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Claims  |
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What is claimed is:
1. An adaptive control system, for a plant where its input distribution
matrix is known and a number of effective inputs is the same as a number
of independent outputs, comprising:
state output detection means for detecting a state output value of a plant;
known dynamics value production means for producing a known dynamics value
by substituting said state output value of said plant into a known part of
a dynamic equation of said plant;
unknown dynamics value production means for producing an unknown dynamics
value by adding a derivative value of said state output value of said
plant, negative quantity of multiplication of an input value of said plant
and an input distribution matrix value of said plant, and negative
quantity of said known value;
non-identity filtering means, except for a time delay element, for
producing a filtered unknown dynamics value which is close to but not
exactly the same as said unknown dynamics value;
reference state output production means for producing a state output value
of a reference model by substituting an input value of said reference
model into a dynamic equation of said reference model;
error value production means for producing an error value by subtracting
said state output value of said plant from said state output value of said
reference model;
error dynamics adjustment value production means for producting an error
dynamics adjustment value by multiplying said error value and a value of
an error dynamics adjustment matrix;
reference model dynamics value production means for producing a reference
model dynamics value by adding multiplication of said state output value
of said plant and a system matrix value of said reference model, and
multiplication of an input value of said reference model and an input
distribution matrix value of said reference model;
value summation means for producing a summed value by adding negative
quantity of said known dynamics value, negative quantity of said filtered
unknown dynamics value, said reference model dynamics value, and negative
quantity of said error dynamics adjustment value; and
control input value production means for producing a control input value to
said plant by multiplying said summed value and a pseudo-inverse matrix
value of said input distribution matrix of said plant.
2. An adaptive control system as claimed in claim 1, in which said
non-identity filtering means comprises a low-pass filter for producing a
filtered unknown dynamics value which is almost the same as said unknown
dynamics value for low frequencies.
3. An adaptive control system as claimed in claim 1, in which said
non-identity filtering means comprises a band-pass filter for producing a
filtered unknown dynamics value which is the same as said unknown dynamics
value at a certain frequency.
4. An adaptive control system as claimed in claim 1, in which said
non-identity filtering means comprises a non-unity-gain filter for
producing a filtered unknown dynamics value which is the same as said
unknown dynamics value in terms of phase.
5. An adaptive control system as claimed in claim 1, in which said
non-identity filtering means comprises a combination of a sampler for
producing a sampled value of said unknown dynamics value, and a
zero-order-holder for producing a filtered unknown dynamics value which is
equal to said sampled value for a sampling period.
6. An adaptive control system as claimed in claim 1, in which said
non-identity filtering means comprises a combination of a sampler for
producing a sampled value of said unknown dynamics value, a
zero-order-holder for producing a held value which is the same as said
sampled value for a sampling period, and a shift operator for producing a
filtered unknown dynamics value which is the same as said held value if
said unknown dynamics value is shifted into the past by amount of said
sampling period.
7. An adaptive control system, for a plant where its input distribution
matrix is known and a number of effective inputs is the same as a number
of independent outputs, comprising:
state output detection means for detecting a state output value of a plant;
non-identity filtering means for producing a filtered plant input value
which is close to but not exactly the same as an input value of said
plant;
adaptive value production means for producing an adaptive value by
subtracting multiplication of said filtered input value and an input
distribution matrix value of said plant from a derivative value of said
state output value of said plant;
reference state output production means for producing a state output value
of a reference model by substituting an input value of said reference
model into a dynamic equation of a reference model;
error value production means for producing an error value by subtracting
said state output value of said plant from said state output value of said
reference model;
error dynamics adjustment value production means for producing an error
dynamics adjustment value by multiplying said error value and a value of
an error dynamics adjustment matrix;
reference model dynamics value production means for producing a reference
model dynamics value by adding multiplication of said state output value
of said plant and a system matrix value of said reference model, and
multiplication of an input value of said reference model and an input
distribution matrix value of said reference model;
value summation means for producing a summed value by adding negative
quantity of said adaptive value, said reference model dynamics value, and
negative quantity of said error dynamics adjustment value; and
control input value production means for producing a control input value to
said plant by multiplying said summed value and a pseudo-inverse matrix
value of said input distribution matrix of said plant.
8. An adaptive control system as claimed in claim 7, in which said
non-identity filtering means comprises a low-pass filter for producing a
filtered plant input value which is the same as said input value of said
plant for low frequencies.
9. An adaptive control system as claimed in claim 7, in which said
non-identity filtering means comprises a band-pass filter for producing a
filtered plant input value which is the same as said input value of said
plant at a certain frequency.
10. An adaptive control system as claimed in claim 7, in which said
non-identity filtering means comprises a non-unity-gain filter for
producing a filtered plant input value which is the same as said input
value of said plant in terms of phase.
11. An adaptive control system as claimed in claim 7, in which said
non-identity filtering means comprises a combination of a sampler for
producing a sampled value of said input value of said plant, and a
zero-order-holder for producing a filtered input value which is equal to
said sampled value for a sampling period.
