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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and apparatus for driving a servo
system which positions a structure which vibrates by a reaction force of a
drive force generated in a positioning operation while suppressing a
residual vibration of the structure.
2. Description of the Related Art
In JP-A-60-171512, means is disclosed to suppress a structure vibration by
utilizing a vibration inertia force of a load weight and using a servo
mechanism. JP-A-60-231205 discloses a method for suppressing a vibration
of a mechanical system without adding a separate vibration suppression
device. In this method, a mechanical system in a positioning control
system is modeled by an electrical circuit, the model is arranged in
parallel to the control system and a signal therein is supplied to a main
loop to suppress a mechanical vibration of a load.
However, in the first prior art technique, although a vibration suppression
effect is attained, a separate vibration suppression device is required.
As a result, the system is complex. In the second prior art technique, no
separate vibration suppression device is required and the system
construction is simpler, but there is no assurance that a positioning
operation is attained in a short time. Further, if there is an error in
the electrical circuit model of the mechanical system, the vibration
suppression effect is reduced.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a method and apparatus
for driving a servo system while suppressing a residual vibration
generated in position control.
It is another object of the present invention to provide a method and
apparatus for driving a servo system which can attain position control in
a short time and reduce a residual vibration of a structure.
It is still another object of the present invention to provide a method and
apparatus for driving a servo system which is simple in construction and
suppresses a residual vibration generated in position control.
The above objects are achieved by the following method and apparatus.
A method for driving a servo system for determining a drive signal for an
actuator for driving a movable unit in accordance with an error between a
target position and a current position of the movable unit, and driving
the actuator by the drive signal to displace the movable unit to a
predetermined position, comprises the steps of:
in response to a move command, calculating a target trajectory for
suppressing a residual vibration of a structure at an end of displacement
of the movable unit by using a model of a controlled object comprising the
movable unit and the structure, a constraint of the actuator and a
boundary condition;
generating target positions at different times in the displacement of the
movable unit based on said target trajectory; and
displacing said movable unit to said predetermined position by using the
generated target positions.
An apparatus for driving a servo system comprises:
a movable unit moving on or with a structure;
an actuator for imparting a drive force to said movable unit;
a control unit for producing a drive signal to said actuator to eliminate a
difference between a target position and an actual position of said
movable unit;
a movement detection device for detecting the actual position of said
movable unit; and
an operation unit including first means for calculating and storing, in
response to a move command, a target trajectory for suppressing a
vibration of said movable unit at or after stop of the movement based on a
stored model of said movable unit and said structure, a constraint for
said actuator and a boundary condition determined by the move command, and
second means for generating target positions of said movable unit during
the movement of said movable unit based on the stored target trajectory
and supplying the target positions at various times to said control unit.
Other objects and features of the present invention will be apparent from
the following description of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows an overall system configuration in one embodiment of the
present invention,
FIG. 2 shows a model of a controlled object in the embodiment of FIG. 1,
FIGS. 3 and 4 are operational flow charts of the embodiment of FIG. 1,
FIG. 5 shows a control block diagram of the embodiment of FIG. 1,
FIGS. 6 to 9 show results of operation in the embodiment of FIG. 1,
FIG. 10 shows a control block diagram in another embodiment of the present
invention,
FIGS. 11 to 13 show signal patterns in the embodiment of FIG. 10,
FIG. 14 shows an operational flow chart in the embodiment of FIG. 10,
FIGS. 15 and 16 show results of operation in the embodiment of FIG. 10,
FIG. 17 shows a control block diagram in other embodiment of the present
invention, and
FIG. 18 shows a model of a controlled object in the embodiment of FIG. 17.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[Embodiment 1]
FIG. 1 shows an embodiment in which the present invention is applied to a
reduction projection exposure apparatus, which reduces a circuit pattern
of LSI or IC and projects the reduced pattern onto a wafer for exposure.
