Fix inaccuracy in comparison of elapsed time (dt)

The inaccuracy is small, but it becomes visible when operating
within tight margins of the `sample_time`, like for example, when
working with a simulated clock in a test environment.

Specifically, `dt` cannot be exactly zero because it is used as
a divider. When it would be zero, it is set to a very small,
conventional value instead, that I've renamed MIN_DT for clarity.

When `dt == MIN_DT` it is really representing the case when it
would be zero. Not taking that value into consideration when
comparing the elapsed time since last computation does effectively
increase `sample_time` by `MIN_DT`. It is not a lot, but it is not
accurate either.

By correcting the comparison, very precise use of `sample_time`
becomes possible. One concrete use case is using simulated time
for testing.

Author: gonzalo-bulnes

simple_pid/pid.py

@@ -12,6 +12,8 @@ def _clamp(value, limits):
 class PID(object):
     """A simple PID controller."""
 
+    MIN_DT = 1e-16
+
     def __init__(
         self,
         Kp=1.0,
@@ -114,11 +116,15 @@ def __call__(self, input_, dt=None):
 
         now = self.time_fn()
         if dt is None:
-            dt = now - self._last_time if (now - self._last_time) else 1e-16
+            dt = now - self._last_time if (now - self._last_time) else PID.MIN_DT
         elif dt <= 0:
             raise ValueError('dt has negative value {}, must be positive'.format(dt))
 
-        if self.sample_time is not None and dt < self.sample_time and self._last_output is not None:
+        if (
+            self.sample_time is not None
+            and dt < self.sample_time - PID.MIN_DT
+            and self._last_output is not None
+        ):
             # Only update every sample_time seconds
             return self._last_output