model-based pressure and torque control for innovative...

Model-Based Pressure and Torque Control for Innovative Pneumatic Soft-Actuators

André Wilkening

FWBI – Friedrich-Wilhelm-Bessel-Institute Research Society

and Institute of Automation, University of Bremen, Germany

Miroslav Mihajlov

ITK Enineering AG, Stuttgart, Germany

Oleg Ivlev

FWBI – Friedrich-Wilhelm-Bessel-Institute Research Society

and Institute of Automation, University of Bremen, Germany

ABSTRACT

This paper describes a model-based pressure and torque control concept for innovative

pneumatically driven actuators with rotary elastic chambers. These soft-actuators have been

developed to operate in human environment, especially for physical interaction with people in

service and rehabilitation tasks. Owing to the inherent compliancy of the working chambers,

these actuators possess additional (compared to conventional fluidic actuators) nonlinearities,

causing specific problems related to their modeling and control. The pressure and torque control

concepts were investigated and tested by using a knee motion therapy device as test-bed. The

torque control is used to compensate the weight of the device mechanics as well as the patient’s

lower leg. Next step is the realization of "Assist-as-Need" behaviour for rehabilitation tasks.

NOMENCLATURE

p chamber pressure bar

m mass flow rate Nl/min

V chamber volume m3

R gas constant 287 J/kgK

7th International Fluid Power Conference Aachen 2010

1

T temperature 297 K

U voltage V

torque Nm

1 INTRODUCTION

Actuators with inherent compliance (soft-actuators) are predestinated for service and

rehabilitation tasks. The well-known fluidic artificial muscles belong to this category and

their working principle is quite analogous to the biological one. Different designs of

pneumatic muscles are reviewed in /Dae02/. This type of muscles generate pulling

forces, for the realization of a revolute joint a mechanical transmission is necessary

which leads to complex kinematic structures. One example is the realization of an

exoskeleton for use in physiotherapy /Tsa03/. In contrast to that, actuators with rotary

elastic chambers (REC-actuators) present a revolute type of artificial muscle and have

been developed preliminary for working in direct environment with humans /Ivl09/. Due

to the design, the actuators can be directly integrated in revolute robot joints, without

any additional transmission elements. However, all kinds of fluidic actuators behave

strongly nonlinear which not only depends on the air compressibility in the chambers.

Thus, an exact control becomes a difficult task. This paper describes a model-based

pressure and torque control using low-noise servo-valves. For rehabilitation tasks a low-

noise therapy device is desirable. Hence, the PWM controlled switching valves used in

/Mih08/ are unsuitable. As fundamental base, the nonlinear characteristics of REC-

actuators and of servo-valves have been determined in experimental manner. The

pressure control was investigated, using two different types of servo-valves, and

compared to pressure proportional valves. Furthermore a model-based torque control

was developed using a knee motion therapy device as test-bed, to achieve a

compensation of gravitation of patient’s lower leg and mechanics. This successfully

tested torque control can be used as a base for prospective rehabilitation tasks.


2

2 PNEUMATIC SOFT-ACTUATORS

By means of passive inherent compliance the REC-actuator is predestined to operate in

service or rehabilitation tasks. The mode of operation is quite similar to conventional

single vane fluidic motors, which consist of two chambers and a fixed rotary vane. A

general difference is the replacement of the rigid chambers by the elastic chambers.

Due to strongly nonlinearities of soft-actuators, which not only depends on the air

compressibility in the chambers, control becomes a difficult task. Unfortunately, because

of the material properties of the membrane the actuator hysteresis effects are

unavoidable. The actuator with pleated Rotary Elastic Chambers (pREC), which can be

seen in Figure 1, has a diameter of 100 mm and a height of 90 mm. Owing to the two

half cylinders made of aluminium and the ultra slim bearing the actuator housing is

lightweight and of high stiffness. The weight of one chamber is 50 g and the total

actuator weight is approximately 500 g. Effective working range is currently limited to an

angle of ± 45°, while the maximal torque is 20 Nm developed at the working pressure of

5 bar.

Figure 1: pleated Rotary Elastic Chamber (pREC) actuator

3 MODEL-BASED PRESSURE CONTROL USING MASS FLOW MAPS OF SERVO-

VALVES

This section describes the model-based pressure control law for pneumatic pREC-

actuators developed in /Mih08/, which has been realized and tested using servo-valves

instead of on-off valves. To compensate nonlinearities of servo-valves an inverted model


3

of determined flow map of valves has been used, similar to /Wol06/. To verify the

properties of low-noise servo-valves, a model was created in an experimental manner,

because theoretical mass flow equations are only approximations of current mass flow.

