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This is to certify that the

thesis entitled

PRECISE CONTROL OF ELECTRORHEOLOGICAL
FLUIDS IN COMPOSITESTRUCTURES

presented by

Kara R. McGregor

has been accepted towards fulfillment
of the requirements for

MS

degree in ME

 

 

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1/96 animus-p.14

PRECISE CONTROL OF ELECTRORHEOLOGICAL FLUIDS

IN COMPOSITE STRUCTURES
By

Kara R. McGregor

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1997

ABSTRACT
PRECISE CONTROL OF ELECTRORHEOLOGICAL FLUIDS
IN COMPOSITE STRUCTURES
By

Kara R. McGregor

Electrorheological (ER) fluids have variable viscosity, heat transfer and electrical
properties based on an internal organizational state which can be changed with the
application of an electric field. ER fluids have not attained widespread use due to
relatively slow, nonlinear, and unpredictable response. Fast, linear and predictable
response is needed for applications to systems such as variable shock absorbers and
controllable heat exchangers. It is imperative that simple and accurate methods be
developed to control ER fluids.

This study presents a new method for the remote measurement of fluid activation
state and a control strategy to provide fast and precise control in a graphite-epoxy
composite structure. Electrical conductivity changes are used here for an accurate sensor
of fluid activation state. Laboratory results clearly showed the conductivity of the
system rose to levels consistent with the state of the fluid. The precision control strategy
used conductivity feedback to adjust the electric field input to achieve the level of
chaining desired in any fluid. Response speed was increased by over 170% while

decreasing system error from 100% to 0.2% after 60 seconds.

Copyright by
Kara Renee McGregor
1997

ACKNOWLEDGMENTS

I would like to express my gratitude to Dr. Clark Radcliffe for his expert guidance
throughout my research. He constantly challenged me to expand my mind to find both
the answers and the questions that represent this body of work. My master's committee
member's, Dr. Ranjan Mukherjee and especially Dr. John R. Lloyd who provided me with
both a laboratory and patient guidance, will always have my sincere thanks. They added
the balancing voices that gave this work the perspective it needed.

I would also like to express my thanks to the other members of our team of
researchers that gave me both their assistance and their friendship. Ruth Andersland and
Jeff Hargrove answered all my questions and got me started on the right path. My lab
mates, Brooks Byam, Charles Birdsong and Omar Hayes deserve recognition for all their
daily help and listening ears. Above all, I would like to thank Gloria Elliott who
collaborated on much of the video work and shared her research, answers and questions
with me.

This research was funded by the State of Michigan Research Excellence Fund,
administered through the Composite Materials and Structures Center at Michigan State
University.

Finally, I would like to thank my family for their love and support. My parents,
F. Scott McGregor and Tamyra Jackson, my brother Erik, my sister Kristen, and my
grandparents Kenneth and Betty Lou Jackson. 1 would also like to thank Tom Oliver
without whose love, patience and housekeeping skills I am not sure I would have survived

the last year.

iv

TABLE OF CONTENTS

LIST OF TABLES .............................................................................................................. vii
LIST OF FIGURES ............................................................................................................ viii
NOMENCLATURE ........................................................................................................... x
INTRODUCTION ............................................................................................................. 1
FEED-FORWARD AND FEEDBACK SYSTEMS COMPARED .............................. 5
ELECTRICAL CONDUCTIVITY SENSOR DESIGN .................................................. 6
ER Fluid Preparation ............................................................................................... 7
ER Fluid Composite Structure ................................................................................ 7
ER Fluid Video Slide Assembly .............................................................................. 8
ER Fluid State Sensor .............................................................................................. 8
ELECTRICAL CONDUCTIVITY AS A STATE SENSOR ........................................ 9
PROPORTIONAL FEEDBACK CONTROL ................................................................. 12
ER FLUID FEEDBACK CONTROLLER SYSTEM .................................................... 13
MEASURED FEEDBACK RESPONSE: PROPORTIONAL CONTROL .................. 14
PROPORTIONAL - INTEGRAL FEEDBACK CONTROL ......................................... 17
MEASURED CLOSED LOOP RESPONSE: PI CONTROL ............................................ 18
CONCLUSIONS ................................................................................................................. 20
APPENDIX A ................................................................................................................... 22

V

APPENDIX B .................................................................................................................... 24

LIST OF REFERENCES .................................................................................................. 37

vi

LIST OF TABLES

Table 1 - Comparisons of feed-forward and proportional feedback control
gain and time constants for ER fluid electrical conductivity
measurements (10% by weight) .................................................................... (16)

vii

LIST OF FIGURES

Figure 1 - Microscopic views of particle chaining over time under a voltage of
1000 VDC(Elliott, 1997) ............................................................................. (2)

Figure 2 - Laboratory measurement of zeolite ER fluid response using a
prototype optical sensor feed-forward control, pulse train

zeolite-fluid (1% Vol. Fraction, Dry) (after Tabatabai, 1993). ................... (3)
Figure 3 - F eed-forward control system ...................................................................... (5)
Figure 4 - Feedback control system ............................................................................ (6)
Figure 5 - ER fluid composite structure ...................................................................... (7)
Figure 6 - ER fluid slide assembly for the microscope (Elliott, 1997 and

Hargrove, 1997) .......................................................................................... (8)
Figure 7 - Transient electrical conductivity of the ER fluid in the video slide

assembly under increasing field strengths (10% by weight) ....................... (9)
Figure 8 - Transient electrical conductivity measurements of the ER fluid

under a varying field (10% by weight) ........................................................ (10)
Figure 9 - Transient electrical conductivity measurements of the ER fluid

under increasing field strengths ( 10% by weight) ............................. (1 1)
Figure 10 - System flow chart ....................................................................................... (13)

Figure 11 - Proportional control of the ER fluid at a desired
electrical conductivity of 0.5 uSiemens and increasing levels of
proportional control (10% by weight) ........................................................ (14)

Figure 12 - Proportional controller action and response of the ER fluid at a
desired electrical conductivity of 0.5 uSiemens at KP = 30 (10%
by weight) ................................................................................................... (15)

viii

Figure 13 - PI control of the ER fluid at a desired electrical
conductivity of 0.5 uSiemens for KP = 3 and increasing levels
of integral control (10% by weight) ............................................................ (18)

