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      Robust control of heart rate for cycle ergometer exercise

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          Abstract

          The objective was to assess the performance and robustness of a novel strategy for automatic control of heart rate (HR) during cycle ergometry. Control design used a linear plant model and direct shaping of the closed-loop input-sensitivity function to achieve an appropriate response to disturbances attributable to broad-spectrum heart rate variability (HRV). The controller was evaluated in 73 feedback control experiments involving 49 participants. Performance and stability robustness were analysed using a separately identified family of 73 plant models. The controller gave highly accurate and stable HR tracking performance with mean root-mean-square tracking error between 2.5 beats/min (bpm) and 3.1 bpm, and with low average control signal power. Although plant parameters varied over a very wide range, key closed-loop transfer functions remained invariant to plant uncertainty in important frequency bands, while infinite gain margins and large phase margins (> 62 ) were preserved across the whole plant model family. Highly accurate, stable and robust HR control can be achieved using LTI controllers of remarkably simple structure. The results highlight that HR control design must focus on disturbances caused by HRV. The input-sensitivity approach evaluated in this work provides a transparent method of addressing this challenge.

          Graphical Abstract

          Heart rate control using a cycle ergometer

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          Nonlinear modeling and control of human heart rate response during exercise with various work load intensities.

          The first objective of this paper is to introduce a nonlinear system to model the heart rate (HR) response during and after treadmill walking exercise. The model is a feedback interconnected system that has components to describe the central and peripheral local responses to exercise and their interactions. The parameters of the model were experimentally identified from subjects walking on a treadmill at different speeds. The stability of the obtained nonlinear model was mathematically proven. The modeling results demonstrate that the proposed model can be useful in examining the cardiovascular response to exercise. Based on the nonlinear model, the second objective is to present a computer-controlled treadmill system for the regulation of HR during treadmill exercise. The proposed nonlinear controller consists of feedforward and feedback components. The designed control system was experimentally verified and the results demonstrated that the proposed computer-controlled treadmill system regulated the HR of the experimental subjects according to two different exercising HR profiles, indicating that it can play an important role in the design of exercise protocols for individuals.
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            Identification and control for heart rate regulation during treadmill exercise.

            This paper proposes a novel integrated approach for the identification and control of Hammerstein systems to achieve desired heart rate profile tracking performance for an automated treadmill system. For the identification of Hammerstein systems, the pseudorandom binary sequence input is employed to decouple the identification of dynamic linear part from input nonlinearity. The powerful epsilon-insensitivity support vector regression method is adopted to obtain sparse representations of the inverse of static nonlinearity in order to obtain an approximate linear model of the Hammerstein system. An Hinfinity controller is designed for the approximated linear model to achieve robust tracking performance. This new approach is successfully applied to the design of a computer-controlled treadmill system for the regulation of heart rate during treadmill exercise. Minimizing deviations of heart rate from a preset profile is achieved by controlling the speed of the treadmill. Both conventional proportional-integral-derivative (PID) control and the proposed approaches have been employed for the controller design. The proposed algorithm achieves much better heart rate tracking performance.
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              Heart-rate recommendations: transfer between running and cycling exercise?

              With the expanding use of portable heart rate (HR) monitors in endurance sports, HR is increasingly used as a marker for exercise intensity. Hereby, HR at the so-called individual anaerobic threshold (IAT) is one possible reference point. However, once determined, it is often attempted to apply HR recommendations from one type of ergometry to different kinds of exercises. We examined whether HR at IAT and at 4 mmol x l -1 blood lactate is predictable from cycling to running and vice versa. Data of 371 subjects (304 male, 67 female) were analyzed. All subjects underwent an incremental test on a treadmill (TR, starting speed 6 or 8 km x h -1, increments 2 km x h -1 every 3 min) and on a bicycle ergometer (BE, start at 50 Watt, increments 25 or 50 Watt every 3 min). IAT was determined at a net increase of lactate concentration of 1 - 5 mmol x l -1 above lactate concentration at lactate threshold for running (as in: Med Sci Sports Exerc 1998, 30 (10); 1552 - 1557) and 1.0 mmol x l -1 for cycling. A maximum time span of three weeks was allowed between the tests. We found that heart rate at IAT or at 4 mmol x l -1 blood lactate did not correlate between cycling and running. A sports specific test seems to be a prerequisite for reliable heart rate recommendations.
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                Author and article information

                Contributors
                kenneth.hunt@bfh.ch
                Journal
                Med Biol Eng Comput
                Med Biol Eng Comput
                Medical & Biological Engineering & Computing
                Springer Berlin Heidelberg (Berlin/Heidelberg )
                0140-0118
                1741-0444
                30 August 2019
                30 August 2019
                2019
                : 57
                : 11
                : 2471-2482
                Affiliations
                GRID grid.424060.4, ISNI 0000 0001 0688 6779, Institute for Rehabilitation and Performance Technology, Division of Mechanical Engineering, Department of Engineering and Information Technology, , Bern University of Applied Sciences, ; Burgdorf, CH-3400 Switzerland
                Author information
                http://orcid.org/0000-0002-6521-9455
                Article
                2034
                10.1007/s11517-019-02034-6
                6828638
                31471785
                89ca3a5e-e02e-47df-b010-c36f51663efe
                © The Author(s) 2019

                Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

                History
                : 25 March 2019
                : 17 August 2019
                Categories
                Original Article
                Custom metadata
                © International Federation for Medical and Biological Engineering 2019

                Biomedical engineering
                heart rate control,heart rate dynamics,heart rate variability,system identification,physiological control,cycle ergometers

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