IOP PUBLISHING SMART MATERIALS AND STRUCTURES

Smart Mater. Struct. 16 (2007) 418–428 doi:10.1088/0964-1726/16/2/021

Control of electro-rheological fluid basedresistive torque elements for use in activerehabilitation devicesJason Nikitczuk, Brian Weinberg and Constantinos Mavroidis1

Department of Mechanical and Industrial Engineering, Northeastern University,360 Huntington Avenue, Boston, MA 02115, USA2

E-mail: mavro@coe.neu.edu

Received 14 July 2006, in final form 19 December 2006Published 9 February 2007Online at stacks.iop.org/SMS/16/418

AbstractIn this paper we present control algorithms for novel electro-rheological fluidbased resistive torque generation elements that will be used to drive the jointof a new type of portable and controllable active knee rehabilitation orthoticdevice (AKROD) for iso-inertial, isokinetic, and isometric exercising as wellas gait retraining. The AKROD is composed of straps and rigid componentsfor attachment to the leg, with a central hinge mechanism where a gearsystem is connected. The key features of AKROD include: a compact,lightweight design with highly tunable torque capabilities through a variabledamper component, full portability with on-board power, control circuitry,and sensors (encoder and torque), and real-time capabilities for closed loopcomputer control for optimizing gait retraining. The variable dampercomponent is achieved through an electro-rheological fluid (ERF) elementthat connects to the output of the gear system. Using the electricallycontrolled rheological properties of ERFs, compact brakes capable ofsupplying high resistive and controllable torques are developed. In thisproject, a prototype for the AKROD has been developed and tested. TheAKROD’s ERF resistive actuator was tested in laboratory experiments usinga custom-made ERF testing apparatus (ETA). ETA provides acomputer-controlled environment to test ERF brakes and actuators in variousconditions and scenarios including emulating the interaction between humanmuscles involved with the knee and the AKROD’s ERF actuators/brakes. TheAKROD’s ERF resistive actuator was tested in closed loop torque controlexperiments. A hybrid (non-linear, adaptive) proportional-integral (PI) torquecontroller was implemented to achieve this goal.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Electro-rheological fluids (ERFs) are fluids that experiencedramatic changes in rheological properties, such as viscosityand yield stress, in the presence of an electric field. Thefluids are made from suspensions of an insulating base fluidand particles having a size on the order of 0.01–0.1 μm and

1 Author to whom any correspondence should be addressed.2 http://www.coe.neu.edu/∼mavro

volume fraction of the particles between 20% and 60% [1–3].The electro-rheological effect arises from the difference in thedielectric constants of the fluid and particles. In the presenceof an electric field, the particles, due to an induced dipolemoment, rearrange into a more organized manner and formchains along the field lines. The induced structure changes theERF’s viscosity, yield stress, and other properties, allowing theERF to change consistency from that of a liquid to somethingthat is viscoelastic (such as a gel) at response times on the orderof milliseconds.

0964-1726/07/020418+11$30.00 © 2007 IOP Publishing Ltd Printed in the UK 418

Control of electro-rheological fluid based resistive torque elements for use in active rehabilitation devices

Figure 1. Electro-rheological fluid based knee device—prototype ona leg.

Control over the fluid’s rheological properties offers thepromise of many possibilities in engineering for actuationand control of mechanical motion. ERF based controllablebrakes can apply very high electrically controlled resistiveforces and torques while their size (weight and geometricparameters) can remain small. These properties make themsuitable for use in force-feedback systems [4–9] includingvariable resistance rehabilitation devices. So far, the use ofERF actuating/resistive elements and brakes in rehabilitationhas been very limited. The few rehabilitation devicesemploying ERF elements that have been developed so far werefixed based, non-portable, non-wearable systems [10–12].Initial prototypes of portable, variable resistance ERF basedrehabilitation devices for the hand and the knee have beenproposed in [13, 14].

Recently, a new type of portable and controllable activeknee rehabilitation orthotic device (AKROD), shown infigure 1, was developed. The main component of the braceis a resistive brake (or controllable damper) that will be used toresist knee flexion and extension in iso-inertial, isokinetic, andisometric exercises as well as during retraining of gait. Theknee brace is composed of straps and rigid components forattachment to a leg, with a central hinge mechanism where agear system is connected. The key features of the AKRODinclude: a compact, lightweight design with strong, highlytunable torque capabilities, full portability with on-boardpower, control circuitry, sensors, and real-time closed loopcomputer control for optimizing rehabilitation exercises whilein use. The variable damper component is achieved throughan electro-rheological fluid (ERF) element that connects to theoutput of the gear system. A torque sensor and an opticalencoder provide torque and joint position feedback.