Figure 14 - PI controller action and response of the ER fluid at a desired
electrical conductivity of 0.5 uSiemens for KP = 3 and K I = 30
(10% by weight) ......................................................................................... (19)

Figure 15 - Comparisons of the measured and calculated responses of the
ER fluid at a desired electrical conductivity of 0.5 uSiemens for
KP = 3 and K, = 10 (10% by weight) ....................................................... (20)

Figure Al - Comparison of electrical conductivity measurements of two
different ER fluid concentrations under a field strength of 500
VDC/mm (10% by weight) ......................................................................... (22)

Figure A2 - Comparison of electrical conductivity measurements of the same

ER fluid taken under identical field strengths of 700 VDC/mm
before and after twenty-four hours of settling (10% by weight) ................. (22)

Figure A3 - Saturation of an ER fluid under a field strength of 1000 VDC/mm
(10% by weight) ......................................................................................... (23)

Figure A4 - Microscopic views of broken chains in a previously activated ER
fluid ............................................................................................................. (23)

Figure A5 - Proportional controller response of the ER fluid at a desired
electrical conductivity of 0.5 uSiemens for Kp= 65 (10% by
weight) ........................................................................................................ (23)

Figure B1 - Virtual instrument front panel for data acquisition of ER fluids
composite structure .................................................................................... (25)

Figure B2 - Front panel for the data acquisition of the field applied in steps
for the ER fluids composite structure ......................................................... (29)

Figure B3 - Front panel for the proportional-integral controller for the ER
fluids composite structure .......................................................................... (33)

ix

NOMENCLATURE

Arabic Symbols

C = ER fluid state/conductivity

Cd“ desired conductivity

Cfb = ER fluid state of the feedback system

C fl = ER fluid state of the feed-forward system
D = feed-forward controller transfer function
E = error

G = system or plant (ER fluid) transfer function
H = ER fluid state sensor

I = current

K = feedback controller transfer function

K, = feedbackintegral gain

K P = feedback proportional gain

k = system gain

k fb = feedback system gain

N = external system disturbance

S = Laplace transfer variable

T = transfer function

F = fieldlevel

Y = output from controller

Greek Symbols

AC
AF

1'

1,2,

ER fluid state signal
Input voltage change

system time constant

feedback system time constant

INTRODUCTION

Electrically controlled components are essential technology because static
mechanical parts have limited to zero adjustability and designs must be carefully
constructed to meet a variety of conditions. For example, a car suspension system is
designed for a range of loads, as well as road and weather conditions. Heat transfer
systems use fins designed from different materials to conduct heat away from the primary
system. It is impossible, with standard spring and damper combinations and materials
with constant heat transfer properties, to construct a system that will handle all feasible
conditions optimally. To do this we must build systems that are able to dynamically
adjust as the existing conditions change. In a world where technology increases every
day, systems must be increasingly dynamic and adjustable.

Engineers are currently working to develop "smart materials" whose properties
can change over a range of values. One such material is an electrorheological fluid first
recognized by Winslow in 1947. An electrorheological (ER) fluid is a mixture composed
of conducting particles suspended in a non conducting fluid whose rheology changes with
applied electrical field (Winslow, 1962; Klass and Martinek, 1967a). When an electric
field is applied to the fluid the conducting particles link together to form chains parallel to
the field. This chaining results in variable viscosity (Russel, 1980), heat transfer (Zhang
and Lloyd, 1992, Hargrove, 1997) and electrical properties (Klass and Martinek, 1967b;
Hass, 1993) which can be changed with the strength of the electric field.

Progressive particle chaining can be viewed microscopically (Figure 1). An ER

fluid is a substance composed of zeolite particles suspended in silicon oil. The zeolite

particles act as microscopic sponges and trap water molecules in their pocketed surfaces
allowing the particles to form dipoles (Davis, 1992b). Chains of particles develop over
time under a constant electrical field (Figure 1(a) to (c)). The particle distribution is
uniform before the field applied with increasing degrees of chaining alter the field
application. The electrodes are composed of 1 mm and 2 mm gaps, allowing 2 separate
field strengths to be viewed, 1000 VDC/mm and 500 VDC/mm. In figures (b) and (c) it
can be seen that the chains in the lower portion are much more clearly defined and thicker
than those formed in the upper region. This demonstrates that chains are both organized
more quickly and become more concentrated in stronger fields. The difference in the gaps
also produces an area where it is possible to verify that the chains form parallel to the
local field. Therefore, time, field strength and orientation affect the degree of chaining.

Non repeatable and slow response has hindered the use of the changes exhibited in
the field (Lloyd and Zhang, 1994). When activated, the fluid reaches steady state over a
large range of times and values, as indicated by the transmission of light through the ER
fluid under a varying field (Figure 2). With each new field application, the fluid both
responds more quickly and to a greater degree. One can never be sure exactly how
quickly, or to what degree the fluid will respond, making any precision devices

impossible. A method of precisely controlling the fluid and increasing the Speed of the

     

(a) 0 min. (c) 10 min.

Figure 1 - Microscopic views of particle chaining over time under a voltage of 1000 VDC
(Elliott, 1997)

 

 

  

1600 . '0.15 g
1400‘ Key ’0.13 g
m 1200 . ....... E ’0.11 E
§1ooo ‘ —T ’o.09 g
g 800' ‘o.o7 g
.5 600‘ 'o.05 g
E 400 ‘. ’o.oa g
2 200 ’o.o1 .8
o a

 

 

 

 

 

 

  

 

- -' - ' - ' - 1 - ' - 0
0 430 860 1290 1720 2150 2580 3010
Time (s)