12. An adaptive control system as claimed in claim 1, in which said
non-identity filtering means comprises a combination of a sampler for
producing a sampled value of said input value of said plant, a
zero-order-holder for producing a holded value which is the same as said
sampled value for a sampling period, and a shift operator for producing a
filtered plant input value which is the same as said holded value if said
shifted value is shifted into the past by amount of said sampling period.
13. An adaptive control system as claimed in claim 7, in which said
non-identity filtering means comprises a time delay element for producing
a filtered plant input value which is delayed from said input value of
said plant by a certain amount of time.
14. An adaptive control system, for a plant where its input distribution
matrix is known and a number of effective inputs is the same as a number
of independent outputs, comprising:
state output detection means for detecting a state output value of a plant;
known dynamics value production means for producing a known dynamics value
by substituting said state output value of said plant into a known part of
a dynamic equation of said plant;
unknown dynamics value production means for producing an unknown dynamics
value by adding a derivative value of said state output value of said
plant, negative quantity of multiplication of an input value of said plant
and an input distribution matrix value of said plant, and negative
quantity of said known dynamics value;
non-identity filtering means for producing a filtered unknown dynamics
value which is close to but not exactly the same as said unknown dynamics
value;
error value production means for producing an error value by subtracting
said state output value of said plant from a desired state output value
defined as a function of time;
desired error dynamics value production means for producing a desired error
dynamics value by multiplying said error value and a desired error
dynamics matrix value;
value summation means for producing a summed value by adding negative
quantity of said known dynamics value, negative quantity of said filtered
unknown dynamics value, negative quantity of said desired error dynamics
value and a derivative value of said desired state output value; and
control input value production means for producing a control input value to
said plant by multiplying said summed value and a pseudo-inverse matrix
value of said input distribution matrix of said plant.
15. An adaptive control system as claimed in claim 14, in which said
non-identity filtering means comprises a low-pass filter for producing a
filtered unknown dynamics value which is the same as said unknown dynamics
value for low frequencies.
16. An adaptive control system as claimed in claim 14, in which said
non-identity filtering means comprises a band-pass filter for producing a
filtered unknown dynamics value which is the same as said unknown dynamics
value at a certain frequency.
17. An adaptive control system as claimed in claim 14, in which said
non-identity filtering means comprises a non-unity-gain filter for
producing a filtered unknown dynamics value which is the same as said
unknown dynamics value in terms of phase.
18. An adaptive control system as claimed in claim 14, in which said
non-identity filtering means comprises a combination of a sampler for
producing a sampled value of said unknown dynamics value, and a
zero-order-holder for producing a filtered unknown dynamics value which is
equal to said sampled value for a sampling period.
19. An adaptive control system as claimed in claim 14, in which said
non-identity filtering means comprises a combination of a sampler for
producing a sampled value of said unknown dynamics value, a
zero-order-holder for producing a holded value which is the same as said
sampled value for a sampling period, and a shift operator for producing a
filtered unknown dynamics value which is the same as said holded value if
said unknown dynamics value is shifted into the past by amount of said
sampling period.
20. An adaptive control system as claimed in claim 14, in which said
non-identity filtering means comprises a time delay element for producing
a filtered unknown dynamics value which is delayed from said unknown
dynamics value of said plant by a certain amount of time. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to an adaptive control system which controls a
physical plant such as a servo motor, a heat pump and the like with
unknown dynamics and disturbances.
2. Description of the Prior Art
A conventional adaptive control system, the Time Delay Controller (TDC),
has been proposed by K. YOUCEF-TOUMI and O. ITO, the inventor of this
invention, in a paper, "A Time Delay Controller for Systems with Unknown
Dynamics" in pages 904 through 911 of the Proceedings of 1988 American
Control Conference.
The TDC deals with a physical plant expressed in a state space dynamic
equation where an input distribution is known and the number of effective
inputs is the same as the number of independent outputs. For this class of
physical plants, an object of the TDC is to eliminate an error, which is
defined as a difference between a desired output of a reference model and
an actual output of a physical plant. In order to achieve the object, an
unknown dynamics value is estimated using a time delay based on
observation of inputs and state outputs. The TDC cancels the estimated
unknown dynamics value, cancels an undesired known dynamics value, inserts
a desired dynamics value of a reference model, and adjusts dynamics of the
error. The above mentioned paper shows the TDC's excellent robustness
properties to unknown dynamics and disturbances.
However, the TDC has the following three disadvantages from a practical
point of view.
(1) A time delay is difficult to implement.
(2) The controller does not work successfully when either a state output
value, a known dynamics value or an input distribution matrix value
changes quickly.
(3) A reference model is not useful when an output of a physical plant
should continuously follow a certain desired trajectory defined as a
function of time.
SUMMARY OF THE INVENTION
It is the first object of this invention to provide an adaptive control
system which is easy to implement.
It is the second object of this invention to provide an adaptive control
system which works sufficiently even if either a state output value, a
known dynamics value or an input distribution matrix value changes
quickly.