Two types of servo vales were analyzed and compared by using below presented

model-based pressure control, namely the FESTO MPYE-5-1/8LF-010-B servo-valve

and the GAS-Automation WS 15 G1/8 servo-valve. Considering that in a closed

chamber just the dynamic mass flow rate is measurable, two test plants were used

(inflow and exhaust flow) to describe the dynamics in a steady state. Figure 2 shows the

experimental setups.

Figure 2: Experimental setups for measuring, a) inflow rate, b) exhaust flow rate

The adjustable cut-off valve (valve 2) limits the mass flow, which was measured by using

the mass flow sensor ifm electronic SD6000 and for lower mass flows the

SensorTechnics FHA. By independently variegate the servo-valve and the cut-off valve,

different combinations of pressure and mass flow could be achieved. To measure the

actual chamber and supply pressure two SensorTechnics SCX pressure sensors were

used. By means of very high mass flow rates the pressure supply slightly alternates.

Thus, for simplification, it is assumed to be constant. To achieve a model that describes

the complete behaviour of valves, inflow and exhaust flow map were combined. Figure

3 shows the models of the valves. Note, that only the FESTO valve map contains of a

major dead zone, whereby a more precisely closing behaviour is afforded.

a)

b)


4

a)

0 2.5 5 7.5 10

0123456

-200

0

200

voltage [V]pressure [bar]

mas

s flo

w r

ate

[Nl/m

in]

b)

0 2.5 5 7.5 10

0123456

-200

0

200

voltage [V]pressure [bar]

mas

s flo

w r

ate

[Nl/m

in]

Figure 3: Experimentally determined mass flow map of valves, a) FESTO MPYE-5-

1/8LF-010-B, b) GAS-Automation WS 15 G1/8

One obtains a nonlinear function of the mass flow depending on supply voltage and

chamber pressure, whereby the supply pressure is assumed to be constant.

constppUfm ss ,, (1)

The pREC-actuator comes with complex volume characteristic which has a stake in the

pressure dynamics.

2,1,,,,,,; ippfVppufmVpmRTV

p siisiiiiii

i

(2)

Based on the pressure dynamics (2) the control law for the closed loop system is

assumed to be:

i

iiiidpi V

VpppKmRTG

(3)

Thus, the mass flow rate is chosen as:

i

iiiidp

ii

V

VpppK

RT

Vm

(4)

Note that the law based on the feedback linearization approach is composed of two

terms. The first term expresses a volume proportional P controller and the second term

describes a compensation of mass flow rate. This second term should compensate

pressure variation based on a fast change of volume. With the chosen control law a

decoupling of the pressure subsystem and the mechanical subsystem as well as a

compensation of previously described nonlinearities of valves should be given. The

desired mass flow rate in (4) describes a virtual actuating variable, whereby obviously

the real one is the supply voltage of servo-valves, which is obtained by using the


5

inverted model of servo-valves. One achieves a function of supply voltage depending on

the mass flow rate and the chamber pressure.

constppmfU s ,,1 (5)

At first the step responses of applied pressure step references have been compared

using GAS-Automation and FESTO servo-valve. Afterwards the step responses using

FESTO servo-valve MPYE-5-1/8LF-010-B and FESTO pressure proportional valve

MPYE G 1/8 have been compared. Objective was to show the advantage of using

developed model-based pressure control instead of internal pressure control of FESTO

MPYE G 1/8 valves. Finally an analysis of tracking behaviour to sinusoidal reference

pressure signal as well as pressure response to fast angle variation was done by using

those two different types of FESTO valves. Figure 4 shows positive and negative step

responses using FESTO and GAS-Automation servo-valves, whereby step reference

was applied in an interval of pd = [1,5] bar.

a)

0 0.1 0.2 0.3 0.4 0.50

2

4

6

time [s]

pres

sure

[ba

r]

b)

0 0.1 0.2 0.3 0.4 0.50

2

4

6

time [s]

pres

sure

[ba

r]

Figure 4: Closed loop response of pREC-actuator with FESTO servo-valves in red and

with GAS-Automation servo vales in blue, a) positive desired pressures, b) negative

desired pressures

The comparison shows proper results with a more homogeneous performance using

FESTO servo-valves (red curve). Settling times as well as steady state errors are

smaller. This can be explained by better valve characteristics of FESTO valves, in

particular being able to supply a larger flow rate plus the attribute of hard closing. In

contrast the soft closing behaviour of GAS-automation valves leads to damped step

responses (blue curve). For this experiment the pREC-actuator was fixed in its zero


6

position. The following Table 1 presents the results of the pressure step response

comparison.

