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This section
will assist engineers and scientists in gaining a general understanding
of active vibration isolation systems, how they work, when they
should be applied, and what limitations they have. Particular
attention has been given to the semiconductor manufacturing
industry, since many applications have arisen in this field.
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Feedback control
systems have existed for hundreds of years but have had their
greatest growth in the 20th century. During World War II, very
rapid advances were made as the technology was applied to defense
systems. These developments continued, and even today most texts
on control systems feature examples like fighter aircraft control
and missile guidance systems. |
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Active vibration
isolation systems were an extension of the electromechanical
control systems developed for defense. As early as the 1950s,
active vibration cancellation systems were being developed for
applications like helicopter seats. Thus, active control systems
specifically for vibration control have been around for over
40 years! In the precision vibration control industry, active
vibration isolation systems have been available for nearly 20
years. There are many reasons why they have been slow to come
into wider use. |
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Most active vibration
isolation systems are relatively complex, costly, and often provide
only marginal improvements in performance compared with conventional
passive vibration isolation techniques. They are also more difficult
to set up, and their support electronics often require adjustment.
Nonetheless, active systems can provide function which is simply
not possible with purely passive systems. |
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Two things have
lead to the renewed interest in active vibration control systems
in recent years. The first is the rapid growth of the semiconductor
industry, and, second, the desire to produce more semiconductors,
faster, and at a lower cost. Lithography and inspection processes
usually involve positioning the silicon wafer relative to critical
optical (or other) components by placing the wafer on a heavy
and/or fast moving stage. As these stages scan from site to site
on the wafer, they cause the whole instrument to “bounce” on
the vibration isolation system. Even though the motion of the
instrument may be small after such a move (a few mm), the resolution
of the instrument is approaching, and in some cases going below,
1 nm. Instruments with this type of resolution are inevitably
sensitive to even the smallest vibration levels. Active systems
help in these cases by reducing the residual motions of an isolated
payload after such stage motions occur. |
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The second change
which has made active systems more popular has been the advancement
in digital signal processing techniques. In general, an active
system based on analog electronics will outperform a digitally
based system. This is due to the inherent low noise and wide
bandwidths available with high-performance analog electronics.
(A relatively inexpensive operational amplifier can have a 30
bit equivalent resolution and a “sampling rate” of
many MHz.) Analog electronics are also inexpensive. The problem
with analog-based systems is that they must be manually adjusted
and cannot (easily) deal with non-linear feedback or feedforward
applications (see Section
5.4.3). Digital controllers have the potential to automatically
adjust themselves and to deal with non-linear feedback and feedforward
algorithms. This allows active systems to be more readily used
in OEM applications (such as the semiconductor industry). They
can also be programmed to perform a variety of tasks, automatically
switch between tasks on command, and can have software upgrades
which “rewire” the feedback system without lifting
a soldering iron. To further the reader’s understanding
of the costs and benefits of these systems, we have provided a brief
introduction to the terminology and techniques of servo control systems.
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Although the terminology
for active systems is fairly universal, there are some variations.
The following discussion introduces the terminology used by TMC
and should help you with the concepts involved in active systems.
The basis for all active control systems is illustrated in Figure
16. |
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It contains three
basic elements: |
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- The block labeled “G” is called the plant,
and it represents the behavior of your mechanical (or electronic,
hydraulic, thermal, etc.) system before any feedback is
applied. It represents a transfer
function, which is the ratio of the block’s output
to its input, expressed as a function of frequency. This ratio
has both a magnitude and a phase and may or may not be unitless.
For example, it may represent a vibration
transfer function where the input (line on the left)
represents ground motion and the output (line to the right)
represents the motion of a table top.
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Figure
16: A basic feedback loop consists of three elements: the plant,
compensation, and summing junction.
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In this case, the ratio is unitless.
If the input is a force and the output a position, then the
transfer function has units of (m/N). The transfer function
of G has a special name: the plant
transfer function. All transfer functions (G, H, the
product GH, etc.) are represented by complex numbers (numbers
with both real and imaginary components). At any given frequency,
a complex number represents a vector in the complex plane.
The length and angle of that vector represents the magnitude
and phase of the transfer function.
- The block labeled “H” is called the compensation and
generally represents your servo. For a vibration isolation system,
it may represent the total transfer function for a sensor which
monitors the plant’s output (an accelerometer), some electronic
filters, amplifiers, and, lastly, an actuator which produces
a force acting on the payload. In this example, the response
has a magnitude, phase, and units of (N/m). Note that the loop
transfer function for the system, which is the product
(GH), must be unitless. The loop transfer function is the most
important quantity in the performance and stability analysis
of a control system and will be discussed later.
- The circle is a summing junction.
It can have many inputs which are all summed to form one output.
All inputs and the output have the same units (such as force).
A plus or minus sign is printed next to each input to indicate
whether it is added or subtracted. Note that the output of H
is always subtracted at this junction, representing the concept
of negative feedback. The output of the summing junction is
sometimes referred to as the error
signal or error point in
the circuit.
