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Claims  |
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I claim:
1. A system for monitoring the movement of a mass driven by a flexible
element comprising:
a mass moveable along a predetermined path;
a flexible element coupled to the mass;
a motor for driving the flexible element and thereby the mass along a
predetermined path;
a transducer mounted on the mass and in communication with the flexible
element capable of detecting a physical characteristic of the flexible
element representative of velocity of the mass relative to velocity of the
motor; and
means for generating a relative velocity signal therefrom.
2. A system according to claim 1, additionally comprising:
means for generating a target velocity signal in communication with the
motor for controlling rotational output of the motor and thereby the
velocity of the mass; and
means for combining the target velocity signal with the relative velocity
signal and generating a mass velocity error signal.
3. A system according to claim 2, additionally comprising:
means for modifying the target velocity signal in accordance with the mass
velocity error signal.
4. A system according to claim 1, wherein the mass is a shuttle carriage of
an ink jet printer and the flexible element is a cable.
5. A system according to claim 1, wherein the relative velocity transducer
utilizes a magnetic circuit operating according to variable reluctance
principles to generate the relative velocity signal.
6. A system according to claim 5, wherein the relative velocity transducer
comprises:
a base member having a support arm and a mounting arm extending therefrom,
the mounting arm being connected to the flexible element, and the base
member comprising an iron-containing rigid metallic material;
a magnet mounted on the support arm with its poles arranged in a
predetermined orientation;
a pole piece mounted on the magnet having an extending portion extending
toward the mounting arm and forming an air gap between its terminal end
and a surface of the mounting arm; and
a coil wound around the extending portion of the pole piece.
7. A dual loop servo system for monitoring and controlling the movement of
a mass moved along a predetermined path by a motor-driven flexible member
comprising:
an outer servo loop employing linear encoder techniques to generate a
signal indicative of the velocity of the mass; and
an inner servo loop employing a sensor that detects a physical
characteristic of the flexible member representative of the velocity of
the mass relative to the velocity of the motor to generate a relative
velocity signal.
8. A dual loop servo system according to claim 7, wherein:
the sensor comprises a relative velocity transducer mounted on the mass and
connected to the motor-driven flexible member.
9. A dual loop servo system according to claim 8, additionally comprising:
means for generating a target velocity signal in communication with the
motor for controlling rotational output of the motor and thereby the
velocity of the mass as it moves along its predetermined path;
means for combining the target velocity signal with the relative velocity
signal and generating a mass velocity error signal; and
means for modifying the target velocity signal in accordance with the mass
velocity error signal.
10. A dual loop servo system according to claim 8, wherein the relative
velocity transducer utilizes a magnetic circuit operating according to
variable reluctance principles to generate the relative velocity signal.
11. A dual loop servo system according to claim 7, wherein the mass is a
shuttle carriage of an ink jet printer.
12. A dual loop servo system according to claim 7, wherein the mechanical
stiffness of the sensor is significantly higher than that of the flexible
member.
13. A dual loop servo system according to claim 8, wherein the relative
velocity transducer comprises:
a base member having a support arm and a mounting arm extending therefrom,
the mounting arm being connected to the flexible element, and the base
member comprising an iron-containing rigid metallic material;
a magnet mounted on the support arm with its poles arranged in a
predetermined orientation;
a pole piece mounted on the magnet having an extending portion extending
toward the mounting arm and forming an air gap between its terminal end
and a surface of the mounting arm; and
a coil wound around the extending portion of the pole piece.
14. A dual loop servo system according to claim 13, wherein the air gap
formed between the terminal end of the pole piece and the surface of the
mounting arm is from about 5 mils to about 50 mils in width.
15. A dual loop servo system according to claim 13, wherein the coil wound
around the extending portion of the pole piece is a signal coil, and the
system additionally comprises a bucking coil wound in the same direction
as the signal coil around an opposite side of the pole piece and connected
in series with the signal coil, but with opposed polarity.
16. A dual loop servo system according to claim 8, wherein the relative
velocity transducer comprises:
a base member having a support arm and a mounting arm extending therefrom,
the mounting arm being connected to the flexible element, and the base
member comprising an iron-containing rigid metallic material;
a magnetic insulator mounted on the support arm;
a first pole piece mounted on the magnetic insulator having an extending
portion extending toward the support arm and defining an air gap between
its terminal end and a surface of the mounting arm;
a magnet mounted on the first pole piece generally aligned with the support
arm, with its poles arranged in a predetermined orientation; and
a second pole piece mounted on the magnet and generally aligned with the
first pole piece, the second pole piece having an extending portion
extending toward the mounting arm and defining a second air gap between
its terminal end and a surface of the mounting arm; and
a coil wound around the extending portion of the first pole piece.
