Position and cadence tracking of a motorized FES-cycle with an unknown time-varying input delay using saturated FES control
Open accessAbstract
Neurological conditions (NCs) can have debilitating effects on an individual and can impede a person’s ability to perform activities of daily living. A common rehabilitation for individuals with NCs is the use of functional electrical stimulation (FES) to induce muscle contractions to perform a functional task, such as cycling. In this paper, we develop a closed-loop FES cycling controller that yields exponential cadence tracking. Contributions of the work result from the design and analysis innovations to compensate for switching between the different muscles and motor control inputs, compensating for the inherent uncertain nonlinear dynamics, compensating for the time-varying unknown input delay resulting from the complex electrochemical FES muscle torque production process, and compensating for saturation in the evoked torque due to fatigue, available muscle mass, or stimulation sensitivity. The performance of the developed control system was examined through a series of experiments on nine participants (five able-bodied and four with NCs). The experiments resulted in a cadence tracking error of −0.03 ± 1.69 RPM for non-informed passive able-bodied participants and −0.04 ± 1.98 RPM for the participants with NCs, for a desired cadence of 50 RPM. © 2022 Elsevier Ltd. All rights reserved.
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Differential equations with discontinuous right-hand side
Filippov, A. F. (1964) · Translations - American Mathematical Society/Translations · doi:10.1090/trans2/042/13 · Cited by 1,344 · see citing works
Delay Compensation for Nonlinear, Adaptive, and PDE Systems
Krstić, M. (2009) · Systems & control · doi:10.1007/978-0-8176-4877-0 · Cited by 1,064 · see citing works
Paden, B. A., & Sastry, S. (1987) · IEEE Transactions on Circuits and Systems · doi:10.1109/tcs.1987.1086038 · Cited by 748 · see citing works
Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems
Krstić, M. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2034923 · Cited by 393 · see citing works
Global Asymptotic Stabilization of Feedforward Systems With Delay in the Input
Mazenc, F., Mondié, S., & Francisco, R. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.828313 · Cited by 257 · see citing works
Yang, D., Li, X., & Qiu, J. (2019) · Nonlinear Analysis Hybrid Systems · doi:10.1016/j.nahs.2019.01.006 · Cited by 247 · see citing works
LaSalle-Yoshizawa Corollaries for Nonsmooth Systems
Fischer, N., Kamalapurkar, R., & Dixon, W. E. (2013) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2013.2246900 · Cited by 225 · see citing works
Self-citationSchutte, L. M., Rodgers, M. M., Zajac, F. E., et al. (1993) · IEEE Transactions on Rehabilitation Engineering · doi:10.1109/86.242425 · Cited by 184 · see citing works
Zhou, Q. F., Wu, C., & Shi, P. J. (2016) · Fuzzy Sets and Systems · doi:10.1016/j.fss.2016.11.002 · Cited by 154 · see citing works
Electromechanical delay revisited using very high frame rate ultrasound
Nordez, A., Gallot, T., Catheline, S., Guével, A., Cornu, C., & Hug, F. (2009) · Journal of Applied Physiology · doi:10.1152/japplphysiol.00221.2009 · Cited by 153 · see citing works
Hooker, S. P., Figoni, S., Rodgers, M., et al. (1992) · Archives of Physical Medicine and Rehabilitation · doi:10.5555/uri:pii:000399939290037w · Cited by 140
Predictor Feedback for Delay Systems: Implementations and Approximations
Karafyllis, I., & Krstic, M. (2017) · Systems & Control: Foundations & Applications · doi:10.1007/978-3-319-42378-4 · Cited by 135 · see citing works
Stability of switched nonlinear systems with delay and disturbance
Wang, Y., Sun, X., & Mazenc, F. (2016) · Automatica · doi:10.1016/j.automatica.2016.02.015 · Cited by 129 · see citing works
Hooker, S. P., Figoni, S. F., Rodgers, M. M., Glaser, R. M., Mathews, T., Suryaprasad, A. G., & Gupta, S. C. (1992) · PubMed · Cited by 124 · see citing works
Zhou, B., Lin, Z., & Duan, G. (2009) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.1525 · Cited by 106 · see citing works
Saturated control of an uncertain nonlinear system with input delay
Fischer, N., Dani, A. P., Sharma, N., & Dixon, W. E. (2013) · Automatica · doi:10.1016/j.automatica.2013.02.013 · Cited by 102 · see citing works
Self-citationPredictor-Based Compensation for Electromechanical Delay During Neuromuscular Electrical Stimulation
Sharma, N., Gregory, C. M., & Dixon, W. E. (2011) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2011.2166405 · Cited by 96 · see citing works
Self-citationBellman, M. J., Downey, R. J., Parikh, A., & Dixon, W. E. (2016) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2016.2527716 · Cited by 89 · see citing works
Self-citationZhou, B., & Lin, Z. (2011) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2011.2143170 · Cited by 88 · see citing works
Feedback linearization based predictor for time delay control of a high-DOF robot manipulator
Bagheri, M., Naseradinmousavi, P., & Krstić, M. (2019) · Automatica · doi:10.1016/j.automatica.2019.06.037 · Cited by 62 · see citing works
Downey, R. J., Mérad, M., Gonzalez, E. J., & Dixon, W. E. (2016) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2016.2626471 · Cited by 59 · see citing works
Self-citationCycling device powered by the electrically stimulated muscles of paraplegics
Pons, D. J., Vaughan, C. L., & Jaros, G. G. (1989) · Medical & Biological Engineering & Computing · doi:10.1007/bf02442162 · Cited by 57 · see citing works
Ferrante, S., Pedrocchi, A., Ferrigno, G., et al. (2008) · Virtual Community of Pathological Anatomy (University of Castilla La Mancha) · Cited by 50 · see citing works