Figure 2 -Laboratory measurement of zeolite ER fluid response using a prototype
optical sensor feed-forward control, pulse train zeolite-fluid (1% Vol.
Fraction, Dry) (after Tabatabai, 1993).
response are under development.
Previous work (Andersland, 1995; Radcliffe et a1, 1996) demonstrated control of
the ER fluid using light transmissivity as a measure of the chaining state (Figure 2). A
simple proportional feedback controller based on this sensor was developed which
produced a faster and more precise response. The proportional controller, however, was
limited by a signal to noise ratio in the sensor of about 10:1 which in turn limited both the
speed and precision of the system to gains of less than 5. In addition, light transmissivity
is measured through a transparent containment unit that most mechanical applications
could not allow. This investigation continues previous work with two major distinctions.
First, electrical conductivity was used as the state sensor. This sensor allowed a more
representative graphite-epoxy composite structure and generated less noise than exhibited
in the transmissivity sensor. Second, proportional-integral controllers were investigated
to improve the precision of the response.
The internal state of the fluid can be measured directly by the amount of chaining
present, or how well organized the particles are. The chaining state can be qualitatively
identified (Figure 1) as zero to high in microscopic views. The fluid has been described in

closed systems in terms of the viscosity, which is a derived property only obtained when

the fluid is flowing, however, a more direct measurement, dependent only on chaining is
needed.

Past studies of "conductivity effects" have focused on the conductivity of the
particles and the suspending fluids, particularly in relation to one another (Davis, 1992a;
Khusid and Acrivos, 1996). They have used these conductivities and the ratio between
them as one of the main factors for mathematically describing the mechanics behind
particle chaining. This paper uses the electrical conductivity of the ER fluid mixture and
its change over time after the application of an electric field as a measure of particle
chaining state. This investigation equates the change in conductivity with the change in
the state of the fluid much the same as changes in viscosity have been used.

The objective of this study is to demonstrate that 1) electrical conductivity is an
effective measurement of the state of the ER fluid and that 2) a feedback control method
can produce a faster and more predictable response. It will be shown, through the use of
electrical conductivity measures, that the standard or feed forward control of the fluid
reacts too slowly to be useful commercially. Feedback control using conductivity as a
measure of the state of the fluid will adjust the applied field to achieve the desired state

more quickly and accurately than previously possible.

F EED-FORWARD AND FEEDBACK SYSTEMS COMPARED

F eed-forward is the most common method for the activation of any system

(Figure 3). The controller, D(s) = G" (s) , is based upon knowledge of the relationship

between the output and the input of the system, G(S). The total output of the system,
C fl(s) , is represented in the Laplace domain by the system's response to both the

controller action, D(s), and external disturbances, N(s).

C Jgr“) = G(S)[D(S)Cdes(3) + N (8)]
= Cm“) iff D(s) = G"(s) and N(s) = o (1)

14(5)

External
Disturbance

. . Control
Desrred Ou ut . Controlled S stem
cat" i<> Gay Rats“
(Conductivity) “Ski/6(3) I - (ER Fluid) . .
, (Field) , (Conductrvrty)

Figure 3 - F eed-forward control system

(Field, Stress, etc.)

 

 

 

The precision of the feed-forward controller is dependent upon having an accurate,
invertable model of the system and negligible external disturbances. Any noise, N(s), or
imprecision in the model, G(s), will result in proportional errors in the output. The
input/output function must be both known exactly and invertable to allow precise feed-
forward control.

The unpredictable and Slow response of ER fluids is well known. For any given
input, a large range of outputs can be expected, affecting both the speed and the accuracy
of the desired response. Perturbations in the field activating an ER fluid showed a
response that varied in terms of the magnitude as well as the time required to reach steady
state (Figure 2). This indicates the non-linear nature of the system which has yet to be
sufficiently modeled. Without an invertable model of the system, it can easily be seen
that the method of feed-forward control is not effective and a more complicated, precision
control theory is required to attain the desired state. Therefore, we must consider the
other alternative.

Feedback control uses a sensor to measure the system's output, compares it to the
desired output and compensates for any difference by adjusting the input (Figure 4). The

controller, K(s), responds to the error, E(s), which is the difference between the desired
output, Cdes(s) and the actual system response, C fl,(s).

       
  

 

   

  
 

Desired Output + Em? . * Response
Cdes(5) Controller ER Fluid System Cfb(s)
(Conductivity) — K‘s) 0“) , (Conductivity)

 

 

 

Figure 4 - Feedback control system

____ G(S)[K(S)Cd_.,(8) + N(S)]
1+ K (s)G(s)H(s)

 

=Cd,,(s) iff K(s)—)oo and H(s)=1 (2)

The equation for C ,b(s) shows that the accuracy of response no longer requires

any knowledge of the physical system or the disturbances. Only a strong controller,
K(s), and an accurate sensor, H(s) are required to attain the desired response quickly and
precisely. Feedback or precision control is adjustable throughout the activation period,
relying on information gathered from system sensors to adjust the level of input as
needed. Constant and accurate monitoring of the system through sensors is essential to

precision control under changing conditions.

ELECTRICAL CONDUCTIVITY SENSOR DESIGN

The first goal of this study is to establish a fast, simple and accurate electrical
conductivity based sensor of the state of the fluid. The material property, the electrical

conductivity,

C = (3)

<|~

Conductive

Copper Tape
i‘ i - EJ.

 

 

 

 

 

 

 

 

 

 

Graphite-Epoxy Coupons Silicon rubber window

Figure 5 - ER fluid composite structure

ER Fluid Preparation

The manufacture of the ER fluid was accomplished in the laboratory by mixing the
silicon oil and zeolite particles according to the percent by weight chemistry standard.

This equation is given by

 

m .
Percent by weight= mini (4)

m + msilicon

zeolites
Laboratory conditions did not provide the constant humidity environment required to
produce a consistent water content in the zeolite particles. This produced a noticeable
difference in the response of some mixtures. All the solutions in the following

experiments were a ten percent by weight mixture.

ER Fluid Composite Structure

The ER fluid composite structure was composed of two unidirectional graphite-
epoxy composite panels measuring 9 cm x 9 cm separated by a 2 mm thick silicon rubber
insulating material enclosing a space 6.5 cm by 4.5 cm filled with the ER fluid (Figure 5).

This is the first investigation to use of this type of electrode on the ER fluid.

