BACKGROUND OF THE INVENTION
Field of the Invention
[0001] This invention relates to a let-off control device for a weaving machine capable
of achieving desirable controllability in a stable fashion regardless of variations
in rotational speed of the weaving machine.
Description of the Prior Art
[0002] A let-off control device of a weaving machine controls a warp beam via a let-off
motor in such a way that a specific warp tension is maintained. A conventionally known
problem of the let-off control device is that if a simple feedback control system
is configured and a large integration time constant is inserted in a warp tension
detecting system, overall response significantly deteriorates, making it difficult
to achieve a specific degree of controllability. This is because the warp tension
considerably fluctuates during each rotation of a main shaft of the weaving machine
due to a various operations of the weaving machine such as a warp shedding motion
during which a peak warp tension could rise up to as much as twice of the average
warp tension.
[0003] Japanese Unexamined Patent Publication No. 59-157354 proposes a let-off control device
of a weaving machine to overcome the aforementioned problem. This let-off control
device calculates a basic speed of a let-off motor based on the rotational speed of
the weaving machine and warp winding diameter on its warp beam, detects warp tension
at a specific angle of rotation (hereinafter referred to as the crank angle) of a
main shaft during its each successive turn, calculates the amount of speed correction
for the let-off motor based on an moving average of the warp tension, and controls
the speed of the let-off motor based on the basic speed corrected by the calculated
amount of speed correction. A controller for calculating the amount of speed correction
has control elements for performing proportional, integral and differential (control)
actions and calculates the amount of speed correction each time the moving average
of the warp tension is calculated. Therefore, it is not necessary to insert a large
integration time constant in a warp tension detecting system and it is possible to
achieve desirable controllability by using correction control by a feedback control
system based on the moving average of the warp tension in addition to a feed-forward
control system based on the basic speed.
[0004] With the aforementioned let-off control device, so long as the weaving machine operation
speed is maintained at substantially a constant value, a time delay (a lag element;
a time delay), i.e., from the time detecting a warp tension to the time the corrected
speed is output, can be maintained at substantially a constant value. However, it
has become common practice in the recent weaving operation to change the operation
speed of the weaving machine in accordance with the different weaving materials. To
this regard, in the aforementioned let-off control device employing said PID controller,
readjustment of a control gain, in particular a proportional gain, for the PID controller
is necessitated. For instance, when a high speed weaving operation is performed with
the proportional gain (gain value) having suitably adjusted for a low speed weaving
operation, the adjusted time delay factor would be too long for the high speed operation.
In other words, the proportional gain set for the low speed weaving operation will
be too large for the proportional gain needed for the effective control in the high
speed weaving operation. Thus unless the control gain, i.e., not only a proportional
gain but also an integral gain and a differential gain, is changed in accordance with
the speed of the weaving operation, the effective control of the weaving operation
cannot be performed.
[0005] According to the aforementioned prior art technology, however, the controller calculating
the amount of speed correction calculates the amount of speed correction each time
the moving average of the warp tension is calculated, that is, the amount of speed
correction is calculated every rotation of the main shaft of the weaving machine.
Thus, the prior art technology has a problem that it is difficult to maintain desirable
controllability. Because when the rotational speed of the weaving machine changes
due to the particular weaving operation, leading to the change in sampling time (frequency),
what was previously optimum control gain adjusted prior to the change in rotational
speed is no longer the optimum gain for the weaving operation after the change in
rotational speed. It is, thus, highly likely that those previously adjusted gain values
(for the control gain) are in excess or in lack with respect to the optimum values
for the new weaving operation at new rotational speed. Accordingly, with the aforementioned
prior art technology, unless the control gain is readjusted at the time of change
in rotational speed of the weaving machine, it becomes difficult to maintain the desirable
controllability.
SUMMARY OF THE INVENTION
[0006] In view of the foregoing problems of the prior art technology, it is an object of
the invention to provide a let-off control device for a weaving machine which can
consistently achieve good controllability in a stable fashion regardless of a large
variations in rotational speed of the weaving machine by making an operating cycle
of a controller independent of average tension calculating cycle.
[0007] A second object of the invention is to provide a let-off control device for a weaving