To be able to use such ERF powered orthoses inrehabilitation tasks, it is of primary importance to be ableto accurately control the resistive torque applied by the ERFbrake. It is the purpose of this paper to propose anddemonstrate the effectiveness of a new torque controller forERF brakes.

While a lot of research has been performed on the design,modeling and testing of ERF based resistive devices, littlework has been performed on their closed loop control. Mostof the literature in this area studied the position control [15]while very little work has been performed on the force/torquecontrol of these devices. ERF devices are generally usedwith position control as dampers to avoid vibration [16], such

as in vehicle suspensions [17] or for developing anti-seismicbuildings [18]. Position control has also been applied in ERFdevices such as valves [19]. Force control applications ofERFs have been studied [20] where the tip of a robotic fingerwas equipped with an ERF actuated component that acts as anactively controlled damper. This allows optimal absorption ofthe impulse forces at the contact transitions, while the explicitforce control of the finger is left to a conventional DC motor.Finally, the development and experimental verification of anaccurate closed loop torque control for ERF brakes is used withhaptic joysticks in [21]. A non-linear proportional integral (PI)controller with a feedforward loop was proposed for the work.

In this paper, we go a step further than [21] and weextend the capabilities of the non-linear PI controller by addingan adaptive algorithm. Due to various reasons, such asenvironmental temperature or humidity changes, ERFs presenta slight change in their material properties which means thatwhen a closed loop torque controller is used, the control gainsneed to be changed frequently. By adapting the controller tothe new environmental conditions we demonstrate excellentperformance of the controller all the time. Furthermore, in thispaper non-linear controllers are tested on a new ERF brakearchitecture, that of a multiple concentric cylinder concept,instead of the previous ERF brake architecture that was basedon a flat plate concept as described in [21]. Finally, preliminaryresults are obtained on the implementation of our non-linear,adaptive controller on the AKROD prototype.

2. Experimental systems

To test the performance of the controllers we developed twodifferent ERF brakes. The first is a low torque brake consistingof a single set of concentric cylinders. The second brake wasa high torque one based on a multiple concentric cylinderdesign. Both brakes were placed on a custom-made ERFtesting apparatus that allowed us to accurately measure theperformance of the brakes and induce known disturbances tothe system. The low torque brake served as a simple ERFdevice to test the controllers, while the high torque brake wasexactly the one used on the active knee orthosis as shownin figure 1. Finally a prototype of AKROD was developedand tested in closed-loop torque control experiments. In thissection we provide technical details for these experimentalsystems.

2.1. Low torque ERF brake

This brake concept consists of a rotating, cylindrical electrodeplate located concentrically with another fixed cylindricalelectrode plate as shown in figure 2. The inner and outercylindrical electrodes are separated only by a thin layer offluid and applying an electric field across the gap alters thefluid’s properties. More specifically, the fluid’s yield stressis increased. When the rotating cylinder is in motion, thehigher yield stress corresponds to an increased shear stresson the electrode’s surfaces which eventually creates increasedresistive torque to any torque applied externally by a humanoperator.

Figure 3 shows the actual prototype of this brake. Itscharacteristics include an outer cylinder radius of 43.18 mm

419

J Nikitczuk et al

IInnnneerr--CCyylliinnddeerr,,PPoossiittiivvee EElleeccttrrooddee

OOuutteerr--CCyylliinnddeerr,,NNeeggaattiivvee EElleeccttrrooddee,,

FFiilllleedd wwiitthh EERRFF((ccuutt aawwaayy vviieeww ))

Figure 2. Concentric cylinder low torque ERF brake concept.

Figure 3. Prototype of the low torque ERF brake containing a singleset of concentric cylinders.

and an inner cylinder radius of 42.42 mm, resulting in a gapof 0.76 mm in between the electrodes. The overlapping heightof the two electrodes was 18 mm. The brake was capable ofapproximately 375 mN m at 2.5 kV.