Aluminum Electrodes

 

Figure 6 - ER fluid slide assembly for the microscope (Elliott, 1997 and Hargrove, 1997)

ER Fluid Video Slide Assembly

The video device (Figure 6) was a set of aluminum electrodes bolted to a viewing
slide forming a gap of 1 mm. The fluid occupied the space between the electrodes and
was contained by the silicon insulating material. A microscope with a camera attached

was used to record visual images Simultaneously with conductivity data.

ER Fluid State Sensor

The state sensor was composed of data acquisition and control algorithms which
were programmed in a Power Macintosh 7100/80AV using National Instrument's
LabVIEW to create virtual instruments. To activate the system, the desired field was
output to a NB-MIO-16 L board connected to the computer, the output was amplified
200 times by a Trek Model 677A Supply/Amplifier. This field was then applied directly
to the structure to activate the fluid.

The direct measurement of both the field and the resulting system current was
allowed by the amplifier through the back panel of the main device. The NB-MIO-16L
board externally monitored the field and the current and the data was taken via the

LabVIEW Programs. The data was sampled over a specified time and the data was

averaged over discrete time intervals to remove some noise and reduce the number of data
points produced. The conductivity was then computed from the data.

The video apparatus had such a small contact area that a large voltage divider was
used to allow the measurement of a very small current (on the order of nAmps).
Therefore, the voltage across a 10 MQ/l MQ resistor was measured using LabVIEW

programs and converted into a conductivity value.

ELECTRICAL CONDUCTIVITY AS A STATE SENSOR

Chaining can be visually linked with a distinct rise in conductance (Figure 7).
With zero electric field, the particles are randomly distributed in all cases. This initial
state was the same for the three field strengths shown. The same mixture was used in

each trial, but the fluid in the apparatus was changed to provide a consistent starting

 
   
   
 
      

400 VDCI’mm

300 VDCt'mm

Conductivity (nSiemens)
RS

200 VDCme

1 00 200 300 400 500
1 minute Time(S) 8 minutes

 

  

 

I I

Figure 7 - Transient electrical conductivity of the ER fluid in the video slide assembly
under increasing field strengths (10% by weight)

10

 

 

 

 

A 018 ~~ 1— 720
" «~ Conductivit
5 0'16 ——y——* —— 700
0 E i r
g 0.12 A” z \r‘ E
5' 0.10 “r -, . ._ 660 g
'; 0.08 —~ ‘-. + 640 2.
‘6 0.06 ~~ * » g
5 i “r 620 ..
g 0.04 -_ , l
o “I, _. ., -- 600
o 0'02 Field

0.00 i i i 580

0 1000 2000 3000
Timo(e)

Figure 8 -Transient electrical conductivity measurements of the ER fluid under a varying
field (10% by weight)
point. Within one minute of activation, the particles aligned in varying strengths
according to the strength of the applied field. These three Slides can also be seen to
follow the corresponding electrical conductivity measurements. As time proceeds, for
each field there was a distinct rise in conductivity. At eight minutes, slides of the fluid are
again Shown. Closely observed, the chains appear heavier or more developed than the
previous slides. There was also a distinct difference between the successive fields just as
there is in the levels of conductance. The results show the electrical conductivity of the
ER fluid to be proportional to internal chaining in the fluid.

The non repeatable chaining response is demonstrated by means of the electrical
conductivity (Figure 8) as it was with transmissivity (Figure 2) which has been shown to
be a direct measure of chaining (Hargrove, 1997). The gains and time constants decreased
for each perturbation in the electric field. Every application of an electric field had a
direct effect on all subsequent applications, making the entire activation history essential
to determining fluid behavior.

The level of electrical conductivity decreased over time, rising less and less. This

seems to oppose earlier work regarding light transmissivity, which increased over time

ll

 
   
   
 

 

 

3? 0.09 ~—

g 0.08 + ..... .........

.5, 0.07 «- " 700 VDC/mm

" 0.06 ~—

g. 0.05 —~

’5 0.04 w 600 VDC/mm

33 0.03 «f

.3 0.02 500 VDC/mm

g 0.01 *5

0 0.00 + i i + ., __,
0 100 200 300 400 500 600

Time(s)

Figure 9 - Transient electrical conductivity measurements of the ER fluid under
increasing field strengths (10% by weight)

(Figure 2). Both responses may be due in some part to a small degree of settling. The
video data clearly shows that when the field is removed, the chains break from the
electrodes and fall without complete disintegration (Elliott, 1997), this would tend to
increase the settling effect if compared to the dispersed particles. While a settled fluid
would conduct less readily with the particles concentrated at the bottom, light
transmissivity would increase with the majority of the fluid free of particles. This effect
requires further study using simultaneous visual and state measurements to determine the
exact cause or causes.

The conductivity changes due to the application of an electric field are Shown over
time for three larger field strengths (Figure 9). The conductivity was low before the
application of the field corresponding to zero chaining. As time increased, at all field
levels the chaining of the fluid resulted in a noticeable increase in electrical conductivity
proportional to the field applied. In each case, formation of the internal particle chains
allowed electricity to be conducted more easily across the medium, therefore increasing its

conductivity.

12

Moisture content was a significant factor in the response of the ER fluid. Each
mixture, while consistent in percentage, was subject to a range of environmental changes,
especially humidity. Humidity produced both very sensitive and reactive fluids that
saturated at low field strengths, as well as fluids that did not react measurably. This
created an added problem in determining how the fluid would react.

Electrical conductivity can be equated with chain formation for any applied field,
therefore, it is clearly a more direct measurements of the state of the fluid than previous
properties used. The data also gave further evidence that feed-forward control is not a
precision control method for the ER fluid. Conductivity provides an excellent sensor for

a feed-back control strategy.

PROPORTIONAL FEEDBACK CONTROL
Now that an fast accurate sensor has been established, specific control strategies
can be discussed. Referring back to (2), if the controller K(s) is replaced by a constant,

KP, then the equation for the transfer function can be used to predict the closed loop time

constants and gains asng no noise N(s) = 0 and H(s) = 1.