17. A dual loop servo system according to claim 8, wherein the relative
velocity transducer comprises:
a base member having a central mounting arm and two support arms extending
therefrom, the central mounting arm being connected to the flexible
element, and the base member comprising an iron-containing rigid metallic
material;
a magnet mounted on each support arm with its poles arranged in a
predetermined orientation;
a pole piece mounted on each magnet, each pole piece having an extending
portion extending toward the mounting arm and defining an air gap between
its terminal end and a surface of the mounting arm; and
a coil wound around the extending portion of each pole piece, the coils
being wound in the same direction and connected in series with opposed
polarity.
18. A dual loop servo system for monitoring and controlling the movement of
a mass moved along a predetermined path by a motor-driven flexible member
comprising:
a first servo loop employing linear encoder techniques to generate a mass
velocity signal; and
a second servo loop employing a sensor that detects a physical
characteristic of the flexible member representative of the velocity of
the mass relative to the velocity of the motor.
19. A relative velocity transducer that senses velocity of a mass movable
along a predetermined path by a motor-driven flexible element coupled to
the mass relative to the velocity of rotational output of the motor
utilizing a magnetic circuit operating according to variable reluctance
principles.
20. A relative velocity transducer according to claim 19, comprising:
a base member having a support arm and a mounting arm extending therefrom,
the mounting arm being connected to the flexible element, and the base
member comprising an iron-containing rigid metallic material;
a magnet mounted on the support arm with its poles arranged in a
predetermined orientation;
a pole piece mounted on the magnet having an extending portion extending
toward the mounting arm and defining an air gap between its terminal end
and a surface of the mounting arm; and
a coil wound around the extending portion of the pole piece. |
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Claims |
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Description |
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FIELD OF THE INVENTION
This invention relates to methods and apparatus for monitoring and
controlling the motion of a mass, and relates more particularly to
improved feedback systems for providing that the actual position or
velocity of a mass corresponds more closely to its desired position or
velocity profile.
BACKGROUND OF THE INVENTION
The methods and apparatus of the present invention are especially suitable
for monitoring and controlling the position, movement or velocity of an
object driven by a non-rigid means, such as a belt, cable, or the like. An
exemplary system that will be used for illustrative purposes throughout
this disclosure is a shuttle carriage of an ink jet printer driven by a
flexible cable, which is in turn moved by rotational motor drive output.
Precise control is especially challenging where the mass is relatively
large and the cable is, of necessity, flexible and somewhat elastic.
In printer applications, the desired shuttle carriage velocity profile is
conveyed directly to a motor, and the motor generates rotational output
corresponding to the desired velocity profile. A printer carriage is
typically driven by a cable and pulley system or a cogged timing belt
which translates the rotational motor drive output to printer carriage
movement along a linear path. The timing belt or cable is flexible to
accommodate the rotational motor drive output, and it is therefore subject
to forces that cause the actual carriage velocity to deviate from the
desired velocity profile. The flexible nature of the cable generates
undesirable velocity ripples which cause print defects as a result of
variations in ink drop exit velocity from the printer carriage. This
problem is generally aggravated as the mass or object increases in weight
and/or the cable increases in flexibility. In order to generate high
fidelity images, such as during printing operations, the actual carriage
velocity must be closely monitored and controlled to ensure that it
corresponds as closely as possible to the desired velocity profile.
The cable or belt in the printer carriage system is equivalent to a linear
spring that obeys Hooke's law, and deflection can therefore be determined
as a function of the cable force. The cable or belt driven system is
analogous to a mass/spring model system in which the internal damping in
the cable is represented by a dashpot in parallel with the spring. In
contrast to the more common case where one end of the spring is fixed,
however, in the printer carriage mass/spring model system, the other end
of the spring is not connected to mechanical ground. Instead, it is
attached to the motor rotor, and the rotor is related to mechanical ground
through an electromagnetic connection. Substantial deviation of the actual
carriage motion from the desired velocity profile is due to extension or
compression of the spring (belt or cable), and the remainder is due to
errors in the position of the motor rotor.
