Abstract
ABSTRACTHeart rate can be used to define exercise intensity; feedback control systems for treadmills which automatically adjust speed to track arbitrary heart rate target profiles are therefore of interest. The aim of this study was to compare linear (L) and nonlinear (NL) controllers using quantitative performance measures. Sixteen healthy male subjects participated in the experimental L vs. NL comparison. The linear controller was calculated using a direct analytical design that employed an existing approximate plant model. The nonlinear controller had the same linear component, but it was augmented using static plant-nonlinearity compensation. At moderate-to-vigorous intensities, no significant differences were found between the linear and nonlinear controllers in mean RMS tracking error (2.34 vs. 2.25 bpm [L vs. NL], p=0.26) and average control signal power (51.7 vs. m2/s2, p=0.16), but dispersion of the latter was substantially higher for NL (range 45.2 to 56.8 vs. 30.7 to m2/s2, L vs. NL). At low speed, RMS tracking errors were similar, but average control signal power was substantially and significantly higher for NL (28.1 vs. m2/s2 [L vs. NL], p<0.001). The performance outcomes for linear and nonlinear control were not significantly different for moderate-to-vigorous intensities, but NL control was overly sensitive at low running speed. Accurate, stable and robust overall performance was achieved for all 16 subjects with the linear controller. This points to disturbance rejection of very-low-frequency heart rate variability as the overriding challenge for design of heart rate controllers.
Highlights
Fitness training programmes often use heart rate to describe exercise intensity (Garber et al, 2011; Pescatello et al, 2014)
There were no significant differences in the primary outcomes root-mean-square tracking error (RMSE) and P v for the linear (L) and nonlinear (NL) controllers over the main evaluation interval 420 ≤ t ≤ 1800 s: the mean RMS tracking errors were, respectively, 2.34 and 2.25 bpm (p = 0.26, Table 2); the means of the average control signal powers were 51.7 and 60.8 × 10−4 m2/s2 (p = 0.16, Table 2)
Dispersion of RMSE values for the L and NL cases was similar (Table 2, where similar standard deviations can be observed for RMSE, and Figure 3(a)), but the dispersion of P v values was substantially and strikingly higher for the nonlinear controller: the ranges for P v were 45.2 to 56.8 vs. 30.7 to 108.7 × 10−4 m2/s2, L vs. NL (Figure 3(b)); the standard deviations of P v were 3.3 vs. 24.1 × 10−4 m2/s2 (Table 2 and Figure 3(b))
Summary
Fitness training programmes often use heart rate to describe exercise intensity (Garber et al, 2011; Pescatello et al, 2014). It has recently been proposed that the principal design issue for feedback control of heart rate is disturbance rejection of very-low-frequency heart rate variability, VLFHRV (Hunt & Fankhauser, 2016; Sassi et al, 2015): accurate tracking of the heart rate target is important, but, at the same time, the control signal must not be excited too strongly in frequency bands where changes in the treadmill speed would be perceptible to and unacceptable for the runner To address this challenge, a new approach was developed based on shaping of the plant input sensitivity function; in an experimental evaluation with 30 subjects, it was shown that this linear time-invariant approach was able to directly address the principal design challenge of VLF-HRV disturbance rejection and delivered robust and accurate tracking with a smooth, low-power control signal in all subjects (Hunt & Fankhauser, 2016). Controller calculation was based upon a single, approximate linear plant model that was not specific to any of the subjects tested, but was obtained previously in a separate system identification study (Hunt, Fankhauser, & Saengsuwan, 2015)
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