Isometric Torque Control for Neuromuscular Electrical Stimulation With Time-Varying Input Delay
Mérad, M., Downey, R. J., Obuz, S., et al. (2015) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2015.2470637 · Cited by 44 · see citing works
Predictor-based tracking for neuromuscular electrical stimulation
Karafyllis, I., Malisoff, M. A., de Queiroz, M. S., Krstić, M., & Yang, R. (2014) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.3211 · Cited by 40 · see citing works
Asynchronous switching for switched nonlinear input delay systems with unstable subsystems
Wang, Y., Niu, B., Wu, B., et al. (2018) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2018.01.033 · Cited by 40 · see citing works
Downey, R. J., Cheng, T.-H., Bellman, M. J., & Dixon, W. E. (2016) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2016.2543699 · Cited by 39 · see citing works
Self-citationModel-Free Neuromuscular Electrical Stimulation by Stochastic Extremum Seeking
Paz, P., Oliveira, T. R., Pino, A. V., et al. (2019) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2019.2892924 · Cited by 37 · see citing works
Controlling the Cadence and Admittance of a Functional Electrical Stimulation Cycle
Cousin, C. A., Rouse, C. A., Duenas, V. H., & Dixon, W. E. (2019) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2019.2914579 · Cited by 34 · see citing works
Self-citationStability and Robustness Analysis for Switched Systems with Time-Varying Delays
Mazenc, F., Malisoff, M., & Özbay, H. (2018) · SIAM Journal on Control and Optimization · doi:10.1137/16m1104895 · Cited by 26 · see citing works
Continuous Discrete Sequential Observers for Time-Varying Systems Under Sampling and Input Delays
Mazenc, F., & Malisoff, M. (2019) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2019.2930676 · Cited by 23 · see citing works
Characterization of the Time-Varying Nature of Electromechanical Delay During FES-Cycling
Allen, B. C., Stubbs, K. J., & Dixon, W. E. (2020) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2020.3017444 · Cited by 18 · see citing works
Self-citationRobust Cadence Tracking for Switched FES-Cycling With an Unknown Time-Varying Input Delay
Allen, B. C., Cousin, C. A., Rouse, C. A., & Dixon, W. E. (2021) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2021.3070189 · Cited by 18 · see citing works
Self-citationObuz, S., Duenas, V. H., Downey, R. J., Klotz, J. R., & Dixon, W. E. (2019) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2019.2926945 · Cited by 16 · see citing works
Self-citationExtremum Seeking-based Adaptive PID Control applied to Neuromuscular Electrical Stimulation
Oliveira, T. R., COSTA, L. R., Pino, A. V., et al. (2019) · Anais da Academia Brasileira de Ciências · doi:10.1590/0001-3765201820180544 · Cited by 11 · see citing works
Cadence Tracking for Switched FES Cycling with Unknown Input Delay
Allen, B. C., Cousin, C. A., Rouse, C. A., & Dixon, W. E. (2019) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc40024.2019.9029696 · Cited by 10 · see citing works
Self-citationAllen, B. C., Stubbs, K. J., & Dixon, W. E. (2020) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2020.12.2737 · Cited by 9 · see citing works
Self-citationFifteen Papers on Differential Equations
Азбелев, Н. В., Caljuk, Z. B., Dezin, A. A., et al. (1964) · Translations - American Mathematical Society/Translations · doi:10.1090/trans2/042 · Cited by 8 · see citing works
Robust Power and Cadence Tracking on a Motorized FES Cycle with an Unknown Time-Varying Input Delay
Allen, B. C., Stubbs, K. J., & Dixon, W. E. (2020) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc42340.2020.9304066 · Cited by 6 · see citing works
Self-citationAllen, B. C., Stubbs, K. J., & Dixon, W. E. (2021) · Disability and Rehabilitation Assistive Technology · doi:10.1080/17483107.2021.1878295 · Cited by 4 · see citing works
Self-citationSaturated Control of a Switched FES-Cycle with an Unknown Time-Varying Input Delay
Allen, B. C., Stubbs, K. J., & Dixon, W. E. (2020) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2021.04.212 · Cited by 2 · see citing works
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Research works printed but not linked: 1
- Allen, B. C., Cousin, C., Rouse, C., & Dixon, W. E. (2019b). Cadence Tracking for Switched FES Cycling with Unknown Input Delay. In Proc. IEEE conf. decis. control (pp. 60–65). Nice, Fr. · DOI
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- Authors
- Allen, B. C., Stubbs, K. J., & Dixon, W. E.
- Affiliations
- Auburn University (US)
- University of Florida (US)
- Corresponding author
- Allen, Brendon C.
- Venue
- Automatica
- Publisher
- Elsevier BV
- Published
- 2022-05
- Volume
- 139
- Pages
- 110176
- ISSN
- 0005-1098 (ISSN-L)
- OpenAlex
- W4213452388
- Cited by
- 8
- References
- 41
- Citations by year
- 2026: 1 · 2024: 2 · 2023: 1 · 2022: 4
- FWCI
- 0.71
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/legal/tdmrep-license (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (am, 298 d)
- doi.org/10.15223/policy-017 (stm-asf)
- doi.org/10.15223/policy-037 (stm-asf)
- doi.org/10.15223/policy-012 (stm-asf)
- doi.org/10.15223/policy-029 (stm-asf)
- doi.org/10.15223/policy-004 (stm-asf)
- Locations
- Automatica (acceptedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Health Sciences › Medicine › Rehabilitation › Stroke Rehabilitation and Recovery
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- functional electrical stimulation, FES cycling, time-varying input delay, saturated control, neurological disorders, rehabilitation, muscle fatigue, exponential tracking, feedback control, nonlinear dynamics compensation
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