In printer applications, at least two different control architectures have
been implemented. According to one approach, an encoder or tachometer is
mounted on the motor shaft to provide a motor shaft velocity signal. This
system does not provide direct information concerning the position or
velocity of the printer carriage, however, and it cannot correct for
substantial deviation of carriage motion from the desired velocity profile
due to forces exerted on the belt or cable. This approach therefore does
not address a primary source of inaccuracy, since the printer carriage and
the cable or belt are outside the servo loop.
A second control architecture employs a clock track encoder mounted on the
carriage itself that reads a linear encoding strip mounted in fixed
relationship to the carriage. According to this approach, the actual
velocity of the printer carriage is monitored, but the responsiveness of
the system can be unsatisfactory. In other words, the system is not
effective in correcting deviations in the actual carriage position until
the deviations have already occurred and printing errors have been
introduced. This type of control system may thus be suitable for providing
gross control functions, but it is limited in the fine control it can
provide. Additionally, this control architecture presents a difficult
servo system to implement because the resonant mass/spring system is in
the loop.
One important principle of feedback systems design is that the servo system
must not have a phase shift ("around" the loop) of 180.degree. or more for
any frequency for which the system gain is unity or greater. If a higher
phase shift is introduced, the servo system will oscillate rather than
functioning as a linear feedback control system. In systems that
incorporate a mass/spring system, it is easy to consume most of the
180.degree. allowable phase shift on the mass/spring portion of the
system, leaving very little for the rest of the servo system. For this
reason, it is difficult to incorporate mass/spring systems in servo loops.
To provide a stable servo loop in a single loop system incorporating a
mass/spring component, it is generally necessary to reduce the system
bandwidth and loop gain. In a velocity servo loop, loop gain is a good
predictor of the velocity error which will result from a sudden increase
or decrease of drag on the carriage. Similarly, the system bandwidth is
indicative of the speed with which the servo can react to and recover from
an adverse disturbance. Loop gain and bandwidth are therefore critical
characteristics of the servo system, and high performance servo systems
require elevated loop gain and bandwidth characteristics.
SUMMARY OF THE INVENTION
The present invention provides a stable, high performance system for
monitoring and controlling carriage (mass) position or velocity directly.
More particularly, one aspect of the present invention provides a system
for controlling the movement of a mass reciprocated along a linear path by
a motor-driven flexible member using a dual loop servo system. An "outer"
servo loop using conventional linear encoder techniques operates normally,
and is supplemented by an "inner" servo loop which utilizes a sensor that
detects a physical characteristic of the flexible member linking the motor
and the mass representative of the position or velocity of the mass
relative to the position or velocity of the motor. A feedback circuit is
responsive to the sensed physical characteristic for adjusting the target
velocity signal to reduce the variation between the target and actual
velocities of the mass.
In a preferred embodiment, a load cell comprising a strain gauge sensor for
sensing flexure forms part of a coupling member linking the printer
carriage and the cable. Flexure of the coupling member is related to the
load or force on the belt and the distortion of the belt, such as
extension or compression, is proportional to its load. The mechanical
stiffness of the sensor (the ratio of deflection to applied force) is
designed to be much higher than that of the cable or belt.
The flexure sensed by the load cell thus provides a feedback signal
representative of the distortion of the connecting cable or belt. The load
cell distortion is negligible. The feedback signal provides a direct
indication of the carriage position relative to the motor position, which
can be differentiated to produce a signal that is representative of the
carriage velocity relative to the motor velocity. This inner servo loop
signal, referred to herein as a relative carriage velocity signal, is
combined with the outer servo loop carriage velocity signal derived from
the linear encoder to reduce disparities between the actual and target
carriage velocities.
Alternatively, the inner loop may employ a relative velocity transducer to
measure the relative printer carriage velocity directly. One preferred
relative velocity transducer utilizes a magnetic circuit operating
according to variable reluctance principles to generate a relative
carriage velocity signal directly without requiring differentiation of a
relative position signal. The relative carriage velocity signal is used to
generate a velocity error signal that adjusts the target velocity signal
to compensate for distribution of the flexible cable.
A control system having inner and outer servo loops is thus provided
according to the present invention that effectively modulates the motor
drive output so that the actual carriage velocity corresponds more closely
to the desired target velocity profile. These and other features and
advantages of the present invention will become apparent from a reading of
the detailed description with reference t the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a block diagram schematically illustrating one embodiment of a
control system according to the present invention.