 

 

 

 

 

T(s)_ Cfl,(s)_ ka(1+1:s) _ ka _ kfb (5)
Cdes(s) 1+[kKP/(l+t:s)] l+ka+13 1+tfl,s
kK r
whe k = P =>1 d r = =>O K 00
re 1” 1+»ka an 1” 1+ka as P:

This feedback controller is referred to as a proportional controller, is linear in nature, and
can be directly compared to the linear system response. The gains approach precision
and the time constants will become smaller as the proportional controller becomes
sufficiently large.

The performance of the feed-forward controller and proportional controller will be
compared and evaluated by modeling the ER fluid as a first order system where the gain

and the time constant vary widely over a large range of values. These values are

13

dependent upon the length of time that the fluid has been activated, the strength of the
field and other physical factors that have been previously mentioned. The linear model of

the fluid can be expressed in standard form as

 

k C(s)
G = = — 6
(S) 1+T-s F(s) 0
where
AI
= — 7
AF ( )
which is the conductivity adjusted by the separation of the composite plates and
t' = At for 63.2% of steady state (8)

where 4 1: is the settling time at which the system reaches steady state.

ER FLUID FEEDBACK CONTROLLER SYSTEM

The closed loop algorithm (Figure 10) used the same windows and state sensor as
the open loop, but the MB board related the measurements to the Power Macintosh with
LabVIEW programming, averaged the signal and adjusted the output as shown by the
equations developed in the previous section. The control algorithm worked at a maximum
real time speed of 8 Hz. In this medium, this rate is sufficient to get accurate control as

the fluid responded slowly to any input change.

  
   

 

Computer-Bas back C

Field

 

  

 
      

 

  

ER Fluid
(Fggtrfgrwue;d Ammpnofi" wmm ER Fluid Pm‘im
- 0-2 V . .
or Feedb ( ) (System) Chaining

 

 

 

 

 

Figure 10 - System Flow Chart

l4

 

 

 

 

A 0.5 T
g 0.45 if,
5.1;:
5 ° : Kp=60
.3 0-3 t.
g 002: KP=30
o _ , -
:11? _ - I- 5.:15 _. "m -
3 0.05 F " '
0 i i i i i
0 10 20 30 40 50 60
Timo(s)

Figure 11 - Proportional control of the ER fluid at a desired electrical conductivity of 0.5
uSiemens and increasing levels of proportional control (10% by weight)

MEASURED FEEDBACK RESPONSE: PROPORTIONAL CONTROL

Three successively larger levels of proportional control were plotted to determine
the ER fluid's response. The desired level of conductivity was 0.5 uSiemens and as the
controller became stronger, or K P increased, the proximity to the desired value increased
as well as the speed of response. Increasing K P also had a secondary effect, the
fluctuations at the beginning of the response increased. Above K P = 60, they continued
beyond the first few seconds and the system became unstable. Although the precision
increased and the speed of the response increased dramatically, by the time the controller
becomes unstable, the fluid only attained 56% of the desired value.

Investigation of the applied field clearly shows why the conductivity never
reached its desired value. The calibrated measure of the conductivity is the ratio between
the amplifier signals for current and applied voltage. The current signal is a voltage that

represents the actual current in mAmps. The applied voltage is a measure of the input to

15

the amplifier, or the actual applied voltage divided by 200. The signals require a

calibration constant of

=I.1000=L200000
V/200 V

 

to determine the actual desired conductivity from the actual signals.
Cd“ = (200000)(5E - 7Siemens) = 0.1

(8)

(9)

At steady state, 60 seconds, the measured current is 0.07 mAmps and the pre-amplified

voltage is 1.91.

C,=m=o.03..
1.91

The error Signal (Figure 10) is
E(s) = (0.1- 0.0364) = 0.0636

(10)

(11)

This error was multiplied by the controller gain producing the output to the amplifier in

volts,

Y = (0.0636) - 30 = 1.91

 

0-2 Conductivity ~—
0.18 -- _ J. - _ v A A ‘- _ —- L" w v.
0.16 - - _ - _ m.“ t

0-14 * Field
0.12 a

0.1 r'
0.08 W l
0.06 "
0.04 ‘*
0.02 t

o i i If
0 10 20 30 40 50 60

Time(s)

 

Conductivityotsmmens)

 

 

 

di-
~r-

250

200

" 150

100

50

Figure 12 - Proportional controller action and response of the ER fluid at a desired

electrical conductivity of 0.5 uSiemens at KP = 30 (10% by weight)

(12)

Field(VDC/mrn)

16

which corresponds to 382 VDC amplifier output or 191 V/mm field strength as shown
(Figure 12). As the system approaches the desired value, the error signal decreases,
causing the applied voltage to fall. With proportional control, the conductivity never
reaches the desired value because some non-zero error is always required.

Precision, low error, control can only be attained when K ,6 becomes sufficiently
large (6). The proportional controller gain reached its stable limit at about K ,6 =60. The
signal to noise ratio for the sensor was slightly over 60:1, therefore, when amplified by
more than 60, the noise generated in the sensor, when amplified at that level, became the
driving force in the system, generating random, unstable response. The larger stable gains
in this work were a result of this sensor's signal to noise ratio, improved over the
transmissivity sensor which had a signal to noise ratio of 10:1 and limited the maximum
allowable gain to about K p = 5 in prior work (Andersland, 1995; Radcliffe et a1, 1996).

The gains and the time constants for the feed-forward system were computed for
all systems that responded at levels that were able to be read by the standard equipment
described. These were then used to form a model of computed gains and time constants
for the proportional feedback control system (Table 1). The system behaved as predicted
by the model for each level of proportional control. The system gains with the feedback

controller approached one as the proportional constant increased. Andersland (1995) was

Table 1 - Comparisons of feed-forward and proportional feedback control gain and time
constants for ER fluid electrical conductivity measurements (10% by weight)

 

 

 

 

 

 

 

 

Measured Computed
Controller k 1: (s) k t (s)
Feed-forward 0.00458 - 1.13 3. - 119. ----------------------
Feedback. K,» = 15 0.162 0.211 0.0643 - 0.944 0.167 - 111.
Feedback. Kp = 30 0.364 0.215 0.121 - 0.971 0.086 - 104.
Feedback, Kp = 60 0.564 0.165 0.216 - 0.985 0.044 - 93.
Feedback, KP = 600 ............. 0.733 - 0.999 0.004 - 32.

