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Transcript of 1999-01-3000V001
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AV. PAULISTA, 2073-HORSA II - CJ. 2001 - CEP 01311-940 - SO PAULO - SP
SAE TECHNICALPAPER SERIES 1999-01-3000
E
Servo Controller Compensation MethodsSelection of the Correct Technique for
Test Applications
Steve Soderling, Malcolm Sharp and Christoph Leser
MTS Systems Corporation
VII International MobilityTechnologyConference & Exhibit
Sao Paulo, BraziOctober 4 to October 6, 1999
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1999-01-3000
Servo Controller Compensation Methods
Selection of the Correct Technique for Test Applications
Steve Soderling Malcolm Sharp Christoph Leser
MTS Systems Corporation
Copyright 1999 Society of Automotive Engineers, Inc
ABSTRACT
Servo-hydraulic test systems are used to applyprecise loads and displacements to specimens as part of a
program of evaluation in the laboratory. For the test system
to correctly load the specimen the type of servohydraulic
control must be carefully selected. Factors such as accuracy,
repeatability, control range and stability depend on the
matching of the control scheme to the characteristics of the
test stand, specimen and the command profile. This paper
reviews the compensation methods available with particular
reference to practical applications of the different methods in
the laboratory testing of automobiles from components of all
types through sub-systems to full vehicles.
INTRODUCTION
The development of the electro-hydraulic servo
valve by Moog and others in the mid-forties, combined with
the development of strain gage based load cells allowed
precise loads and displacements to be applied using
hydraulic actuators as prime movers. This servocontrol
technology was rapidly adopted in structural and material
test laboratories for the application of loads and
displacements to test specimens. The basic servo control
system uses a closed loop control algorithm where the
instantaneous difference between desired "command"
displacement or load, and the measured "feedback"
displacement or load, the "servo error", is used to drive the
actuator in such a direction as to minimize the error.
Early closed-loop servo systems controlled the
actuator directly from a scaled proportion of the servo error
signal. Later servo control systems incorporated the use of a
feedback signal obtained from the derivative of the servo
error to main dynamic stability of the system at higher
frequencies of operation. Further refinements included the
use of feedback obtained from the integral of the servo error
to minimize the static or following error at low frequencies.
The combination of these control approaches resulted in the
general purpose PID (Proportional, Integral, Derivative)
controller.
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Later servo controllers introduced further feedback-
derived control terms based on velocity feed forward and lagterms (F and L) feedback. In addition, feedback terms for the
correction of inertial mass-related load errors in the system
Mass or Inertia Compensation can be found. Finally, actuator
pressure difference feedback can be used when the stiffness
of the hydraulic oil and inertial mass of the system provides
a resonance pole within the desired control band of the servo
system.
The above servo controller feedback algorithms are
applied directly to the "inner" control loop of the servo
system. The mathematical background and application of
these control schemes are well covered in any of the
available texts on control systems [1, 2] and will not becovered in further detail.
A second family of control algorithms or
compensation schemes has been developed by a number of
hydraulic servo controller manufacturers which are applied
as "outer" control loops around the "inner" control loop.
These compensation schemes are required to provide
increased control accuracy, stability and repeatability in
applications where inner control loop methods prove
inadequate.
and,
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Unlike the inner control loop, where the theory and
application of the control schemes are well documented and
understood, these "outer" loop compensation schemes are
still the source of confusion in the testing community. This
confusion exists not only because of a lack of documentation
on the theory and application of the schemes but also as a
result of a lack of consistency in naming of the methods.
Indeed identical compensation techniques from different
manufacturers exist with different names! The remainder of
this paper reviews practical PID controller use, repeatability
and linearity concerns before describing the outer loop
compensation schemes available and commonly used within
the automotive structural test laboratory.
PRACTICALLIMITATIONSINPID CONTROLLERS
The compensation techniques under review are
control algorithms that compensate for the limitations of (1)
standard PID servo loop controllers when combined with (2)
the characteristics of the real system that it is trying to
control and (3) the accuracy, repeatability and stabilitydemands of the test to be performed.
There are several limitations inherent in the
operation of the standard PID form of the servo controller.
The standard servo loop compares a command and a
feedback and then generates a correction signal proportional
to the difference between them (the P part of PID). Note that
unless there is a difference between command and feedback,
there is no correction signal generated, which means that the
only time feedback can equal command exactly is when the
system is static. Any motion can only be the result of a
correction signal that is produced based on the error in the
servo loop. This means that error is inherent in a standardservo loop. It is required for operation. For quasi-static
operation the use of an integral I term in the control loop can
be used to reduce the servo error but this approach cannot be
applied in situations where accurate control is required above
1-2 Hz.
The inherent error in a standard loop is also reduced
as much as possible by increasing the proportional gain, P,
which causes the loop to produce more correction signal for
a given amount of error. If proportional gain could be
increased to infinity, the loop could run without error.