In FIG. 1, a reticle (circuit pattern) 1 is reduced and projected onto a
wafer 5 on a movable XY stage (movable unit) 4 by an illumination system 2
and a reduction lens 3. The illumination system 2 is supported by an
illumination post 6, and the reticle (circuit pattern) 1 and the reduction
lens 3 are supported by a column 7. Elements of the apparatus such as the
movable unit 4 are mounted on a structure base (structure) 8, and the
structure 8 is held by an anti-vibration table 9 to isolate it from
external vibration. Since up to several tens of circuit patterns are
projected onto the wafer 5, the movable unit 4 on which the wafer 5 is
mounted is moved by a step and repeat method in X and Y directions which
are two orthogonal axes in a horizontal plane. The movement of the movable
unit 4 and the positioning control are effected by supplying to a control
unit 13 a target position supplied from an operation unit 12 and a current
position of th emovable unit supplied from a movement detector 11 such as
a laser range finder so that the control unit 13 produces a drive signal
in accordance with a difference between the target position and the
current position of the movable unit 4 to drive an actuator 10 for moving
the movable unit 4. A drive force of the actuator 10 is transmitted to the
structure 8 on which the apparatus is mounted, as a reaction force, so
that it causes a vibration of the structure. It also vibrates the column 7
which holds the reticle 1 and the reduction lens 3 so that a relative
alignment precision between the reticle 1 and the wafer 5 is lowered.
When a move command to the movable unit 4 is issued, the operation unit 12
changes the target position toward which the movable unit 4 is to be moved
from the current position, with the elapsed time during the movement
period so that a residual vibration of the structure 8 at the time when
the movable unit 4 reaches the final goal and stops thereat. An
aggregation of target positions which vary with time when the movable unit
is moved from the current position to the final goal is called a target
trajectory. A target trajectory which, under a given condition, can
minimize a movement time for the movable unit 4 to reach the final goal
and minimize a residual vibration at the time when the movable unit 4
reaches the final goal and stops thereat, is called an optimum target
trajectory. The operation unit 12 may be a general purpose computer
(particularly, a micro computer), but in FIG. 1 it comprises a target
trajectory operation unit 19 and a target position generation unit 14 to
facilitate understanding. The target trajectory operation unit 19 receives
a move command and a detection signal of a vibration detection device 17
at the end of movement of the movable unit 4 to calculate the optimum
target trajectory. The target position generation unit 14 stores the
optimum target trajectory and supplies to the control unit 13 target
positions at various time points during the movement period of the movable
unit 4 in accordance with the stored optimum target trajectory. Detail of
the operation of the target trajectory operation unit 19 will be explained
later and only brief explanation thereof is given here. The move command
which represents a movement distance from a current position to a final
goal is given to the target trajectory operation unit 19 and the target
position generation unit 14. When the move command is first applied, the
optimum target trajectory has not been derived. The target position
generation unit 14 does not then generate the target position and the
target trajectory operation unit 19 determines a solution of the target
trajectory which minimizes the residual vibration of the structure and
minimizes the movement time of the movable unit 4 within a restricted
condition for the actuator 10 and the movement detection device 11, by
using a model of a system comprising the movable unit 4 and the structure
8 and by a linear programming method, and writes the target position into
the memory of the target trajectory generation unit 14. Then, the target
position generation unit 14 supplies the target position stored in the
memory to the control unit 13 to move and position the movable unit 4. The
target trajectory operation unit 19 detects, by the vibration detection
device 17, the residual vibration of the structure at the end of the
movement of the movable unit 4, that is, when the position of the movable
unit 4 detected by the movement detection device 11 has been moved by the
distance commanded by the move command. If the detected residual vibration
is beyond a permitted level, the target trajectory operation unit 19
corrects a boundary condition of the linear programming method by using
the residual vibration data, recalculates the target trajectory and writes
it into the memory of the target position generation device 14. If the
optimum target trajectory has already been calculated and stored in the
memory of the target position generation unit 14, the target position
generation unit 14 supplies the target position stored in the memory to
the control unit 13 when the move command 19 is issued to move and
position the movable unit 4. The target trajectory operation unit 19
further corrects the boundary condition based on the residual vibration
data in the same manner as that described above, derives a new target
trajectory and writes it into the memory of the target position generation
unit 14.