machine which can automatically set optimum control parameters for a controller for
calculating the amount of speed correction with an additional provision of an automatic
tuning circuit, and thereby achieve desirable controllability with ease.
[0008] To achieve the aforementioned objects, a let-off control device of the invention
for a weaving machine comprises a basic speed calculator for calculating a basic speed
of a let-off motor, an average tension calculator for calculating a moving average
of warp tension detected at a specific crank angle in one or more picks, a controller
for calculating a speed correction value for the let-off motor based on deviation
of average tension fed from the average tension calculator with respect to a target
tension, and a control amplifier for controlling the speed of the let-off motor based
on the basic speed fed from the basic speed calculator and the speed correction value
fed from the controller, wherein the controller operates in synchronism with an operating
cycle which is independent from an operating cycle of the average tension calculator.
[0009] In this construction, the average tension calculator obtains the average tension
by calculating the moving average of the warp tension at the specific crank angle
during multiple picks. Specifically, the average tension calculator detects the warp
tension at the specific crank angle in each successive rotation of a main shaft of
the weaving machine and determines the average tension by calculating the moving average
of the warp tension thus detected during the most recent rotations of the main shaft.
Accordingly, the operating cycle of the average tension calculator is completely synchronized
with the rotations of the main shaft. On the other hand, since the controller operates
in synchronism with the operating cycle which is independent from the operating cycle
of the average tension calculator, there is no likelihood that sampling time varies
and thereby substantial control parameter loses its optimum state even when the rotational
speed of the weaving machine changes. The controller operates according to a clock
signal independent of the rotational speed of the weaving machine and may include
control elements for performing proportional, integral and differential (control)
actions, or those for performing proportional and integral (control) actions only.
[0010] In one aspect of the invention, the controller operates in synchronism with the operating
cycle which is shorter than the operating cycle of the average tension calculator.
[0011] This enables the controller respond to variations in the warp tension and the rotational
speed of the weaving machine without delay as it operates in synchronism with the
operating cycle which is shorter than the rotational period of the main shaft of the
weaving machine.
[0012] In another aspect of the invention, the let-off control device may further comprise
a correction calculator for adjusting the speed correction value fed from the controller
based on the winding diameter of warp on a let-off beam.
[0013] If the speed correction value fed from the controller is adjusted by the correction
calculator based on the winding diameter of warp on the let-off beam, it becomes possible
to achieve good controllability. This is because, although a transfer function of
a mechanical system from the let-off motor to the warp tension varies when the winding
diameter of the warp on the let-off beam decreases due to the consumption of the warp
for instance, the correction calculator can properly compensate for such variations.
[0014] In still another aspect of the invention, the let-off control device may further
comprise a switching circuit which disables the controller when a tuning command is
issues, and an automatic tuning circuit which updates a control parameter of the controller
by producing the tuning command.
[0015] In this construction, the controller can be disabled by the switching circuit and,
then, the automatic tuning circuit can automatically set the control parameter of
the controller by producing the tuning command. Specifically, when the controller
is disabled by the switching circuit, the automatic tuning circuit can transmit an
appropriate driving signal to the let-off motor, find the transfer function of the
mechanical system from the let-off motor to the warp tension by monitoring variations
with time of the warp tension caused by the driving signal, determine the optimum
control parameter for the transfer function, and automatically set it in the controller.
The switcher (switching circuit) may operate the controller hold the speed correction
value output from the controller at zero value, or substantially disable the controller
by open-circuiting its output. When the weaving machine is at rest, the tuning command
should be generated by manual operation or by appropriate automatic means.
[0016] In yet another aspect of the invention, the automatic tuning circuit may include
a proportional controller which generates a driving signal to be delivered to the
let-off motor based on the deviation of the warp tension with respect to the target
tension, and a tension data detector which detects variations in the warp tension
caused by the driving signal fed from the proportional controller. Alternatively,
the automatic tuning circuit may include a signal generator which generates a driving
