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

Figures

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  Figure 1.. Block diagram of control structure for this study. Po(s) is the plant model, C(s) is the feedback compensator, and Cpf(s) is a reference prefilter. The controlled variable (HR) is y, u is the control signal (treadmill speed target), d is a disturbance term than mainly comprises heart rate variability, and n models measurement noise. r is the reference/target HR signal and r′ is the filtered HR reference.

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  Figure 2.. Closed-loop frequency responses for the first test series: input-sensitivity function (Uo), sensitivity function (So) and complementary sensitivity function (To); each function is plotted for compensators C1 and C2. Red dots mark the −3 dB cutoff frequency (bandwidth) for each transfer function. Vertical dashed lines distinguish four frequency bands of HRV (Shaffer & Ginsberg, 2017): ultra-low frequency (ULF, ≤0.003¯ Hz), very-low frequency (VLF, 0.003¯–0.04 Hz), low frequency (LF, 0.04–0.15 Hz) and high frequency (HF, 0.15–0.4 Hz).

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  Figure 3.. Test protocol with HR-reference profiles (HR∗). Upper plot: profile of reference HR signal for the first test series (square wave). Lower plot: heart rate target for the second test series (constant). (a) Reference HR signal for first test series and (b) Reference HR signal for second test series.

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  Figure 4.. The computer-controlled treadmill used in this study.

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  Figure 5.. Measurements with RMSE closest to the mean in the two test series for the two compensator types. For each figure, the upper plot shows the reference heart rate signal (HR∗, black dashed line), the measured heart rate (HR, red line) and the nominal (simulated) heart rate response (HRnom, black line); the lower plots show the control signal, i.e. treadmill speed. The evaluation period for each measurement is denoted by a red horizontal bar. Participant number is denoted as P03, etc. (a) First test series, C1, P08. (b) First test series, C2, P09. (c) Second test series, C1, P03 and (d) Second test series, C2, P03.

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  Figure 6.. Dispersion of samples for RMSE and P∇u from the two test series, with 10 sample pairs from the first test series (Figure 6(a,b)) and eight sample pairs from the second series (Figure 6(c,d)). In each figure, blue and red dots are the outcomes with compensators C1 and C2, respectively, green lines connect sample pairs for each participant, and red bars mark the sample means (given numerically in Tables 2 and 3). D denotes the difference between paired samples (C2–C1) and MD (red horizontal bar) the mean difference. The 95% confidence intervals (CIs) are marked in blue. For P∇u, the value 0 is outwith the 95% CI in both cases, indicating a significantly higher value for C2 (the notation * signifies p<0.05 and ∗∗∗∗ means p<0.0001). For RMSE, the value 0 is inside the 95% CI in both cases, indicating that the values for C2 are not significantly lower (p>0.05). (a) RMSE for first test series. (b) P∇u for first test series. (c) RMSE for second test series and (d) P∇u for second test series.