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It can be shown
that the closed-loop transfer function for
the system is given by Equation
16. This is perhaps the single most important relationship
in control theory. The denominator 1+GH is called the characteristic
equation, since the location of its roots in the complex
plane determine a system’s stability. There are several
other properties which are immediately obvious from the form
of this equation. |
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 [16] |
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First, when the loop
gain (the magnitude |GH|) is much less than one, the
closed-loop transfer function is just the numerator (G). For
large loop gains ( |GH| >> 1), the transfer function is
reduced or suppressed by the loop gain. Thus the servo has its
greatest impact on the system when the loop gain is above unity
gain. The frequency span between the unity
gain frequencies or unity
gain points is the active
bandwidth for the servo. In practice, you are not allowed
to make the loop gain arbitrarily high between unity gain points
and still have a stable servo. In fact, there is a limit to
how fast the gain can be increased near unity gain frequencies.
Because of this, the loop gain for a system is usually limited
by the available bandwidth. |
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Another obvious
result from Equation
16 is that the only frequencies where the closed-loop transfer
function can become large is where the magnitude of |GH|  1,
and its phase becomes close
to 180°. As the quantity GH nears this point, its value
approaches (-1), the denominator of Equation
16 becomes small, and the closed-loop response becomes large.
The difference between the phase of GH and 180° at a unity
gain frequency for GH is called the phase
margin. The larger the phase margin, the lower the amplification
at the unity gain points. It turns out, however, that larger
phase margins also decrease the gain of the servo within its
active bandwidth. Thus, picking the phase margin is a compromise
between gain and stability at the unity gain points. Amplification
at unity gain will always happen for phase margins less than
60°. Most servos are designed to have a phase margin between
20° and 40°. Amplification at a servo’s unity
gain frequencies appear like new resonances in the system.
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The previous section
provided a qualitative picture of how servos function and introduced
the broad concepts and terminology. In reality, most active vibration
cancellation systems are much more complex than the simple figure
shown in Figure 16.
There are typically 3 to 6 degrees-of-freedom (DOF) controlled:
three translational (X, Y, and Z motions), and three rotational
(roll, pitch, and yaw). In addition, there may be many types
of sensors in a system, such as height sensors for leveling the
system and accelerometers for sensing the payload’s motions.
These are combined in a system using parallel or nested
servo loops. While these can be represented by block diagrams
like that in Figure 16 and
are analyzed using the same techniques, the details can become
quite involved. There are, however, some general rules which
apply to active vibration cancellation servos in particular. |
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Multiple
Sensors. Although you can have both an accelerometer
measuring a payload’s inertial motion, and a position
sensor measuring its position relative to earth, you can’t
use both of them at any given frequency. In other words,
the active bandwidth for a position servo cannot overlap with
the active bandwidth for an accelerometer servo. Intuitively,
this is just saying that you cannot force the payload to track
two independent sensors at the same time. This has some serious
consequences. |
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Locking a payload
to an inertial sensor (an accelerometer) makes the payload quieter;
however, the accelerometer’s output contains no information
about the earth’s location. Likewise, locking a payload
to a position sensor will force a payload to track earth more
closely – including earth’s vibrations. You cannot
have a payload both track earth closely and have good vibration
isolation performance! For example, if you need more vibration
isolation at 1 Hz, you must increase the gain of the accelerometer
portion of the servo. This means that the servo which positions
the payload with respect to earth must have its gain lowered.
The result is a quieter platform, but one that takes longer to
move back to its nominal position when disturbed. This is discussed
further in Section
5.6. |
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Gain
Limits on Position Servos. As
mentioned above, position sensors also couple ground vibration
to a payload. This sets a practical limit on the unity gain
frequency for a height control servo (like TMC’s
PEPS® Precision Electronic Positioning System).
To keep from degrading the vibration isolation performance
of a system, the unity gain frequency for PEPS is
limited to less than 3 Hz. This in turn limits its low-frequency
gain (which determines how fast the system re-levels after
a disturbance). Its main advantages are more accurate positioning
(up to 100 times more accurate than a mechanical valve), better
damping, better high-frequency vibration isolation, and the
ability to electronically “steer” the payload using
feedforward inputs (discussed later). It will not improve how
fast a payload will re-level.* PEPS can
also be combined with TMC’s PEPS-VX® System,
which uses inertial payload sensors to improve vibration levels
on the payload. |
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Structural
Resonances. Another important
concern in active vibration isolation systems is the presence
of structural resonances in the payload. These resonances
form the practical bandwidth limit for any vibration isolation
servo which uses inertial sensors directly mounted to the
payload. Even a fairly rigid payload will have its first
resonances in the 100-500 Hz frequency range. This would be
acceptable if these were well damped. In most structures,
however, they are not. This limits the bandwidth of such servos
to around 10-40 Hz. Though a custom-engineered servo can do
better, a generic off-the-shelf active vibration cancellation
system rarely does.