signal to be delivered to the let-off motor, and a regression analyzer which performs
regression analysis of variations in the warp tension caused by the driving signal
fed from the signal generator.
[0017] If the automatic tuning circuit includes the proportional controller and the tension
data detector, the automatic tuning circuit finds and analyzes a step response of
a feedback control system formed of the proportional controller and a controlled system
by means of the tension data detector, and thus determines the transfer function of
the controlled system, and find the optimum control parameter.
[0018] If the automatic tuning circuit includes the signal generator and the regression
analyzer, the automatic tuning circuit can perform regression analysis of the variations
in the warp tension by means of the regression analyzer after the signal generator
has transmitted the driving signal to the let-off motor, determine the transfer function
of the controlled system using results of the analysis, and find the optimum control
parameter. The driving signal output from the signal generator to the let-off motor
may be of a fixed level maintained for a specific time period so that appropriate
variations with time of the warp tension would be obtained.
[0019] In a further aspect of the invention, the let-off control device may further comprise
a compensating circuit for improving response to the target tension.
[0020] The compensating circuit would help improve response to the target tension. It forms
a control system having two degrees of freedom together with the controller and would
optimize response of the controller not only to external disturbances but also to
variations in the warp tension.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021]
FIG. 1 is a general block diagram of a let-off control device of a weaving machine
according to a preferred embodiment of the invention;
FIG. 2 is a block diagram showing a let-off control device according to another embodiment
of the invention;
FIG. 3 is a block diagram showing a principal portion of the let-off control device
of FIG. 2;
FIG. 4 is an equivalent block diagram of FIG. 3;
FIG. 5 is a diagram showing the operation of the let-off control device of FIG. 2;
FIG. 6 is a block diagram showing a principal portion of the let-off control device
of FIG. 2 as an alternative configuration to the block diagram of FIG. 3;
FIG. 7 is a diagram showing the operation of the let-off control device of FIG. 2
incorporating the configuration of FIG. 6; and
FIG. 8 is a block diagram showing a let-off control device according to still another
embodiment of the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION
[0022] Specific embodiments of the present invention are now described with reference to
the accompanying drawings.
[0023] Referring to FIG. 1, a let-off control device (hereinafter referred to simply as
the control device) 10 of a weaving machine comprises as its principal elements a
basic speed calculator 11, a controller 14, a control amplifier 17 and an average
tension calculator 18. An output of the control device 10 is connected to a let-off
motor M.
[0024] The let-off motor M is connected to a warp beam WB via a reduction gear unit GD.
Warp threads W fed from the warp beam WB are pulled out over a tension roller TR and
separated into two sets of warp threads, upper warp threads W1 and lower warp threads
W2, by a heddle which is not illustrated. The tension roller TR is associated with
a detector LD, such as a load cell, which detects warp tension Y exerted on the tension
roller TR on a real-time basis. The warp beam WB is associated with a winding diameter
sensor DS which detects winding diameter D of (the warp W on) the warp beam WB.
[0025] Weft density A of an in-process fabric, gear ratio m of the reduction gear unit GD,
rotational speed N of the weaving machine and the winding diameter D fed from the
winding diameter sensor DS are entered to the basic speed calculator 11, where the
weft density A and the gear ratio m are set on an unillustrated setter while the rotational
speed N of the weaving machine is output from an unillustrated rotational speed detector.
[0026] An output of a target tension setter 12 is connected to the controller 14 via an
summing point 13. Also, an output of the controller 14 is connected to the let-off
motor M via a correction calculator 15, an summing point 16 and the control amplifier
17. Outputs of the average tension calculator 18 and the basic speed calculator 11
are connected to a subtracting terminal of the summing point 13 and to an adding terminal
of the summing point 16, respectively. An output of a tachometer generator TG which
is directly connected to the let-off motor M is fed back to the control amplifier
17. Further, a clock signal Sc is input from an unillustrated clock generator to the
controller 14, and data on the winding diameter D output from the winding diameter
sensor DS branches off and is entered to the correction calculator 15.
[0027] A main shaft MS of the weaving machine is associated with a dog MS1, and a proximity
switch DT is disposed face to face with the dog MS1. An output of the proximity switch
DT is connected to the average tension calculator 18, to which the warp tension Y
is entered from the detector LD.
[0028] When the weaving machine is in steady-state running conditions, the basic speed calculator
11 calculates basic speed Vo (rpm) of the let-off motor M as follows:

