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Research Papers

Robust Adaptive Control of the Nonlinearly Parameterized Human Shank Dynamics for Electrical Stimulation Applications

[+] Author and Article Information
Ruzhou Yang

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
Baton Rouge, LA 70803

Marcio de Queiroz

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: mdeque1@lsu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received June 9, 2017; final manuscript received February 6, 2018; published online March 30, 2018. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 140(8), 081019 (Mar 30, 2018) (15 pages) Paper No: DS-17-1296; doi: 10.1115/1.4039366 History: Received June 09, 2017; Revised February 06, 2018

In this paper, we introduce two robust adaptive controllers for the human shank motion tracking problem that is inherent in neuromuscular electrical stimulation (NMES) systems. The control laws adaptively compensate for the unknown parameters that appear nonlinearly in the musculoskeletal dynamics while providing robustness to additive disturbance torques. The adaptive schemes exploit the Lipschitzian and/or the concave/convex parameterizations of the model functions. The resulting control laws are continuous and guarantee practical tracking for the shank angular position. The performance of the two robust adaptive controllers is demonstrated via simulations.

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Figures

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Fig. 1

Shank with electrode stimulation of the quadriceps muscle group

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Fig. 2

Reference trajectory qd(t) used in each simulation

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Fig. 3

Muscle fatigue gain over time. After 160 s, the muscle fatigues to approximately 60% of its original strength.

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Fig. 4

Simulation 1: tracking error e(t)

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Fig. 5

Simulation 1: control input u(t)

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Fig. 6

Simulation 1: parameter estimates θ̂(t)

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Fig. 7

Simulation 1: parameter estimates ϕ̂(t)

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Fig. 8

Simulation 1: parameter estimates Ψ̂(t) for LPB control (left column) and parameter estimates λ̂(t) for CCPB control (right column)

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Fig. 9

Simulation 2: tracking error e(t); bottom plots show the steady-state error

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Fig. 10

Simulation 2: control input u(t)

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Fig. 11

Simulation 2: parameter estimates θ̂(t)

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Fig. 12

Simulation 1: parameter estimates ϕ̂(t)

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Fig. 13

Simulation 2: parameter estimates Ψ̂(t) for LPB control (left column) and parameter estimates λ̂(t) for CCPB control (right column)

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Fig. 14

Simulation 2: disturbance term dl(t)

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