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Although we have
alluded to “position” and “acceleration” servos,
in reality these systems can take many different forms. In addition,
the basic performance of the servo in Figure
16 can be augmented using feedforward. The following sections
introduce the most common configurations and briefly discuss
their relative merits.
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Figure 17: The
basic inertial feedback loop uses a payload sensor and a force
actuator, such as a loudspeaker “voice coil,” to
affect the feedback. Feedforward can be added to the loop at
several points.
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By far the most
popular type of active cancellation system has been the inertial
feedback system, illustrated in Figure
17. Note that the pneumatic isolators have been modeled here
as a simple spring. Neglecting the feedforward input
and the ground motion sensor (discussed
in Section 5.4.3),
the feedback path consists of a seismometer, filter, and force
actuator (such as a loudspeaker “voice coil”). The
seismometer measures the displacement between its test
mass and the isolated payload,
filters that signal, then applies a force to the payload such
that this displacement (X1 - X2) is constant – thereby
nulling the output of the seismometer. Since the only force acting
on the test mass comes from the compression of its spring, and
that compression is servoed to be constant (X1 - X2 0),
it follows that the test mass is actively isolated. Likewise,
since the isolated payload is being forced to track the test
mass, it must also be isolated from vibration. The details of
this type of servo can be found in many references.** |
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The performance
of this type of system is always limited by the bandwidth of
the servo. As mentioned previously, structural resonances in
the isolated payload limit the bandwidth in practical systems
to 10-40 Hz (normally towards the low end of this range). This
type of system is also “AC coupled” since the seismometer
has no “DC” response. As a result, these servos
have two unity gain frequencies – typically
at 0.1 and 20 Hz. This is illustrated in greater detail in Section
5.6. As a result, the servo reaches a maximum gain of around
20-40 dB at ~2 Hz – the natural frequency of the passive
spring mount for the system. The closed-loop response of the
system has two new resonances at the ~0.1 and ~20 Hz unity gain
frequencies. Due to the small bandwidth of these systems (only
around two decades in frequency), the gain is not very high
except at the natural (open-loop) resonant frequency of the
payload. The high gain there completely suppresses that resonance.
For this reason, it is helpful to think of these systems as inertial
damping systems, which have the property of damping the
system’s main resonance without degrading the vibration
isolation performance. (Passive damping can also damp this resonance
but significantly increases vibration feedthrough from the ground.)
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These servos are
also limited in how low their lower unity gain frequency can
be pushed by noise in the inertial sensor. This is described
in detail in the reference of Footnote
2. Virtually all commercial active vibration cancellation
systems use geophones for
their inertial sensors. These are simple, compact, and inexpensive
seismometers used in geophysical exploration. They greatly outperform
even high-quality piezoelectric accelerometers at frequencies
of 10 Hz and below. Their noise performance, however, is not
adequate to push an inertial feedback system’s bandwidth
to below ~0.1 Hz. To break this barrier, one would need to use
much more expensive sensors, and the total cost for a system
would no longer be commercially feasible. |
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Another low-frequency “wall” which
limits a system’s bandwidth arises when the inertial feedback
technique is applied in the horizontal direction. (Note that
a six degree-of-freedom [DOF]
system has three “vertical” and three “horizontal” servos.
Horizontal DOFs are those controlled using horizontally driving
actuators – X, Y, and twist [yaw]). This is the problem
of tilt to horizontal coupling.
If you push a payload sideways with horizontal actuators and
it tilts, the inertial sensors read the tilt as an acceleration and
try to correct for it by accelerating the payload – which,
of course, is the wrong thing to do. This effect is a fundamental
limitation which has its roots in Einstein’s Principle
of Equivalence, which states that it is impossible
to distinguish between an acceleration and a uniform gravitational
field (which a tilt introduces). The only solution to this problem
is to not tilt a payload when you push it. This is very difficult
to do, especially in geometries (like semiconductor manufacturing
equipment) which are not designed to meet this requirement. Ultimately,
one is forced to use a combination of horizontal and vertical actuators
to affect a “pure” horizontal actuation. This becomes
a “fine tuning” problem, which even at best yields
marginal results. TMC prefers another solution. |
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Passive
Horizontal Systems. Rather than use an active system
to obtain an “effective” low resonant frequency,
we have developed a passive isolation
system capable of being tuned to as low as 0.3 Hz in the horizontal
DOFs. Our CSP® (Compact
Sub-Hertz Pendulum System) is not only a more reliable
and cost-effective way to eliminate the isolator’s 1-2
Hz resonance, but it also provides better horizontal vibration
isolation up to 100 Hz or more – far beyond what is practical
for an active system. Unfortunately, such passive techniques
are very difficult to implement for the vertical direction.
TMC recommends the use of systems like our PEPS-VX® Active
Cancellation System to damp the three “vertical” DOFs.