where the weft density A is expressed in picks per inch and π represents " a ratio
of the circumference of a circle to its diameter".
[0029] The proximity switch DT detects a specified crank angle

during each rotation of the main shaft MS and causes the average tension calculator
18 to operate. The average tension calculator 18 successively detects the warp tension
Y at the specified crank angle θo and obtains a moving average of the warp tension
Y (= Y1, Y2 ....., Yn) for the n most recent rotations (n≧1) of the main shaft MS
and then outputs average tension Ya = avg (Y1, Y2, ....., Yn) to the summing point
13, where n represents the number of rotations of the main shaft MS, Y1, Y2, .....,
Yn indicate detected values of the warp tension Y at the crank angle θo during the
successive rotations of the main shaft MS, and avg (Y1, Y2, ....., Yn) is the average
of the individual values of the warp tension Y (= Y1, Y2, ....., Yn). Thus, a signal
corresponding to a deviation, "

(subtracting Ya entered from the average tension calculator 18 from a target tension
Yo fed from the target tension setter 12)" is input to the summing point 13, and then
the signal corresponding to the deviation Δya is output to the controller 14.
[0030] The controller 14 has control elements for performing proportional, integral and
differential (control) actions, for instance. It operates in synchronism with a specific
operating cycle according to the clock signal Sc and thereby calculates speed correction
value Vc based on the deviation ΔYa. The controller 14 performs sampling control operation
according to the clock signal Sc, wherein control parameters of the individual control
elements, such as proportional gain, integration time constant (integral gain) and
differentiation time constant (differential gain), are optimally set with respect
to maximum winding diameter Do of the warp W on the warp beam WB.
[0031] The correction calculator 15 adjusts the speed correction value Vc fed from the controller
14 to speed correction value Vc1 based on the winding diameter D of the warp W on
the warp beam WB as follows:

[0032] A signal corresponding to a summation, "Vo + Vc1 (a summation of a basic speed Vo
fed from the basic speed calculator 11 and a speed correction value Vc1 fed from the
correction calculator 15)" is input to a summing point 16 and then a signal corresponding
to the summation value is output to the control amplifier 17.
[0033] The summing point 16 and the control amplifier 17 controls the speed of the let-off
motor M based on the basic speed Vo fed from the basic speed calculator 11 and the
speed correction value Vc1 fed from the correction calculator 15, whereby the warp
beam WB can be controllably driven such that the average tension Ya equals the target
tension Yo (

). In this control operation, the tachometer generator TG detects rotational speed
Vm of the let-off motor M and feeds it back to the control amplifier 17, thereby constituting
a speed minor loop.
[0034] The average tension calculator 18 is caused to operate once every rotation of the
main shaft MS through the dog MS1 and the proximity switch DT. On the other hand,
the controller 14 operates in synchronism with the operating cycle determined by the
clock signal Sc which is generated at fixed rate, independently of the operating cycle
of the average tension calculator 18. Therefore, there is not any likelihood that
the substantial control parameters will fluctuate due to variations in the rotational
speed N of the weaving machine. Here, it is preferable that pulse frequency of the
clock signal Sc be determined such that the operating cycle of the controller 14 becomes
smaller than the operating cycle of the average tension calculator 18 which is determined
by the rotational speed N of the weaving machine.
Other Embodiments
[0035] The control device 10 of FIG. 1 may further comprises a switching circuit 19 and
an automatic tuning circuit 20 as shown in FIGS. 2 and 3.
[0036] The switching circuit 19 is inserted between the correction calculator 15 and the
summing point 16. A tuning command St is entered from an unillustrated weaving machine
control circuit. This tuning command St is further delivered to the automatic tuning
circuit 20 and to the correction calculator 15 and the switching circuit 19 through
the automatic tuning circuit 20.
[0037] The aforementioned warp tension Y and simulated target tension Ys fed from an unillustrated
step signal generator are entered to a proportional controller 21 of the automatic
tuning circuit 20, and an output signal of the proportional controller 21 is entered
to another adding terminal of the summing point 16 as a driving signal Sd. The warp
tension Y branches off and is entered to a tension data detector 22 of the automatic
tuning circuit 20 as well, and an output of the tension data detector 22 is connected
to the controller 14 of the control device 10 via a transfer function calculator 23
and a parameter setter 24. The tuning command St branches off and is entered to the
proportional controller 21 and the tension data detector 22 as well.
[0038] If the tuning command St occurs when the weaving machine is at rest, the switching
circuit 19 disconnects the summing point 16 from the correction calculator 15 and
substantially disables the controller 14 as a consequence. At this time, the proportional
controller 21 can drive the let-off motor M by outputting the driving signal Sd based
on deviation ΔY (= Ys - Y) of the warp tension Y with respect to the simulated target
tension Ys, and the tension data detector 22 can detect variations with time of the
warp tension Y caused by the driving signal Sd. Since the rotational speed N of the
weaving machine is equal to zero (N = 0) at this point, the basic speed Vo fed from
the basic speed calculator 11 is equal to zero (Vo = 0).
[0039] The proportional controller 21 of this embodiment forms a direct feedback control
system for a controlled system from the let-off motor M to the warp tension Y as shown
in FIG. 4, in which g represents proportional gain, F(s) represents a transfer function
of the controlled system, and s represents a Laplacian operator.
[0040] Referring to FIG. 4, it is assumed here that the transfer function F(s) of the controlled
system is expressed as follows:

