Comparison of linear and nonlinear feedback control of heart rate for treadmill running

Abstract

Heart 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. 60.8 × 10-4 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 108.7 × 10-4 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. 138.7 × 10-4 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.