 

 

 

 

 

 

17

able to achieve about 0.87 gains while this investigation only achieved 0.56 due, in part, to
the use of a non-zero operating point about which the desired transmissivity level was
specified. The time constants decreased consistently and were still within the predicted
range. The measured time constants were over 14-17 times smaller than the smallest feed-
forward time constant and were an improvement over Andersland's increase of over 5
times, consistent with the use of higher gains.

The analytical results (Table 1) clearly show that a higher level of control is need
to attain the desirable levels of speed and precision. The controller could approach the
desirable level with an acceptable degree of precision if the gains were extremely high,
over 600. This control gain would only be possible if the noise in the sensor were less

than 0.6% of the signal

PROPORTIONAL - INTEGRAL FEEDBACK CONTROL

A controller design must compensate both for the slowness of response and the
lack of precision and the experiments clearly showed the problems encountered with
simple proportional control. A controller that provides both speed and precision at lower
controller gains than required by the proportional controller is needed. A proportional-
integral (PI) controller provides dynamic compensation which will improve both the
transient and the steady-state response, providing precision even at the lowest gains. The
transfer function for such a controller can be expressed as below with adjustable

proportional and integral gains, K P and K, respectively.

 

 

K(s)= Y(s) =K +_1_<_,_= Kps+K, = KP(s+K, /K,.)

E(s) P s s s (13)

The closed loop transfer function of the entire controlled system assuming zero noise

N(s) = 0, and H(s) = 1.

18

A 0.6 T

 

0.5 t
0.4 t
0.3 ‘—
0.2 r” i

0.1

 

ConductivityatSiemens

 

 

 

Time(s)

Figure 13 - PI controller response of the ER fluid at a desired electrical conductivity of 0.5
uSiemens for KP = 3 and increasing levels of integral control (10% by weight)

Cfl,(s) _ kK(s)/(1+t-s) _ k(K,+Kps)

T(s) = _ .. 2
(Za6(8) 1-thKKSJNfl-ttsil ts -+(1-tkdtp)s4-kkg

 

 

(14)

whereas s=>0 , T(s)=>1

The transfer function T(s) no longer depends on the strength of the controller for
precision, at steady state the desired state will be attained. It is also no longer linear,
therefore, it can not be compared directly to the system response as with the
proportional controller. Simulations that evaluate the transfer function at the feed-

forward gains and constants were used to predict the behavior of the ER fluid controller.

MEASURED CLOSED LOOP RESPONSE: PI CONTROL

Proportional-integral control is Shown (Figure 13) for constant proportional
control held nominally at three and three successively larger integral controls. As the
integral constant increased (starting at 1 second) it had two effects, it decreased the time
to the desired state while it simultaneously increased the precision. At very low integral

control it took a long time to get to the desired state, clearly longer than shown. A slight

l9

 

 

 

 

,3 0.6 T 800

: Co ductivity ,,

o 0.5 — -_-'A'. 700 A
«El —- -_ 600 g
a 0.4 Field ,_ a
a 500 o
3.; 0 3 «~ 400 g
> v
*5 0.2 .. “’ 30° 3;
g 0 1 q? -- 200 E
5 ' t 100

° 0 -._..___ i . l 0

 

0 10 20 30 40 50 60
Tlrne(s)

Figure 14 - PI controller action and response of the ER fluid at a desired electrical
conductivity of 0.5 uSiemens for KP = 3 and K, = 30 (10% by weight)

overshoot was seen at K, = 50, which indicated that the upper limits of the integral
portion of the controller had been reached.

The applied field required to obtain the desired response is Shown (Figure 14 ).
There was a quick rise then the field began to fall slightly after reaching the desired value
of conductivity, in contrast to proportional control (Figure 12). The conductivity rise
showed no overshoot and the desired value was reached and precisely held in about 7
seconds. The speed of the response is slower than the those found with proportional
control, but still 1.71 times faster than the shortest settling time for feed-forward control.
The precision of the response is a significant improvement over both the feed-forward
and proportional controls in terms of steady state.

The maximum error attributed to overshoot (alter attaining the desired state)
ranged from 3.4% to 6.2%. After 60 seconds, the errors ranged from 0.2% to 3.8%, a
dramatic improvement over both feed-forward and proportional feedback control. Feed-
forward control illustrated the problems in the prediction of the attained state, it was
never certain what level of conductivity would be reached. Proportional feedback control

was much more predictable, but the error in reaching steady state after 60 seconds was

20

 

 

 

 

 

0.7
7’. 0.6 1
G
E Upper Limit ._ ..
a
3 0.4 a
E:
'; _
E 0'3 I Measured
E 0.2
8 0.1 Lower Limit
0 I 1 T l I
0 10 20 30 40 50 60
Time“)

Figure 15 - Comparisons of the measured and calculated responses of the ER fluid at a
desired electrical conductivity of 0.5 uSiemens for KP = 3 and K, = 10 (10%
by weight)

still 44% at the highest level of control. Proportional-integral control provides a

combination of speed and precision with little dependence on the size of the error that

determined that PI control was the most appropriate method investigated here to control
the ER fluid precisely.
The Simulated response of the proportional integral controller were found using

the open loop gains and time constants (Table 1) to evaluate the transfer firnction (14).

The simulations formed limits between which the measured response for KP = 3 and

K, = 10 were found (Figure 15). The upper limit clearly shows an overshoot, while the

lower limit is a very slow rise to steady state. The measured response of the PI controller

also fell within the predicted limits of the model.