Then, transfer function G(s) from the simulated target tension Ys to the warp tension
Y is

where α and β are constants,

and

.
[0041] The state of warp tension Y versus time in response to the step response of the aforementioned
automatic tuning circuit 20 is expressed in Fig. 5. From Fig. 5, it is clearly seen
that the warp tension Y varies for time t≧T1, in which T1 is a delay time of the actual
controlled system. When the steplike simulated target tension Ys is given at time
t = 0, the warp tension Y rises from its initial value Y1 up to a peak value Ym during
a rise time T2 after the delay time T1 and settles and remains at a final value Y2
thereafter. The proportional gain g of the proportional controller 21 is properly
set such that the warp tension Y exhibits an apparent peak value Ym and the peak value
Ym would not diverge.
[0042] For time t≧0, the step response y(t) of the transfer function G(s), i.e., a transfer
function y(t) which is converted into a time domain from a transfer function G(s)
in response to a step response, is given by

where


[0043] Adapting the step response y(t) to a portion time t≧ T1 of the curve of FIG. 5, a1
and a2 are obtained as follows:

where ln is a symbol for natural logarithm. It is then possible to determine the
transfer function G(s) by substituting

[0044] Since the transfer function F(s) contains an integral element F1(s) (= D/s) which
corresponds to a rotational system from the let-off motor M to the number of rotations
of the warp beam WB, transfer function F2(s), which excludes the integral element,
of a mechanical system is calculated from the number of rotations of the warp beam
WB as follows:

Transfer function Fo(s) of the actual controlled system can be expressed as a first-order
lag of a time constant T associated with the delay time T1 as follows:

Then, from a comparison between the transfer functions F2(s) and Fo(s),

It is possible to determine the transfer function Fo(s) of the actual controlled
system in the aforementioned fashion.
[0045] When the transfer function Fo(s) of the actual controlled system has been determined
as shown above, optimum control parameter PD of the controller 14 having the control
elements for performing proportional, integral and differential (control) actions
can be calculated as follows, for instance:

or

where Kp is the proportional gain, Ti is the integration time constant (integral
gain) and Td is the differentiation time constant (differential gain). Of the above
equations, (7a) to (7c) are for optimizing response to external disturbances while
(8a) to (8c) are for optimizing response to a target value.
[0046] When the tuning command St occurs and the switching circuit 19 disables the controller
14, the steplike simulated target tension Ys is applied to the proportional controller
21 at time t = 0 of FIG. 5, and the proportional controller 21 generates the driving
signal Sd to be delivered to the let-off motor M. The tension data detector 22 collects
data on variations with time of the warp tension Y caused by the driving signal Sd
throughout the time period t≧0 and outputs the delay time T1, the peak value Ym of
the warp tension Y and the final value Y2 to the transfer function calculator 23.
The transfer function calculator 23 can determine the transfer function F(s) using
equations (1) to (4) and further determine the transfer function Fo(s) using equations
(5) and (6).
[0047] On the other hand, the parameter setter 24 can calculate the optimum control parameter
PD for the transfer function Fo(s) using equations (7a) to (7c) or (8a) to (8c) and
update set it to the controller 14. The controller 14 is then caused to resume its
operation by resetting the tuning command St and thereby closing the switching circuit
19. Here, the delay time T1 output from the tension data detector 22 is delivered
up to the parameter setter 24.
[0048] Since the optimum control parameter PD set in the aforementioned fashion is calculated
for the controlled system containing the integral element F1(s) (= D/s), however,
the speed correction value Vc output from the controller 14 is corrected by the correction
calculator 15 according to the winding diameter D of the warp W on the warp beam WB.
More specifically, referring to FIG. 2, the correction calculator 15 calculates the
speed correction value Vc1 as follows, using the winding diameter D (=D1) at the point
in time when the tuning command St occurs or when the controller 14 resumes the aforementioned
corrective control operation after the tuning command St has been reset:

[0049] The automatic tuning circuit 20 may include a signal generator 25 and a regression
analyzer 26 instead of the proportional controller 21 and the tension data detector
22 as shown in FIG. 6. The warp tension Y is entered to the regression analyzer 26
and an output of the signal generator 25 is delivered to the summing point 16 as a
driving signal Sd for the let-off motor M. The output of the signal generator 25 branches
off and is entered to the transfer function calculator 23 as well. The tuning command
St branches off and is entered to the regression analyzer 26 and the signal generator
25, and an output of the regression analyzer 26 is delivered up to the transfer function
calculator 23.
[0050] Generally, when a steplike input of a specific level V (= V1) is given to a controlled
system of transfer function

at time t = 0 for a specific time period τ, variation with time Y(t) of output Y
is given by

where




and X2 is assumed to be equal to zero (X2 = 0) when X2<0. By performing nonlinear
regression analysis on equation (9) above, it is possible to determine parameters
α and B and, then, parameter β which is given by

.
[0051] When the transfer function F(s) has been determined as described above, the transfer
function Fo(s) of the actual controlled system containing the delay time T1 can be
determined from equations (5) and (6) and, then, the optimum control parameter PD
of the controller 14 for the transfer function Fo(s) can be calculated from equations
(7a) to (7c) or (8a) to (8c).
[0052] Specifically, when the tuning command St occurs and the switching circuit 19 is opened,
the signal generator 25 generates the driving signal Sd of the specific level V (=
V1) for the specific time period τ at time t = 0 of FIG. 7. The regression analyzer
26 collects data on variations with time of the warp tension Y caused by the driving
signal Sd and determines parameters α and B by performing regression analysis on a
time-varying curve which varies from initial value Y3 of the warp tension Y to its
final value Y4 during a period including the delay time T1 and time

to τ - T1. The regression analyzer 26 excludes the influence of the delay time T1
by substituting

in equation (9). In FIG. 7, a solid line shows an example of an actual time-varying
curve of the warp tension Y and a broken line shows an example of plotting obtained
from equation (9) by regression analysis of the time-varying curve. Also in FIG. 7,
the level V1 of the driving signal Sd and signal length τ are properly set such that
the let-off motor M turns the warp beam WB in its forward running direction and the
warp tension Y smoothly varies from the initial value Y3 to the final value Y4 which
is not equal to 0.
[0053] Referring to FIG. 6, the transfer function calculator 23 can determine the parameter
β using the parameters α and B fed from the regression analyzer 26 and the level V1
of the driving signal Sd fed from the signal generator 25 and then determine the transfer
function Fo(s) of the actual controlled system containing the delay time T1 from equations
(5) and (6), wherein the delay time T1 can be obtained from the regression analyzer
26 as part of the data on variations with time of the warp tension Y (FIG. 7). Therefore,
the parameter setter 24 may calculate the optimum control parameter PD of the controller
14 and set it to the controller 14, and the controller 14 may resume its operation
when the switching circuit 19 is closed by resetting the tuning command St in exactly
the same way as described above.
[0054] Although the tuning command St is generated by manual operation at the time of, such
as, replacement of the warp beam, in the foregoing discussion, it may be produced
by appropriate automatic means. For example, provision may be made to monitor one
or more parameters, such as the winding diameter D of the warp W on the warp beam
WB or the deviation ΔYa of the warp tension Y, which could influence let-off control
operation, and when any of these parameters considerably varies with time, the tuning
command St may be produced automatically generated based on a judgment that tuning
operation needs to be performed again.
[0055] In the block diagrams of FIGS. 1 and 2, a compensating circuit 31 may be inserted
between the target tension setter 12 and the summing point 13 as shown in FIG. 8.
The compensating circuit 31 forms a control system having two degrees of freedom together
with the controller 14. Specifically, when response to external disturbances of the
controller 14 is to be optimized by equations (7a) to (7c), for example, the compensating
circuit 31 can improve response to the target tension Yo by incorporating control
elements for performing proportional and differential (control) actions with the same
proportional gain Kp and differentiation time constant Td as those of the controller
14 and also optimize response to a target value.
[0056] Although the present invention has been fully described by way of example with reference
to the accompanying drawings, it is to be understood that various changes and modifications
will be apparent to those skilled in the art. Therefore, unless otherwise such changes
and modifications depart from the scope of the present invention hereinafter defined,
they should be construed as being included therein.