U.S. patent application number 10/131875 was filed with the patent office on 2003-10-30 for method and system for controlling mechanical systems exhibiting discontinuity in inertial loading.
Invention is credited to Chaffee, Mark A..
Application Number | 20030201747 10/131875 |
Document ID | / |
Family ID | 29248637 |
Filed Date | 2003-10-30 |
United States Patent
Application |
20030201747 |
Kind Code |
A1 |
Chaffee, Mark A. |
October 30, 2003 |
METHOD AND SYSTEM FOR CONTROLLING MECHANICAL SYSTEMS EXHIBITING
DISCONTINUITY IN INERTIAL LOADING
Abstract
A technique is provided for adapting feedback control system
performance to applications involving changing inertial loads. A
modified gain profile is applied for a control system block that
includes isolated torque scaling. The torque scaling block
facilitates the generation of gain profiles specifically adapted to
the changing inertial conditions of the load. Dilatory effects of
backlash and similar load discontinuity can be avoided, therefore,
by appropriately applying gain profiles to reduce gain within a
region of reduced load.
Inventors: |
Chaffee, Mark A.; (Etna,
NH) |
Correspondence
Address: |
Alexander M. Gerasimow
Allen-Bradley Company, LLC
1201 South Second Street
Milwaukee
WI
53204-2496
US
|
Family ID: |
29248637 |
Appl. No.: |
10/131875 |
Filed: |
April 24, 2002 |
Current U.S.
Class: |
318/630 |
Current CPC
Class: |
G05B 13/024
20130101 |
Class at
Publication: |
318/630 |
International
Class: |
G05B 011/01 |
Claims
What is claimed is:
1. A method for controlling a mechanical system exhibiting
backlash, the method comprising: generating control signals for
application to an actuator in accordance with a first gain level
when a normal inertial load is applied to the actuator; and
reducing the gain level to a second level when a reduced inertial
load is applied to the actuator within a backlash range of
motion.
2. The method of claim 1, wherein the first gain level is based
upon inertia of the load and inertia of the actuator.
3. The method of claim 2, wherein the second gain level is based
upon inertia of the actuator only.
4. The method of claim 1, wherein the gain level is reduced
linearly from the first level to the second level.
5. The method of claim 4, wherein the gain level reaches a minimum
at a midpoint of the backlash range of motion.
6. The method of claim 1, wherein the control signals are generated
in nested velocity and torque control loops.
7. A method for controlling a mechanical system exhibiting backlash
behavior, the method comprising: determining a backlash range of
motion; determining a first gain level to be applied to an actuator
during normal loading; determining a second gain level to be
applied to the actuator during backlash loading, the second gain
level being less than the first gain level; and generating a gain
profile to be applied to the actuator within the backlash range of
motion based upon the first and second gain levels.
8. The method of claim 7, wherein the gain profile includes a
backlash region in which a gain level is reduced from the first
level to the second level.
9. The method of claim 8, wherein the backlash region is centered
at a midpoint of the backlash range of motion.
10. The method of claim 9, wherein the gain level within the
backlash region is reduced linearly from the first level to the
second level.
11. The method of claim 7, comprising the further step of storing
the gain profile for generation of control signals to be applied to
the actuator.
12. The method of claim 8, wherein gain levels within the backlash
region are determined by subtracting the second gain level from the
first gain level and dividing the resulting value by one half the
backlash range.
13. The method of claim 7, wherein the first gain level is
determined based upon inertia of a load and inertia of the
actuator.
14. The method of claim 13, wherein the second gain level is
determined based upon inertia of the actuator only.
15. A system for controlling a machine, the system comprising: an
actuator coupled to the machine and configured to drive the machine
in response to control signals; and a controller coupled to the
actuator and configured to apply control signals to the actuator,
the controller applying control signals based upon a first gain
level when a normal inertial load is coupled to the actuator, and
reducing the gain level to a second level when a reduced inertial
load is applied to the actuator within a backlash range of
motion.
16. The system of claim 15, further comprising a position sensor
coupled to the controller, wherein the control signals are a
function of position of the actuator as detected by the position
sensor.
17. The system of claim 15, wherein the first gain level is based
upon inertia of the load and inertia of the actuator.
18. The system of claim 17, wherein the second gain level is based
upon inertia of the actuator only.
19. The system of claim 15, wherein the gain level is reduced
linearly from the first level to the second level.