CONCLUSIONS

Feed-forward and feedback controllers for an ER fluid structure were examined

experimentally, and the responses were analytically compared using a model of the ER

21

fluid response. The traditional method of feed-forward control was found ineffective for
the ER fluid both analytically and in practice. The experiments clearly showed that
neither the level nor the speed of response for feed-forward control was adequate for the
fluid to be useful commercially. Electrical conductivity proved to be a more direct
method of measuring the internal state of the ER fluid, therefore, a feedback controls
approach using an electrical conductivity based sensor produced an effectively controlled
ER fluid response. Proportional and proportional-integral feedback control were
examined to determine the most effective approach. Proportional control produced a
significant decrease in time constants, 1400-1700%, but only attained 56% of the desired
electrical conductivity level. The proportional-integral controllers were found to be most
effective in terms of precision, they decreased the fastest settling time by up to 170% and
attained up to 99.8% of the desired state. All measured results were within the predicted
model limits. The conclusions of this study provide a means for the control of viscosity,
electrical and heat transfer properties to be used in further applications.

With precise control and increased speed, the ER fluid can be used in commercial
applications. Future work should include the investigation of the optimum control
strategy for specific fluid concentrations as well as for known water content. It is also
important to proceed with simultaneous visual and state measurement techniques to
determine the chaining mechanisms behind some of the unusual observed behaviors.
Proportional-integral feedback control allows the use of ER fluid properties through
increasing the Speed of response by at least 170% and an decreasing the system steady

state error from 100% down to 0.2%.

APPENDIX A

APPENDIX A

Some of the response trends associated with the ER fluid were seen in
experiments with the conductivity. The presence of these trends give further evidence to
the validity of conductivity as an ER fluid sensor. These are shown here for reference

because they are important to the overall understanding of ER fluids.

0.05 ~~
0.04 «-
0.04 «—
0.03 .-
0.03 4-
0.02 +
0.02 4»
0.01 —~
0.01 + .
0.00 '

Cond uctivity(p81emens)

 

“l"

l J l l
I I

0 100 200 300 400 500 600
Time(s)

—0-

Figure A1 - Comparison of electrical conductivity measurements of two different ER fluid
concentrations under a field strength of 500 VDC/mm (10% by weight)

 

 

ConductivityolSIemens)

 

 

 

v T—T—T'?W
1 l a
4 0 0 5 0 0 6 0 0

Time(s)

Figure A2 - Comparison of electrical conductivity measurements of the same ER fluid
taken under identical field strengths of 700 VDC/mm before and after twenty-
four hours of settling (10% by weight)

22

23

I; A!

-. .

 

O 100 200 300 400 500 600
Tlme(s)

Figure A3 - Saturation of an ER fluid under a field strength of 1000 VDC/mm (10% by
weight)

 

Figure A4 - Microscopic views of broken chains in a previously activated ER fluid

 

 

 

 

1 ..ll 11.11 11.11.1111 “I Ill 11 111111 I ll 1111111111111 1111111111111 1111‘
-0.5 0 1 o 0 . . t t .0
rimem

Figure A5 - Proportional controller response of the ER fluid at a desired conductivity of
0.5 uSiemens for KP= 65 (10% by weight)

APPENDIX B

APPENDIX B

The programs for both the data acquisition and control are shown here for
clarity. The front panels associated with the three devices demonstrate the capabilities of
each. Programmed as virtual instruments in National Instruments LabVIEW, they act as
mechanical devices with the ability to sent and receive data. Three programs were used: a
simple data acquisition program for a constant applied field (Figure B1), a data acquisition
program for a step field (Figure BZ), and a proportional-integral controller (Figure B3).

The simple data acquisition program first specifies the device(NB-MIO-l6 L
Board) and the input and output channels on the board. There are channels for the output
of a field, and inputs for the current and applied field sensors. Data acquisition is
determined by the amount of time the field is to be active and the rate at which the data is
sampled. The ntunber of points to be plotted on the graph was included to reduce the
data points to a reasonable number and to provide a means to average the data over
discrete time intervals. When the program has completed the data acquisition, it polls the
user to specify a spreadsheet file to send the data to. When the data has been saved to
the file, any error incurred during the program cycle is displayed along with a graph of the
data.

The data acquisition program for the step field operated in much the same way
with a few exceptions. First, the timing depends on the number of steps taken and the
time allowed for each step which are both entered on the front panel. Second, the high
and low voltages are also required.

The controller also specifies the input and output channels and the device, and
the timing is specified as well as the sampling frequency. In this case, the user is not
allowed to dictate the number of points on the graph 100 was designated as the number of
points to average. An upper limit was also placed on the sampling rate. These two

factors prevented the user from specifying a controller speed beyond the virtual

24

25

instruments capacity. The desired conductivity was input in Siemens and there are knobs

that allow adjustments for both proportional and integral control.

provided to limit the output field.

saturation voltage was

Also included here is the program used to simulate the proportional-integral

transfer function. This program was written and executed in Matlab. The data was then

transferred to an Excel file where the plots were integrated with the measured data.

Data Acquisition for the ER Composite Structure

 

 

  
 
  

Number of Points on the Graph

Field

'

i Field Output Channel

 
 
 
 

  
 

: Current input Channel

Field Input Channel

 

 

Sampling Rate

1

Run Time

A

1

‘7

Hours-
Minutes-

Seconds —

 

 

 

 

 

 
    

1.0 2.0 3.0 4.0 5.0 6.0 ?.0 8.0 9.0

10.0

Figure Bl - Virtual instrument front panel for data acquisition of ER fluids composite

structure

 

 

 

 

 

 

 

 

 

 

11:43.1 "argum-

I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

Begin Sampling the data

 

 

27

process the data and
the 20 array

Zero "to output Clear the butter

Carmine the ID army: by column

the time any

 

 

 

 

Graph Data on the Front Panel

 

29

Data Acquisition for the ER Composite Structure

 

 

Device

IE:

Current Channel

Field Input Channel

Field Output Channel

 

 

Sampling Rate
1 00.00

Number of Steps

IZI

Step Time

Run Time Units

Hours- ‘
Minutes-i
Seconds- v

 

 

 

 

 

 

500 .0

 

Low Voltage
1 000 .0

500 .0 1 500 .0

 

”-0 2000.0

High Voltage
1 000 .0

500.0 1 500.0

 

0-0 2000.0

1

 

C0nductance (11. Siemens)

 

1 000 .0 1 500 .0

2000 .0

  

