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The traditional proportional-integral-derivative (PID) algorithm forregulation suffers from a tradeoff: placing the sensor near the sample beingregulated ensures that its steady-state temperature matches the desiredsetpoint. However, the propagation delay (lag) between heater and sample canlimit the control bandwidth. Moving the sensor closer to the heater reduces thelag and increases the bandwidth but introduces offsets and drifts into thetemperature of the sample. Here, we explore the consequences of using twoprobes---one near the heater, one near the sample---and assigning the integralterm to the sample probe and the other terms to the heater probe. The\textit{split-PID} algorithm can outperform PID control loops based on onesensor.

Split PID control: two sensors can be better than one