20. The system of claim 19, wherein the gain level reaches a
minimum at a midpoint of the backlash range of motion.
21. The system of claim 15, wherein the control signals are
generated in nested velocity and torque control loops.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention relates generally to the field of
mechanical systems, such as rotationally driven equipment. More
particularly, the invention relates to a technique for more
smoothly or accurately controlling movement of such mechanical
systems to compensate for discontinuities in inertial loading.
[0002] A wide range of mechanical systems exist and are presently
in use for driving various types of loads. Many systems include
rotary machinery, such as engines or motors which drive loads
either linearly or in rotation through the intermediary of various
power transmission components. Such components may serve to
appropriately locate a load with respect to a source (e.g. transfer
position of application of forces) or may serve to alter the speed
of the input source and, therewith, the reflected inertia of the
load. In either case, it is generally desirable to provide for
smooth control over a wide range of speeds and torques, with the
ability to reverse directions of movement and hold accurate
position where appropriate. In conventional power transmission
systems, components interposed between a prime mover and a load may
include various types of gear boxes, chain drives, servo drives,
clutches, and so forth.
[0003] Depending upon the design and operation of the power
transmission components in such systems, conditions may exist or
develop in which the reflected load inertia is discontinuous. In a
typical example, a gearbox, chain drive, or similar power
transmission component, may exhibit a characteristic generally
referred to as "backlash." Backlash may be considered a
discontinuity in inertial loading due to a reduction in contact
between two or more elements over a portion of a movement range. In
a gearbox, for example, backlash may develop due to a loss of
contact between neighboring gear teeth which generally intermesh to
transmit rotary motion. The backlash may not be particularly
noticeable when the load is driven. While the load is accelerating
and decelerating the gear teeth are normally engaged. In most cases
load friction keeps the gear teeth engaged even when the load is
driven at a constant speed. However, when the system is held
static, or when there is minimal friction applied to the load
moving at constant speed, backlash may be result in sudden changes
in the reflected load inertia which can lead to servo control
instability. Another problem with backlash is the difficulty in
maintaining accurate control in servo applications.
[0004] At present, servo tuning and adaptive control are key
control technologies enabling drive and motion products to be
easily applied to industrial motion control applications,
particularly to power transmission applications. The objective of
servo tuning algorithms, sometimes refer to in the industry as
"auto-tuning" when applied to the motion control, is automatically
to achieve a well tuned, "application-ready" position or velocity
servo loop. The servo loop generally refers to the control loop
which is established to maintain a desired position or velocity as
indicated by an input or command signal. Servo tuning is typically
accomplished through foreknowledge of the motor-mechanical system
or through the application of a minimal motion profile to an
unknown motor-mechanical system. In either case, servo tuning
algorithms result in servo loops that are generally tuned for a
fixed load inertia.
[0005] One of the main objectives of adaptive control algorithms,
sometimes referred to as "adaptive tuning," is to maintain
acceptable servo control performance levels despite significant
variations in parameters associated with the motor-mechanical
system. One common adaptive control problem that motion control
engineers face is compensating for a variable system inertia, such
as that present in discontinuous inertia situations such as that
described above, and in particular in situations where backlash is
present. Adaptive control algorithms compensate for these
variations by continuously measuring the inertia of the system or
by calculating the inertia based on the current position, time, or
control state.
[0006] Traditional servo loop topologies do not make the task of
developing auto-tuning or adaptive control algorithms a
straightforward process. Servo control loops generally need to
interface to a wide variety of drive power structures, motors, and
mechanical systems, as well as to feedback devices. With
traditional servo loop technologies, a variation in any of these
components affects multiple gain parameters. When these variations
occur in real time, such as due to discontinuities in inertial
loading, modification of multiple gain parameters using adaptive
control is awkward.
[0007] There is a need, therefore, for improved approaches to
control of systems in which varying or inconsistent inertia loading
may be present. There is a need, at present, for a straightforward
approach to the control of loads in mechanical systems in which
there is variation in load inertia. In particular, there is a need
to compensate for discontinuous variation in load inertia as a
function of position such as exhibited by mechanical backlash.