PZT-based active systems, such as TMC’s STACIS®,
use another approach which allows for active control of horizontal
DOFs (see Section 5.4.4).
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The performance
of the inertial feedback system in Figure 17 can be improved
with the addition of feedforward.
In general, feedforward is much more difficult than feedback,
but it does offer a way to improve the performance of a system
when the feedback servo is limited in its bandwidth. There are
two types of “feedforward” systems which are quite
different, though they share the same name. |
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Vibrational
Feedforward. This scheme involves the use of
a ground motion sensor and is illustrated in Figure
17. Conceptually, it is fairly simple: If the earth moves
up by an amount  z,
the payload feels a force through the compression of the spring
equal to Ksz.
The ground motion sensor detects this motion, however, and
applies an equal and opposite force to the payload. The forces
acting on the payload “cancel,” and the payload
remains unaffected. “Cancel” is in quotes because
it is a greatly abused term. It implies perfect
cancellation – which never happens. In real systems,
you must consider how well these two forces cancel.
For a variety of reasons, it is difficult to have these forces
match any better than around 10%, which would result in a factor
of 10 improvement in the system’s response. Matching
these forces to the 1% level is practically impossible. The
reasons are numerous: The sensor is usually a geophone, which
does not have a “flat” frequency response. Its
response must be “flattened” by a carefully matched
conjugate filter. The gain of
this signal must be carefully matched so the force produced
by the actuator is exactly equal in magnitude to the forces
caused by ground motion. These gains, and the properties of
the “conjugate filter,” must remain constant to
within a percent with time and temperature. Gain matching is
also extremely difficult if the system’s mass distribution
changes, which is common in a semiconductor equipment application.
Lastly, the cancellation level is limited by the sensor’s
inherent noise (noise floor). |
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Another limiting
factor to vibrational feedforward is that it becomes a feedback system
if the floor is not infinitely rigid (which it is not). This
is because the actuator, in pushing on the payload, also pushes
against the floor. The floor will deflect with that force, and
that deflection will be detected by the sensor. If the level
of the signal produced by that deflection is large enough, then
an unstable feedback loop is formed. |
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Because of the
numerous problems associated with vibrational feedforward, TMC
has not pursued it. Indeed, though available from other vendors,
we know of no successful commercial application of the technique.
It is possible, however, with ever more sophisticated DSP controllers
and algorithms, that it will be more appealing in the future.
The technique which is successfully used is command
feedforward. |
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Command
Feedforward. Also shown in Figure
17, command feedforward is only useful in applications
where there is a known force being applied to the payload,
and a signal proportional to that force is available.
Fortunately, this is the case in semiconductor manufacturing
equipment where the main disturbance to the payload is a moving
stage handling a wafer. |
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The concept here
is very simple. A force is applied to the payload of a known
magnitude (usually from a stage acceleration). An electronic
signal proportional to that force is applied to an actuator
which produces an equal and opposite force. As mentioned earlier,
there is a tendency in the literature to overstate the effectiveness
of this technique. Ridiculous statements claiming “total
elimination” of residual payload motions are common. As
in vibrational feedforward, there is a gain adjustment problem,
but all issues concerning sensor noise or possible feedback
paths are eliminated. This is true so long as the signal is
a true command signal from
(for example) the stage’s motion controller. If the signal
is produced from an encoder reading the stage position, then
it is possible to form an unstable feedback loop. These systems
can perform very well, suppressing stage-induced payload motions
by an order of magnitude or more and will be further discussed
in Section 5.7.
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Figure
18 shows the concept of a “quiet pier” isolator
such as TMC’s STACIS® line
of active isolators (Patent Nos. 5,660,255 and 5,823,307).
It consists of an intermediate
mass which is hard mounted to the floor through a piezoelectric
transducer (PZT). A geophone is mounted to it, and its signal
fed back to the PZT in a wide-bandwidth servo loop. This makes
a “quiet pier” for supporting the payload to be
isolated. Isolation at frequencies above the servo’s active
bandwidth is provided by a  20Hz
elastomer mount. This elastomer also prevents piers from “talking” to
each other through the payload (a payload must rest on several
independent quiet piers). This system has a unique set of advantages
and limitations. |
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The vibration isolation
performance of the STACIS® system
is among the best in the 0.6-20 Hz frequency range, subject to
some limitations (discussed below). It also requires much less
tuning than inertial feedback systems, and the elastomer mount
makes the system all but completely immune to structural resonances
in the payload. Alignment of the payload with external equipment
(docking) is not an issue because the system is essentially “hard
mounted” to the floor through the 20 Hz elastomers. The
settling time is very good because the response of the system
to an external force (a moving stage) is that of the 20 Hz elastomer
mount. This is comparable to the best inertial feedback systems.