The operation of FIG. 1 is explained with reference to a model of FIG. 2
and flow charts of FIGS. 3 and 4. FIG. 2 shows a model of a system
comprising the movable unit 4 and the structure 8. In FIG. 2, the movable
unit 4 is moved by a drive force u of the actuator 10 and the structure 8
receives a reaction force of the drive force u and vibrates at a vibration
frequency and a damping coefficient determined by a spring 21 of the
structure and a viscosity resistance 22 of the structure. Kinetic
equations of the model are given by:
m.sub.1 x.sub.1 +B.sub.1 (x.sub.1 -x.sub.2)=u (1)
m.sub.2 x.sub.2 +B.sub.2 x.sub.2 +kX.sub.2 =-u+B.sub.1 (x.sub.1 -x.sub.2)
(2)
where m.sub.1 is a mass of the movable unit 4, m.sub.2 is a mass of the
structure 8, x.sub.1 is a position of the movable unit 4, x.sub.2 is a
position of the structure 8, u is a drive force of the actuator 10,
B.sub.1 is a damping constant of the movable unit drive system, B.sub.2 is
a damping constant of the structure 8, k is a spring constant of the
structure 8, X.sub.1 is a velocity derived by differentiating X.sub.1
once, X.sub.1 is an acceleration/deceleration derived by differentiating
X.sub.1 twice, X.sub.2 is a velocity derived by differentiating X.sub.2
once, and X.sub.2 is an acceleration/ deceleration derived by
differentiating X.sub.2 twice.
The equations (1) and (2) are represented by a state equation as follows.
X=AX+bu (3)
where
##EQU1##
An upscript T represents transposition of vectors.
A constraint required in moving the movable unit 4 by a distance X.sub.s
uniquely determined by the move command while suppressing the residual
vibration of the structure 8 at the end of the movement of the movable
unit 4 is that the velocity X.sub.1 of the movable unit 4 is smaller than
a maximum velocity V.sub.max that is measurable by the movement detection
device and the drive force u of the actuator 10 does not exceed a maximum
drive force U.sub.max. Namely,
.vertline.x.sub.1 .vertline..ltoreq.V.sub.max (4)
.vertline.u.vertline..ltoreq.U.sub.max (5)
The movable unit 4 is stationary at time t=0 and has been moved by the
distance X.sub.s at the end of the movable unit movement time t=T.sub.f
and is stationary at that moment, and the residual vibration of the
structure 8 should be zero at that moment. Accordingly, boundary
conditions at an initial time t=0 and an end time t=T.sub.f are given by:
X.sub.0 =[R.sub.o 0 0 0 ].sup.T (6)
x.sub.f =[R.sub.0 +X.sub.s 0 0 0 ].sup.T (7)
where R.sub.0 is a target position of the movable unit in a stationary
state of the movable unit prior to the movement thereof, and also the
position of the movable unit, and x.sub.O and x.sub.f and state vectors x
at the initial time t=0 and the end time t=T.sub.f.
If a drive force u of the actuator which meets the constraint and boundary
conditions of the equations (4) to (7) is derived, it is possible to
obtain a control solution for moving the movable unit 4 by x.sub.s and
stopping it thereat while suppressing the residual vibration of the
structure 8. The state variable x and the drive force u are represented by
an output vector y as follows.
y=C.sub.x +D.sub.u (8)
where
##EQU2##
The above constraint and boundary conditions are represented as follows.
Y.sub.min .ltoreq.Y.ltoreq.Y.sub.max (0<t<T.sub.1) (9)
X=X.sub.0 (t=0) (10)
y.sup.(f).sub.min .ltoreq.Y.ltoreq.Y.sup.(f).sub.max (t=T.sub.1) (11)
where Y.sub.min : possible minimum value of the output vector y
y.sub.max : possible maximum value of the output vector y
y.sup.(f).sub.min :possible minimum value of the output vector y at the end
time
y.sup.(f).sub.max : possible maximum value of the output vector y at the
end time
x : state variable vector
##EQU3##
The drive force u which moves the movable unit 4 by x.sub.s step while
suppressing the residual vibration of the structure 8 can be derived by a
linear programming method based on the constraint and boundary condition
of the formulas (9) to (11). To this end, the state equation (2) is split
by a sampling period T.sub.s as follows.
X.sub.k+1 =AX.sub.k +Bu.sub.k (12)
Y.sub.k =Cx.sub.k +Du.sub.k (13)
where
k: number of times of sampling
x.sub.k+1 : state variable vector at (k+1)th sampling
x.sub.k : state variable sample at k-th sampling
u.sub.k : drive force for the actuator at k-th sampling
y.sub.k : output vector at k-th sampling
I: unit matrix
A=exp (AT.sub.s), C=C, D=D
B=(exp (AT.sub.s) - I) A.sup.-1 b (FIG. 3 step 100)
The state vectors x.sub.k and output vectors y.sub.k at times t=kT.sub.s
(k=0, 1, 2, . . .) are represented as follows.
##EQU4##
By applying the formulas (14) and (15) to the formulas (9), (10) and (11)
and formatting them with respect to u.sub.i (i=O, N), the following linear
inequalities are derived.