2500 .0

Number 01' Points on the Graph

fluids composite structure

Figure B2 - Front panel for the data acquisition of the field applied in steps for the ER

 

3000 .0

0 Potnleleycb

30

 

 

 

 

 

 

 

 

Configure the butter for data aqulsltion

l

 

Begin Sampling the data

 

m
m

Smu Freq D
I unplanned C]
m:

I’m
I‘<- a

I Polmucycln 1:12.77

Supt Freq '0

I ammo-a D
m:
rm

I Pow- a

I Polntucyclo a

Errol Freq e

I unplellrud .
I

I 01011 O
I Foam/cycle 9

in .C .7

 

L 9’1

31

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

     

 

 

 

 

1'; Lou
_ Field
i“ ”W
HUG
but.
Itarnalea t voltage or 6 cyc as
during which data is read and averaged.
T III 10
a 20
10 El 52 m c v v
no I [mail I .‘ v»
1 10- L"
Fla
1’5 Flold
r u Dela
Zero the court Clo-I lhI butler
m
Yuk _ 19 1D
10 El E2 c c V
s 0..
e I I _I_,~ I e

QDaWbC to ID 1WI‘bC

 

 

l

 

'"l

 

 

 

m l

Rearrange the data arrays(two 20 a Fl/b G)
into 2 10 arrays 1 Rla'b

2‘. Low
Field

, ”V1
Field

 

 

I Points/cycle

32

 

 

 

 

 

 

 

 

 

 

 

Graph Data on the From Panel

 

 

 

 

33

Pl Controller for ER Fluid Composite Structure

 

 

Input
Sampling Frequencg

Current Output DEVI-39
1:1 El

 

 

Kield Output Field Input Run Time
Hours- ‘5

Controller Specifications Minutes-«i
Seconds- v

Window Conductivity Desired

Saturation Voltage

Kp Control Ki Control .. 200000
40.0 60.0 40.0 60.0

 

 

 

 

 

Error

         

IIEJI
|:::J

 

 

 

 

 

 

Conductivitg

 

5.015 5
0.0E+0-

 

 

 

 

 

 

Figure B3 - Front panel for the proportional-integral controller for the ER fluids
composite structure

 

34

 

 

mumwmnmmm

_~- ttntlon Volta - e

 

Nahum» Control Operation. m

 

Calculate the saturation voltage

 

 

 

Vol.9.

Initialize the system at 100 VDC

Configure the ND and the buffer to recieve incoming data.

 

35

n r

 

 

 

 

 

J l

 

Clear the butter. shut down the amplifier and send data to a file

 

 

Calculate the time array

Sort the data into a 20 array and graph the conductivity

 

36

PI Transfer Function Simulator
Written in Matlab

% simulates the transfer function for the proportional integral control
% with proportional control equal to three and integral control equal to
% ten. The response will be plotted for the range of values

% corresponding with the range of gain and time constants shown in

% experiments with a ten percent ER fluid.

k1=l.12968;
k2=0.00458;
kp=3;
ki=10;
tau1=3;
tau2=119;

num1=[kl *kp k1*ki];
denl=[taul (1+k1*kp) k1*ki];
t=[0:0.125:60];

[y] ,x1,t]=step(numl,den1 ,t);
ylfi'l

num2=[k2*kp k2*ki];
den2=[tau2 (1+k2*kp) k2*ki];
[y2,x2,t]=step(num2,den2,t);
y2=y2

LIST OF REFERENCES

LIST OF REFERENCES

Andersland, Ruth M., 1995, "Feedback Control of Electrorheological Fluids," Michigan
State University, January

Davis, L. C., 1992a, "Finite-element analysis of particle-particle forces in
electrorheological fluids," Journal oprplied Physics, 60(3), January

Davis, L. C., 1992b, "Polarization forces and conductivity effects in electrorheological
fluids," Journal of Applied Physics, 72 ,August

Elliott, Gloria, 1997, "Controllable Heat Transfer in Electrorheological Fluid Composites:
An Investigation," Michigan State University, May 9

Hargrove, Jeff, 1997, "An Experimental Study of Radiative Heat Transfer Through
Electrorheological Fluids," Michigan State University, May

Hass, K. C., 1993 "Computer simulations of non equilibrium structure formation in
electrorheological fluids," Physical Review 47(5), May

Khusid, Boris and Acrivos, Andreas, 1996, "Effects of Conductivity in Electric-Field
-Induced Aggregation in Electrorheological Fluids," Physical Review 52(2), August

Klass, Donald L. and Martinek, Thomas W., 1967a "Electroviscous Fluids. 1. Rheological
Properties" Journal of Applied Physics, 38, January

Klass, Donald L. and Martinek, Thomas W., 1967b, "Electroviscous Fluids. 11. Electrical
Properties" Journal of Applied Physics, 38, January

Lloyd, J. R., and Zhang, C., 1994, "A Discussion On The Use Of Electrorheological
Fluids In The Control of Heat Transfer Processes, " Proceedings of the First
ISHWT-ASME Heat and Mass Transfer Conference, Bombay, India, Tata
McGraw-Hill, pp. 67-77, Jan.,. 57.

Phillips, Charles L. and Harbor, Royce D., 1991, Basic Feedback Control Systems,
Prentice Hall, New Jersey.

37

38

Radcliffe, Clark J., Lloyd, John R., Andersland, Ruth M., and Hargrove, Jeff, 1996,
"Feedback Control of Electrorheological Fluids," ASME

Russel, W. B., 1980, "Review of the Role of Colloidal Forces in Rheology of
Suspensions," Journal of Rheology, 24

Winslow, W. M., 1947, Translating Electrical Impulses into Mechanical Force, US.
Patent 2,417,850, March 25.

Winslow, W. M., 1962, Field Responsive F orce Transmitting Compositions, US. Patent
3,047,507, July 31.

Zhang, C., and Lloyd, J .R., 1992, "Measurements of Radiation Heat Transfer in
Electrorheological Fluid Based Composite Materials," Developments in Radiative
Heat Transfer, HTD Vol. 20, 1992 National Heat Transfer Conference, San Diego,
CA, Aug. 8-11, pp. 55-62.

      
    

 

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