SUMMARY OF THE INVENTION
[0008] The present invention provides a novel control technique
designed to respond to these needs. The technique is particularly
well suited to the control of rotational systems, such as
motor-driven loads including gear boxes, chain drives, ball-screws,
or any other power transmission components which may be subject to
discontinuities in load inertia. However, it should be borne in
mind that the invention is susceptible to application in a more
wide range of settings. That is, linear or other power transmission
applications may also benefit from the technique, particularly
where inertia loading may vary or where servo systems may require
rapid adaptability to changing loads or speeds. In an exemplary
embodiment, the invention is applied to a power transmission system
including a gear box that exhibits backlash. Other systems,
however, may exhibit similar control issues, and the invention is
intended to address similar problems in all such applications.
[0009] In accordance with one aspect of the invention, a method for
controlling a mechanical system exhibiting backlash includes
generating control signals for application to an actuator in
accordance with a first gain level. The first gain level is applied
when a normal inertia load is applied to the actuator. The gain
level is then reduced to a second level when a reduced inertial
load is applied to the actuator within a backlash range of motion.
Various profiles may be provided for transitioning between the
first and second levels, and the gain levels may be adapted to the
specific application and loading.
[0010] A system is also provided by virtue of the present
technique. The system may include an actuator coupled to a machine
and configured to drive the machine in response to control signals.
A controller is coupled to actuator and is configured to apply
control signals to the actuator, with the controller applying the
control signals based upon a first gain level when a normal
inertial load is coupled to the actuator, and reducing the gain
level to a second level when a reduced inertial load is applied to
the actuator within a backlash range of motion.
[0011] Again, a broad understanding of the term backlash is
contemplated in accordance with the present technique. That is, the
technique may be generally applied within a range of motion which
is susceptible to sudden and significant variations in inertial
loading, such as due to a change in contact two or more machine
elements.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] The foregoing and other advantages and features of the
invention will become apparent upon reading the following detailed
description and upon reference to the drawings in which:
[0013] FIG. 1 is a diagrammatical overview of a machine system
including one or more power transmission components and a load
which is susceptible to changes in inertial loading and which will
be controlled in accordance with the present technique;
[0014] FIG. 2 is a detailed representation of a section of two
intermeshing gears illustrating one source of discontinuity in
inertial loading due to backlash;
[0015] FIG. 3 is an exemplary profile of an inertia discontinuity,
which can result from backlash in systems as that illustrated in
FIG. 2;
[0016] FIG. 4 is a simplified velocity servo loop block diagram for
a system of the type illustrated in FIG. 1;
[0017] FIG. 5 is a simplified position loop block diagram for the
system of FIG. 1;
[0018] FIG. 6 is a graphical representation of Bode magnitude plots
for each of the loops in a system of the type illustrated in FIG.
5;
[0019] FIG. 7 is a modified block diagram for the system,
illustrating introduction of a torque scaling factor to facilitate
compensation for variable inertia conditions; and
[0020] FIG. 8 is a graphical representation of an exemplary gain
profile for the torque scaling in a system of the type illustrated
in FIG. 7 for addressing discontinuous inertial loading.
DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS
[0021] Turning now to the drawings, and referring first to FIG. 1,
an exemplary motion control system is illustrated and represented
generally by reference numeral 10. While many various system
configurations may be envisaged for implementation of the present
techniques, the system illustrated in FIG. 1 includes a drive 12
such as an electric motor, coupled to power transmission components
14 and therethrough to a load 16. The power transmission
components, again, may include a wide variety of individual
elements, such as couplings, gear reducers, chain drives, pulleys,
clutches, and so forth. In general, however, the power transmission
components serve to transmit mechanical force from the drive 12 to
the load 16. In a typical application, power transmission
components may include a gear reducer which is driven by an
electric motor to power a pulley, conveyor, pump, or any other
mechanical load.
[0022] A control circuit 18 receives a variety of input signals and
generates output signals for controlling the operation of the
system. As will be appreciated by those skilled in the art, control
circuits such as that illustrated diagrammatically in FIG. 1 may
include general purpose or application-specific computers, various
interface circuitry, user interfaces, and so forth. Control circuit
18 may receive signals of various natures depending upon the design
of the system. However, in the illustrated embodiment power
conductors 20 which supply incoming power to drive 12 also
originate input signals via sensors to the control circuit 18 as
indicated at reference numeral 22. The sensors will typically
include sensors for current and voltage through the power
conductors. Of course, various upstream circuit components may be
included in the system and are not illustrated in FIG. 1, such as
protective devices, power supplies, switch gear, and so forth.
