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SMEDEMA: Real Time Programming 1977
SUBRAMANYAM: Computer Applications in Large Scale Power Systems
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ROBERT MAXWELL
Publisher at Pergamon Press
CONTROL ASPECTS OF
PROSTHETICS
AND
ORTHOTICS
Proceedings of the IF A C Symposium
Ohio, USA, 7-9 May 1982
Edited by
R. M. CAMPBELL
Bio-Medical Engineering Center
The Ohio State University
Columbus, Ohio, USA
Published for the
INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL
by
PERGAMON PRESS
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Copyright© 1983 IFAC
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First edition 1983
British Library Cataloguing in Publication Data
Control aspects of prosthetics and orthotics.
1. Biomedicai engineering—Congresses
I. Campbell, R.M. II. International Federation
of Automatic Control
610'.28 R856.A1
ISBN 0-08-029350-6
In order to make this volume available as economically and
as rapidly as possible the authors' typescripts have been
reproduced in their original forms. This method unfor
tunately has its typographical limitations but it is hoped
that they in no way distract the reader.
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
CONTROL ASPECTS OF PROSTHETICS AND ORTHOTICS
Organized by
The Ohio State University Bio-Medical Engineering Center
The Central Ohio Bio-Medical Engineering Community Council (COBECC)
Sponsored by
International Federation of Automatic Control in conjunction with the Seventh
Midwest Bio-Medical Engineering Conference with the participation of:
IEEE - Control Systems Society (CSS)
IEEE — Engineering in Medicine and Biology Society (EMBS)
International Technical Program Committee (IPC)
Robert McGhee, Columbus, Ohio, USA (Chairman)
Emanuel Biondi, Milan, Italy
Antonio Pedotti, Milan, Italy
Adam Morecki, Warsaw, Poland
Maciej Nalecz, Warsaw, Poland
A. M. Petrovsky, Moscow, USSR
Pierre Rabischong, Montpelier, France
George Saridis, W. Lafayette, Indiana, USA
Rajko Tomovic, Belgrade, Yugoslavia
Gerhard Vossius, Karlsruhe, Germany
Herman R. Weed, Columbus, Ohio, USA (EMBS)
Baxter Womack, Texas, USA
Copyright © IFAC Control Aspects of Prosthetics and Orthotics SESSION 1: FUNCTIONAL MUSCLE
Ohio, USA, 1982
AND NERVE STIMULATION
Chairman: Professor P. Hunter Peckham
Case Western Reserve University, Cleveland, Ohio
A DISCRETE-TIME SERVOMECHANISM FOR THE
REGULATION OF FORCE AND POSITION DURING
FUNCTIONAL NEUROMUSCULAR STIMULATION
G. F. Wilhere, P. E. Crago, and R. C. Chang
Applied Neural Control Laboratory, Department of Biomedicai Engineering, Case Western
Reserve University, Cleveland, Ohio, USA
Abstract. Orthoses employing electrically stimulated mus
cles could be improved by the incorporation of closed-loop
control systems to regulate the output of the muscle. The
electrically stimulated muscle is modeled as a sampled data
system and a digital controller is designed to satisfy sta
bility, repeatability, linearity, and step response criteria
over a wide range of recruitment gains. The digital con
troller can be implemented with a microprocessor and is
amenable to adaptive control techniques.
Simulation studies were conducted to evaluate the controller
design. It was concluded that the design technique used can
compensate for the muscle recruitment nonlinearities.
Keywords. Force Control; Sampled data systems; Nonlinear
control systems; Orthotics; Simulation
INTRODUCTION DESCRIPTION OF SYSTEM MODEL
Functional Neuromuscular stimulation (FNS) In an FNS orthosis muscle force may be
can restore hand function to patients par controlled in two ways, pulse area modula
tially paralyzed by spinal cord injury tion (recruitment) and/or pulse frequency
(Peckham et al, 1980). At present all modulation, PFM, (temporal summation).
clinically deployed FNS orthoses are Pulse area for rectangular pulses is the
open-loop systems. Open-loop systems are product of pulse amplitude and pulse dura
limited because the controller has no in tion (width). When modulating pulse area
trinsic means of compensating for flucua- pulse width modulation, PWM, is preferable
tions at the system output. Past attempts to pulse amplitude modulation. This
to develop closed-loop control systems statement is based on the fact that at any
utilized continuous time proportional or given force pulse width modulation re
proportional-plus-integral controllers. quires less charge transfer per stimulus
Although adequate system response charac pulse than pulse amplitude modulation
teristics could be obtained, repeatable (Crago et al, 1980b). It has been demon
performance could not be ensured due to strated that one method of obtaining a
variations in muscle input-output proper linear relationship between command and
ties over time. force is to use only PWM over the first
two-thirds of the total force range and
A discrete time closed-loop controller has only PFM over the remaining one-third
been designed to meet specified perfor (Crago et al, 1980a). This paper will re
mance criteria. This type of system is port on a controller which uses only PWM.
