Analysis of the Delayed Central Nervous System Action in the Regulation of a Third-order Muscle-Tendon Model

This paper presents the analysis of a third-order linear time-invariant delay differential equation representing the regulation of a muscle-tendon system. The Central Nervous System action is modeled as a delayed proportional-derivative controller exploiting the multiplicity-induced-dominancy property. The stability analysis is illustrated via the software P3δ.

[1]  T. Dao,et al.  Biomechanics of the Musculoskeletal System , 2014 .

[2]  L. Stark,et al.  Muscle models: What is gained and what is lost by varying model complexity , 1987, Biological Cybernetics.

[3]  D. Piovesan,et al.  A Third-Order Model of Hip and Ankle Joints During Balance Recovery: Modeling and Parameter Estimation , 2019, Journal of Computational and Nonlinear Dynamics.

[4]  Silviu-Iulian Niculescu,et al.  On the Dominancy of Multiple Spectral Values for Time-delay Systems with Applications , 2018 .

[5]  Silviu-Iulian Niculescu,et al.  Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design , 2020, ESAIM: Control, Optimisation and Calculus of Variations.

[6]  Marimuthu Palaniswami,et al.  Computational intelligence for movement sciences : neural networks and other emerging techniques , 2006 .

[7]  Silviu-Iulian Niculescu,et al.  Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system , 2017 .

[8]  S. Niculescu,et al.  On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant , 2020, IFAC-PapersOnLine.

[9]  G. Pólya,et al.  Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions , 1976 .

[10]  John G Milton,et al.  The delayed and noisy nervous system: implications for neural control , 2011, Journal of neural engineering.

[11]  D. Thelen Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. , 2003, Journal of biomechanical engineering.

[12]  S. Niculescu,et al.  Multiplicity-induced-dominancy for delay-differential equations of retarded type , 2020, Journal of Differential Equations.

[13]  S. A. Campbell Time Delays in Neural Systems , 2007 .

[14]  Matthew Millard,et al.  Flexing computational muscle: modeling and simulation of musculotendon dynamics. , 2013, Journal of biomechanical engineering.

[15]  Gabor Stepan,et al.  Delay effects in the human sensory system during balancing , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  F. J. Alonso,et al.  A comparison among different Hill-type contraction dynamics formulations for muscle force estimation , 2016 .

[17]  O. Schmitt The heat of shortening and the dynamic constants of muscle , 2017 .

[18]  Gregory S. Sawicki,et al.  A Simple Model to Estimate Plantarflexor Muscle–Tendon Mechanics and Energetics During Walking With Elastic Ankle Exoskeletons , 2016, IEEE Transactions on Biomedical Engineering.

[19]  Silviu-Iulian Niculescu,et al.  Tracking the Algebraic Multiplicity of Crossing Imaginary Roots for Generic Quasipolynomials: A Vandermonde-Based Approach , 2016, IEEE Transactions on Automatic Control.

[20]  Davide Piovesan,et al.  Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics. , 2011, Journal of biomechanical engineering.

[21]  Irinel-Constantin Morarescu,et al.  Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains , 2015, Syst. Control. Lett..

[22]  Silviu-Iulian Niculescu,et al.  Characterizing the Codimension of Zero Singularities for Time-Delay Systems , 2016, Acta Applicandae Mathematicae.

[23]  Roberto Bortoletto,et al.  Lower Limb Stiffness Estimation during Running: The Effect of Using Kinematic Constraints in Muscle Force Optimization Algorithms , 2014, SIMPAR.

[24]  G. Pólya,et al.  Series, integral calculus, theory of functions , 1998 .

[25]  Alberto Pierobon,et al.  Critical damping conditions for third order muscle models: implications for force control. , 2013, Journal of biomechanical engineering.

[26]  Alberto Pierobon,et al.  Third-Order Muscle Models: The Role of Oscillatory Behavior In Force Control. , 2012, International Mechanical Engineering Congress and Exposition : [proceedings]. International Mechanical Engineering Congress and Exposition.

[27]  Guilherme Mazanti,et al.  Partial Pole Placement via Delay Action: A Python Software for Delayed Feedback Stabilizing Design , 2020, 2020 24th International Conference on System Theory, Control and Computing (ICSTCC).

[28]  W S Levine,et al.  An optimal control model for maximum-height human jumping. , 1990, Journal of biomechanics.