Other sensors are provided in the system for detecting parameters
such as position and speed. In the illustrated embodiment sensors
24 and 26 provide for feedback of position and speed signals both
upstream and downstream of the power transmission components 14.
The power transmission components 14 may also originate feedback
signals, such as position, speed, temperature, vibration, and so
forth that may be fed into a control circuit for control,
monitoring or diagnostic purposes. Finally, feedback signals may
originate from the load as indicated at reference numeral 30, such
as to provide indications of position, speed, load (e.g. weight),
and so forth. Based upon these signals, and upon signals received
from the drive itself, the control circuit 18 determines
appropriate output control signals for regulating operation of the
drive and applies these signals to the drive as indicated at
reference numeral 32. Of course, intermediate components may be
provided between the control circuit and the drive, such as for
isolation, signal conditioning, and so forth. In general, however,
the control circuit will apply control signals to the drive in
accordance with predetermined control algorithms which may include
closed loop position control, velocity control, torque control, or
a combination of these.
[0023] Through the control algorithms executed by control circuit
18, various adaptations may be made to the dynamic characteristics
of the drive, the power transmission components and the load
itself. In particular, the control circuitry is specifically
adapted to accommodate power transmission trains in which
discontinuities or significant changes in inertial loading may
occur. In particular, such significant changes in loading may be
the result of loss of contact between power transmission
components, such as due to effects known as backlash. FIG. 2
illustrates a typical situation that may result in such
backlash.
[0024] As shown in FIG. 2, in a gear reducer, gearing represented
generally by reference numeral 34, will include intermeshing gears
36 and 38, each having teeth designed to contact one another to
transmit torque from a driving gear to a driven gear. In the
illustration of FIG. 2, for example, gear 36 may be driven by gear
38, by contact of tooth 40 of gear 38 with tooth 42 of gear 36. In
convolute gearing, rolling contact is generally maintained as
indicated generally at reference numeral 44.
[0025] Due to wear, manufacturing tolerances, and other mechanical
causes, spacing or gaps may develop within the gearing, such as
between tooth 40 and a subsequent tooth 46 on gear 36. The gap,
indicated at reference numeral 48 in FIG. 2, may not pose
significant problems when the gears are driven in a single
direction and relatively steady loading. However, if the process
calls for changes in direction of rotation, or for the gears to
remain static, driven gear 38 may experience a significant
reduction in inertial loading due to the presence of gap 48. That
is, the gap will represent a range of positions over which gear 38
is generally not loaded.
[0026] FIG. 3 is a graphical representation of the discontinuity in
inertial loading, which can result from backlash in gearing or
other power transmission components. As shown in FIG. 3, the
graphical representation indicated at reference numeral 50
illustrates inertia experienced by the drive components of the
system. The position or angle axis 52 indicates the linear or
rotary position of the driving member, while the load axis 54
indicates inertial loading of the driving members. As can be seen
from the profile of the loading 50, under load the driving members
experience a relatively elevated load level 56 which, of course,
may vary somewhat depending upon the characteristics of the load
and the application. However, a substantially reduced load 58 is
experienced over the backlash range 60.
[0027] The present technique permits adaptation of control signals
delivered by a control circuit 18 (see FIG. 1) to accommodate
substantial changes in loading of the type illustrated graphically
in FIG. 3. The control scheme is preferably implemented through
nested control loops. In a present embodiment, the control servo
loops may consist of three "nested" control loops. The inner-most
loop is referred to as a current or torque servo loop. Surrounding
the torque loop is a velocity servo loop and, finally, surrounding
the velocity loop is a position servo loop. The characteristics of
these control loops in a present embodiment will now be described
in greater detail.