##EQU5##
In solving the linear equalities (16) by the linear programming method, if
N is small, it is not possible to meet the boundary condition at the time
t=T.sub.f in N steps and the linear programming method is disabled. By
determining N.sub.0 above which the linear programming method is enabled,
it is possible to obtain the drive force u as time sequence data u.sub.k
(k=0, 1, 2, . . . )which can move the movable unit 4 by the distance
x.sub.s in a minimum time while suppressing the residual vibration of the
structure. The number of steps N.sub.0 for the minimum time is searched by
a binary method depending on whether the linear programming method is
enabled or disabled to determine control solutions u.sub.k (k=0, 1, 2, . .
. N.sub.0) for the minimum time (FIG. 3 step 101).
Detail of the step 101 of FIG. 3 (search of the number of steps N.sub.0 for
the minimum time by the binary method) is explained with reference to a
flow chart of FIG. 4. First, in order to search the number of steps
N.sub.0 for the minimum time which enables the linear programming method,
by the binary method, the number of steps which disables the linear
programming method is set to N.sub.min and the number of steps which
enables the linear programming method is set to N.sub.max (FIG. 4 step
107). At a mid-point of the number of steps N.sub.min at which the linear
programming method is disabled and the number of steps N.sub.max at which
the linear programming method is enabled, that is, at a point N=(N.sub.min
+N.sub.max)/2, the linear inequalities (16) are derived by the linear
programming method (FIG. 4 steps 108 and 109). If the linear programming
method is enabled at N and disabled at N-1, it is the control solution for
the minimum time and the operation is now terminated (FIG. 4 step 110). If
the control solution for the minimum time is not obtained in the step 110,
whether the solution by the linear programming method is enabled or not at
N is determined (FIG. 4 step 111). If the solution by the linear
programming method is enabled in the step 111, N.sub.max is substituted by
N (FIG. 4 step 112), and if it is disabled, N.sub.min is substituted by N
(FIG. 4 step 113). By repeating the steps 108, 109, 110, 111, 112 and 113,
the search area is narrowed and it eventually reaches the number of steps
N.sub.0 for the minimum time so that the control solutions u.sub.k (k=1,
0, . . . N.sub.0) for the minimum time are obtained (FIG. 4 step 114).
In an actual positioning control system, it is necessary to construct a
closed loop control system in order to keep the state in a steady state.
As shown in FIG. 5, the closed loop control system feeds back the position
x.sub.1 of the movable unit 4 and the velocity X.sub.1 thereof. FIG. 5
shows a control block diagram of the embodiment of FIG. 1. In FIG. 5, an
adder 47 produces an error between the target position .gamma. supplied
from the operation unit 12 and the movable unit position x.sub.1. An
amplifier 25 amplifies the error by a factor of G.sub.p to produce a
target velocity corresponding to the error. An adder 49 produces an error
between the target velocity and the movable unit velocity x.sub.1
amplified by an amplifier 24 by a factor of G.sub.v. The movable unit
velocity x.sub.1 is determined by a state observer 23 based on the movable
unit position x.sub.1 and an output of a power amplifier 51. The output of
the adder 49 (velocity error) is amplified by the power amplifier 51 and
it is supplied to an actuator 10 as a drive signal. The actuator 10 is
driven by the drive signal with a drive force u represented by
u=G.sub.a {G.sub.p (.gamma.-x.sub.1)-G.sub.v x.sub.1 } (17)
where
G.sub.a : gain of the amplifier 51
G.sub.p : gain of the amplifier 25
G.sub.v : gain of the amplifier 24
A control unit 13 receives the target position .gamma. and the movable unit
position x.sub.1 to produce the drive signal u represented by the formula
(17).
On the other hand, the optimum target position .gamma..sub.k at each
sampling point on the optimum target trajectory is derived based on the
drive force u.sub.k at the sampling point derived by the linear
programming method and the state x.sub.k, as shown below.
##EQU6##
x.sub.1 (k): x.sub.1 at k-th sampling x.sub.1 (k): x.sub.1 at k-th
sampling
x.sub.2 (k): x.sub.2 at k-th sampling
x.sub.2 (k): x.sub.2 at k-th sampling
The optimum target trajectory which is an aggregation of the optimum target
positions .gamma..sub.k derived by using the linear programming method is
calculated by the target trajectory operation unit 19 and stored in the
memory in the target position generation unit 14 (FIG. 3 step 102). The
target position generation unit 14 supplies to the control unit 13 the
optimum target positions .gamma..sub.k for the respective time points from
the stored optimum target trajectory at every sampling pitch so that the
control unit 13 drives the actuator to position-control the movable unit 4
(FIG. 3 step 103).
