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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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+=+

==

(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

h(t, ) = h() for -

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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

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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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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

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desired

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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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(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.