advantageous because it is easily imple
mented on a microprocessor based system, In the control system the interpulse in
and it is amenable to adaptive control terval or sampling period is determined by
techniques that can automatically compen the fusion frequency. The fusion frequen
sate for variations in the muscle parame cy is defined as the stimulus frequency at
ters. which there is a 10% ripple in the con
traction force.
A muscle twitch can only be elicited by a
pulsed input, hence the absense of a
zero-order hold in the system. In addi
tion, since the pulse widths are much
1
2 G. F. Wilhere, P. E. Crago and R. C. Chang
MUSCLE
CONTROLLER 1
I FORCE
COMMA! V—^—> DCZ) «•^ X r -> G(Z)
K- *PI IPI 1 ^
^
Fig. 1 Block diagram of the closed-loop F(z) XD(z)G(z)
(3)
digital control system for the re
gulation of muscle force. C(z) 1 + XD(z)G(z)
Let D(z) = H(z)/G(z).
smaller than the interpulse interval the
input to the muscle can be approximated as Then,
an impulse train.
F(z) XH(z)
The muscle can be modelled as a low pass (4)
filter with a pure delay (Bawa et al, C(z) 1 + XH(z)
1976) of the form:
Let H(z) be a generalized model of the
c -Ds form (Kuo, 1963):
G(s) = V (1)
aiz - a
(s+a)(s+b) H(z) = i i0 ? (5)
The discrete time transfer function, as
(z - l)(z - b )
obtained from the modified Z-transform, is Q
of the form:
The system transfer function becomes:
_-!gii_! go) F(z) X(aiz - aQ)
G(z) (2) (6)
<z + S2)(z + g3) C(z) z2 - (l+b0-xai)z + bö-Xa0
The recruitment characteristic is a Note that a^ is a scaling factor and the
time-varying nonlinear relationship product Xa^ is chosen £o be equal to (1
between stimulus area and the portion of -*zi)/ui - P^1 - p ))? where p»
the muscle activated. The causes of the
p , z^ are the closed loop poles and
nonlinearities are believed to be the
zero. This choice of Xa, will ensure a
orientation of the intramuscular electrode
zero steady-state error at the sampling
with respect to the numerous motor nerve
instants. From the characteristic equa
bundles and the range of stimulus thres
tion of equation (6) a root locus can be
holds for the nerves within these bundles
constucted which defines the system per
(Crago et al, 1980b). The regions of sa
formance for variations in the recruitment
turation correspond to the maximum and
gain, X. From this root locus the range
minimum muscle forces. The time-varying
of X can be determined for which the spec
property is primarily the result of
ified performance criteria will be satis
changes in the relative positions of the
fied. The goals of the design process
electrode and the nerve bundles. A
were to: 1) minimize the percent
piece-wise linear approximation of a "typ
overshoot and time to maximum overshoot
ical" recruitment characteristic is dep
>T , of the step response, and 2) to
icted in Fig. 2. χ
maximize the range of X. This was accom
plished by optimizing the angle alpha as
CONTROLLER DESIGN
defined by Lindorff (1959) ,i.e. the re
lative positions of the real zero and com
The controller design was based on the
plex poles in the Z-plane.
Truxall synthesis method (Truxall, 1955),
i.e. a factor in the controller transfer
It was determined that a recruitment gain
function is the reciprocal of the plant
ratio equal to ten (maximum allowed
(muscle) transfer function. An extension
gain/minimum allowed gain) would be suffi
of this design technique was necessary to
cient to cover the range of possible
compensate for the recruitment charac
changes in the recruitment characteristic.
teristic nonlinearity.
