Heart rate control using first- and second-order models during treadmill exercise.

Heart rate control using first- and second-order models was compared using a novel control design strategy which shapes the input sensitivity function. Ten participants performed two feedback control test series on a treadmill with square wave and constant references. Using a repeated measures, counterbalanced study design, each series compared controllers C1 and C2 based on first- and second-order models, respectively. In the first series, tracking accuracy root-mean-square tracking error (RMSE) was not significantly lower for C2: 2.59 bpm vs. 2.69 bpm (mean, C1 vs. C2), p = 0.79. But average control signal power was significantly higher for C2: $11.29\times {10}^{-4}{m}^2/s^2$ vs. $27.91\times {10}^{-4}{m}^2/s^2$ , $p=3.1\times {10}^{-10}$ . In the second series, RMSE was also not significantly lower for C2: 1.99 bpm vs. 1.94 bpm, p = 0.39; but average control signal power was again significantly higher for C2: $2.20\times {10}^{-4}{m}^2/s^2$ vs. $2.78\times {10}^{-4}{m}^2/s^2$ , p = 0.045. The results provide no evidence that controllers based on second-order models lead to better tracking accuracy, despite the finding that they are significantly more dynamic. Further investigation using a substantially larger sample size is warranted.