a novel closed-loop control approach for a flywheel and
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A Novel Closed-loop Control Approach for a
Flywheel and Electrical Clutch Assist Mechanism in
FES Cycling
S. C. Abdulla and M. O. Tokhi Department of Automatic Control and Systems Engineering
University of Sheffield
Sheffield, UK
cop11sca@sheffield.ac.uk
Abstract— A closed-loop control approach is proposed to control
a flywheel and electrical clutch mechanism to assist paralyzed
legs during functional electrical stimulation (FES) cycling by
stimulating the quadriceps muscle group. Fuzzy logic control is
used to control pedaling movement of legs by controlling the
pulse width of the stimulus. The proposed control approach with
the new assist mechanism significantly reduces the cadence error
and produces smoother pedaling movement as compared with
cycling without assistance. The results show that the new
mechanism has reduced the overall stimulation intensity on leg
muscles by approximately 43% and hence delays the occurrence
of muscle fatigue. The new mechanism promotes smooth,
coordinated and prolonged FES cycling for disabled individuals.
Keywords— Flywheel and clutch, assist mechanism, FES
cycling, closed-loop control, fuzzy logic
I. INTRODUCTION
Functional electrical stimulation (FES) has widely been
used for training paralyzed limbs. Several researches have
shown the importance of FES in improving the health of the
disabled by reducing muscle atrophy, improving blood
circulation in the limb, preventing bone loss and pressure sores,
as well as improving the self-image of the individual [1-5].
FES can be described as a train of pulses applied to the motor
units of a muscle to cause muscle contraction and generate
movement in paralyzed limbs. Stimulating the muscle with
FES can be done by using a stimulator with either implanted or
surface electrodes. Using surface electrodes is more common
because they are cheaper and safer as compared with implanted
electrodes [6]. One of the problems associated with FES is the
rapid appearance of muscle fatigue that terminates the training
session.
One of the common forms of training by FES that is widely
used in rehabilitation clinics is FES cycling which is
considered as an attractive and enjoyable choice for the
disabled due to its simplicity as compared with standing and
walking. One of the handicaps that are encountered during FES
cycling is the two dead points, i.e. a point of transition between
knee extension and flexion moment [6], that cause rapid
change in the speed and consequently unsmooth, i.e. jerky,
pedaling movement.
To provide a comfortable, smooth and prolonged exercise
for paraplegics researchers have focused on improving the
mechanical design of the cycling ergometer [6-9] and the
closed-loop control approach [10-13] as well as stimulating
different combinations of muscle groups [7][10][14]. As an
assist mechanism, some researchers used an auxiliary motor
[14-15] to help passing the cycling dead spots as well as assist
the leg pedal when muscle fatigue occurs. Others used a crank
arm to provide hybrid training as well as help the leg passing
the dead spots [6]. Others utilized an elastic spring to provide
assistance [16]. In a previous work [17], a novel assist
mechanism, represented by a flywheel and electrical clutch, has
been introduced. The flywheel, as energy storage device, is
engaged with the bicycle shaft by the clutch to absorb the
excessive energy in the system and store it as kinetic energy.
Also it re-engages with the shaft to discharge its energy into the
system and speed up the movement.
In this work a novel closed-loop control approach is
proposed to control the engagement and disengagement of the
flywheel by the clutch in FES cycling. A comparison between
FES cycling, by stimulating the quadriceps muscle group,
with/without the new assist mechanism is introduced and
assessed.
II. SYSTEM DESCRIPTION
A. Humanoid-bicycle model
A humanoid-bicycle model, with a flywheel and an
electrical clutch mechanism, was developed using Visual
Nastran 4D dynamic simulation software. The humanoid
model was built using the standard anthropometric dimensions
introduced by [18]. The dimensions of the bicycle used were
taken from a real cycling ergometer. Standard ball bearings
friction was added to crank shaft holder of the bicycle for more
realistic results. The electrical clutch mechanism was modeled
as an on/off constraint between the flywheel and the crank
shaft of the bicycle using the same software. Detailed Sponsored by The Ministry of Higher Education and Scientific Research/
KRG-IRAQ.
information about the humanoid-bicycle model can be obtained
from previous work of the authors [17].