For a sampling period equal to 80 ms., an
From Fig. 1, the overall transfer func
tion for the system is:
A Discrete-time Servomechanism 3
1.50T
1.0T
\\ ALPHA
UJ \\ 2.00
UQ: \\ \\ --1296..0 030 - -
o
u. 1.00 4 W
a
LU
N x
<
.5 + Σ
<
0.50 +
Σ
a:
o
z
20 T
0.5 1.0 1.5
NORMALIZED PULSE WIDTH
Fig. 2 A piece-wise linear approximation 5 15
of a "typical" recruitment charac O
teristic. I
CO
£ 10
o
initial damping ratio of 0.7, a T not
ffiax
greater than 1.4 s. and percent overshoot
not greater than 20.0% a recruitment gain 5 +
ratio equal to 10.42 could be obtained
when alpha equaled -19.03 degrees. These
constraints on the transient step response
are considered adequate for hand control. 0.2 0.4 0.6 0.8 1.0
RECRUITMENT GAIN
This result is portrayed graphically in
Fig. 3. 1.0
SIMULATION STUDIES
The discrete-time system has been simulat ω
ed on a PDPll/23 computer to study the re x
lationship between Tmax> percent <
overshoot; and the recruitment gain. In
all of these simulations the parameters a: 0.5 +
<
for the muscle transfer function, equation
(2), were GQ = 50, D - 10 ms., a = 11 CD
rad/s., and b = 13 rad/s. The values for
<
the muscle poles were interpolated from
experiments performed by Bawa, Mannard,
and Stein (1976). For these muscle poles
the fusion frequency was estimated to be
12.5 Hz.
0.5 1.0
REAL AXIS
The responses to two different types of
commands were examined. First, the step Fig. Graphs of T χ (top), percent
response was examined since this is the overshoot (middle), and the
command for which the performance criteria closed- loop poles (bottom) as a
are defined. Second, a "truncated ramp" function of normalized recruitment
command was examined since this is expect gain and for three different
values of the angle alpha. The
ed to be the command utilized in the FNS
zeros are located on the real axis
orthosis. For evaluating the effects of
at 0.62, 0.52, and 0.77 for alphas
the recruitment nonlinearity two ap
equal to -19.03, -26.0 and 2.0 de
proaches were taken. First, systems with
grees, respectively.
linear, nonsaturating recruitment charac
teristics were studied. These responses
predict the incremental responses obtained
in real-life systems for commands small
enough that the recruitment characteristic
could be considered linear. Second, sys
tems with "typical" real life recruitment
characteristics were studied.
4 G. F. Wilhere, P. E. Crago and R. C. Chang
1.0
1.0T
§0.5
LU
0. 5 1.0 1.5 2.0 0.5 1.0 1.5 2.0
TIME (S.)
TIME (S.)
1.0T 1.0·
0.5 1.0 1.5 2.0 0.5 1.0
TIME (S.) TIME <S. )
Fig. 4 System step responses for the max Fig. 5 System response to a 400 ms.
imum (top) and the minimum (bot truncated ramp for the maximum
tom) allowed recruitment gains. (top) and minimum (bottom) allowed
recruitment gains.
A Discrete-time Seromechanism 5
System responses for step inputs at the Crago, P.E., J.T. Mortimer, and G.B.
minimum and maximum allowable linear re Thrope (1980b). Modulation of Muscle
cruitment gains are shown in Fig. 4. At Force by Recruitment During Intramus
both ends of the recruitment range the cular Stimulation. IEEE Trans.
transient responses conform to the speci Biomed. Eng., BME-27, 679-684.
fied criteria ^max not greater than 1.4 Kuo, B.C. (1963)." The Analysis and
s. and percent overshoot not greater than Design of Sampled Data Control
20.0%) and the steady-state error at the Systems. Prentice-Hall, New Jersey.
sampling instants is zero. System Lindorff, D.P. (1959). Application of
responses for 400 ms. truncated ramp in Pole-zero Concepts to Design of Sam-
puts at the minimum and maximum allowable pled-Data Systems. I.R.E. Trans, on
recruitment gains are shown in Fig. 5. Aütorn. Control, AC-4, 173-184.
As expected, the responses to this type of
Peckham, P.H., E.B. Marsolais, and J.T.
input equaled or exceeded the system step
Mortimer (1980). Restoration of key
responses in performance.
grip and release in the C6 tétraplégie
patient through functional electrical
Step responses for the nonlinear recruit stimulation. The Journal of Hand
ment characteristic in Fig. 2 are shown Surgery, 5_, 462-469.
in Fig. 6. For a step of amplitude equal
to 0.5 only the first segment of the re
cruitment characteristic, which has a gain
of 10.0, is traversed. For a step of am
plitude equal to 3.5 only the second seg
ment, which has a gain of 1.0, is tra
versed. And. for a step equal to 2.0,
portions of both of these segments are
traversed. In each of these cases the
response satisfies the specified perfor
mance criteria. It should be noted that
in the actual FNS orthosis the regions of
saturation in the recruitment characteris
tic are only encountered at the extremes
of the muscle force range.