2.2. High torque ERF brake

Shear forces are directly proportional to the surface area ofthe electrodes, so to maximize the torque/force output from anERF-based resistive element, the surface area of the electrodesneeds to be increased while the volume of the whole systemis as small as possible. In this project, we used a novel wayto maximize the surface area of the electrodes while keepingthe resistive element’s overall size as small as possible. Weemployed the concept of two electrodes, each one being a setof multiple concentric cylinders. One of the electrodes servedas the fixed one and was located on the external side of theresistive element, while the second electrode served as therotating one that could ‘mate’ with the fixed one so that severalconsecutive pairs of concentric cylinders are formed. Figure 4shows each one of the electrodes, fixed and rotating, witheach one’s concentric cylinders already ‘mated’. The multipleconcentric cylinder design for the two electrodes allows formaximum shearing surface area while maintaining a compactoverall volume for the resistive element. The actuation ofthe viscous fluid occurs within the very small gap betweenconsecutive cylinders of the fixed and rotating electrodes andis consequently creating a resistive torque on the rotating shaft.By manipulating the strength of the electric field applied onthe fluid, at each pair of consecutive concentric cylinders, thetorque can be easily controlled.

Figure 5 shows the actual prototype of this brake. It usedfive concentric rotating electrode plates and was significantlystronger than the single concentric cylinder pair brake. It wasapproximately 165 mm in diameter, with a gap of 1.27 mmbetween each of the electrodes, and 38 mm high. It is capableof approximately 8 N m at 2.5 kV.

2.3. ERF testing apparatus

Two ERF brakes were tested in laboratory experimentsusing the ERF testing apparatus (ETA) shown in figure 6.The ETA provides a computer-controlled environment totest ERF actuators and brakes in various conditions and

Figure 4. Multiple concentric cylinder high torque ERF brake concept.

420

Control of electro-rheological fluid based resistive torque elements for use in active rehabilitation devices

Figure 5. Prototype of the high torque ERF brake based on amultiple concentric cylinders concept.

scenarios including emulating the interaction between humanmuscles involved with the knee brace’s ERF brakes. Thebrake’s rotating electrode is driven by a computer-controlledcommercially available DC motor that can emulate externalinputs to the ERF brake including torques produced at a humanknee joint. ETA also includes a torque sensor to measuretorques produced by the ERF, an optical encoder to determinethe ERF brake’s angular position and speed, a thermocouplefor temperature measurements, and a Trek model 610C highvoltage power supply that includes feedback sensors for precisereadings of current and applied voltage. The testing programalso includes algorithms that automate data testing over longtime intervals.

2.4. Active knee rehabilitation orthotic device (AKROD)

To complete the verification of the control, it was implementedwith a third system, an ERF knee device. A multiple concentriccylinder ERF brake was designed and fabricated and was thenattached via a 6.2:1 planetary gear and sensory system to astandard rehabilitation style brace. Based on the electric fieldsent to the ERF elements, a corresponding bias force to theknee joint is experienced by the user. A CAD rendering of thebrace, gears, and sensory system can be seen in figure 7 (top)with the fabricated components in figure 7 (bottom).

The knee orthosis includes a sensory system, which wasrequired for the control algorithm. The first is an opticalencoder for measuring the angle and velocity of the knee(found on the inside of the ERF brake, see figure 7 (top)). Thesecond sensor is a torque sensor for measuring the resultanttorque between the patient’s knee and the ERF brake. Torquesensors capable of accurately reading the forces a humanknee produces are inherently large and awkward to conceal.To overcome this, a sensory system, utilizing two miniaturecompression sensors, was developed and incorporated into thedesign. The two miniature compressor sensors are arrangedin opposite directions to measure torque via a force from amoment arm in both flexion and extension (see figure 7 (top)).Currently, electrical power to the orthosis is provided usinga tether for off-the-wall power acquisition. A Trek model610C high voltage power supply was used to amplify the inputvoltage to the levels needed to activate the ERF brake. In the

Figure 6. ERF testing apparatus (ETA).

future, a fully portable power supply/high voltage amplifiersystem will be developed and implemented.

3. Non-linear PI torque control: method and testing

The non-linear PI torque control developed in [21] isimplemented in this section in the low torque single concentriccylinder pair ERF brake. The experimental results demonstratethe need for an adaptive control scheme that is described insection 4.