B. Muscle model
The human musculoskeletal muscles, that are responsible
for producing voluntary movement, have been widely
described in the literature [19-20]. In this work, it is preferred
to use the model featured in [21], which is simple to implement
and accurate enough as it has been derived from data obtained
experimentally from paraplegics and healthy subjects. The
model is represented by a single-pole transfer function that
mimics the behaviour of the quadriceps muscle group
stimulated by an electrical stimulus. This muscle model is
implemented using simulink/matlab software with fixed
stimulation frequency of 33Hz, while the pulse width is kept
variable. The resultant muscle torque is fed to the knee joints of
the humanoid-bicycle model to produce leg movement. Further
information about this muscle can be found in detail in [21].
III. CONTROL STRATEGY
The amount of torque, generated by applying FES signal on
leg muscles, can be controlled by a closed-loop control
approach to maintain smooth and coordinated pedaling
movement. The controllers can be used to alter, according to a
feedback signal, the pulse width of FES signal, control the
amount of muscle contraction and produce the required
movement. In this work, it is aimed to perform a cycling
cadence of 35 rpm, the lowest cycling speed used clinically
[10]. The actual cycling speed is measured using a speed
sensor, in the humanoid-bicycle model, located at the bicycle
crank, i.e. shaft, to measure the angular velocity of the crank.
This feedback signal is compared with a reference of 35 rpm
and the resultant error signal is fed to the controllers to
accordingly alter the pulse width and control the movement of
the legs to follow the reference.
A. FES cycling without assistance (Scenario I)
The aim is for paraplegics to perform FES cycling, by
stimulating the quadriceps muscle group of each leg, without
assistance. The difficulty in this scenario arises from the fact
that stimulating the quadriceps of each leg leads to knee
extension only and no flexion movement can be generated.
Although, at certain positions, knee extension can speed up the
pedaling movement, at other positions it can also produce
opposite action and retard the movement, as in Fig. 1. To
govern a required cadence, the muscle should be stimulated
twice per cycle; first to speed up the movement and second to
retard it if necessary [16]. The cycling movement of each leg
can be divided into three phases; push, resist and rest. The push
phase is the period at which the knee extension can speed up
the cycling, while the resist phase is the period at which the
knee extension produces resistance to the movement. The rest
phase is the phase at which the leg is left without stimulus to
get rest before the next stimulus is due.
For simplicity, the stimulation phases are defined according to
the crank angle of the bicycle measured by a position sensor.
Considering the 0° of the crank as the horizontal point at which
the right leg is situated close to the hip, the phases are defined
as; right push phase between 20° and 80°, the right resist phase
between 150° and 200°, the left push phase between 200° and
260°, the left resist phase between 330° and 20°. Since the
amount of pushing required to speed up the cycling may differ
from that of resist, four fuzzy logic controllers are used as
shown in Fig. 2.
The cadence error and its derivative are fed to the
controllers after being normalized by input scaling factors. The
two normalized FLC inputs are fuzzified using a fuzzy set of
five equally distributed, with 50% overlapping, Gaussian
membership functions. The fuzzy output, results from the fired
fuzzy rules of the FLC, changes to crisp values using the centre
of area defuzzification method. The output is defuzzified using
five equally distributed Gaussian membership functions. The
output of each controller, after being scaled by output scaling
factors, is added with a constant reference pulse width. The
values of constant pulse width together with the input/output
scaling factors are determined heuristically as G1=G10=
0.0034, G2=G11=0.007, G3=G12=70, G4=G7=0.002,
Fig. 2. The control block diagram of scenario I
Fig. 1. Stimulation phases according to knee position
G5=G8= 0.0067, G6=G9= -45, R1=R4=60, R2=70, R3=50.
The performance of this control approach can be evaluated
from Figs 3-5. It’s clear from Figs 3-4 that each muscle is
stimulated twice per cycle; once for push and once for resist
phase. Also both muscles received approximately equal amount
of stimulation and produced the same torque in successive
cycles which is a good indicator of a coordinated pedaling
movement.
From Fig. 5 it is clear that the control strategy was successful
in producing cycling movement. However, the dead points
resulted in rapid changes in the crank cadence.