[0028] A complete model for a velocity servo drive and motor in
accordance with aspects of the present technique includes the
electrical and mechanical time constance of the motor, and can be
rather cumbersome in implementation and analysis. However, in the
present approach, a simplification of the analysis is based upon
assuming that the motor is a pure inertia load, and that the
current/torque loop is a simple single-pole filter having a time
constant T. The time constant of the model represents the sum of
the delays through the velocity loop. Thus, the closed loop
bandwidth of the lumped model for the torque servo loop may be
represented by the relationship:
BW(torque)=1/T. (1)
[0029] The resulting simplified velocity servo loop block diagram
may be represented as illustrated in FIG. 4. As shown in FIG. 4, a
velocity command signal indicated by reference numeral 62 is
applied to the loop, with an output signal 64 resulting from the
loop. The output signal and command signal are combined at a
summing junction 66. The combination is applied to a
proportional/integral controller 68. The transfer function for the
proportional/integral controller may be represented by the sum:
Kp+Ki/s. (2)
[0030] The output of the proportional/integral controller is
applied to a torque amplifier 70. The transfer function for the
torque amplifier may be represented by the value:
1/(Ts+1). (3)
[0031] The output of the torque amplifier is then applied to the
motor load 72, which may be modeled as the as a lumped inertial
load, J, where J is the sum of the motor inertia and the reflected
load inertia as seen by the motor:
1/Js. (4)
[0032] The output signal 64 results from the motor load and is fed
back to the summing junction 66 as indicated at reference numeral
74 in FIG. 4.
[0033] As will be appreciated by those skilled in the art, the
transfer functions and values indicated for the velocity loop are
in the S-domain. The value Kp represents the proportional gain, Ki
is the integral gain, T, again is the sum of all delays around the
closed loop system (torque loop delay, computational delay,
sampling delay, etc.), and J is the total system inertial. The
system inertia expressed in torque units per acceleration unit, can
be thought as including the gain of the drive amplifier and the
gain of the feedback transducer, as well as the motor reflected
load inertia.
[0034] It should be understood that the foregoing model does not
address the impact friction, damping, mechanical compliance on
servo behavior, nor does it address non-linear effects such as
mechanical backlash or dead band, discussed in greater detail
below. The usefulness of the model is based on the fact that
inertia is the dominant factor in most servo control applications,
and is the focus for the following development.
[0035] A set of general equations for Ki and Kp can be developed
from the foregoing model as functions of T, J, and the classical
damping factor .zeta.. The unity-gain bandwidth of the velocity
servo loop is found to be given by the ratio of the proportional
gain and the inertia, that is, Kp/J. The velocity loop equations,
in terms of the foregoing nomenclature, may be written as
follows:
BW(vel)=Kp(vel)/J=1/4.zeta..sup.2*1/T; (5)
Kp(vel)=J*1/4.zeta..sup.2* 1/T=J*BW(vel); (6) and
Ki(vel)=1/J*1/4.zeta..sup.2*Kp.sup.2(vel). (7)
[0036] With these relationships in hand, a similar set of general
equations can be used to compute a complete set of proportional and
integral parameters for the outer position servo loop.
[0037] The position loop block diagram may be illustrated as shown
in FIG. 5. A position command signal is applied to the system as
indicated at reference numeral 76 to produce a position output 78.
The two are combined at summing junction 80, and the resultant
signal is applied to the proportional integral/controller 82. The
transfer function for the proportional/integral controller 82 may
be identical to that indicated above for the controller 68 of FIG.
4. Output from the positional integral controller is applied to the
velocity loop 84. The transfer function for the velocity loop may
be written in terms of Damping Factor, .zeta., and Natural
Frequency, .omega..sub.n, as follows: 1 n 2 s 2 + 2 ?? n s + n 2 .
( 8 )
[0038] The output of the velocity loop is applied to a position
accumulator 86, which may be considered to have a transfer
function:
1/s. (9)
[0039] The position accumulator output is the position signal 78,
which is fed back to summing junction 80 as indicated at reference
numeral 88 in FIG. 5.
[0040] A rigorous mathematical analysis of the position loop model
demonstrates that the most practical measure of bandwidth for the
position servo loop is given by proportional gain for the position
loop, that is Kp (pos), which represents the unity gain bandwidth
of the position servo loop. The position loop equations, then, may
be written in terms of the values described above as follows:
BW(pos)=Kp(pos)={fraction
(1/16)}*1/.zeta..sup.2*1/T=1/4.zeta..sup.2*BW(ve- l); (10)
Kp(pos)=BW(pos); (11) and
Ki(pos)=1/4.zeta..sup.2*Kp.sup.2(pos). (12)
[0041] It should first be noted that the bandwidth formulas for the
three control loops are related to one another by the classical
damping factor of the second order velocity servo loop. The nested
loop bandwidth relationship may be expressed:
BW(pos)=1/4.zeta..sup.2*BW(vel)=1/4.zeta..sup.2*1/4.zeta..sup.2*BW(torque)-
. (13)
[0042] As can be seen from the foregoing analysis, to achieve a
given damping for the closed loop system response, the servo loops
may be tuned such that each loop has a bandwidth that is a factor
of 1/4.zeta..sup.2 less than the bandwidth of the next inner loop.
