  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
\textit{split-PID} algorithm can outperform PID control loops based on one
sensor.