3.1. The method

A block diagram of the closed loop torque controller developedin [21] is seen in figure 8. The details described in [21] will besummarized here to explain the process behind employing thenon-linear PI controller.

Using figure 8 as a reference, the desired torque, denotedby Td, is given as an input by the user. Td is then compared withthe torque obtained from the torque sensors. The resultant errorbetween them is then fed into the controller. The controller is aPI (proportional integral) block. A feedforward loop is addedto the output of the controller, resulting in TPI, which is then fedinto an inverse model of the system shown by equation (1) [21].In addition to the PI control output, TPI, being fed into theinverse model, several other variables are used and/or must becomputed. Vlim, T0, and k, all functions of velocity, are foundthrough sensory feedback that supplies the velocity value. Vlim

is defined as the limiting voltage of the system where belowthis value the ERF system is reactionless. The torque, T0,is defined as the friction torque or the torque apparent in thesystem when the voltage is equal to zero. The inverse modelof equation (1) is derived from equation (2) which is a genericdescription of the torque output of an ERF system based on thevariables, Vlim, T0, k, and input voltage, V

V (T , θ ) = Vlim(θ) +√

TPI − T0(θ )

k(θ )(1)

T = T0 + k(V − Vlim)2. (2)

421

J Nikitczuk et al

Figure 7. Electro-rheological fluid based knee device—top: CAD rendering of brace, gears, and sensory system; bottom: assembledprototype and close-up views of its components.

By solving the equation in terms of voltage, V , producingan inverse model (1), the output of the controller is now anactuation signal for the ERF brake. The variables Vlim, T0,and k are specific to each ERF system. In order to determinethese constants, graphs similar to the one in figure 9 are foundusing the ERF test apparatus described in the previous sectionand shown in figure 6. They are created by setting the motor

at a constant speed and slowly ramping up the voltage tothe ERF brake. By plotting the changing voltage against thetorque readings, all three variables can be found as functionsof the velocity. Equations (3a)–(3c) give the three equationsfound specific for the low torque ERF brake and test bedused for control development. The ERF brake was filled with3365S fluid, from Smart Technology Limited [22], and all tests

422

Control of electro-rheological fluid based resistive torque elements for use in active rehabilitation devices

Figure 8. Block diagram of the non-linear PI torque control of an ERF brake.

Figure 9. Graph for finding variables Vlim, To, and k.

throughout this work were performed using the same fluid

Vlim = (0.0001 ∗ velocity) + 0.72 (3a)

T0 = (0.0252 ∗ velocity) + 21.30 (3b)

k = (0.026 ∗ velocity) + 19.47. (3c)

The units in equations (3a)–(3c) are volts for Vlim, mN mfor T0 and deg s−1 for the velocity.

3.2. Results

To begin testing, the integral and proportional gains of the PIcontroller were found experimentally. The proportional andIntegral gains were appropriately set to be Td ∗ 0.000 17 andTd ∗ 0.000 48 (s−1), respectively, where Td is the numericalvalue of the desired torque. Using these gains, numeroustests were performed for varying desired torques and motorvelocities. The motor was allowed to speed up to the userdefined velocity, then the controller was started and proceededto achieve the desired torque. Nearly all results from theseexperiments are well represented by figure 10. Again, theseresults were obtained with the low torque brake.

The average settling time of the system is in the range of0.2 s. However large oscillations (as seen in figure 10) areobtained during the transient state. This is identified to be dueto the unmodeled dynamics of the system. More specificallyfor the dynamics issue, a spring-like behavior was exhibited bythe ERF brake being tested due to the virtual ‘impact force’that it experienced when going from a no-field state to the high

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Time (seconds)

To

rqu

e (m

N m

)

Torque vs. Time(for desired torque of 240 mNm)

Figure 10. Initial torque versus time relationship with non-linear PIcontroller for 240 mN m.

voltage activated state in the fluid reaction time, less than amillisecond. The fact that the fluid properties model was quiteinaccurate and dependent on numerous other variables besidesthe ones taken into consideration (temperature, humidity, etc.)generally increased the effect of the virtual ‘impact force’(higher required voltage computed than necessary).

