Page 276 - Programming Microcontrollers in C

Timer Operations 261

30000000
RPM =
Counts
Neither calculation is convenient in a microcontroller. The numerator
is larger than an int but smaller than a long. Both Counts and
RPM have a range that can be contained in an int. One would expect
that the conversion to time should be done on the input speed. That
way, the division would be done only once for each speed setting. If
the measured times were converted to RPM each time a time were
measured, the computer program would be loaded with complicated
divisions in its real time application portion. But let’s examine the
nature of the error with the different types of measures. Suppose the
input RPM were converted to time and the measurements were based
on time. Then the error signal, which is the difference between the
measured value and the desired value, would have a wrong sense.
That is if the motor is moving too slowly, then the error signal would
be negative, which would cause the motor to go even slower. If the
calculation were done based on RPM and the motor were going too
slow, the error signal would be positive. In this case, the control would
drive the motor faster which is the needed correction.
The difficulty with the time-based system could be solved by
using the negative value of the error signal for the feedback control.
A simple analysis will show the potential problem with this approach.
Suppose that we work with two counts, C and C . Let us use the
d m
value K for the constant in the above equation. Therefore,

 1 1 

e= C –C= K – 
d m
 RPM d RPM m 
The error signal is seen to be

 RPM – RPM 
e=K  m d 
 RPM * RPM m 
d
When the two speeds are nearly the same, this expression is very
nearly proporstional to the difference between the two speeds. However,
when one of the speeds deviates significantly from the other, it will
cause the resultant error signal to be less sensitive to difference than
would be expected. Also, there is the problem that occurs if the motor
is stopped and the error signal in that case is undefined.