Page 284 - Programming Microcontrollers in C

Timer Operations 269

close the loop and regulate the motor speed. The relation that can be
derived from the above data is

RPM + 12528
PWM_count =
7.875
This expression is accurate to about 1% across the range of
interest. The measured data is the input capture count, which we will
call p. What we must do is to calculate a new value for the
PWM_count from a measured p. An error in p is called p and this
expression means a change in p. The PWM_count will be designated
as pc and also means a change in pc. We shall now attempt to arrive
at an equation that expresses the necessary change in pc to correct
for an error in p. The error in p is the difference between the desired
cycle time and the measured cycle time. RPM in the above expression
is converted to cycle time p by noting that the RPM is 60000 / shaft
cycle time in milliseconds, and that the clock is ticking 500 times per
millisecond. Therefore, we have
1  12528 + 60000* 500 
p=  
c
7.875  p 
If there is a error in the cycle time say, ∆p, then the change in
pc, ∆pc, is seen to be

3809500
p + ∆p =1591+
c c
p+ ∆p
This expression, after some simplification and approximation
reduces to

∆p
–
∆p= 3809500 +
c 2 (5-1)
p
This value calculated by the above expression will be used to change
the PWM_count that drives the motor. The data contained in
measured_period are placed there by the input capture interrupt
service routine. It is assumed that the data there are always current.
The calculation to determine the PWM_count correction is
substantial. We shall use this approach here to determine the
correction, but recognize that there is another approach that probably
requires less total calculation. This approach is to use a lookup table.