From these results, the following observations couldbe made. First, a large oscillating transient response wasdescribed and was due to the system’s unmodeled dynamics.As the ERF brake is not an active device but rather only apassive one, the PI was incapable of compensating for errorsby opposing the vibrations with an active force in the oppositedirection. This resulted in large oscillations which eventuallydamped out with time. This would certainly be a cause forconcern when actually implementing the controller in practicalapplications. Previous work in [21] did not exhibit theselarge ‘impact forces’ due to the much weaker ERF brakeand lower voltages utilized. Second, as the fluid propertieschange slightly on a daily basis, this could largely affect theERFs performance. Due to various environmental reasons,such as temperature or humidity changes, ERFs change theirmaterial properties slightly (e.g. shear stress and viscosity)that in turn will affect the resistive torque output of theERF brake. This means that, when a closed loop controlleris used, the coefficients of the model in equations (1)–(3)need to be changed frequently. By adapting the controllerto the new environmental conditions instead, it is possibleto experimentally demonstrate excellent performance of thecontroller all the time. This meant that the gains of the PI

423

J Nikitczuk et al

0

100

200

300

400

500

600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (seconds)

To

rq

ue

(m

N m

)

Torque vs. Time

(for desired torque of 240 mNm)

Figure 11. Torque versus time plot of the non-linear PI controllerwith step logic function.

controller had to be changed daily for the same response tobe realized day to day.

4. Adaptive non-linear PI torque control: methodand testing

4.1. Step logic

To eliminate the large oscillations experienced by the systemduring the ‘transient stage’, a simple solution was found. Astep logic function was implemented at the output of theinverse model. This prevented the controller from supplyinga virtual ‘impulse’ but rather increase the voltage in a seriesof steps. In other words a maximum voltage differential wasset which limited the increase of the output voltage sent to thebrake. The technique used in this step is very similar to a zero-order-hold function that approximates a signal (in our case acontrol signal) with a series of step inputs where each stepinput is applied for the duration of the sampling interval andthen its value is changed rapidly to the value correspondingto the next discrete sample value. The result of adding thiscomponent is seen below in figure 11. It was very effectiveand from the graph two important verifications can be made.The first is the obvious inaccuracy of the model, which is thereason for the large overshoot. The second is the effectivenessof the PI control to pull the overshoot down to the desiredtorque (steady state settling down to the desired torque whichis denoted by the red (horizontal) line).

4.2. Adaptive control algorithm

An adaptive component was developed for the controller totake into account the changes in the ERF material properties.The adaptive algorithm worked to minimize the effect of theinaccurate model on the controller. This addition servedto make the controller less dependent on the system andits model by adjusting over time to the current conditions.More specifically, it enabled the controller to compensate forinaccuracies in the model that caused overshoots or slow risetime, training it to achieve an optimal response.

The adaptive control was based on a B-spline technique.A B-spline is similar to a Bezier curve in that it obtains acontinuous function, from a set of known control points ornodes. In a B-spline curve, changes to these certain pointswill affect points in the immediate vicinity of that change. By

changing a series of nodes gradually, the whole curve can bechanged. The B-spline modeling is given by the followingequation:

C(k) =n∑

i=0

Ni, j (k) ∗ Pi (4)

where C(k) is the curve function, Pi are the control points, k isthe variable against which the model is defined, (torque in thiscase), n + 1 is the number of points found by the spline, and jis the order of the curve ( j = 2 used here). The basis functionis given by the term Ni, j (k) which is defined as:

Ni, j (k) = k − ki

ki+ j − kiNi, j−1(k) + ki+ j+1 − k

ki+ j+1 − ki+1Ni+1, j−1(k)

(5)where

Ni,0(k) ={

1 if ki � k � ki+1

0 otherwise.(6)

This recursive formulation for the B-spline basis functionlends itself well to digital implementation and increasing theprecision of the curve is simply a matter of adding furtheriterations (i.e. increasing j).

In this system 11 control points, or nodes, were chosen.The control points for the B-spline are stored in a file and readat the beginning of each test cycle. These values are then usedto interpolate the 90 values of the spline curve. The propercompensation term is selected from this curve for the desiredtorque and used throughout the test for adjusting the modelaccordingly. Immediately following the test, the first inflectionpoint’s underdamped or overdamped characteristics, namelyovershoot or slow rise time, are used to proportionally changethe proper control point(s) and thus the compensation termsfor the next test. The proportional factor used was based on agolden section optimization method, 0.618. This is added tothe output of the PI controller.