This bandwidth relationship may be illustrated as shown in FIG.
6.
[0043] FIG. 6 shows a series of functions 90 displayed over a
frequency range along axis 92 and a magnitude range along axis 94.
The Bode magnitude plots of FIG. 6 represent a damping factor
.zeta.=1. A unity magnitude value is represented by the dashed line
96 in FIG. 6. Plot 98 crosses the unity magnitude level at the
position servo loop bandwidth value Kp(pos). The plot 100 crosses
the same line at the velocity loop bandwidth value Kp(vel)/J.
Finally, the plot 102 crosses the unity magnitude value at the
torque loop bandwidth 1/T. The plots indicate that the closer the
outer servo bandwidth is run to that of the inner loop, the more
under damped the frequency response becomes. The bandwidth of both
the position and velocity servo loops are, therefore, ultimately
limited by the drive model time constant T, which may be estimated
as the lump sum of all delays through the velocity loop. As
indicated above, the time constant T may generally be considered to
include servo computational delays, output filter time constants,
current loop time constants, feedback sample delays, feedback
filter time constants, and so forth. With the proper value of T
established, it has been found through simulation studies and
laboratory tests that the above equations work quite well in
characterizing the frequency response of the system using the
nested proportional/integral servo loop topology.
[0044] It may be noted from the discussion above that the
proportional gain for each of the control loops is directly
proportional to the unity-gain bandwidth of the loop. Because the
unity-gain bandwidth is an important metric of servo performance,
it is desirable to make use of this relationship. In the case of
the velocity servo loop, however, the scaling factor is the inertia
value J, which varies from application to application and can vary
as a function of time or position in a given application. In the
present approach, the proportional gain value is equal to the
unity-gain bandwidth of the corresponding servo loop. To achieve
this end, the scaling factor J must first be eliminated from the
above equations.
[0045] The torque integrator scaling factor J can be eliminated by
adding a new gain term, called torque scaling, into the velocity
servo model as shown in FIG. 7. As indicated in FIG. 7, the model,
as in the velocity loop model of FIG. 4, calls for application of a
velocity command signal at reference numeral 62 and a velocity
output at reference numeral 64 fed back to a summing junction at
reference numeral 66. Again, the output of the summing junction is
applied to the proportional/integral controller 68. However, the
output of the controller is applied to a torque scaling block 104.
By setting the torque scaling gain of block 104 equal to the system
inertia, J, the term 1/J is canceled from the proportional gain
equation. The output of the torque scaling of block 104 is applied
to the torque amplifier 70 and therefrom to the motor load 72 as
indicated above for the block diagram of FIG. 4.
[0046] Through the use of the torque scaling in the present
technique the gain equations defined above can be simplified to the
following:
Kp(vel)=BW(vel); (14) and
Ki(vel)=1/4.zeta..sup.2*Kp.sup.2(vel); (15)
[0047] for the velocity loop gains, and
Kp(pos)=BW(pos); (16) and
Ki(pos)=1/4.zeta..sup.2*Kp.sup.2(pos); (17)
[0048] for the position loop gains. It can be seen from these
equations, that the gain values are no longer dependent upon the
system inertia, J, and the loop bandwidths are solely determined by
the proportional gains.
[0049] As long as the torque scaling value matches the inertia of
the system, J, the values for Kp and Ki should not vary
significantly from application to application. In fact, because the
model for a given servo drive or controller is known, the gains can
be established using the foregoing equations based on the desired
damping factor without prior knowledge of the motor, load, or
feedback resolution. Thus, the problem of tuning the servo loop or
compensating the servo loop for the system inertia variation has
been simplified to the adjustment of a single value, the torque
scaling gain. As described more fully below, accommodation of
discontinuities or significant changes in inertia, such as due to
backlash, can be provided by appropriately adjusting the torque
scaling gain in accordance with the present technique.