FIG. 6 shows changes in time of the movable unit position x.sub.1, the
movable unit velocity x.sub.1 and the structure position x.sub.2 when the
servo system drive apparatus calculates the optimum target trajectory to
control the position. If the characteristic of the controlled object is
perfectly known, it is possible to completely suppress the residual
vibration of the structure at the time of stop.
However, the optimum target trajectory derived above represents the model
of the controlled object by the formulas (12) and (13), and the
characteristic of the model represented by those formula is usually
different from the characteristic of the actual controlled object. If
there is a difference between the actual characteristic and the model
characteristic, the optimum target trajectory determined by the model is
not always be optimum. As a result, if the position control is done by
using the optimum target trajectory determined by the calculation, the
residual vibration is involved at the time of stop. If the residual
vibration exceeds a permissible level .epsilon., it causes a trouble.
Accordingly, the operation unit 12 receives the detection result of the
residual vibration to determine whether it exceeds .epsilon.. This is the
step 104 of FIG. 3. If the residual vibration exceeds .epsilon., the
target trajectory is amended. In the present embodiment, a boundary
condition x.sub.f at the end of the movement of the movable unit (stop)
t=T.sub.f is modified based on the residual vibration data derived when
the movable unit is driven in accordance with the stored optimum target
trajectory (FIG. 3 step 105). The boundary condition x.sub.f is amended in
the following manner.
##EQU7##
where
z: number of times of iterative modification
x.sub.2.sup.(j) and x.sub.2.sup.(j) :and velocity of the structure at the
end of movement of the movable unit in the j-th modification of the
boundary condition
Based on the boundary condition modified by the formula (19), the optimum
target trajectory is derived by the target trajectory operation unit 19 by
the linear programming method, and the target trajectory stored in the
target position generation unit 14 is removed. The movable unit 4 is
repeatedly driven (FIG. 3 step 103) until the residual vibration becomes
lower than .epsilon. (FIG. 3 step 104). Through such learning control, the
movable unit 4 can be precisely position-controlled in a minimum time
while the residual vibration of the structure 8 is suppressed, even if an
identification error is included. FIGS. 7 to 9 show responses to the
learning control. They show that the position control which minimizes the
residual vibration in the minimum time is attained by the repetitive
learning control.
[Embodiment 2]
Another embodiment of the present invention is now explained. FIG. 10 shows
a control block diagram of other embodiment which corresponds to FIG. 5.
The overall system configuration is similar to that of FIG. 1.
In FIG. 10, most elements are identical to those of FIG. 5 and the
explanation thereof is omitted. In FIG. 10, a velocity pattern generator
55 which receives an output of an adder 47 (position error) to generate a
velocity pattern corresponding to the position error is provided. The
velocity pattern thus produced and the velocity signal x.sub.1 are
supplied to an adder 49 which produces a velocity error. This velocity
error is applied to a bangbang element 59 which produces a predetermined +
or - value depending on a sign (+ or -) of the velocity error. A power
amplifier 51 receives this value and amplifies it by a factor of G.sub.a
to produce a drive signal. The actuator 10 drives the movable unit 4 by
the drive signal. In the present embodiment, the velocity pattern is
accelerated to a maximum measurable speed V.sub.max and decelerated when
it proximates the final goal as shown in FIG. 11.
A method for suppressing the residual vibration of the structure which
vibrates even after the end of movement of the movable unit by a reaction
force of a drive force acting on the movable unit 4. In order to move the
movable unit 4 by the distance x.sub.s in the minimum time, the target
position generation unit 14 generates a stepwise target position which
changes from the pre-movement target position R.sub.0 to the final target
position R.sub.0 +x.sub.s. In order to suppress the residual vibration,
the target position is divided in time into two parts as shown in FIG. 12
so that the target position is tentatively set to an intermediate target
position R.sub.0 +X.sub.m, and it is switched to the final target position
R.sub.0 +x.sub.s at the time T.sub.m. By generating the time-divisioned
target positions, the velocity pattern of the movable unit repeats the
maximum acceleration and maximum deceleration pattern twice as shown in
FIG. 13. The acceleration/ deceleration patterns are adjusted such that
the residual vibration generated in the structure by the first half
intermediate target position R.sub.0 +X.sub.m and the residual vibration
generated by the latter half final target position R.sub.0 +x.sub.s cancel
to each other to suppress the residual vibration at the end of movement of
the movable unit 4. The acceleration/deceleration patterns are represented
by two parameters, the displacement X.sub.m before the intermediate target
position and the switching time T.sub.m, and it is important to balance
those two parameters. In order to determine the parameters, a learning
control method is used to repeatedly amend the target trajectory by the
target trajectory operation unit 19 based on the vibration data detected
by the vibration detection device 17. The learning control method is now
explained.