The block diagram of the hybrid controller is shown abovein figure 12. It consists of the PI control as well as the adaptivecomponent. The error signal is fed into the PI control. Theoutput of the PI control is then added to the torque desired(Td) along with the compensation term from the adaptivecomponent. The compensation term which is added has beencalculated according to the basis function obtained from theprevious test cycle. The output is then fed into the ERF brakethrough the inverse model. In this way the adaptable routinecalculates compensation factors that are used to drive the initialmodel predicted torques to produce results closer to the desiredtorque. In other words, the adaptive component compensatesfor the inaccuracies in the model that cause overshoots or slowrise time and can be trained to achieve an optimal response.

4.3. Results

Tests were conducted for various torques at numerous constantvelocities. All results in this section were obtained with the lowtorque brake. The torque was varied from 120 to 400 mN m. Atthe beginning of each test the system read the values of storedweighting factors. These acted as the inputs to the B-splinealgorithm which constructed the spline curve from the 11 nodepoints. Not until the first inflection point occurred in thetorque versus time data, was the PI component of the controller

424

Control of electro-rheological fluid based resistive torque elements for use in active rehabilitation devices

Figure 12. Closed loop block diagram of the hybrid controller.

Spline Curve(at initilization)

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

0 20 40 60 80 100

Initial Torque vs. Time(for desired torque of 200 mN m)

0

100

200

300

400

500

600

0 0.2 0.4 0.6 0.8 1Time (seconds)

To

rqu

e (m

N m

)

Figure 13. Adaptive control—left: initial spline curve indicating the torque correction (in mN m); right: torque versus time plot.

Spline Curve (adapting)

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

0 20 40 60 80 100

Adapting Torque vs. Time(for desired torque of 200 mN m)

0

100

200

300

400

500

600

0 0.2 0.4 0.6 0.8 1

Time (seconds)

To

rqu

e (m

N m

)

Figure 14. Adaptive control—left: adapting spline curve indicating the torque correction (in mN m); right: corresponding torque versus timeplot (first out of three training tests required).

activated. The system stored the maximum overshoot orundershoot during the transient stage and compared it withthe desired torque. The difference between these two valueswas used to proportionally alter the weighing factor for thatparticular desired torque for use in the next test cycle. Thenew weighting factors are stored and these are then used forconstructing the spline curve for the next cycle. For eachsubsequent cycle, the response is further improved.

The collected data shown in figures 13–15 display asystem being trained for a desired torque of 200 mN m.Figure 13 corresponds to the stage when the system is runfor the first time. Since the weighing factors are initializedto zero, the spline curve obtained is a straight line along the xaxis. As the compensation factor corresponding to this is 0, theadaptive component of the hybrid controller does not affect the

controller’s output and therefore a large overshoot is obtainedduring the transient state.

The PI control is initiated once the first inflection pointoccurs (in this case the overshoot point). It effectively bringsdown the output to an accurate steady state. The inflectionpoint (or overshoot) is used to compute the shift in the B-splinecurve. This new spline curve with its new node points are usedas inputs for the next test cycle which are shown in figure 14. Itcan be seen that the adaptive component has started acting andit contributes towards decreasing the overshoot. The overshootdisappears when the system is fully trained, five test cyclesfor the test shown, and these results can be seen in figure 15.Performing the same operation with various other torques theaverage rise time was found to be 0.08 s while the settling timewas 0.1 s. The average steady state error was around 0.17%.

425

J Nikitczuk et al

Spline Curve (final)

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

0 20 40 60 80 100

Final Torque vs. Time(for desired torque of 200 mN m)

0

100

200

300

400

500

600

0 0.2 0.4 0.6 0.8 1Time (seconds)

To

rqu

e (m

N m

)

Figure 15. Adaptive control—left: final spline curve indicating the torque correction (in mN m); right: corresponding torque versus time plot.

Torque vs. Time

(for desired torque 360 mNm)

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5 6 7 8 9 10

Time (seconds)

To

rq

ue (

mN

m)

Torque vs. Time

(for desired torque of 240 mNm)

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5 6 7 8 9 10Time (seconds)

To

rq

ue (

mN

m)

Figure 16. Disturbance response of final controller at two different desired torques.