However, the issue of stability becomes apparent long before
we reach this point. Real world control systems have massand when combined with the finite force and velocities
available from the hydraulic fluid, performance limits will be
reached. As the frequency of operation is increased these
factors result in an increasing lag between the servo error
driving the system and what the physical system is capable
of accomplishing. When proportional gain is high and the
output lag in the system approaches 180% out of phase with
the servo error input the control loop becomes unstable and
oscillates. There are many techniques used to enhance
stability that use signals proportional to the derivative (D
term of PID) or double derivative of the feedback (that is
differential pressure (delta P) or acceleration). These
techniques enable the proportional gain to be increased
somewhat, but there is always a limit beyond which the loop
becomes unstable.
Because control test systems are real, physical
systems with mass and limited force and velocity capability,
their response, that is, the ratio of actual output to command
input, is not constant over an infinite frequency band.
Although the servo-control loop attempts to main a 1:1 ratio
between actual output and command input, this response
ratio starts to reduce or "rolls off" above a certain frequency.
This roll-off is usually set initially by the limited velocity
capability of the system and subsequently by the limitations
in the forces it can apply to accelerate the system mass.
Additionally, many real world test control systems have
resonances or anti-resonances within particular frequencybands as a result of the finite stiffness of the test system,
fixturing, or indeed the test specimen itself. If these
resonances occur within the desired frequency range of
control for the test they become a real problem.
Lastly there may be a complex mechanical system
between the actuator and the feedback parameter of interest
(remote parameter). Real systems may also have elements
that have non-linear input/output relationships, for example,
variable spring rate, lash, or non-repeatable input/output
relationships, such as specimen degradation. The linearity
and repeatability issues resulting from these will be
discussed later.
All of these issues make it difficult, or in some
cases impossible, for a standard PID servo controller to
ensure that actual system response and the commanded
system response are equal.
Compensation techniques make use of measurement
of the desired and actual system response measurement and
knowledge of the physical system measurement to correct
the above limitations by (1) modifying the input command or
(2) the servo loop control parameters. In general, the
compensation algorithm is a process that is designed to
reduce the difference between desired and achieved responseof the test system, in some cases degrading some aspect of
the achieved response to obtain improvements in another.
These algorithms can be extremely simple or very
complex. For example, with peak/valley amplitude control,
the program correction is based on computing (desired peak
actual peak) * convergence gain which is quite simple to
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understand and use. At the other end of the complexity
spectrum, iterative deconvolution methods use a measured
linear frequency domain system model to iteratively
correct the system command inputs to achieve the desired
system response outputs. This command correction is
obtained from the deconvolution of the response error and
the above mentioned linear system model.
CRITICAL ISSUES FOR COMPENSATION
TECHNIQUES
Three key issues must be addressed when choosing
a compensation technique. These are repeatability, linearity,
and inside vs. outside the servo loop.
REPEATABILITY - System repeatability is
important because none of the compensation techniques can
work well for a system that does not exhibit some level of
repeatability in it's input/output relationship. Very often we
will specify an accuracy level based on the system
repeatability, for example for iterative deconvolutioncompensation methods optimum accuracy is often specified
to be no better than two times the error of the systems
repeatability. A system is repeatable if exactly the same
output is achieved each time the system is excited with a
specific input. The extent to which this output differs is the
extent to which the system is not repeatable.
It is important not to confuse a repeatability issue
with a specimen degradation issue. A repeatability issue will
appear as a random variation in the output while a
degradation issue will show a definite trend. Many
compensation techniques can handle degradation, depending
on how quickly it occurs.
Any system whose characteristics are likely to vary
randomly will have repeatability problems. Examples of this
are systems with high noise levels in their output, systems
with "uncontrolled inputs", such as an output sensitive to
ambient temperature but where temperature is uncontrolled,
or systems with backlash or indeterminate frictional
characteristics (slip/stick). In systems with these
characteristics, the best accuracy that can possibly be
achieved will be in the range of twice the level of non-
repeatability.
LINEARITY - A clear understanding of the testsystem behavior is often required, as many of the
compensation techniques require linear system behavior to
function, and their accuracy is directly related to the degree
of linearity the system exhibits. The simplest way to review
the importance of linearity is to list characteristics of
multiple-input-multiple-output linear systems [3], denoted in
the section that follows as the operator h, and review their
implications from the control aspect as follows:
Homogeneous
)( 11 cxhcy = (1)
The relationship c between any input x and any
outputy, at any specific frequency, is proportional, that is if
you double the input, the output is doubled. This does not
mean that a linear system must have the same output/input
ratio h at every frequency. A system could have an
output/input ratio of 1 at 5 Hz and a ratio of 0.3 at 10 Hz. It
can still be linear as long as a change in the input results in a
proportional (based on the ratio at that frequency) change in
the output.
The characteristics of the system must be the same
for motion or loading in both the positive and negative
directions. An example of a specimen that has this type ofnon-linearity is a shock absorber, which has a different
resistance in the rebound and compression directions.
Because c is constant for any specific frequency, the
system cannot generate in the output signal frequencies that
are not contained in the input signal. This means that a 10
Hz input cannot create anything but a 10 Hz output. The
amplitude and phase may be different, but the frequency
must be 10 Hz and there can be no harmonics created.