ts(s) ess(mbar)

FESTO MPYE-5-1/8LF-010-B ≤0.12 ≤30

GAS-Automation WS 15 G1/8 ≤0.21 ≤50

Table 1: Specific values of the step responses using FESTO and GAS-Automation

servo-valves

To show the improvement, the FESTO servo-valve MPYE-5-1/8LF-010-B and the

FESTO pressure proportional valve MPYE G 1/8 with internal pressure control have

been compared. At First the pressure step responses are shown in Figure 5.

a)

0 0.1 0.2 0.3 0.4 0.50

2

4

6

time [s]

pres

sure

[ba

r]

b)

0 0.1 0.2 0.3 0.4 0.50

2

4

6

time [s]

pres

sure

[ba

r]

Figure 5: Closed loop response of pREC-actuator with FESTO servo-valve MPYE-5-

1/8LF-010-B in red and with FESTO pressure proportional valve MPYE G 1/8 in blue, a)

positive desired pressures, b) negative desired pressures.

The model-based pressure control (red curve) shows a much shorter reaction time as

the internal pressure control (blue curve). Table 2 summarizes the results of above

shown step response comparison. Steady state errors are larger as twice the number,

when using the internal pressure control.

ts(s) ess(mbar)

FESTO MPYE-5-1/8LF-010-B ≤0.12 ≤30

FESTO MPYE G 1/8 ≤0.32 ≤70

Table 2: Specific values of step responses using FESTO servo-valve and FESTO

pressure proportional valve


7

A further attribute of performance is the pressure response to fast angle variation, which

can be seen in Figure 6.

a)

0 2 4 61.5

2

2.5

3

3.5

time [s]

pres

sure

[ba

r]

0 2 4 6

-20

0

20

40

angl

e [°

]

b)

0 2 4 61.5

2

2.5

3

3.5

time [s]

pres

sure

[ba

r]

0 2 4 6

-20

0

20

40

angl

e [°

]

Figure 6: Closed loop response to fast angle variations, a) FESTO MPYE-5-1/8LF-010-B

and the model-based pressure control, b) FESTO MPYE G 1/8 with internal pressure

control

Figure 7 shows a sinusoidal pressure reference tracking. Two types of pressure control

methods were analyzed and compared by using a frequency of 1 Hz, 6 Hz and 10 Hz.

The Offset is chosen to 2.5 bar and the amplitude to 1 bar.

a)

0 1 2 323

0 1 2 323

pres

sure

[ba

r]

0 1 2 323

time [s]

b)

0 1 2 323

0 1 2 323

pres

sure

[ba

r]

0 1 2 323

time [s]

Figure 7: Sinusoidal pressure reference tracking, above: frequency = 1Hz, central:

frequency = 6Hz, below: frequency = 10Hz, blue curve: reference pressure, red curve:

actual pressure, a) FESTO MPYE-5-1/8LF-010-B and the model-based pressure

control, b) FESTO MPYE G 1/8 with internal pressure control

The comparison shows far better performance of the model-based pressure control,

whereby even with a frequency of 10 Hz a tracking is achieved. In contrast, the internal

pressure control shows a weakness already with using low frequencies. For higher

frequencies a tracking is not given any more.


8

4 MODEL-BASED TORQUE CONTROL FOR REHABILITATION DEVICES

Robot assisted motion therapy applications require an enhanced attention to patient’s

safety. Hence, a demand for safe robot solutions, using the properties of soft, i.e.

inherently compliant actuators, is increasing. To perform preliminary functional tests and

to investigate prospective patient-centred (assistive) control strategies the proof-of-

concept prototype with pREC-actuators has been used, which is shown in Figure 8. As

a passive load a leg dummy filled with a synthetic material to get a realistic weight of the

lower leg is applied. The thigh and the lower leg are connected through a single-axis

mechanical knee joint from Otto-Bock. The active forces occurring while patient activities

have been simulated manually. The test-bed is driven by two pREC-actuators to double

the maximum actuator torque and beyond that, the plant consists of two pressure

sensors, one angular encoder and two servo-valves.

Figure 8: Test-bed for knee motion therapy equipped with two pREC-actuators

As base for assistive control concepts a model-based torque control has been

developed. Objective was to achieve compensation of gravitation of mechanics and

patient’s lower leg, without using expensive torque sensors. Due to this advantage

rehabilitation after heavy neurological injuries or strokes will be possible. Instead of

torque sensors inverted torque characteristics of actuators are used. Note that torque

characteristics of pREC-actuator are nonlinear functions of chamber pressure and actual

vane angle.

sppf ,, (6)


9

Besides these characteristics the actuator turns out to possess hysteresis behaviour.