The stiffness of the elastomer mount also makes STACIS® almost
completely immune to room air currents or other forces applied
directly to the payload and makes it capable of supporting very
high center-of-gravity payloads. |
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STACIS® can
support, and is always compatible with, tools incorporating any
type of built-in passive or active pneumatic vibration isolation
system. |
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Unfortunately,
the PZT has a range of motion which is limited (around 20-25  m).
Thus the servo saturates and “unlocks” if the floor
motion exceeds this peak-to-peak amplitude. Fortunately, in
most environments, the floor motion never exceeds this amplitude.
To obtain a good vibration isolation characteristic, the active
bandwidth for the PZT servo is from ~0.6 to ~200 Hz. This high
bandwidth is only possible if the isolator is supported by a
very rigid floor. The isolator needs this because it depends
on the intermediate mass moving an amount proportional to the
PZT voltage up to a few hundred Hz. If the floor has
a resonance within the active bandwidth, this may not be true.
Most floors have resonances well below 200 Hz, but this is acceptable
as long as the floor is massive enough
for its resonance not to be significantly driven by the servo.
The proper form of the floor specification becomes floor
compliance, inin/lbf
(orm/N).
In general, STACIS® must
be mounted directly on a concrete floor. It will work on raised
floors or in welded steel frames only if the support frame is
carefully designed to be very rigid. Another problem is “building
sway,” the motion at the top of a building caused by wind.
This is often more than 25 mm on upper floors, so the system
can saturate if used in upper stories (depending on the building’s
aspect ratio and construction).
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Figure 18: This
method involves quieting a small “intermediate mass” with
a high-bandwidth servo, then mounting the main payload on that “quiet
pier” with a passive 20 Hz rubber mount.
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There are many other
types of active vibration isolation systems. |
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The first broad
class of “alternate” active systems are the hybrids.
One of these is a hybrid between a quiet pier and a simple pendulum
isolator. Here, a 3-post system contains only three PZTs which
control the vertical motion at each post actively (thus height,
pitch, and roll motions of the payload are actively controlled).
The “horizontal” DOFs are isolated using simple pendulums
hanging from each 1-DOF quiet pier. This system has only about
one-fifth the cost of a full-DOF quiet pier system because of
the many fewer PZTs. On the other hand, the pendulum response
of these systems in the horizontal direction is sometimes less
than desirable. |
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There are also
hybrids of the STACIS®/quiet
pier type of system with inertial
feedback systems to improve the dynamic performance of the elastomer
mount. These systems have additional cost and must be tuned
for each application). For more information see the STACIS® 2000 page.
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Broadly, there
two different types of applications: vibration critical or settling
time critical. These are not the same and each has
different solutions. Some applications may be both, but since
their solutions are not mutually exclusive, it is fair to think
of both types independently. It is important to note, however,
that since the solutions are independent, so are their costs.
Therefore you should avoid buying an active system to reduce
vibration if all you need is faster settling times, and vice-versa.
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Vibration critical
applications are actually in the minority. This means the number
of applications which need better vibration isolation than a passive system
can provide is quite small. Passive
vibration isolation systems by TMC are extremely effective
at suppressing ground noise at frequencies above a few Hz. There
are only two types of applications where the vibration isolation
performance of a passive isolator is a problem. |
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First, it is possible
that the level of ground noise is so high that an instrument
which is functional in most environments becomes ground noise
sensitive. This usually only happens in buildings with very weak
floors or in tall buildings where building sway becomes an issue.
This is an unusual situation, since most equipment (such as semiconductor
inspection machines) usually come with a “floor spec” which
vendors are very hesitant to overlook. |
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The second type
of applications are those with the very highest degree of intrinsic
sensitivity. Prime examples are atomic force and scanning tunneling
microscopes (AFMs and STMs). These have atomic scale resolutions
and are sensitive to the smallest payload vibrations. |
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In both these
situations the isolation performance of passive mounts is usually
adequate, except for the frequency range from about 0.7 Hz to
3 Hz where a passive mount amplifies ground
motion. This is a convenient coincidence, since active systems
(such as the inertial feedback scheme) are good at eliminating
this resonant amplification. Again, it is important to avoid
an active vibration cancellation system unless you have
an application which you are sure has a vibration isolation
problem that cannot be solved with passive isolators. Most
semiconductor equipment today has a different issue: settling
time.
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Settling
time critical applications are those where the vibration
isolation performance of a passive pneumatic isolator is completely
adequate, but the settling time of
the isolator is insufficient. It is easy to determine if yours
is such a system. If it works fine after you let the payload
settle from a disturbance (stage motion), then you only have
a settling time issue. (See Section
5.8). Before continuing, however, it is important to understand
what is meant by “settling
time.” |
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Settling
Time. The term settling
time is one of the most abused terms in the industry,
primarily because it lacks a widely accepted definition. A
physicist might define the settling time as the time for the
energy in the system to drop by 1/e . This is a nice, model-independent
definition. Unfortunately, it is not what anybody means
when they use the term. The most common definition is the “time
for the system to stop moving.” This is the worst of
all definitions since it is non-physical, model and payload
dependent, subjective, and otherwise completely inadequate.