Additive
)(
)();(
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xxhyy
xhyxhy
+=+
==
(2)
If an output of the system for one inputx1 isy1 and
for another input x2 is y2 then the result of applying both
inputs simultaneously has to bey1 +y2. This is frequently not
the case for multi-axis systems where the effect of one input
modulates the effects of another. For example, the side
loading of an elastomer engine mount may radically affect i ts
stiffness in another direction.
Physically Realizable
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using some forms of predictive or feed forward control
may not meet this criterion.
Constant Parameter
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The major disadvantage with outside-the-loop
techniques is that they cannot reject disturbances, but depend
upon a consistent relationship between command and
feedback to function properly. They can be designed to
handle external disturbances such as cross-coupling due to
other system inputs, but only when they employ system
models that establish specific relationships between inputs
and outputs of different channels. When something
unexpected happens, the accuracy suffers.
Fortunately, most of automotive structural testing is
not prone to unexpected disturbance effects and outside- the-
loop techniques work well. In cases where the user can
afford the test time to allow these techniques to converge on
the correct input levels these techniques work extremely well
and offer the best general approach to non-deterministic,
multiple-input structural test applications.
A REVIEW OF CURRENTLY AVAILABLE
COMPENSATION TECHNIQUES AND
APPLICATIONS
A wide variety of compensation techniques are
available commercially. Each technique has attributes that
make it effective or desirable in some applications but not
others. Some require linear systems. Some work with peaks
only and dont preserve signal shape. Some are simple to set
up and run while others require trained, experienced
operators. When choosing the correct technique for the
application, it is usually desirable to choose the simplest
technique that will perform the function. For example, an
"iterative deconvolution" compensation approach will
provide accurate signal reproduction in almost any
application, but it is time-consuming and would beunnecessarily complicated for a cyclic test that only needs to
ensure that peaks are achieved. In applications such as these
a peak/valley amplitude controller technique or null pacing
would be more applicable, quicker, and easier to use.
The following section describes the compensation
techniques in use in automotive structural and material
testing applications, listing key attributes and some
appropriate applications.
NULL PACING - There are two types of null
pacing: static and dynamic
Amplitude
Time
SNPstarts
SNPends
Command
Feedback
Segment #1 SNP Hold Segment #2
Tolerance
Error
Note SNP = Static Null PacingTS-K102
Figure 2, Static Null Pacing
Static Null Pacing - In this approach the error
(difference) between the command and the sensor feedback
is monitored. If the error is too large because of system
velocity or force constraints the compensation algorithm
holds or null paces the command at a steady output level,
allowing the system to attain the target command level. As
the error comes within tolerance, static null pacing resumes
the command.
Dynamic Null Pacing - In this approach the error
(difference) between the command and the sensor feedback
is also monitored. If the error is too large because of system
velocity or force constraints, dynamic null pacing reduces
the command frequency, allowing the system additional time
to track the command. As the error comes within tolerance,
dynamic null pacing resumes the command.
Attributes of null pacing:
Works with linear or non-linear specimens. Works with cyclic or arbitrary end level waveforms,
rainflow matrix depletion, and similar. Does not require
a periodic waveform.
Guarantees to meet peaks within a specified tolerancethe first time without overshooting.
Pre-measurement of system performance is not required. Will work with mixed control modes. Since it does not over program, it typically runs slower
than a compensation method that does.
The difference between static and dynamic null
pacing is that the static version holds the maximum program
level until the feedback is within error tolerance withoutregard for wave shape, while the dynamic version attempts
to maintain wave shape by slowing the frequency enough
that the peak levels are within tolerance. Normally, dynamic
null pacing will slow a test down more than static null
pacing.
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Null pacing is used in one of two applications. In
the first, the user does not care about wave shape but simply
wants to get his test performed as quickly as possible,
meeting the peak within a specified tolerance on every cycle,
and using the maximum performance of his hydraulic
system. In this case, he will design his cyclic test with
frequencies faster than his system can reproduce. He will
then rely on the null pacing algorithm to slow the test down
just enough that his hydraulic system can reproduce the peak
levels. Static null pacing would normally be used in this
case because wave shape is irrelevant and the user wants the
test to run as quickly as possible.
The other application is where the user wants to
ensure that he meets the peak within a specified tolerance on
every cycle, but cannot tolerate the possibility of
overshooting the peak (which can happen with peak valley
amplitude control or other over programming techniques).
In this case, dynamic null pacing would be used if wave
shape were an issue, otherwise static null pacing would run
faster.
PEAK/VALLEY/MEAN (PVM) CONTROL -
PVMamplitude controlmonitors the command and feedback
to detect any peak amplitude under- or overshoot or mean-
level divergence. If under- or overshoot is detected, PVM
compensates by boosting or reducing the command
amplitude. If mean-level divergence is detected, PVM
compensates by adjusting the command mean level.