Therefore it can be seen that the problems faced initiallydue to the presence of only the PI controller have beenresolved. The oscillations obtained initially due to the systemdynamics have been dealt with by the introduction of a steplogic function at the output of the inverse model. The additionof an adaptive component to the controller takes care of theinaccuracies in the mathematical model of the system andmakes the controller less dependent on the system. This inturn drastically improves the ‘transient response’ of the systemafter several training sessions. Also, although in equation (4)it is clear that the output of the curve will be more accurateif the order of the equation is increased, a B-spline curve ofonly order 2 was used and demonstrated excellent behavior.Therefore increasing the order would only be an unnecessarycomplication and an optimal adaptive algorithm has beenattained.

4.4. System response to disturbances

The system was also tested for external disturbance response.This was performed by introducing external disturbances whilethe system was being tested. It can be seen in figure 16that the controller is extremely effective at compensating forsystem disturbances and effectively drives the output in adirection which makes it quickly return to the desired torque.It is important to note, the weighing factors for the adaptivecomponent are not changed during these disturbance tests. Thealgorithm does not consider a disturbance which is not in thetransient state as an overshoot/undershoot. Therefore, as the

Figure 17. Non-linear PI torque control of high torque ERF brake.

first inflection point has already been experienced, any largedisturbances are purely compensated for by the PI control.

5. Tests with the high torque brake and the AKROD

The same controllers as described in sections 3 and 4 weretested with the high torque brake and the knee brace. Basictests with the simple non-linear PI torque control wereperformed and a good representation of the results found canbe seen in figure 17.

It was similarly seen that the high torque brake’s torquewas well maintained, but only after the transient oscillationsdamped out. To solve this, the same procedures were

426

Control of electro-rheological fluid based resistive torque elements for use in active rehabilitation devices

Figure 18. Adaptive non-linear PI torque control with the hightorque ERF brake.

Torque vs. Time(for desired torque of 10,000 mN m)

-2

0

2

4

6

8

10

12

0 1 2 3 4 5

Time (seconds)

Torq

ue

(Nm

)

Figure 19. Adaptive non-linear PI torque control on ERF kneedevice—user is shown going from a resting position to being resisteda desired 10 N m during an extension or flexion exercise.

performed with first the step logic function component beingadded to the algorithm and finally, the adaptive routine beingadded. Figure 18 shows the final results. The control’seffectiveness was equally as impressive and helps verify therobustness of an adaptive non-linear PI torque control for ERFbrakes.

The knee device was then worn while exercises in bothextension and flexion were performed. Once activated, theadaptive non-linear PI torque control created a resistance to theuser’s motions that was felt as a smooth and continuous forceby all tested. The results can be seen graphically in figure 19(where the user is shown going from a resting position tobeing resisted 10 N m during an extension or flexion exercise).The control produced accurate resistive forces and respondedwell to the inconsistent forces produced by the human. Thisfinal verification of the adaptive non-linear PI torque controlconfirms its effectiveness with human-interactive ERF devices.

6. Conclusions

The aim of this project was to create a controller whichcould accurately control the torque output of ERF brakes.It was verified that the basic non-linear PI control is aneffective method but with unsatisfactory initial transientresponse capabilities. The problems arose from severalfactors, including unmodeled dynamic system behavior andERF material property changes. To overcome these issues twocomponents were added to the non-linear PI control. The firstwas a step logic function. This was seen to be very efficient

at eliminating the oscillations due to the virtual ‘impact force’the system experienced.

The second component added was an adaptive algorithm.It was based on a B-spline concept that trained itselfto compensate for inaccuracies in the model and varyingenvironmental changes. The final controller was tested ona test bed under various conditions. It was seen that thefinal hybrid controller, with all components included, providedexceptional results, with low rise times and very good steadystate response for two different ERF brakes. Finally, thecontrol was used with an ERF knee device and showed morethan satisfactory results. The unique method of using adaptiveroutines combined with non-linear PI control is thereforeproven to be a very efficient means of control for all rotarybased ERF brake systems.

Acknowledgments

This work was supported by the National Science Foundation(CMS-0422720). Any opinions, findings, conclusions orrecommendations expressed in this publication are those of theauthors and do not necessarily reflect the views of the NationalScience Foundation. The authors would like to thank Mr A Dasand Mr H Vyas for their assistance in the implementation of thecontrol algorithms in the early stages of this work.

