Robust Discrete-Time H∞ Control for Unsupported Paraplegic Standing: Experimental Results

This paper develops a design approach, based on sampled data H ∞ -robust feedback control, for stabilisation of the upright posture of paraplegic persons standing. The subject stands in a special apparatus which braces the knee and hip joints. Stabilising torque at the ankle joint is produced by electrical stimulation of the paralyzed calf muscle of both legs using surface electrodes. The goal in this setup is for the subject to stand without the need to hold on to an external support for stability: we call this “unsupported standing”. The apparatus allows measurement of ankle moments and inclination angle. The control structure therefore has an inner loop providing high-bandwidth control of ankle moment, and an outer loop which stabilises the inclination angle. This problem involves a significant degree of uncertainty because of the nonlinear and time-varying response of the electrically stimulated muscles. We therefore focus here on robust H ∞ -control design for the angle control loop, using a discrete-time formulation.

[1]  M. Munih,et al.  Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle , 1998, IEEE Transactions on Biomedical Engineering.

[2]  Siva S. Banda,et al.  Robust control systems design using H-infinity optimization theory , 1992 .

[3]  P. Khargonekar,et al.  STATESPACE SOLUTIONS TO STANDARD 2 H AND H? CONTROL PROBLEMS , 1989 .

[4]  K.J. Hunt,et al.  New results in feedback control of unsupported standing in paraplegia , 2004, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[5]  E. Condie,et al.  Functional Electrical Stimulation: Standing and Walking After Spinal Cord Injury , 1990 .

[6]  M Munih,et al.  Variation of recruitment nonlinearity and dynamic response of ankle plantarflexors. , 2000, Medical engineering & physics.

[7]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[8]  I. Postlethwaite,et al.  State-space formulae for discrete-time H∞ optimization , 1989 .

[9]  Henrik Gollee,et al.  Robust control of electrically-stimulated muscle using polynomial H∞ design , 2001 .

[10]  K. Glover,et al.  State-space formulae for all stabilizing controllers that satisfy and H ∞ norm bound and relations to risk sensitivity , 1988 .

[11]  Henrik Gollee,et al.  Design of feedback controllers for paraplegic standing , 2000 .

[12]  Marko Munih,et al.  Optimal control of ankle joint moment: toward unsupported standing in paraplegia , 1998, IEEE Trans. Autom. Control..

[13]  R. Asgharian.  A robust H/sup /spl infin// power system stabilizer with no adverse effect on shaft torsional modes , 1994 .

[14]  T. Basar,et al.  A dynamic games approach to controller design: disturbance rejection in discrete time , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[15]  Michael Green,et al.  Discrete time H∞ control , 1989 .

[16]  T. L. Hill,et al.  Some self-consistent two-state sliding filament models of muscle contraction. , 1975, Biophysical journal.

[17]  J. Mortimer,et al.  The Effect of Stimulus Parameters on the Recruitment Characteristics of Direct Nerve Stimulation , 1983, IEEE Transactions on Biomedical Engineering.

[18]  W. Durfee,et al.  Methods for estimating isometric recruitment curves of electrically stimulated muscle , 1989, IEEE Transactions on Biomedical Engineering.

[19]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[20]  M Munih,et al.  Apparatus and methods for studying artificial feedback-control of the plantarflexors in paraplegics without interference from the brain. , 1997, Medical engineering & physics.

[21]  M Munih,et al.  Feedback control of unsupported standing in paraplegia--part I: optimal control approach. , 1997, IEEE transactions on rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[22]  H Gollee,et al.  Feedback control of unsupported standing. , 1999, Technology and health care : official journal of the European Society for Engineering and Medicine.

[23]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[24]  A. Huxley.  Muscle structure and theories of contraction. , 1957, Progress in biophysics and biophysical chemistry.

[25]  S. Skogestad,et al.  Performance weight selection for H-infinity and μ-control methods , 1991 .