Attributes of PVM control:
Will over program. Compensates for peaks and mean level.
Works with linear or non-linear specimens. Works to match end levels without regard for wave
shape.
Pre-measurement of system performance is not required. Maintains correct peak, valley and mean loads as
specimen degrades.
Requires some cycles for initial convergence. Numberdepends on the system characteristics.
Requires cyclic waveform, but does not have to besinusoidal. Will not work with arbitrary end-level style
command inputs.
Will work with mixed control modes. Multiple channels can use PVM, but the compensation
on one channel does not account for the actions of otherchannels. This means that inaccuracies can result if
there is significant cross-coupling between channels.
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PVM amplitude control is typically used in cyclic
or block/cyclic applications to control peak and mean loads
on the specimen primarily for cyclic fatigue testing. It is the
most commonly used compensation method in the testing
world. The cycle block used in block cycle tests usuallycontain many cycles (>10) because the compensation
algorithm requires some cycles for to achieve initial
convergence on the correct values. This technique is not
generally applicable to low-cycle fatigue tests where short 1
or 2 cycle blocks are needed. Null pacing methods are more
suitable for these applications.
AMPLITUDE PHASE CONTROL (APC) - APC is
a compensation technique that monitors the feedback and
command to detect any gross amplitude or phase lag
differences between command and feedback exist. If
amplitude differences of this type are detected, APC
compensates by boosting the command amplitude. If phaselag is detected, APC compensates by altering the command
phase.
Attributes of amplitude phase control:
Will over program. Pre-measurement of system performance is not required. Works best with a linear system and specimen. Compensates for amplitude and phase, important in
multiple input tests where the phase relationship
between inputs is important.
Uses the integral of the PID loop to maintain meanlevel. This is satisfactory as long as the linearity
requirement is met. Corrects for specimen degradation provided it does not
take place too quickly.
Requires some cycles for initial convergence. Thenumber depends on the system characteristics.
Requires a cyclic, sinusoidal waveform (or a sine sweepif rate is low enough.) Works to match end levels
without regard for wave shape, but assumes sinusoidal
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shape. Peaks will overshoot if significant harmonic
distortion is present in the feedback signal.
Will work with mixed control modes. Multiple channels can use APC, but the compensation
on one channel does not account for the actions of other
channels. This means that inaccuracies can result if
there is significant cross-coupling between channels.
APC is most effectively used in cyclic or block
cyclic testing on multi-channel systems where phase
relationships between channels are critical. Cyclic blocks
usually contain many cycles (>10) because the compensation
algorithm requires some minimum number of cycles to
converge initially. It is not appropriate for 1 or 2 cycle
blocks.
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Figure 5, Example for Before and After Compensation
Systems using APC must be substantially linear. If
they are not, then the feedback will typically have significant
harmonic content and the actual peaks will overshoot the
desired. This is because the APC algorithm works only on
the fundamental frequency of a signal and tries to match the
amplitude of the fundamental frequency of the actual signal
with the desired signal. When harmonics are present, they
will add to the fundamental frequency and this typically
causes the overshoot. A non-linear system may also cause
significant inaccuracy in the mean level when using APC.
APC will also work with sine sweeps, but the sweep
rate must be kept below the APC algorithm update rate or the
APC correction will not keep up. The actual sweep rates
must be determined experimentally on each system, but
typically linear sweep rates must be slower than 1 Hz per
second and logarithmic sweep rates slower than 1 octave per
minute.
ADAPTIVE HARMONIC CANCELLATION
(AHC) - A non-linear system will often produce harmonicsin its feedback signals even when the program is a clean
sinusoid. AHC is a compensation algorithm designed to
remove these unwanted harmonics from a sinusoidal
feedback signal. It uses a technique developed in the
adaptive noise control field that adds a signal to the
program with the correct amplitude, phase and frequency to
completely cancel the unwanted harmonic signal. Adding a
sufficient number of harmonically related correction signals
could theoretically eliminate all the harmonics distortion.
Because cancellation occurs at the system output by
means of a signal at the system input, the phase response of
the system must be known. Before the compensationalgorithm can be applied, it must learn the systems phase
response by exciting the system with a sine sweep or a
random signal over the frequency range of operation and
measure the system response. This training frequency
range must be high enough that all of the harmonics required
to be cancelled are included, that is to cancel a third
harmonic on a 30 Hz signal, the training frequency range
must extend to at least 90 Hz.
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Large Third Harmonic
Attributes of the adaptive harmonic cancellation:
Pre-training is required. Works with non-linear systems to remove harmonics in
sinusoidal signals.
Handles specimen degradation if it does not happen tooquickly.
Requires some cycles for initial convergence. Thenumber depends on the system characteristics.
Requires cyclic, sinusoidal waveform or sine sweep ifthe rate is slow enough.
Multiple channels can use AHC, but the compensationon one channel does not account for the actions of other
channels. This means that inaccuracies can result if
there is significant cross coupling between channels.
