Feedback control of heart rate during treadmill exercise based on a two-phase response model

This work investigated automatic control of heart rate during treadmill exercise. The aim was to theoretically derive a generic feedback design strategy that achieves a constant input sensitivity function for linear, time-invariant plant models, and to empirically test whether a compensator C(2) based on a second-order model is more dynamic and has better tracking accuracy than a compensator C(1) based on a first-order model. Twenty-three healthy participants were tested using first and second order compensators, C(1) and C(2), respectively, during 35-minute bouts of constant heart rate treadmill running. It was found that compensator C(2) was significantly more accurate, i.e. it had 7% lower mean root-mean-square tracking error (1.98 vs. 2.13 beats per minute, p = 0.026), and significantly more dynamic, i.e. it had 17% higher mean average control signal power (23.4 × 10(−4) m(2)/s(2) vs. 20.0 × 10(−4) m(2)/s(2), p = 0.011), than C(1). This improvement likely stems from the substantially and significantly better fidelity of second-order models, compared to first order models, in line with classical descriptions of the different phases of the cardiac response to exercise. These outcomes, achieved using a treadmill, are consistent with previous observations for the cycle ergometer exercise modality. In summary, whenever heart rate tracking accuracy is of primary importance and a more dynamic control signal is acceptable, the use of a compensator based on a second-order nominal model is recommended.