The residual vibration of the structure 8 is first defined. The residual
vibration is a vibration at the end of the movement of the movable unit 4,
and it is represented by the position and velocity of the structure. The
position and velocity of the structure are represented by y.sub.1 and
y.sub.2, respectively. The displacement X.sub.m to the intermediate target
position and the switching time T.sub.m are represented by P.sub.1 and
P.sub.2, respectively. The parameters (P.sub.1, P.sub.2) are called time
division target parameters, and (y.sub.1, y.sub.2) are called residual
vibration parameters. The time division target parameters (P.sub.1,
P.sub.2) drive the movable unit 4 to cause the residual vibration
(y.sub.1, y.sub.2) in the structure 8. Thus, they have the following
input/output relationship.
##EQU8##
where f.sub.1 and f.sub.2 indicate that y.sub.1 and y.sub.2 are functions
of P.sub.1 and P.sub.2, respectively. The input/output relationship
represented by the formula (20) is approximated by the following linear
equation.
##EQU9##
where upper script j represents the number of times of drive for learning
control, and P.sub.i0 is a deduction parameter deducted from the residual
vibration data y.sub.k.
By more exactly identifying the input/output relationship represented by
the formula (21) in the process of the learning control, the time division
target parameters which suppress the residual vibration of the structure
are obtained. A method for identifying the input/output relationship and a
method for deriving the parameter for suppressing the residual vibration
are now explained.
The input/output relationship of the formula is identified by determining
a.sub.ik and b.sub.i of the formula (21) such that a parameter error
between the time division target parameter p.sub.i (i=1, 2) and the
deduction parameter p.sub.i0 (i=1, 2) is minimized. The following
evaluation function representing the parameter error is defined.
##EQU10##
where W.sub.j is a weight factor for weighting data which includes many
past errors ih the iteration of the learning control. The weight factor
W.sub.j is represented by
W.sub.j =f.sub.s.sup.j-k (f.sub.S <1) (23)
By placing the formula (21) in the formula (22), we get
##EQU11##
A condition which minimizes the evaluation function of the formula (24) is
given by
##EQU12##
By solving the formulas (25) and (26), the following relation is obtained.
Mq=f (27)
where
##EQU13##
The input/output relationship represented by the formula (21) is determined
as a.sub.ik and b.sub.i which are obtained by deriving
q=M.sup.-1 f (28)
from the formula (27).
The time division target parameter which causes the residual vibration of
the structure 8 to zero is deducted by putting yk to zero in the formula
(21).
P.sub.io.sup.(j) =b.sub.i (i=1, 2) (29)
As described above, by repetitively identifying the input/output
relationship from the residual vibration data and generating the target
position represented by the time division target parameter which results
in zero residual vibration deducted by the formula (29), the residual
vibration of the structure can be suppressed. In order to identify the
input/output relationship, the input/output data of the time division
target parameter and the residual vibration parameter are required. For
the first learning, at least three different input/output parameters are
required. Accordingly, at the first learning, the movable unit is driven
by at least three different time division target parameters, and the
input/output relationship is identified based on the resulting residual
vibration parameter and time division target parameter.
A learning control method for determining the two parameters, the
displacement X.sub.m to the intermediate target position and the switching
time T.sub.m for generating the time division target position which
suppresses the residual vibration of the structure 8 is explained with
reference to a flow chart of FIG. 14.
For the first learning, the movable unit 4 is positioned to the three
different time division target positions and the residual vibration data
thereof are detected. Based on the three input/output data, the
input/output relationship is identified from the formula (28), and a new
time division target parameter is derived from the formula (29). The
target position is stored in the memory of the target position generation
unit 14. If the number of times of drive is no less than three, the
learning starts from a step 121 of FIG. 14 (FIG. 14 step 12 | | |