A typical application of AHC is to work in
conjunction with APC to control the acceleration levels on a
multiple degree of freedom vibration table using a cyclic
sinusoidal or sweep program to provide acceleration
controlled vibration in a single degree of freedom. The AHC
removes the harmonics so that APC can do a good job of
controlling the amplitude. In this type of test, for example
resonance searches on a test specimen, it is often importantto minimize the harmonic content of the acceleration signal
so that using APC (which cannot correct for harmonic
distortion) is a viable alternative.
AHC can also cancel the fundamental frequency of
an external disturbance. For example, in large multiple-axis
table systems, horizontal movement of a large specimen with
a center of gravity high above the table can generate
significant disturbance loads into the pitch axis. By tuning
the pitch harmonic cancellation to the frequency of
horizontal movement, these pitching disturbances can be
completely eliminated.
ARBITRARY END-LEVEL COMPENSATION
(ALC) - ALC is an adaptive compensation technique that
improves the peak and valley amplitude tracking accuracy of
specimen loading profiles generated from Markov from-to
matrix data. This approach is also known as from-to matrix
compensation.
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ALC compensates for peak and valley errors by
building (and continually updating) a matrix of amplitude
compensation factors. The matrix is two-dimensional, with
its axes mapped to either full scale or a sub-range of full
scale. Each axis is divided into 16, 32, or 64 equal parts, with
each part representing a fraction of the defined range. The
horizontal axis is labeled From-Level and the vertical axis
is labeled To-Level. With each pass of the spectrum, the
peak/valley errors are calculated, and an estimatedcompensation factor is stored in the matrix. Before the
command generator generates a segment, it notes the From
and To levels, and refers to the matrix to determine how
much to over-program the segment.
In order to run the test as fast as possible, the
compensation algorithm builds a second matrix to store
frequency compensation factors. The command generator
uses these factors to maintain the optimum loading profile
replay speed.
The matrix compensation factors are updated during
each pass of the spectrum. Depending on the convergence
rate, it may take a number of cycles before the feedback
amplitude tracks the command to within tolerance. It may
take multiple passes of the spectrum before the complete
spectrum tracks to within specified tolerance.
Attributes of arbitrary end-level compensation:
Works with linear or non-linear specimens.
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Works with cyclic or arbitrary end level waveforms,matrix depletion or similar. Does not require a periodic
waveform.
Will over-program. Works to match end levels without regard for wave
shape.
Will optimize frequency as well as amplitudes tominimize test time. Pre-training is not required. Will work with mixed modes. ALC can be used on multiple input tests, but the
compensation on one input does not account for the
actions of other inputs. This means that inaccuracies
can result if there is significant cross-coupling between
channels.
ALC is typically used in fatigue testing applications
to control amplitudes for matrix depletion tests. A matrix
depletion test is similar to a block/cycle test except that there
are often only one or two cycles of a particular amplitudebefore switching to a new amplitude. There are not enough
cycles in a row at any particular amplitude to establish the
right compensation factor in a PVM or APC control. The
ALC table remembers the last compensation factor for each
amplitude programmed and updates this as the test
progresses. ALC is used where the user wants to test faster
than null pacing would allow and is willing to live with an
occasional amplitude overshoot.
SPECTRUM AMPLITUDE CONTROL (SAC) -
SAC is an extension of ALC where the matrix is a three-
dimensional from-to-next matrix instead of the from-to
matrix in the ALC method. This gives SAC the ability to
handle reversals better than ALC and is can provide better
ultimate accuracy than ALC.
Attributes and typical applications are the same for
SAC as they were for ALC.
DYNAMIC PROPORTIONAL GAIN - Dynamic
proportional gain is an inside the loop technique that
adjusts the proportional gain based on the peak level of error
in the system.
SPRING RATE BASED GAIN CONTROL - This
is an inside the loop technique that works in a load frame
style test or any test that has a fixed spring specimen wherespecimen stiffness is the critical parameter determining servo
loop gain. It continuously monitors the stiffness of the
specimen and uses this information plus information on the
rig stiffness to adjust the proportional and integral gains of
the servo controller. This process occurs fast enough so that
it can do a good job of maintaining the loop at optimum
tuning even as the specimen spring rate changes rapidly.
Attributes of spring rate based gain control:
Will not over-program. Does not work with program orcommand inputs at all.
Works to maintain amplitude and wave shape. Works only with a load control spring specimen test
where specimen spring rate is the critical parameter
determining servo loop performance. Will not functionon inertial reaction test systems such as a vibration table
or full vehicle tire coupled system.
Will not track peaks as accurately as an outside-the-looptechnique like PVM. It can be used in conjunction with
PVM to improve peak accuracy.
Works best for single-channel applications. Can handlesome level of cross coupling depending upon the level
of tuning that can be achieved without loop instability.
This is very dependent on the specific system, but in
general this will not handle cross-coupling as well as a
technique like AIC or iterative deconvolution that
develop specific cross channel models.
