The traditional proportional-integral-derivative (PID) algorithm for regulation suffers from a tradeoff: placing the sensor near the sample being regulated ensures that its steady-state temperature matches the desired setpoint. However, the propagation delay (lag) between heater and sample can limit the control bandwidth. Moving the sensor closer to the heater reduces the lag and increases the bandwidth but introduces offsets and drifts into the temperature of the sample. Here, we explore the consequences of using two probes—one near the heater, one near the sample—and assigning the integral term to the sample probe and the other terms to the heater probe. The split-PID algorithm can outperform PID control loops based on one sensor.

1.
J.
Bechhoefer
,
Rev. Mod. Phys.
77
,
783
(
2005
).
2.
K. J.
Åström
and
R. M.
Murray
,
Feedback Systems: An Introduction for Scientists and Engineers
(
Princeton University Press
,
2008
).
3.
S.
Skogestad
and
I.
Postlethwaite
,
Multivariable Feedback Control
(
John Wiley and Sons
,
2005
).
4.
J.
Bechhoefer
,
Y.
Deng
,
J.
Zylberberg
,
C.
Lei
, and
Z.-G.
Ye
,
Am. J. Phys.
75
,
1046
(
2007
).
5.
K. J.
Åström
and
B.
Wittenmark
,
Adaptive Control
, 2nd ed. (
Dover Publications
,
2008
).
You do not currently have access to this content.