Feedback control of heart rate during treadmill exercise with dead time modelling and compensation

We investigated whether inclusion of dead time in heart rate (HR) response models gives better fidelity and whether feedback controllers that include dead time compensation give more dynamic control and improved HR control accuracy. Dynamic models with and without dead time were obtained from system identification experiments with 30 participants. Feedback controllers with and without dead time compensation were compared. There was a small yet significant improvement in model fit for first-order models with dead time (P1D) compared to those without (P1): the mean fit was 56.1 % vs. 55.4 %, P1D vs. P1, p=0.0043. Root-mean-square tracking error (RMSE) was slightly, but not significantly, lower for controllers with dead-time compensation (C1D) than for those without (C1): the mean RMSE was 2.14 bpm vs. 2.20 bpm, C1D vs. C1, p=0.27. Average control signal power (P∇u) was significantly higher for controllers with dead-time compensation: median P∇u was 2.32×10−4 m2 /s2 vs. 2.16×10−4 m2 /s2, C1D vs. C1, p=0.046. Dead time modelling gave significantly better fidelity, albeit the effect size was small. Feedback control with dead time compensation gave a significantly more dynamic control signal and slightly, but not significantly, better tracking accuracy.