Spring rate based gain control will be most effective
in a static pull or low cycle fatigue test where a specimen is
stressed into its plastic region. When this happens, the
specimen stiffness can change dramatically, drops as the
plastic region is entered and increases at turnaround when
the elastic region is re-entered. It should control the wave
shape quite well in this situation, although it may require
help from a PVM technique to accurately achieve the peak
loads.
It can also be used in high cycle fatigue tests to
improve control once a crack begins to grow. In this case,
there is really no benefit over a standard PVM technique
unless wave shape is critical to the user.
ADAPTIVE INVERSE CONTROL (AIC) - AIC is
a compensation technique that uses an inverse model of the
test system to improve response accuracy where the response
of the test system is approximately linear. It works well for
all types of functions, but its most effective use is with
random or time history signals that have broad band
frequency content.
AIC compensation is based on the concept that any
system with transfer function, T(), combined with a filter
with transfer function, T-1 (), has an overall transfer
function of unity. If a compensation filter with transferfunction, T
-1 (), is placed between the function generator
and the servocontroller as shown in the diagram below, then
the overall system response should be equal to the desired
signal produced by the function generator.
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PID
plant T
response = desired
de s
FG
desired
T-1
compensation filter
Figure 8, AIC compensation concept
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igure 9, AIC compensation implementation
(road profile control)
The adaptive inverse controller places this filter and
continuously updates its characteristics to maintain optimum
tracking even as the servocontrol system changes. The
diagram above shows how this works for a single channel
system where the adaptive control mode is the same as the
PID control mode.
In this example, a road profile (called the desired
profile) is to be replicated at the tire patch of a vehicle. Thedynamics of the test system (the combination of PID
controller, actuator, and test specimen) are represented by afrequency response function (FRF) called T(). The
presence of these dynamics causes tracking errors, especially
at higher frequencies. By placing a compensation filter with
an FRF of T-1() between the function generator and the test
system, an overall FRF of unity (perfect tracking) can be
achieved.
In general, the inverse FRF of the test system is not
known and can change over time. AIC uses an inverse test
system identifier to measure it online during the test by
observing the input and output of the test system (the driveand response). The inverse system identifier controls the
compensation filter whose coefficients are continuously
updated to provide minimum errors while the compensation
algorithm is tracking. If desired, adaptation can be frozen
or switched off after the optimum coefficients have been
found or left in tracking to follow changes in system or
specimen dynamics. The process is automatic; the operator is
not required to perform any calculations.
The diagram below is modified to show AIC
connected for mixed mode operation. In this example, the
servoloop is still controlling displacement, but AIC is
controlling acceleration on the spindle of a vehicle.
Everything works the same as in the previous example
except that the desired signal is now an acceleration signal
and the AIC compensation filter converts it into a
displacement-based signal that drives the servosystem to
produce the proper acceleration response.
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Figure 10, AIC compensation implementation
(spindle control)
AIC is an effective digital control technique for
improving tracking accuracy in servohydraulic test systems
whose behavior is primarily linear.
Attributes of Adaptive Inverse Control:
Will over-program. Pre-training is not required, but can be used to speed
convergence.
Works only with a linear system and specimen. Matches amplitude and signal shape. Compensates for amplitude and phase, which is essential
in multi-channel simulations.
Works on the dynamic component of a signal only. TheDC component is left to the servoloop.
Handles specimen degradation if it does not happen tooquickly. Does not converge as quickly as APC or PVM
so degradation must be even slower for AIC.
Requires some time for initial convergence. Theamount of time depends on the system characteristics.
In general, convergence is slower for AIC than for the
cyclic compensation techniques of APC and PVM.
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Will work with cyclic, sinusoidal waveform or sinesweeps, but is most effective with random or time
history signals with broad band frequency content.
Will work with mixed modes. AIC can work in a single or independent channel mode
or in a cross-coupled mode. Cross-coupling is handled
well as long as the cross coupling is linear.
AIC is ideally suited in a 4-post test application
where a user wants to ensure that a road profile is played the
same on multiple systems. In this case, the primary system
develops a desired file for the actuator displacement signals
(typically using an iterative deconvolution technique). This
file is exported to other systems and played as a desired file.
These systems use AIC to ensure that the files are
reproduced accurately without having to use an iterative
deconvolution technique. The systems can have different
tuning and even different actuator/valve combinations. As
long as the system has enough hydraulic power to reproduce
the signal, AIC will compensate for the control differences.
Other applications for AIC include:
Acceleration control on a vibration table where thedesired signal is random or a time history
A fast sine sweep. In this case, AIC is pre-trained usinga random function generator over the frequency range of
the sweep and is put into frozen mode. The sweep
will now run quite accurately until the system begins to
change. At this point, the AIC must be re-trained with
the random function generator to maintain accuracy.
Any component test that is reasonably linear and usesrandom or time history signals for excitation.
ON-LINE ITERATION (OLI) - OLI is intended tocomplement basic adaptive inverse control, providing a way
of handling nonlinear system applications. Basic AIC relies
on the compensation filter. This filter is linear, so it can only
compensate a system that is mainly linear. Not all the
tracking error can be removed in all cases. For example, non-
linearity can often arise in mixed mode applications where
the desired control parameters are remote from the actuators.