FIG. 2 is a fragmentary diagram illustrating a coupling member for joining
the belt to the carriage that incorporates a strain gauge sensor.
FIG. 3 is a simplified diagram illustrating a suitable bridge circuit for
the strain gauge sensor of FIG. 2.
FIG. 4 is a diagram illustrating the spring/mass model of the printer
system shown in FIG. 1.
FIG. 5 is a block diagram schematically illustrating the loop topology for
the system of FIG. 1 using a strain gauge sensor of the type shown in FIG.
2.
FIG. 6 is a more detailed block diagram showing the loop topology/of the
system of FIG. 5.
FIGS. 7, 8 and 9 are Bode plots illustrating the predicted operation of the
system of FIG. 6 based upon Laplace transforms of the system components.
FIG. 7 shows the Bode plot for the control system with the outer loop
disabled; FIG. 8 shows the control system with the inner loop disabled;
and FIG. 9 illustrates total control system operation.
FIG. 10 shows a block diagram schematically illustrating another embodiment
of the control system of the present invention employing a relative
velocity transducer.
FIGS. 11-15 illustrate various embodiments of relative velocity transducers
suitable for use with the present invention.
FIG. 16 is a block diagram illustrating the loop topology for the system of
FIG. 10 using a relative velocity transducer of the type shown in FIGS.
11-15.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
FIG. 1 illustrates schematically a control system 10 of the present
invention for monitoring and controlling the movement of a carriage 12
mounted on a bar 14. Bar 14 is rigidly mounted to a framework at mountings
16, and carriage 12 is reciprocated on a linear path defined by bar 14. A
target velocity signal is output by a motor driver 38 and conveyed by a
conductor 40 as input to a motor 18 for controlling the velocity of
carriage 12 as it reciprocates on bar 14. Rotational output from motor 18
drives a continuous timing belt 20 mounted on a motor pulley 22 and an
idler pulley 24. A coupling member 26 is mounted on carriage 12 and belt
20 to convey the movement of belt 20 to carriage 12.
Referring again to FIG. 1, carriage 12 also has an optical encoder 36
mounted on it which reads a linear encoding strip 37 mounted fixedly
relative to bar 14 as carriage 12 reciprocates along bar 14. The optical
encoder provides information for the outer servo loop of the control
system. The frequency of the pulse train generated by the encoder is
indicative of the velocity of the carriage. The pulse train is converted
to an analog signal in a frequency-to-voltage converter. This signal is
fed through a loop filter, as will be described, to produce an analog
velocity signal which is processed in motor driver 38. Motor driver 38
compares the actual carriage velocity to the target velocity and modulates
the input to motor 18, thereby modulating the linear velocity of carriage
12. As described earlier, this type of servo loop provides only relatively
coarse control and is difficult to incorporate in a control system as a
result of the mass/spring characteristics of the system.
Carriage velocity fine control must be provided by detecting changes in
carriage velocity as they occur or, if possible, anticipating changes in
the carriage velocity before they actually occur and correcting for them.
Disparities in the actual carriage velocity from the desired velocity
profile are largely attributable to the flexible character of the belt or
cable drive system, and the applicant's efforts have been directed to
sensing distortion of the flexible belt or cable drive system in an effort
to anticipate changes in the carriage velocity.
The control system of the present invention employs an inner servo loop in
combination with the outer servo loop described above. According to one
embodiment, coupling member 26 serves as a carriage position sensor by
sensing forces exerted on the coupling member by the belt. Coupling member
26, shown in FIG. 2, comprises a mounting bracket 28 having an internal
opening. A clamp end 28a is fixedly mounted on belt 20 by a clamping plate
30 and appropriate mounting means for rigidly mounting the clamping plate
on end 28a. Extending from opposite ends of clamp end 28a are elongate
flexible arms 28b and 28c. These arms extend to a carriage mounting end
28d having flared flanges which are fixedly attached to carriage 12, as
shown. Strain gauges 32 and 34 are mounted to the flexible arms 28b and
28c. Suitable strain gauges are well known in the art and include those
sold under the proprietary name of Transducer-Class strain gauges, model
number EA-13-T043P-10C sold by Measurements Group, Inc. of Raleigh, N.C..
Mounting bracket 28 is preferably made of 7075 T6 extruded aluminum, with a
width across end 28a of approximately 0.7 inches. The flexible arms have a
length of about 1/2 inch in the uniform thickness region. It will be
understood by those skilled in the art that other strain gauges and
alternative designs and dimensions for coupling member 26 are suitable for
use in accordance with the present invention. For instance, four strain
gauges could be employed, with the additional two being mounted on the
inside surfaces of arms 28b and 28c.
