31 2 Automated oxygen control in preterm infants, how does it work and what to expect Proportional-integral-derivative Proportional-integral-derivative (PID) control is a longstanding mathematical approach widely used in industry (e.g. automotive cruise-control, thermostats). The proportional term reflects the current error; the integral term reflects the sum of previous errors; and the derivative term accounts for the direction the SpO2 error is heading (Figure 2). The computation includes a unique coefficient for each of the P, I and D terms, thus balancing their relative influence. The sum of the P, I and D terms – which may be opposite in sign – determines the magnitude of the change in FiO2. Although PID control is more abstract and its function more difficult to understand, it makes use of the breadth of available oxygenation information. However, the choice of PID coefficients is vital, as inappropriate coefficients could lead to major fluctuations or oscillations in oxygen saturation and result in oxygen control that is worse than manual titration.21 Oxygen saturation trend 100 90 80 70 Time SpO Proportional error - 0.08 0.005 - 0.01 sum baseFiO PID Terms new FiO Integral Derivative slope Figure 2: The three components of the PID algorithm hidden in the oxygen saturation trend.

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