In these cases, there can be specimen sub-systems between
the actuators and the control transducer that are quite non-
linear. A good example is control of spindle acceleration
with a 4-poster system.
The following figure shows the basic onlineiteration system. It is a real time implementation of the
iterative deconvolution process. Desired, drive and response
files are all equivalent in OLI and iterative deconvolution
processes. In OLI, the AIC compensation filter (called Drive
Correction Filter in the diagram) plays the same role as the
inverse FRF in iterative deconvolution. The drive is played
directly into the PID controller. Simultaneously, the desired
signal is played and compared to the system response to
develop a response error. The response error is then
convolved with the AIC compensation filter and multiplied
by a user-specified iteration gain to create a drive correction
signal. That signal is summed with the current drive signal to
create a new drive file. This process is repeated until the
response error is reduced to meet specification or a system
characteristics minimum is reached.
OLIs advantage is that each time a point for the
current drive is played, a corresponding point for the next
drive is calculated. This all happens in real time so that
when iteration n is finished, iteration n+1 is ready to go. As
a result of this iterations with OLI go much faster than
iterations with iterative deconvolution.
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Attributes of OLI:
Will over-program. Pre-training is required to establish the AIC
compensation filter. Works with linear or non-linear systems and specimens. Matches amplitude and signal shape. Compensates for amplitude and phase, which is essential
in multi-channel simulations.
Does not handle specimen degradation automatically.Requires re-iteration and may require re-training of the
AIC filter if degradation is significant. Typically, users
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do not do this and tend to let the originally developed
drive play for the duration of the test.
Requires some number of iterations for convergence.The amount depends on the system characteristics.
Requires experienced, knowledgeable operators toachieve good results.
Requires good editing and analysis tools in the time andfrequency domain to achieve good results. Works only with time history signals. The time history
signals can be created from sine waves, sine sweeps,
random, or arbitrary signals, but they must be fixed time
histories that can be repeated exactly in the iteration
process.
Will work with mixed modes. It was designed formixed modes with control parameters remote from the
actuators.
Handles linear and non-linear cross-coupling betweenchannels.
The OLI process is typically used for multi-channel
simulations of field data, just like iterative deconvolution.
Note that additional data editing and analysis function are
often necessary to use OLI effectively. OLI really replaces
only the model measurement and iteration parts of iterative
deconvolution process.
ITERATIVE DECONVOLUTION - With the
advent of minicomputers and lower cost array processor
technology in the mid-seventies a technique was developed
[4] that used an iterative technique, based on the
deconvolution of response error with a linear frequency
domain estimate of the system, the frequency response
function (FRF), to converge toward accurate recreation of
measured service responses in the laboratory. Such were theadvantages of this compensation technique for accurate
reproduction of both amplitude and phase in the response of
non-linear, coupled, multiple-input systems that several
commercial versions of the algorithm were developed.
Examples include, Remote Parameter Control, RPC from
MTS Systems Corporation, Iterative Transfer Function
Correction, ITFC from Schenck, SPiDAR from Instron
Corporation and more recently Time Waveform Replication
TWR from LMS International.
Recently a similar method, but employing a time
domain state-space ARX model of the system [5], instead of
the linear frequency domain FRF model used in the iterativedeconvolution and OLI techniques, has been developed and
is available commercially as the Kelsey Instruments Limited
QanTiM package.
Initially the application of the iterative
deconvolution method was the control of laboratory full
vehicle automotive test systems, either tire or wheel spindle
coupled. The control challenge is to simulate or reproduce
service loading conditions on these test systems the desired
specimen responses, accelerations, loads and displacements,
by applying loads remote from the point of measurement.
Conventionally the only service loads that can be measured
and recorded on a vehicle in service or on the proving
ground are on the body or on the suspension components but
the actual loading into the vehicle is the tire contact patch
with the road. At a minimum a non-linear tire spring is
introduced into the control scheme. Additionally, the
responses measured are frequently due to load inputs from
more than one tire patch. By using an iterative deconvolution
approach both the non-linear spring effects and the cross-
coupling can be compensated and accurate full vehicle
responses simulated in the laboratory. Subsequently, the
technique has found wide application in automotive sub-
system and component testing where testing of the specimen
involves recreation of specimen loading due to multiple
input applied through a non-linear system.
It is important to note that both the amplitude andphase of both the multi-axial input and output in the
laboratory test have to be preserved to allow the multi-axial
service loading effects on the specimen to be accurately
reproduced. This limits the options available to the
laboratory test engineer to accelerate the test beyond what
would take place in service. The most common method is to
examine the desired response loads and strains and use to a
time history editor to remove those sections of the service or
proving ground load histories that provide low damage to the
specimen. The software tools to perform this task, either
manually or through some fatigue sensitive editing routine,
are usually provided as part of the iterative deconvolution
package. Depending on the mix of severity of the service orproving ground road surfaces test accelerations of the
order of five to ten times real time are possible.