A representative strain gauge bridge circuit 42 is illustrated in FIG. 3.
The two strain gauges 32 and 34 are connected in a bridge formation with
resistors 44 and 46, and are driven by a reference voltage source 48. The
strain gauges are connected as shown so that upon flexing of arms 28b and
28c during movement of carriage 12, one gauge senses a force due to
compression, and the other senses a force due to tension. In the reverse
direction, each strain gauge senses the opposite form of force. The two
strain gauges thus, when strained, produce a differential voltage which is
fed into a differential amplifier 50. The amplifier produces an output
signal representative of the load on the strain gauge sensor. This load is
also directly proportional to the elongation of belt 20 between pulley 22
and carriage 12. The strain gauge sensor thus detects the shift in
position of the carriage relative to the rotor due to belt distortion.
FIG. 4 illustrates the spring/mass model of the system of FIG. 1. The motor
rotor is represented by the variables having a subscript 1, and the
carriage is represented by the variables having a subscript 2. Rotary
units have been used throughout this analysis. The rotor has a torque T
and mass moment of inertia J.sub.1, and the rotary position of the in the
Laplace domain. The carriage has a calculated mass moment of inertia
J.sub.2 and has a rotary position represented by .theta..sub.2 in the time
domain and .THETA..sub.2 in the Laplace domain. Theoretical dashpots
B.sub.1 and B.sub.2 have effective positions between the frame and the
rotor and carriage, respectively, and represent damping forces. The belt
is represented by a spring having a coefficient K.sub.12 and a dashpot
having a coefficient B.sub.12, representing internal damping in the belt.
Prior to making a physical prototype of the control system illustrated in
FIGS. 1-3, the mass/spring dynamics and compensation of the proposed
system were modeled as shown in FIG. 4, and simulated on a computer system
having the proprietary name LSAP available from California Scientific
Software. The mass/spring model was based upon the following physical
parameters. Drive pulley 22 has 32 teeth at 0.08 pitch; the timing belt
has 535 teeth; and the axes of the idler and motor pulleys are 20.12
inches apart. The stiffness of the belt, experimentally measured as the AE
constant, was determined to be 1.069.times.10.sup.4 LB. The effective
translational stiffness deployed on the pulleys is K.sub.TOT
=1.332.times.10.sup.3 LB/IN. In rotary coordinates, the stiffness
coefficient K.sub..THETA. =K.sub.TOT .times.R.sup.2 =221.1 LB-IN/RADIAN.
This results in a fundamental frequency for the belt/pulley/carriage
combination of f.sub.N =80 Hz.
A damping coefficient was calculated on the basis that force is
proportional to velocity and inversely proportional to the length of the
belt, or F=c'x/L. Solving this equation for c', c'=2.9948 LB-SEC/IN. A
total damping coefficient is calculated as c.sub.TOT
=3.732.times.10.sup.-1 LB-SEC/IN. In rotary coordinate units, c.sub.74
=6.19.times.10.sup.-2 LB-IN-SEC/RAD=B.sub.12.
The equations for rotary motion of the motor rotor and the carriage are:
J.sub.1 .theta..sub.1 =-K.sub.12 (.theta..sub.1 -.theta..sub.2)-B.sub.12
(.theta..sub.1 -.theta..sub.2)-B.sub.1 (.theta..sub.1)+T
J.sub.2 .theta..sub.2 =K.sub.12 (.theta..sub.1 -.theta..sub.2)+B.sub.12
(.theta..sub.1 -.theta..sub.2)-B.sub.2 (.theta..sub.2)
Where .theta. represents position, .theta. represents velocity, and .theta.
represents acceleration, all in the time domain.
Assuming steady state conditions, these equations, after grouping terms and
converting to the Laplace domain, are as follows:
[J.sub.1 S.sup.2 +(B.sub.12 +B.sub.1)s+K.sub.12 ].THETA..sub.1
(s)-(B.sub.12 s+K.sub.12).THETA..sub.2 (s)=T
-(B.sub.12 s+K.sub.12).THETA..sub.1 (s)+[J.sub.2 s.sup.2 +(b.sub.12
+B.sub.2)s+K.sub.12 ].THETA..sub.2 (s)=0
where .THETA. represents position and s represents the independent variable
in the Laplace domain.