B. FES cycling with a flywheel and electrical clutch
mechanism (Scenario II)
In this scenario it is aimed to perform FES cycling by
stimulating the quadriceps only with the help of a new assist
mechanism represented by a flywheel and an electrical clutch.
The flywheel, as energy storage device, is used to assist and
retard the cycling when necessary and to replace muscle
stimulation in the resist phase. The electrical clutch engages the
flywheel with the crank to absorb the excessive energy
produced by the leg and to store it as kinetic energy in the
flywheel. Also the flywheel, loaded with energy, is engaged by
the clutch to discharge its energy into the crank and support the
cycling in case the energy of the leg is not enough to pedal.
In this scenario, two fuzzy logic controllers are used to
control the amount of stimulation during the pushing phase,
while the resist phase is replaced by the assist mechanism. The
control block diagram can be seen in Fig. 6. The input/output
scaling factors and the reference pulse width used in this
scenario are the same as these of scenario I.
The flywheel engagement and disengagement is
implemented in a closed-loop approach as shown in Fig. 7. The
engagement logic is constructed depending on the
instantaneous values of the crank angular velocity and the
angular velocity of the flywheel during the cycling. If the
angular velocity of the crank is greater than the required
cadence, i.e. the crank is fast and excessive energy is available
in the system, and if the angular velocity of the flywheel is less
than that of the crank, i.e. the flywheel is ready to resist, the
clutch will engage the flywheel with the crank to absorb the
energy and slow down the movement. Also, if the angular
velocity of the crank is less than the required cadence, i.e.
needs assistance, and the angular velocity of the flywheel is
greater than that of the crank, i.e. the flywheel is ready to
assist, the clutch will engage the flywheel to discharge its
energy into the crank and speed up the system.
Fig. 6. The control block diagram of scenario II
Fig. 5. The angular velocity of the crank
Fig. 4. Muscle torque of left leg
Fig. 3. Muscle torque of right leg
The performance of this control strategy can be seen from
Figs 8-14. Figs 8-9 show the engagement and disengagement
of the flywheel, by the clutch, for assist and resist periods.
From Fig. 10 and Fig. 11 it is clear that each leg was stimulated
once per cycle while there was an increase in the torque
produced by the muscles which indicates an increase in the
work done by the muscle. It can be seen from Fig. 12 that the
energy absorption and energy release of the flywheel during
resist and assist periods respectively and the corresponding
effect on the angular velocity of the crank, as in Fig. 13. It is
clear from Figs 12-13 that the flywheel mechanism was
successful in reducing the crank speed when a resist action was
required and also was successful in speeding up the crank when
an assist action was required.
Fig. 14 shows a comparison between the cadence error in
both scenarios. It is clear that the flywheel mechanism was
effective in reducing the error in the crank cadence as well as
reducing the rapid change in the angular velocity at the cycling
dead points and consequently produced smoother cycling
Fig. 13. The angular velocity of the crank
Fig. 12. The angular velocity of the flywheel
Fig. 11. Muscle torque of right leg
Fig. 10. Muscle torque of left leg
Fig. 9. Flywheel engagement (resist period)
Fig. 8. Flywheel engagement (assist period)
Fig. 7. The flywheel engagement mechanism
cadence. From Fig. 15 it can be seen that the new assist
mechanism reduced the overall stimulation (from 600µs to
338µs) on the muscles. Reducing the stimulation intensity on
the muscle delays the appearance of muscle fatigue, and hence
the new mechanism promotes extended FES cycling exercise.
IV. CONCLUSION
Coordinated FES cycling can be performed by stimulating
single muscle group, the quadriceps only. Using a closed-loop
control approach, a flywheel and electrical clutch mechanism
can be utilized to assist the legs and improve the cycling
performance. The new assist mechanism has shown superior
performance in terms of reducing the cadence error and the
sharp change in speed at the cycling dead points which results
in smoother and more comfortable cycling. The introduced
control approach with the new assist mechanism has reduced
the overall stimulation intensity on leg muscles by
approximately 43% which promotes delayed muscle fatigue
and prolonged FES cycling exercise.
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Fig. 15. Integral of stimulation intensity in both scenarios
Fig. 14. Cadence error in both scenarios
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