[0050] The system inertia value J can be calculated from datasheets
associated with a drive amplifier, motor, mechanical linkage, and
feedback device. Various commercial control programming tools are
available for performing such calculations, such as a tool
commercially available under the designation MotionBook, from
Rockwell Automation Inc. Alternatively, a simple auto-tuning
algorithm can directly and accurately measure the value J. This
algorithm may compute the acceleration and deceleration rates when
a constant torque command is applied to the motor. The acceleration
time, ta, needed to reach a programmed velocity may be measured,
and after reversing the torque command, the deceleration time td
may be measured to return to a zero velocity. Based upon such
measurements, the system inertia J can be calculated in accordance
with the relationship 2 J = 2 To ( Vo / ta + Vo / td ) * (
RatedTorque ) RatedSpeed / Sec . ( 18 )
[0051] The auto-tuning routine can also compute the maximum
acceleration and maximum deceleration values used by the motion
control planner functions. Because the auto-tuning algorithm torque
profile is used to actually measure the acceleration and
deceleration rates for a known torque output value, the maximum
acceleration and deceleration rates may be determined by
extrapolating the computed values based upon an input that would
have achieved full torque output. The auto-tuning algorithm
typically sets the maximum acceleration and maximum deceleration
parameters somewhat lower than the full limit, such as at
approximately 85% of the calculated maximum rates, to ensure
unsaturated acceleration and deceleration ramps.
[0052] While the auto-tuning algorithm is an affective mechanism
for determining inertia value J, at the time the system is
commissioned, changes over time in the system inertia or position
may occur. To address such changes, traditional approaches included
running the system with a fixed set of "non-optimized" gains to
guarantee stability, or applying and adaptive tuning algorithm
which continuously adjusts the various gains of the loop based upon
the observed behavior of the axis while moving. Through the use of
the torque scaling approach described above, it has been found that
an effective mechanism for compensating for variations in system
inertia is readily available. The adaptive control problem is
affectively reduced to ensure that the torque scaling value
accurately reflects the system inertia value. The servo bandwidth
is therefore maintained despite inertia variations.
[0053] As noted above, in certain control applications, one or more
axes may involve inertial loads which vary significantly over time
or within a span of linear or angular position movements. For
example, an "unwinder" is a common name for a class of applications
in the high-packaging industry where sheet material is being
unwound from a spool. The material is fed at constant linear rate
using pitch rollers such that, over the course of time, the spool
diameter shrinks. The spool represents a significant reflected load
inertia to the motor driving the application. As the spool diameter
shrinks, the inertia of the spool decreases according to a
relationship which may be expressed:
J=1/2*mass*radius.sup.21/2*.pi.*density*length*radius.sup.4.
(19)
[0054] In this exemplary application, because the inertia varies
with the fourth power of the spool radius, the total range of
inertia variation can be considerable. If the servo axis is tuned
with a fully loaded spool, it is highly likely that the axis will
become unstable before the spool is emptied. On the other hand, if
the gains are tuned based upon an empty spool to ensure stability,
the servo axis will be seriously under-tuned when attempting to
control a fully loaded spool. An effective adaptive tuning
algorithm is therefore desirable to maintain servo bandwidth
independent of the spool inertia. Adaptive tuning algorithms that
rely on state observer methods are ill-suited for this class of
time-varying inertia application. Observer methods require access
to feedback that is "rich" in frequency content, such as found when
the axis is undergoing rapid acceleration or deceleration. An
unwinder, by contrast, runs at a fixed line speed during normal
operation.
[0055] Quite often in applications such as unwinders, a sensor is
provided that measures the diameter of the spool such that material
can be unwound at a fixed speed independent of the spool diameter.
The application program of the motion controller accomplishes this
by regularly updating electronic gear ratios as the diameter
changes. Leveraging this approach, the spool diameter can also be
used in the application program to regularly computer the inertia
value based upon equation 19 above. These computed inertia values
are regularly applied to the torque scaling gain in the present
technique while the axis is moving. Because the inertia changes
very little in the short interval between updates (which may be on
the order of 100 msec), disturbance to the axis is negligible.
[0056] In another industrial control context, changes in inertia
with the position of an axis may occur. Articulating arm robots
represent one such application. Control difficulties in such
applications are further complicated by the fact the inertia of
some of axes associated with the arm of a robot can vary with the
position of the associated axis, and also with the position of
other axes in the arm. A number of packaging applications also
exist wherein similar problems arise from axes having multiple
linkage points in variable inertia.
