Heart rate control during treadmill exercise using input-sensitivity shaping for disturbance rejection of very-low-frequency heart rate variability

Background Automatic and accurate control of heart rate (HR) during treadmill exercise is important for prescription and implementation of training protocols. The principal design issue for feedback control of HR is to achieve disturbance rejection of very-low-frequency heart rate variability (VLF-HRV) with a level of control signal activity (treadmill speed) which is sufficiently smooth and acceptable to the runner. This work aimed to develop a new method for feedback control of heart rate during treadmill exercise based on shaping of the input sensitivity function, and to empirically evaluate quantitative performance outcomes in an experimental study. Methods Thirty healthy male subjects participated. 20 subjects were included in a preceding study to determine an approximate, average nominal model of heart rate dynamics, and 10 were not. The design method guarantees that the input sensitivity function gain monotonically decreases with frequency, is therefore devoid of peaking, and has a pre-specified value at a chosen critical frequency, thus avoiding unwanted amplification of HRV disturbances in the very-low-frequency band. Controllers were designed using the existing approximate nominal plant model which was not specific to any of the subjects tested. Results Accurate, stable and robust overall performance was observed for all 30 subjects, with a mean RMS tracking error of 2.96 beats/min and a smooth, low-power control signal. There were no significant differences in tracking accuracy or control signal power between the 10 subjects who were not in the preceding identification study and a matched subgroup of subjects who were (respectively: mean RMSE 2.69 vs. 3.28 beats/min, p = 0.24; mean control signal power 15.62 vs. 16.31 × 10 −4 m 2 /s 2 , p = 0.37). Substantial and significant reductions over time in RMS tracking error and average control signal power were observed. Conclusions The input-sensitivity-shaping method provides a direct way to address the principal design challenge for HR control, namely disturbance rejection in relation to VLF-HRV, and delivered robust and accurate tracking with a smooth, low-power control signal. Issues of parametric and structural plant uncertainty are secondary because a simple approximate plant model, not specific to any of the subjects tested, was sufficient to achieve accurate, stable and robust heart rate control performance.