Thus, to determine torque characteristics of pREC-actuator an experimental method

was used. Rising hysteresis is noticeable relating to the rising pressure. To create an

interpolated and extrapolated model, which is shown in Figure 9.a, the mean values of

these characteristics have been used. The main idea of model-based torque control is to

use inverted torque characteristics of actuators as a mapping of pressure. In case of

compensation of gravitation, the desired torque equals the torque of payload, included

patient’s lower leg plus device mechanics, which have been calculated in analytical

manner. By using the delta principle the desired torque is apportioned to the upper and

lower chamber. The outputs of the inverted torque models are pressure values that are

used as desired pressure values of the previously presented model-based pressure

control. The structure is shown in Figure 9.b.

a)

0 1 2 3 4 5 66-25

-500

2550

0

10

20

pressure [bar]angle [°]

torq

ue [

Nm

]

b)

dT1 dP1

dP2 2,1, PP

2,1 UU

dT2

0T

Figure 9: a) Interpolated and extrapolated torque characteristic of pREC-actuator, b)

Structure of model-based torque control

To prove the developed concept the leg dummy was manually moved while measuring

angle, velocity, desired and actual torque as well as the resulting torque error, which are

shown in Figure 10. The maximum torque error in motion yields to e<|0.18| Nm, with a

maximum angle change of 48.61 °/s. Under static conditions this error decreases to

e<|0.01| Nm.


10

a)

0 5 10 15-20

-10

0

10

20

time [s]

angl

e [°

]

b)

0 5 10 15-60

-40

-20

0

20

40

60

time [s]

velo

city

[°/

s]

c)

0 5 10 151

2

3

4

time [s]

torq

ue [

Nm

]

d)

0 5 10 15

-0.2

-0.1

0

0.1

0.2

0.3

time [s]

torq

ue e

rror

[N

m]

Figure 10: Compensation of gravitation of patients lower leg and mechanics of test-bed;

a) angle, b) velocity, c) desired (blue curve) and actual (red curve) torque, d) torque

error

CONCLUSION

A model-based pressure control was investigated and tested, whereby corresponding

valve and torque characteristics have been determined. A model-based pressure control

law was analyzed by using two types of servo-valves. Results of developed pressure

control using FESTO MPYE-5-1/8LF-010-B servo-valve were compared with the results

using internal pressure control of the FESTO MPYE G 1/8 valve. Comparison shows

proper results with a homogeneous performance using the developed model-based

pressure control. Based on this control a model-based torque control has been

developed and tested by using a knee motion therapy device as test-bed. The main idea

was to use inverted torque characteristics instead of expensive torque sensors.

Objective was to achieve compensation of gravitation of patient’s lower leg combined

with the mechanics, to obtain a fundamental base for prospective rehabilitation tasks.


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ACKNOWLEGMENT

This work is supported by the German Federal Ministry of Education and Research

(BMBF) through the grant 16SV2290 (joint research projects PortaSOR “New generation

of portable soft robotic arms”) and the grant 01EZ0769 (KoBSAR “Compact assistive-

restorative motion therapy devices, based on fluidic soft actuators with rotary elastic

chambers”).

REFERENCES

/Dae02/ Daerden, F. and Lefeber D., Pneumatic artificial muscles: actuators for

robotics and automation, European Journal of Mechanical and

Environmental Engineering, 47(1), 2002, 10–21, 2002

/Tsa03/ Tsagarakis N., Caldwell D., Development and Control of a ‘Soft-Actuated’

Exoskeleton for Use in Physiotherapy and Training, Autonomous Robots,

15, pp 21-33, 2003

/Ivl09/ Ivlev, O., Soft Fluidic Actuators of Rotary Type for Safe Physical Human-

Machine Interaction, 11th IEEE Int. Conf. on Rehab. Robotics (ICORR

2009), Kyoto, Japan, pp.1-5, 23-26 June 2009

/Wol06/ Wolbrecht E.T., Leavitt J., Reinkensmeyer D.J., Bobrow J.E., Control of

a Pneumatic Orthosis for Upper Extremity Stroke Rehabilitation,

Proceedings of the 28th IEEE EMBS Annual International Conference,

New York City, USA, Aug 30-Sept 3, 2006

/Mih08/ Mihajlov, M. Modelling and Control Strategies for Inherently Compliant

Fluidic Mechatronic Actuators with Rotary Elastic Chambers, Ph.D. thesis,

Institute of Automation, Univ. of Bremen., Bremen, Germany, ISBN 978-3-

8322-7275-3, 2008


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