Nonetheless, it can be used with some qualifications. |
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In theory, a disturbed
harmonic oscillator’s motion decays exponentially, which
is infinitely long lived. When in the context of a vibration
isolator, one could think of the time when a system “stops
moving” as the time required for the RMS motion of the
system to reach a constant value, where the system’s motion
is dominated by the feedthrough of ground vibration. This is
neither what people mean by settling time, nor is it model independent,
since the “time to stop moving” depends on the magnitude
of the initial disturbance and the level of ground noise. In
fact, there is no definition of “settling time” as
a single specification which can be used to define system performance
in this context – passive or otherwise. |
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This is the definition
used by TMC: Settling time is the
time required for a payload subjected to a known input to decay
below a critical acceleration level. This is an exact
definition that requires three numbers: The known
input is the initial acceleration of the payload immediately
after the disturbance (stage motion) stops. The critical
acceleration level is the maximum acceleration level the
payload can tolerate and still successfully perform its function.
The settling time is the
time required after the disturbance for the payload’s motion
to decay below the critical acceleration level. Notice that we
use a critical acceleration level and not a
maximum displacement. It is not displacement of a payload which
corrupts a process, but acceleration, since acceleration is what
introduces the internal stresses in a payload which distort the
structure, stage positioning, optics, etc. Of the three numbers,
this is the most critical to understand, since it fundamentally
characterizes the rigidity of your instrument. |
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For the product
specifications on this web site, the critical acceleration and
input levels are unknowns. For this reason, we
quote our settling time specifications as the time required
for a 90% reduction in the initial oscillation amplitude.
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Though inertial
feedback systems can be used to reduce the settling time and
improve vibration isolation performance, they have several significant
drawbacks. As already mentioned, implementing a horizontal inertial
feedback system is strongly limited by the tilt to horizontal
coupling problem (Section
5.4.2). Another problem is that these systems (with the exception
of PZT-based systems) have relatively poor position settling
times. |
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Figure
19 shows the response of a payload to an external disturbance.
It is based on a model of an idealized 1-DOF system and is
only meant to qualitatively demonstrate the performance of
a multi-DOF system. Both curves represent the same active system,
except the first plots the ratio of displacement to applied
force, and the second plots the ratio of acceleration to applied
force, both as a function of frequency. The only difference
is that the first graph has been multiplied by two powers of
frequency to produce the second. The curves show, respectively,
what a position sensor and an accelerometer would measure as
this system was disturbed. Please note that the magnitude
scales on these graphs have an arbitrary origin and are only
meant for reference. |
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Figure 19: The
curves show that the position response is dominated by a low-frequency
resonance, while the acceleration response is dominated by a
high-frequency peak. Note that the peak in the open-loop response
is the same.
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| The curves show
that the position response is dominated by a low-frequency resonance,
while the acceleration response is dominated by a high-frequency
peak. This is a counter-intuitive result, since the peak in the
open-loop (purely passive) response is at the same frequency
in both cases. |
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The good news is
twofold. As promised, this system does a good job of suppressing
the open-loop resonance in the system. In fact, it is even providing
a substantial amount of additional isolation in the 0.5-5 Hz
frequency range. The second piece of good news is that the acceleration
curve is dominated by a well-damped resonance at around 20 Hz
. If we assume the amplitude of the acceleration decays as: |
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|
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where A0 is
the initial amplitude and  =
Q / ( v).
If the quality factor Q is approximately 2, then ≈ 32
ms. Quite good. For any payload which is sensitive to acceleration
(which most are), the settling time for this system will be improved
by an order of magnitude by this servo. |
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The problem with
this system is illustrated in the first set of curves. They show
the position response is dominated by a peak at ~0.1 Hz . Assuming
the same Q as above, this means the decay constant t is approximately
6.5 seconds! Even though the servo has been designed with a large
phase margin to get the Q down to 2, the low frequency of the
peak means it takes a long time to settle in position. Although
payloads are most sensitive to accelerations, there are two notable
cases where a long position settling time is a problem. |
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First, a long position
settling time in the roll or pitch DOF of a payload can look like
a horizontal acceleration. This is due to Einstein’s Principle
of Equivalence: As a payload tips, then the direction
that gravity acts on the payload changes from purely vertical
to some small angle off vertical. By principle this is identical
to having a level payload which is being accelerated by
an amount equal to the tip angle (in radians) x g . In other
words, each mrad of tilt
turns into a mg of horizontal
acceleration. Many instruments, such as electron microscopes,
are sensitive to this. |
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Another significant
problem is docking the payload.