Solving for the position variable transforms of the motor and carriage as
well as the velocity of the carriage results, after considerable
manipulation, in the following equations for the position of the first and
second masses, the relative position of the masses, and the velocity of
the second mass, respectively, where the notation .THETA..sub.2 (s)/T(s)
indicates the velocity of the second mass, e.g., the carriage, expressed
as the Laplace domain transfer function:
##EQU1##
The values for these variables, based upon the physical parameters set
forth above are as follows:
##EQU2##
FIG. 5 shows a block diagram of a control system 10 as shown in FIG. 1
employing a strain gauge or the like in an inner servo loop, based on the
transfer function concept just presented. The transfer functions for
relative position, i.e. (.THETA..sub.2 (s)-.THETA..sub.1 (s))/T(s) and
velocity of the carriage, i.e. .THETA..sub.2 (s)/T(s), provide a model of
the inner servo loop mass/spring damping of the physical operating system.
Target velocity signal generator 52 feeds a target velocity signal through
a signal combiner 54, a compensator 56, and another signal combiner 58.
The signal from combiner 58 passes through a power amplifier 60 which
processes the signal for driving motor 18. The output of motor 18 is the
torque applied to belt 20. This torque acts through the mass spring
damping effects of the motor and belt as represented by inner servo and
outer servo blocks 62 and 66, respectively.
Based upon the position and velocity variable transforms set forth above
and utilizing a control system as shown schematically in FIG. 1, the inner
servo loop detects a physical characteristic of the flexible member
linking the motor and the carriage to provide a signal indicative of the
carriage position relative to the motor position at block 62. The relative
position signal is fed through a position transfer block 64 comprising a
position compensator 65 and a pole/zero compensator 78 which converts the
relative position signal represented by (.THETA..sub.2 (s)-.THETA..sub.1
(s) to a relative velocity signal (.THETA..sub.2 (s)-.THETA..sub.1 (s).
The pole zero compensator acts like a differentiator at low frequencies.
The relative velocity signal is then used to generate an inner loop
velocity error signal at combiner 58.
The outer servo loop employs a linear encoder to produce a signal
indicative of carriage velocity The carriage velocity signal is input
through a velocity transfer gain circuit 68. An outer loop velocity signal
is thereby generated and fed into signal combiner 54, where an outer loop
velocity error signal is derived for reducing the variation of the actual
velocity from the target velocity. The target velocity signal generated by
target velocity signal generator 52, the outer loop velocity error signal
derived at signal combiner 54, and the inner loop velocity error signal
derived at signal combiner 58 are all combined to modify input to motor
18. In this fashion, the actual carriage velocity, and hence the actual
carriage position at any time point, corresponds more closely to the
desired carriage velocity, and hence the desired carriage position at the
corresponding time point.
The transfer equations discussed previously were used to generate the
actual control system 70 shown in FIG. 6. The components which are the
same as those shown in FIG. 5 are given the same reference numerals.
Compensator 56 comprises two lowpass filters having poles at 500 Hz and a
gain block 72 scaled to correspond to the overall loop gain desired. This
is preferably set at 50 for the system shown. A scaler gain of 2/15 as
shown in block 74, adjusts the target velocity signal for input into power
amp 60. The power amp has a gain factor of 2 amp/volt and a pole at 1000
Hz (shown as P.sub.1000). The motor used has a torque factor of 0.5875
lb-in/amp. The velocity transfer gain shown in box 68 has a scale factor
of 0.0306.
The inner servo loop applies a strain gauge sensitivity factor of 223 at
block 74. An amplifier pole at 30,000 Hz (P.sub.30,000)is represented by
filter 76. A pole/zero compensator 78 provides a circuit having a zero at
40 Hz (Z.sub.40) and a pole at 2000 Hz (P.sub.2000) to convert the strain
gauge relative position signal to a relative velocity signal. Capacitive
coupling represented by block 80 has a zero at 0 Hz (Z.sub.o) and a pole
at 0.016 (P.sub.0.016). A 1000 Hz (P.sub.1000) lowpass filter 82 is then
coupled to the inner loop gain 84 which is preferably set at 10. The
transfer functions are effected in this system as previously discussed.