References

[1] Block H and Kelly J P 1988 Electro-rheology J. Phys. D: Appl.Phys. 21 1661–77

[2] Conrad H 1998 Properties and design of electrorheologicalsuspensions MRS Bull. 23 35–42

[3] Gast A P and Zukoski C F 1989 Electrorheological suspensionsas colloidal suspensions Adv. Colloid Interface Sci. 30 153

[4] Kenaley G L and Cutkosky M R 1989 Electrorheologicalfluid-based robotic fingers with tactile sensing Proc. 1989IEEE Int. Conf. on Robotics and Automation (Scottsdale,AR) (Piscataway, NJ: IEEE) pp 132–6

[5] Wood D 1998 Editorial: tactile displays: present and futureDisp. Technol. Appl. 18 125–8

[6] Monkman G J 1992 Electrorheological tactile display Presencevol 1, No. 2 (Cambridge, MA: MIT Press)

[7] Taylor P M, Hosseini-Sianaki A and Varley C J 1996 Surfacefeedback for virtual environment systems usingelectrorheological fluids Int. J. Mod. Phys. B 10 3011–8

[8] Sakaguchi M and Furusho J 1998 Force display system usingparticle-type electrorheological fluids Proc. 1998 IEEE Int.Conf. on Robotics and Automation (Leuven, Belgium, May1998) (Piscataway, NJ: IEEE) pp 2586–90

[9] Bose H, Berkemeier J and Trendler A 2000 Haptic systembased on electrorheological fluid Proc. ACTUATOR 2000Conf. (Bremen, Germany, June 2000)

[10] Sakaguchi M, Furusho J and Genda E 1999 Basic study onrehabilitation training system using ER actuators Proc. IEEEInt. Conf. on Systems, Man and Cybernetics vol 1(Piscataway, NJ: IEEE) pp I-135–40

[11] Koyanagi K, Furusho J, Ryu U and Inoue A 2003 Developmentof a rehabilitation system for the upper limbs in a NEDOproject Proc. IEEE Int. Conf. on Robotics and Automationvol 3 (Piscataway, NJ: IEEE) pp 4016–22

[12] Kikuchi T, Furusho J and Oda K 2003 Development ofisokinetic exercise machine using ER brake Proc. IEEE Int.Conf. on Robotics and Automation vol 1 (Piscataway, NJ:IEEE) pp 214–9

[13] Khanicheh A, Muto A, Triantafyllou C, Weinberg B,Astrakas L, Tzika A and Mavroidis C 2005 MR compatibleERF driven hand rehabilitation device ICORR 2005: Proc.9th IEEE Int. Conf. on Rehabilitation Robotics (Chicago, IL,June–July 2005)

427

J Nikitczuk et al

[14] Nikitczuk J, Weinberg B and Mavroidis C 2005 Rehabilitativeknee orthosis driven by electro-rheological fluid basedactuators Proc. 2005 IEEE Int. Conf. of Robotics andAutomation (Barcelona, Spain, April 2005) (Piscataway, NJ:IEEE)

[15] Choi S B 1999 Control of ER devices Int. J. Mod. Phys. B13 2160–7

[16] Powell J A 1995 ERF as a means of vibration suppressionProc. Int. Conf. on Vibration and Noise (April 1995) pp 1–8

[17] Rettig U and Von Stryk O 2001 Numerical optimal controlstrategies for semi-active vehicle suspension with ERFdampers Fast Solution of Discretized Optimization Problems(ISNM vol 138) ed K-H Hoffmann, R H W Hoppe andV Schulz (Basle: Birkhauser) pp 221–41

[18] Gavin H P 2001 Control of seismically-excited vibration usingER materials and Lyapunov methods IEEE Trans. Autom.Control 9 27–36

[19] Nakano M, Minagawa S and Hagino K 1999 PMW flow ratecontrol of ER valve and its application to ER actuatorcontrol Int. J. Mod. Phys. B 13 2168–75

[20] Akella P and Cutkosky M 1995 Contact transition control withsemiactive fingertips IEEE Trans. Robot. Autom. 11 859–67

[21] Vitrani M, Nikitczuk J, Morel G and Mavroidis C 2004 Torquecontrol of electro-rheological fluidic actuators for hapticvehicular instruments control Proc. 2004 IEEE Int. Conf. onRobotics and Automation (New Orleans, LA, April–May2004) (Piscataway, NJ: IEEE)

[22] Smart Technology Limited, http://www.smarttec.co.uk/erf.htm

428