The development of a typical iterative
deconvolution compensation test takes place in six steps.
1. Record Service or Proving Ground Data - The specimenis instrumented to measure its response to service
loading, where the service loading is represented by
running the vehicle at a proving ground. The specimen
responses are recorded as a time history on a tape
recorder or equivalent recording device.
2. Digitize and Analyze Data - The recorded time history istransferred to the computer-based analysis system. This
may involve digitizing an analog time history recording.
Using the analysis tools provided in the iterative
deconvolution software package the data is checked for
accuracy and possibly reduced in length using the
editing tools described earlier. The output of this step is
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a set of multi-channel digitized time history records or
files containing the "desired response" of the laboratory
test system.
3. Measure the System Frequency Response Function -The instrumented test specimen is fixed in the laboratory
test system. A set of drive signals are developed to
excite the specimen in the test system and the specimen
response measured through the same instrumentation as
used to measure the service load data. Typically the
drive signal developed is a set of uncorrelated shaped
random multi-channel time histories although input-by-
input random and transient excitation methods may also
be used. Using FFT based spectral analysis methods a
linear estimate of the frequency domain response
function or a time domain ARX model of the complete
test system plus specimen is computed. These linear
Multiple-Input Multiple-Output (MIMO) models of the
system contain the amplitude and phase of the input-
output characteristic of the system between all inputs
and outputs over the frequency control band of interest.This system model is then mathematically inverted to
become an output-input model in preparation for the
next step in the process. Some application packages
allow the computation of a system model where the
number of outputs exceeds the number of inputs. In this
case the system is over-determined and the general
approach is to compute a pseudo-inverse where
residual errors are minimized in a least squares [6]
sense.
4. Apply Drive Estimate to the System - Each of thedesired response time histories is convolved with the
inverted system model, that is deconvolved with theforward system model to provide an estimate of the
system drive signal required to produce the response.
Note that this estimate is based on a linear model and
therefore may be substantially in error. From safety
considerations this drive estimate is scaled, typically by
half, and applied to the test system. The resulting
response of the specimen is measured.
5. Calculate Error and Iterate - The desired specimenresponse is subtracted from the response achieved on the
test system due to the drive signal and a response error
signal calculated. The response error signal is convolved
with the inverse system model and a linear estimate ofthe drive error signal results. A scaled proportion of this
drive error is added to the previous drive signal to
produce a better estimate of the drive signal required to
produce the desired response, scaling being employed to
reduce the possibility of overshoot and instability in the
iterative process. The modified drive signal is then used
to run the test system and the new response recorded. A
new response error is calculated as described above and
the process repeated (iterated) until the response error
is reduced to an acceptable value, that is, when the
achieved response on the test system has converged onto
the desired service load response. This process is
repeated for all separate service load recordings made.
The final sets of drive signals files for each response
signal file are combined into a durability test schedule.
6. Execute Durability Schedules - The final step is to runthe durability test schedule into the test system and
monitor the performance of the test specimen over the
laboratory simulated service life.
Attributes of iterative deconvolution control:
Will over-program. Requires use of computer (typically a PC) and an
analog-to-digital, digital-to-analog conversion device to
drive the test system and measure the responses.
Pre-training required through measurements of thesystem transfer function using multi-channel orthogonal
white noise or input-by-input excitation.
Works with non-linear systems that exhibit a moderatedegree of cross coupling between inputs and outputs.
Matches achieved system amplitude and phase to thedesired responses.
Number of iterations required for a given accuracy ofreproduction can be reduced through modification of
system frequency response function at each iteration
step.
While the various commercially available iterativedeconvolution packages differ in the detail of how they
measure and calculate the system model, if during the
development of the test they all converge to the same
degree of accuracy on the desired response then all the
resulting tests will be of the same accuracy and the same
duration.
Differences in implementation and algorithms used inthe iterative deconvolution packages available may
result in reduced test development times or, in some
extreme control cases, the ability to converge on the
desired response. In practical terms, however, any
reduction in test development and test execution time
due to the algorithms employed is small compared to
that obtained by combining an experienced user with a
simple and error reducing software interface to the
application.
REFERENCES
[1] Katsuhiko Ogata: Modern Control Engineering,
Prentice Hall, 1970.
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[2] Howard L. Harrison and John G. Bollinger:
Introduction to Automatic Controls, Harper & Row
Publishers, 1969.
[3] J.S. Bendat and A. G. Piersol: Random Data Analysis
and Measurement Procedures. 2nd
Edition, Wiley-
Interscience, 1986.
[4] B.W. Cryer, P.E. Nawrocki and R.A. Lund: A Road
Simulation System for Heavy Duty Vehicles, SAE
Paper 760361, Automotive Engineering Congress and
Exposition, February 1976.
[5] A. D. Raath and K. Locking: Advances in Service Load
Simulation Testing, Engineering Integrity Society
Conference Paper, October 1995
[6] J. W. Fash, J. G. Goode and R. G. Brown: Advanced
Simulation Testing Capabilities, SAE 921066, 1992.