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Research Papers

Optimal Control of the Spine System

[+] Author and Article Information
Yunfei Xu

Department of Mechanical Engineering,Michigan State Universityxuyunfei@egr.msu.edu

Jongeun Choi1

Department of Mechanical Engineering, and Department of Electrical and Computer Engineering, Michigan State University, 2459 Engineering Building, East Lansing, MI 48824-1226jchoi@egr.msu.edu

N. Peter Reeves

Department of Surgical Specialties,Michigan State Universityreevesn@msu.edu

Jacek Cholewicki

Department of Surgical Specialties,Michigan State Universitycholewic@msu.edu

1

Corresponding author.

J Biomech Eng 132(5), 051004 (Mar 25, 2010) (10 pages) doi:10.1115/1.4000955 History: Received May 20, 2009; Revised December 17, 2009; Posted January 06, 2010; Published March 25, 2010; Online March 25, 2010

The goal of this work is to present methodology to first evaluate the performance of an in vivo spine system and then to synthesize optimal neuromuscular control for rehabilitation interventions. This is achieved (1) by determining control system parameters such as static feedback gains and delays from experimental data, (2) by synthesizing the optimal feedback gains to attenuate the effect of disturbances to the system using modern control theory, and (3) by evaluating the robustness of the optimized closed-loop system. We also apply these methods to a postural control task, with two different control strategies, and evaluate the robustness of the spine system with respect to longer latencies found in the low back pain population. This framework could be used for rehabilitation design. To this end, we discuss several future research needs necessary to implement our framework in practice.

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Figures

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Figure 1

A subject balancing on an unstable seat. The upper body angle and angular velocity (θ1, θ̇1) and the lower body (seat) angle and angular velocity (θ2, θ̇2) were collected during the experiment.

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Figure 2

The dynamic model of postural control during unstable sitting

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Figure 3

The trunk torque disturbance measured at the 5% of the maximum voluntary effort and the associated power spectral density

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Figure 4

The block diagram of the spine system. Mm, Bm, Km, and Tm are matrices defined in Eq. 3. K is the feedback controller. ECD is the excitation-contraction dynamics. ñi and d̃ are the sensor noise and the disturbance input, respectively. Wni and Wd are the sensor noise dynamics and the disturbance dynamic, respectively. Pτ is the approximated delay.

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Figure 5

The closed-loop system. P is the generalized plant and K is the controller.

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Figure 6

Trajectories (θ1,θ2,θ̇1,θ̇2) from simulation studies with original gains (dotted lines), with H2 gains and r=0.001 (dashed lines), and with H2 gains and r=0.5 (solid lines)

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Figure 8

Optimal control with r=0.001: way points of optimized gains and their associated H2 norms versus the number of iterations

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Figure 9

Optimal control with r=0.5: way points of optimized gains and their associated H2 norms versus the number of iterations

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Figure 10

The case of the true time delay τ1=0.0175 s: trajectories (θ1,θ2,θ̇1,θ̇2) from simulation studies with original gains (dotted lines), with H2 gains and r=0.001 (dashed lines), and with H2 gains and r=0.5 (solid lines)

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Figure 11

The case of the true time delay τ2=0.02 s: Trajectories (θ1,θ2,θ̇1,θ̇2) from simulation studies with original gains (dotted lines), with H2 gains and r=0.001 (dashed lines), and with H2 gains and r=0.5 (solid lines)

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Figure 12

The flowchart of the proposed rehabilitation planning

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Figure 7

Control efforts from simulation studies with original gains (dotted line), with H2 gains and r=0.001 (dashed line), and with H2 gains and r=0.5 (solid line)

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