a series of ones and
zeros inside the microcontroller. In the real physical world that we live and
experience, signals are continuous. But we have been forced to convert to digital
because the signal processing and modern control systems are carried out by digital controllers.
T refers the sampling time in seconds. The value of T must be selected carefully
to suit the system being controlled. it is as if we have a shutter in front of
us. We open the shutter every T seconds, read
the world, store the values and close the shutter.
During this time, we convert the signal to digital and do all the other necessary processing.
Remember that we also need to send out to the real physical world the outputs.
so the results of the processing will produce output signals.
these will also be sent out to the physical system at times of T seconds.
The same shutter analogy can be used for the output signals.
T seconds in the world of microcontrollers is a relatively long time.
Once the inputs and outputs are transferred, plenty of time remains for the microcontroller
to do many other tasks. It is also worth remembering that the type of controller used is different between
the two systems. When building the controllers for analogue
control systems, it is customary to use operational amplifiers.
Even analogue computers (that are built using operational amplifiers) were used to solve
differential equations. Using operational amplifiers integrator and
differentiators can be built and used to implement blocks as the P, I and D blocks in controllers.
On the other hand, the basic control block in digital control systems is the microcontroller
or the microprocessor.