Bode Plots for these types of systems provide a coordinated amplitude vs.
frequency and phase vs. frequency presentation. The loop gain of the
system is established by setting the zero dB (unity gain) line on the Bode
Plot for the system. FIGS. 7, 8 and 9 illustrate various Bode Plots for
the control system as provided by a computer simulation using the transfer
functions to model the mass/spring damping dynamics.
FIG. 7 shows the Bode plot for the control system with the outer loop
disabled. A resonant peak is shown to exist on magnitude curve 86 at just
past 206 Hz and there is zero dB gain at -135.degree. phase shift or
45.degree. phase margin as illustrated on phase curve 88.
FIG. 8 shows the control system with the inner loop disabled, thereby using
only the outer loop velocity feedback signal. The magnitude and phase are
shown by curves 90 and 92, respectively. This Bode plot shows an
undesirable resonant peak which would force the 0 dB line (unity gain) to
only 45 Hz. The resonant peak exhibited by the single loop servo system
illustrated in FIG. 8 generally requires an undesirable reduction in band
width and loop gain to maintain the system in a stable condition, that is,
in a linear feedback mode rather than an oscillation mode.
Combined inner and outer loop control system operation is represented by
the Bode plot shown in FIG. 9. Here it is clear that there is no resonant
frequency peak in magnitude curve 94, and there is the desired zero dB
gain at -135.degree. phase shift and approximately 150 Hz, identified by
phase curve 96. The inner/outer servo loop topology of the control system
of the present invention removes the resonant peak caused by the
mass/spring system and provides a stable servo control system.
The system of FIG. 6 has been reduced to practice and found to perform
substantially as expected. This system can therefore be seen to be very
stable and effective in controlling operation of the motor and carriage to
obtain the desired velocity travel characteristics of the carriage. It
will be appreciated that such a control system can be developed for any
motor-driven mass where the path must be controlled. Further, although a
load cell comprising a strain gauge sensor mounted on the coupling member
was used to determine the positional change of the mass due to the flexure
of the belt or cable, other devices may also be used to provide a signal
representative of the cable flexure.
Although the strain gauge sensor described above is suitable for many
applications and permits modulation of the target velocity profile so that
actual carriage velocity corresponds more closely to the desired velocity,
strain gauge sensors exhibit some inherent disadvantages. Strain gauge
transducers are prone to drifting and thus must be monitored and
frequently calibrated to assure high accuracy performance. Additionally,
strain gauge transducers generate a relative position signal which
requires signal differentiation to provide a relative velocity signal. The
differentiated signal is generally high frequency noise sensitive. For
some applications, therefore, it may be preferred to employ different
types of position or velocity transducers.
FIG. 10 shows a general block diagram illustrating a control system
utilizing inner and outer servo loops according to the present invention
and including a relative velocity transducer that produces a signal
directly indicative of relative carriage velocity. Control system 11 of
the present invention is similar to control system 10 illustrated in FIG.
1, but the inner servo loop employs a relative velocity transducer in
place of the strain gauge sensor. Coupling member 27 is mounted on
carriage 12 and cable 20 to accurately convey the movement of cable 20 to
movement of carriage 12. Optical encoder 36 mounted on carriage 12 reads
linear encoding strip 37 and provides velocity information for the outer
servo loop of the control system.
In contrast to the system shown in FIG. 1, coupling member 27 in system 11
comprises a relative velocity transducer that senses carriage velocity
relative to motor velocity directly without requiring differentiation of
relative position signal. Preferred relative velocity transducers comprise
magnetic circuits that operate using variable reluctance properties.
Preferred relative velocity transducers are described with reference to
Figs. 11-15.
Relative velocity transducer 100 shown in FIG. 11 comprises base member 102
having a mounting arm 104 and a support arm 106 extending therefrom. Base
member 102 is rigidly, mechanically mounted to carriage 12. The terminal
end of mounting arm 104 is rigidly mounted to cable 20, such as by
anchoring a fastener passing through cable 20 in fastener receiving means
108. Arrow 109 indicates the direction of motion of cable 20 (and thus
carriage 12).
Base member 102 is formed from a rigid, metallic material. Suitable
materials include sintered iron, nickel-iron alloys, and other
iron-containing alloys. Ideally, the transducer must be many times stiffer
than the belt or cable whose extension it is measuring. Iron-containing
metals resulting in a transducer stiffness of from about 20,000 to about
50,000 lb/in are preferred.
Support arm 106 is shorter than mounting arm 104, and a magnet 112 is
mounted at the terminal end thereof in a specified orientation. Magnet 112
is preferably a | | |