[0057] Difficulty in applying adaptive tuning approaches to this
type of application stems from calculating and applying
compensation rapidly enough to keep pace with the rapid motion of
the machine. Packing machines routinely run at rates of 1000
products per minute, for example, which implies a cycle time of 60
msec. Since the mechanism can go through its full inertia variation
within each cycle, new inertia values are needed at the servo
update rate to provide effective compensation. Such rates may be
too fast for adaptive tuning algorithms that employ state
observers. The applications may also require updates at rates,
which are too fast for an application program to compute the
inertia and update the torque scaling parameter.
[0058] A solution to high-speed inertia compensation problems in
such applications and in accordance with the present technique,
employs a motion controller electronic cam functionality to
generate a position-dependent inertia function. Numerical
relationships between inertia and axis position can be established
through the use of commercially available graphical cam editors.
With a cam table thus computed, the inertia value can be mapped to
the servo's torque scaling parameter and sent to the servo loop
with the command position reference at the motion planner update
rate. Assuming, for example, the motion planner update rate is
comparable to the servo update rate (such as on the order of 250
.mu.sec), the torque scaling value can be applied directly with
little disturbance to the output of the servo loop. If the motion
planner updates significantly slower than the servo update rate,
fine interpolation can be employed to manage disturbances due to
step changes in the torque scaling value. Again, however, the
changing inertia can be compensated for by use of the present
torque scaling technique.
[0059] As mentioned above, a number of applications also include
inconsistencies or substantial changes in inertial loading due to
characteristics such as backlash. If the servo loop is tuned for
peak performance with a load applied in such applications, the axis
will be at best under-damped and at worst unstable in the condition
where the gear teeth, or similar mechanical components, are not
engaged. In the worst case, the motor axis and the input gear
oscillate considerable between the limits imposed by the output
gear teeth, as indicated by reference numeral 60 in FIG. 3
discussed above. The net effect can be an audible buzzing when the
axis is at rest. If the condition persists, the mechanical
components, including the gear reducer, may wear prematurely. To
prevent this condition, the conventional approach has been to
de-tune the servo such that the axis is stable without the gear
reducer load applied. Unfortunately, a system performance suffers
from this approach.
[0060] Due to its non-linear, discontinuous nature, adaptive tuning
algorithms generally fall short of addressing the backlash problem.
However, the present technique has been found to provide an
effective compensation mechanism for such applications by use of
the torque scaling gain which can be adapted to the backlash
profile.
[0061] As represented in FIG. 8, a gain profile 106 is applied for
torque scaling to accommodate changes in loading of the type
illustrated in FIG. 3. The profile 106 of FIG. 8 includes
application of gains at an elevated level 56 to accommodate normal
loading as described above with respect to FIG. 3. However, over
the backlash range 60, altered gains may be applied to reduce the
tendency of the system to oscillate between loaded positions. In
the illustrated embodiment, the profile is tapered from the normal
gain level 56 to a reduced gain level 58, generally corresponding
to the motor inertia alone. A linear ramp 108 is employed in the
present embodiment between the upper gain level 56 and the lower
gain level 58, with a similar linear ramp 110 being applied from
the lower gain level to the loaded gain level at the opposite side
of the backlash region 60. An inflection point 112 may correspond
generally to the center of the backlash region 60. While other
profiles, such as cubic profiles, stepped profiles, and so forth
may be applied, it has been found that the linearly ramped profile
illustrated in FIG. 8 provides excellent results. Moreover, the
tapered profile of FIG. 8 may be preferred over a stepped profile
because as the position error exceeds the backlash distance, a step
profile may create a large discontinuity in the torque output. The
modified gain profile of FIG. 8 may be applied when the
acceleration command to the servo loop is zero, that is, when no
acceleration or deceleration is commanded that would engage the
teeth of the gearbox, or similar mechanical components.
Alternatively, the profile may be applied when there is simply no
commanded motion. As noted above, during such periods, the affects
of the discontinuity in loading may not be present or problematic.
It has been found that the use of the modified gain profile of FIG.
8 can entirely eliminate the ill-affects of gear reducer buzz
without sacrificing any performance of the servo system.
[0062] While the invention may be susceptible to various
modifications and alternative forms, specific embodiments have been
shown in the drawings and have been described in detail herein by
way of example only. However, it should be understood that the
invention is not intended to be limited to the particular forms
disclosed. Rather, the invention is to cover all modifications,
equivalents, and alternatives falling within the spirit and scope
of the invention as defined by the following appended claims.
* * * * *