Experimental Heart Rate Regulation in Cycle-Ergometer Exercises

Abstract

The heart rate can be effectively used as a measure of the exercise intensity during long duration cycle-ergometer exercises: precisely controlling the heart rate (HR) becomes crucial especially for athletes or patients with cardiovascular/obesity problems. The aim of this letter is to experimentally show how the nonlocal and nonswitching nonlinear control that has been recently proposed in the literature for the HR regulation in treadmill exercises can be effectively applied to cycle-ergometer exercises at constant cycling speed. The structure of the involved nonlinear model for the HR dynamics in cycle-ergometer exercises is mathematically inspired by the structure of a recently identified and experimentally validated nonlinear model for the HR dynamics in treadmill exercises: the role played by the treadmill speed is played here by the work load while the zero speed case for the treadmill exercise is here translated into the cycling operation under zero work load. Experimental results not only validate the aforementioned nonlinear model but also demonstrate the effectiveness--in terms of precise HR regulation--of an approach which simply generalizes to the nonlinear framework the classical proportional-integral control design. The possibility of online modifying the HR reference on the basis of the heart rate variability (HRV) is also suggested and experimentally motivated.

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

“…It can readily be shown that the nonlinear structure NL (Figure 1(b)) is identical to a linear PI compensator augmented with the static square-root compensation function (see Figure 1(c)), as proposed in the original references for this approach (Paradiso et al, 2013;Scalzi et al, 2012). To see this, consider the transfer function C PI from e to x in Figure 1…”

“…An alternative control approach based on the v 2 -nonlinear model from Cheng et al (2008) was developed and applied to both treadmill and cycle-ergometer exercise: see Scalzi, Tomei, and Verrelli (2012) and Paradiso, Pietrosanti, Scalzi, Tomei, and Verrelli (2013), respectively. This method countered the plant nonlinearity using the inverse nonlinearity, that is, the square-root function √ .…”

Heart rate regulation during cycle-ergometer exercise via event-driven biofeedback

“…Heart rate (HR) can be used as an index to monitor the exercise intensity [18]. This fact makes it simpler to develop a control system to steer the human HR to a predetermined and individual exercise prescription, represented as a target HR profile, instead of directly employing the exercise intensity in kJoules or Watts and exercise rate (ER) as control parameters.…”

Repetitive Learning Control Design for LED Light Tracking

“…with a robust control algorithm in [26] and its modifications in [23]. Although the aforementioned papers constitute relevant solutions to general light control problems, when tracking of desired luminous color and intensity reference signals is repeatedly considered in the presence of completely uncertain dynamics-with the aim of reproducing a lighting profile similar to the one corresponding to a day cycle (in real world or even in virtual set scenarios) or, more interestingly, with the aim of benefiting from chromotherapy repetitive lighting profiles-possibly complex periodic output reference signals (with known period) naturally arise and repetitive learning control techniques 2 can be successfully used (see [8], [19] for recent theoretical results and [6], [7], [20], [21] for recent significant applications). In contrast to general nonlearning ones, repetitive learning controls are not model-based and actually use, in a repetitive uncertain scenario, the richness of information which error signals possess from previous executions [2] and [9]: while classical robust controllers can only theoretically achieve, through a proper choice of the control gains, exponential convergence of the output regulation or tracking error into residual sets whose size can be made arbitrarily small, repetitive learning controls are additionally able to guarantee asymptotic convergence to zero of the output regulation or tracking error in the presence of uncertainties.…”