EXPERIMENTAL EVALUATION
At present, the controller is implemented
to run in real time on the laboratory com
puter. Animal studies will begin shortly.
Future efforts will be directed toward
controlling antagonistic muscles and to
designing a controller with variable sam
pling period to extend the linear operat
ing range over the remaining third of the
muscle force range.
ACKNOWLEDGEMENTS
This work is funded under contract TIME CS. )
N01-NS-0-2330 from the Neural Prothesis
Fig. 6 Step responses of varying ampli
Program of NIH-NINCDS. The work was per
tude for the nonlinear recruitment
formed in the Applied Neural Control La
characteristic in Fig. 2.
boratory, Dr. J.T. Mortimer, Director.
The authors would like to thank the
members of the laboratory and Dr. Bruce
Walker and Dr. Howard Chizeck of the Sys
tems Engineering Department for helpful
comments and criticism.
REFERENCES
Bawa, P., A. Mannard, and R.B. Stein
(1976). Effects of Elastic Loads on
the Contractions of Cat Muscles.
Biol. Cybernetics, 22, 129-137
Crago, P.E.; J.T. Mortimer, and P.H.
Peckham (1980a). Closed-loop Control
of Force During Electrical Stimulation
of Muscle. IEEE Trans. Biomed.
Eng.. BME-27, 306-312.
Copyright © IFAC Control Aspects of Prosthetics and Orthotics
Ohio, USA, 1982
COOPERATION OF MUSCLES UNDER DYNAMIC
CONDITIONS WITH STIMULATION CONTROL
A. Morecki*, K. Kedzior*, E. Biezanowska*, A. Dabrowska* and
R. Pasniczek**
^Institute of Aircraft Engineering and Applied Mechanics, Technical University
of Warsaw, Warsaw, Poland
** Metro polit an Center of Rehabilitation, Warsaw, Poland
Abstract. This work presents some improvements introduced in
the method of determination of cooperation of muscles, i.e.
a new universal form of description, which permits to simulate
the work of a muscle within a full range of working parameters
(length, velocity, excitation), under static and dynamic condi
tions as well as during a single or tetanous contraction. In
experimental research it is important to determine the proper
characteristics of a muscle, i.e. EMG versus muscular force,
in other words the relationship between a natural stimuli and
a force. An improved and extended method of determining the
amplitude and phase characteristics of muscles is given in the
work. The measurements were conducted on a special test rig with.i
on-line data processing.
While comparing the results of digital simulation with those
obtained from an experiment, it is important to formulate
(guess) a criterion if such exists , followed by the organism
in working muscles in a determined order. Assuming that the
fundamental citerion observed in rapid movements is minimiza
tion of time duration of motion, this criterion was used for
determining the cooperation of muscles serving the human elbow
joint.
This part of work aims also at the use of digital simulation
for controlling the paralysed groups of muscles of tetrap1 egic's
extremity. In current investigations the main attention is put
on the controlling of the prehension, which is induced by sti
mulation of the extensors and flexors of the digits with implan
ted stimulators. The investigations show that the patient needs
a mobility of the wrist joint. Therefore a new design has been
started in which the external orthostesis is fitted in an actu
ator making the flexion and the extension on the wrist possible.
Keyword s. bionics; computer control; dynamic response; transfer
function; e 1ectromyography ; minimum principle; models; optimal
control; implanted stimulators.
INTRODUCTION ly, stimulation or muscle potentials
are the input to the system, and tor
Cooperation of muscles under dynamic que is the output. The torques exer -
conditions has been given relatively ted by the actuators can be determi
small attention. Recently, however, ned after comparing the value of a re
a few works were pub 1 i shed (Morecki , 1971 ) sultant torque with that exerted by
in which various models of coopera a natural limb within a given range
tion were proposed, but so far no ef of mot i on.
fective control criterion was formula
The accordance of torques is quite
ted .
satisfactory, but does not furnish
Mathematical model of cooperation lends information about criterion used by
from models used in theory of control CNS while performing a given motion.
(Kedzior, 1^70) ; a joint is treated This work presents more precise mo
as an object with a known transfer dels of cooperation, and confirms
function, and its muscles as actua hypothesis of minimum time control.
tors with adequate properties. Usual
7