This is a common process where the payload must be periodically
positioned relative to an off-board object with extreme accuracy – typically
20 to 200 mm. It can take an inertial feedback system a very
long time to position to this level. There are two possible
solutions to this. The first is to run the servo at a lower
gain setting, sacrificing some isolation performance (which
may not be needed) for a better position settling time. The
second approach is to turn off the servo for docking. Servos,
unfortunately, do not like to be turned on and off
rapidly – especially when their nominal gain is as high
as the one illustrated here.
Back
to Technical Background Index |
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For settling
time sensitive applications, there is another option which is
less expensive and avoids the problems associated with the inertial
feedback method. As discussed in Section
5.4.3, command feedforward can
be used to reduce the response of a payload to an external disturbance.
You can use this technique with or without using the
inertial feedback scheme in Figure
17. This section deals with the latter option.
Back
to Technical Background Index |
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There are many advantages
to using a feedforward only system. Some of these are: |
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- You do not spend extra money on improved
vibration isolation performance which you do not need. The
system is less expensive because you avoid the cost of six
inertial sensors and a feedback controller.
- The position stability of the payload is
improved because it is now represented by the open-loop
curves of Figure
19. There are also no issues about docking, since “turn-on
transients” of the inertial feedback system are avoided.
The feedforward system can remain on and the payload docked
(using products like TMC’s AccuDock™)
with no problems.
- Since feedforward does not use any feedback,
it is completely immune to resonances on the isolated payload.
- Using adaptive controllers, the amount
of feedforward can be tuned to ensure at least a factor of 10
reduction in the response of the payload to a disturbance (stage
motion). This is comparable to what a well-tuned inertial feedback
system can do.
Back
to Technical Background Index |
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Despite being more
robust, less expensive, and easier to setup, there are still
some disadvantages to the feedforward only option. Some of these
are: |
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- As mentioned in Section
5.4.3, you are required to match the force capability
of your disturbance (moving stage). Electromagnetic drivers
which can do this can be expensive, difficult to align, have
a high power consumption, and have some stray magnetic fields
which can cause problems in some applications.
- For moving X – Y stages, the feedforward problem is non-linear due
to twist couplings. For example, a payload will twist clockwise
if there is an X-acceleration when the stage is in the full – Y
position but counterclockwise when the stage is in the full
+ Y position. Therefore, there are feedforward terms proportional
to XŸ and Y ¨X. This requires the use of a DSP-based
controller.
- To keep the system running well, there should be a self-adaptive
algorithm which keeps the gains properly adjusted. This is done
by monitoring the motion of the payload and correlating it with
the feedforward command inputs. This type of algorithm is non-linear and
can be unstable under certain
circumstances. In particular, with pure sinusoidal stage motion,
stage accelerations become indistinguishable from payload tilting
due to the shifting weight burden caused by the stage (the Principle
of Equivalence again).
- This method requires some work on the customer’s or
stage manufacturer’s part to provide an appropriate set
of command feedforward signals. These can be either analog or
digital in form, but they must come from the stage motion controller.
- The isolation from floor vibration is no better than it is
for a passive system (though, as mentioned, you may not need
any improvement).
Back
to Technical Background Index |
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Determining your
need for an active isolation system varies depending on whether
you have a vibration or settling time critical application. Both
can be difficult, and in either case, you need to know something
about your system’s susceptibility to vibrational noise. |
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In vibration critical
applications, it is insufficient to simply ask “does my
system work?” If your system does not work with passive
systems, or if the performance is inadequate, then you need to
identify the source of the problem. For AFM/STM type applications,
it may be obvious. The raw output of the stylus is dominated
by a 1.5 Hz noise and that is correlated with the payload motion,
and you know your isolators have their resonance at
that frequency. Other times it may be much less clear. For example,
you may see a 20 Hz peak in your instrument, and that correlates
with noise on the payload – but is it coming from the ground?
Many HVAC systems in buildings use large fans which operate in
this frequency range. If they do, they produce both acoustic
noise and ground noise which are correlated with noise on the
payload. So what is the source of the problem? Ground noise or
acoustics? It can be impossible to tell. Keep in mind, however,
that if your problem is at 20 Hz, inertial feedback active systems
will not help you, since they do not have any loop gain at that
frequency. PZT-based isolators like STACIS® may
be the only solution in this frequency range. |
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Settling time critical
applications are more straightforward. To determine if you need
an active system (which we assume to be feedforward only), there
are three steps: |
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- Step one: Determine the critical
acceleration level for your process (as discussed earlier
in Section 5.5.2).
A simple way to do this might be to move your stage and wait
different amounts of time before making a measurement. If
you know how long you need to wait and know the acceleration
level of the payload after the stage stops, then you can derive
this number. For a new instrument, the critical acceleration
level can be very difficult to determine, and you might have
to rely on calculations, modeling, and estimates.
- Step two: Estimate
the initial acceleration level of the payload by multiplying
your stage acceleration by the ratio of your stage mass to
total isolated payload mass.
- Step three: Compare
the numbers from steps one and two. If the critical acceleration
level is above the initial payload reaction, then any TMC passive
system should work for you. If it is below, then you need to
compare the ratio of the initial to critical acceleration levels,
and use Equation 17 to
determine if the system can settle fast enough.
- If your allowed settling time is insufficient
to get the attenuation you need, then you might want to try
a system with higher passive damping. TMC’s MaxDamp® isolators
have a decay rate up to five times faster than conventional
pneumatic isolators (a Q-factor five times lower). This does
sacrifice some vibration isolation but is often a good tradeoff.
- If MaxDamp® isolators
will not work, then you will need an active system (passive
isolation systems have run out of free parameters to solve the
problem).
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There are certain
extreme examples which can determine your need very quickly.
For example, if your critical level is below the initial payload
acceleration and you want “zero” settling time,
then you need an active system. However, if the ratio of the
initial to critical level is more than 10 (with “zero” time),
then you will either be forced to re-design your instrument
or allow for a non-zero settling time. Active systems are not panaceas – they
can not solve all problems.
Back
to Technical Background Index |
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If you are designing
a new system, there are several general considerations which
will make your system function optimally, whether it is active
or not. |
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You should always
use four isolators to support a system (rather than three), and
they should be as widely separated as possible. This dramatically
improves both the tilt stability and tilt damping in a system
with only a marginal cost increase. It simplifies the design
of the frame connecting the isolators, reduces the frame fabrication
costs, gives better access to the components under the payload,
and improves the overall stiffness of the system (assuming that
your instrument has a square footprint). |
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You should use a
center-of-mass aligned system whenever possible. This means putting
the plane of the payload’s center
of gravity (CG) in the same plane as the moving stage’s
CG, and both of these should be aligned with the effective support
point for the pneumatic isolators. This greatly reduces the pitch
and roll of the payload with stage motions and can reduce the
cost of an active system by making it possible to use lower force
capacity drivers in the vertical direction. Note that the “effective
support point” for most isolators is slightly below the
top of the isolator. Consult a TMC
Sales Engineer for the exact location of this point for different
isolation systems. A system’s performance will also be
improved by designing the payload such that the isolators support
roughly equal loads. |
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The cost of the
isolation system can be reduced by several means. The moving
mass should be reduced as much as possible – this reduces
the forces required to decelerate it and thus reduces the cost
of the magnetic actuators in the active system. You should also
make the payload as rigid as possible to reduce the system’s
overall susceptibility to payload accelerations. Lastly, you
can increase the static mass of the system, which will improve
the ratio of static to active mass and thus reduce the payload’s
reactions to stage motions. |
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It is quite possible
that all of these steps, taken together, will allow you to avoid
the use of an active system entirely.
Back
to Technical Background Index |
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The challenges created
by Moore’s Law*** will
require improved collaboration between systems engineers, integrators,
stage manufacturers, and semiconductor tool manufacturers. There
also needs to be a significant improvement in the awareness of
the problem. This is simply a legacy of the by-gone days where “blind
integration” of systems was sufficient. System engineers
need to significantly shift their design goals for systems, since
the conflict with high system throughputs and vibration isolation
systems are fundamental, and active systems only improve the
performance of systems by a certain factor. If the methods of
design are not changed, then there may be a day in the not too
distant future when even active systems will not work. Then you
are really out of luck, since there is no next generation
technology to turn to. Indeed, TMC already sees specifications
which cannot be met even with the most optimistic assumptions
about active system performance. |
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Active systems are
relatively expensive. The costs are driven by components like
the magnetic or PZT actuators. Their prices are high because
of the cost of their materials (rare
earth NdFeB magnets or piezoelectric
ceramics). The cost of power amplifiers can be high. When
considering costs, it is important to realize that there is no
such thing as an incremental active solution. The active system,
if you need one, must match the forces generated by your stage
motions. A system capable of less simply will not work. |
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TMC is striving
to improve active isolation systems. Our goal is to make them
more reliable, easier to install, maintain, and configure, and
to make them self-configuring whenever possible. This will reduce
system costs, engineering times, and speed the production of
your systems. |
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TMC has a staff
of Sales
Engineers who can help you with any questions raised in
this presentation or assist you in the design of an isolation
system.
Back
to Technical Background Index |
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The Technical
Background section of this web site was prepared with assistance
from
Dr. Peter G. Nelson, Manager of
Research and Development for TMC. |
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* This is an
approximate statement, since PEPS is a linear system, and mechanical
valves are very non-linear. PEPS generally levels faster for
small displacements and slower for large ones.
Back
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** See for example,
P.G. Nelson, Rev. Sci. Instrum., 62, p.2069 (1991).
Back to 5.4.1 and Back
to 5.4.2 |
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*** Gordon Moore,
co-founder of Intel Corp., has pointed out that the density
of semiconductors (in terms of transistors/area) has roughly
doubled every 18 months, on average, since the very earliest
days of commercial semiconductor manufacturing (even 1960 or
earlier!).Back
< back
to Section 1.0 |
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