It is the third object of this invention to provide an adaptive control
system which makes a plant output continuously follow a desired trajectory
defined as a function of time.
In order to achieve the first object, the invention provides an adaptive
control system, for a plant where its input distribution matrix is known
and the number of effective inputs is the same as the number of
independent outputs, comprising:
state output detection means for detecting a state output value of a plant;
known dynamics value production means for producing a known dynamics value
by substituting said state output value of said plant into a known part of
a dynamic equation of said plant;
unknown dynamics value production means for producing an unknown dynamics
value by adding a derivative value of said state output value of said
plant, negative quantity of multiplication of an input value of said plant
and an input distribution matrix value of said plant, and negative
quantity of said known value;
non-identity filtering means, except for a time delay element, for
producing a filtered unknown dynamics value which is close to but not
exactly the same as said unknown dynamics value;
reference state output production means for producing a state output value
of a reference model by substituting an input value of said reference
model into a dynamic equation of said reference model;
error value production means for producing an error value by subtracting
said state output value of said plant from said state output value of said
reference model;
error dynamics adjustment value production means for producting an error
dynamics adjustment value by multiplying said error value and a value of
an error dynamics adjustment matrix;
reference model dynamics value production means for producting a reference
model dynamics value by adding multiplication of said state output value
of said plant and a system matrix value of said reference model, and
multiplication of an input value of said reference model and an input
distribution matrix value of said reference model;
value summation means for producing a summed value by adding negative
quantity of said known dynamics value, negative quantity of said filtered
unknown dynamics value, said reference model dynamics value, and negative
quantity of said error dynamics adjustment value; and
control input value production means for producing a control input value to
said plant by multiplying said summed value and a pseudo-inverse matrix
value of said input distribution matrix of said plant.
In order to achieve the second object, the invention provides an adaptive
control system, for a plant where its input distribution matrix is known
and the number of effective inputs is the same as the number of
independent outputs, comprising:
state output detection means for detecting a state output value of a plant;
non-identity filtering means for producing a filtered plant input value
which is close to but not exactly the same as an input value of said
plant;
adaptive value production means for producing an adaptive value by
subtracting multiplication of said filtered input value and an input
distribution matrix value of said plant from a derivative value of said
state output value of said plant;
reference state output production means for producing a state output value
of a reference model by substituting an input value of said reference
model into a dynamic equation of a reference model;
error value production means for producing an error value by subtracting
said state output value of said plant from said state output value of said
reference model;
error dynamics adjustment value production means for producting an error
dynamics adjustment value by multiplying said error value and a value of
an error dynamics adjustment matrix;
reference model dynamics value production means for producing a reference
model dynamics value by adding multiplication of said state output value
of said plant and a system matrix value of said reference model, and
multiplication of an input value of said reference model and an input
distribution matrix value of said reference model;
value summation means for producing a summed value by adding negative
quantity of said adaptive value, said reference model dynamics value, and
negative quantity of said error dynamics adjustment value; and
control input value production means for producing a control input value to
said plant by multiplying said summed value and a pseudo-inverse matrix
value of said input distribution matrix of said plant.
In order to achieve the third object, the invention provides an adaptive
control system, for a plant where its input distribution matrix is known
and the number of effective inputs is the same as the number of
independent outputs, comprising:
state output detection means for detecting a state output value of a plant;
known dynamics value production means for producing a known dynamics value
by substituting said state output value of said plant into a known part of
a dynamic equation of said plant; unknown dynamics value production means
for producing an unknown dynamics value by adding a derivative value of
said state output value of said plant, negative quantity of multiplication
of an input value of said plant and an input distribution matrix value of
said plant, and negative quantity of said known dynamics value;
non-identity filtering means for producing a filtered unknown dynamics
value which is close to but not exactly the same as said unknown dynamics
value;
error value production means for producing an error value by subtracting
said state output value of said plant from a desired state output value
defined as a function of time;
desired error dynamics value production means for producing a desired error
dynamics value by multiplying said error value and a desired error
dynamics matrix value;
value summation means for producing a summed value by adding negative
quantity of said known dynamics value, negative quantity of said filtered
unknown dynamics value, negative quantity of said desired error dynamics
value and a derivative value of said desired state output value; and
control input value production means for producing a control input value to
said plant by multiplying said summed value and a pseudo-inverse matrix
value of said input distribution matrix of said plant.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be better understood from the following description
taken in connection with the accompanying drawings in which:
FIG. 1 is a schematic view showing a conventional motor system which is
controlled by an adaptive control system of the present invention;
FIG. 2 is a block diagram of a servo system embodying the present
invention;
FIGS. 3a and 3b are block diagrams showing feedback loops in FIG. 2;
FIGS. 4a and 4b are simplified block diagrams of FIGS. 3a and 3b,
respectively;
FIGS. 5a through 5c are a block diagram, a frequency response diagram and a
time response diagram, respectively, of a low-pass filter which is used as
a non-identity filter in FIG. 2;
FIGS. 6a through 6c are a block diagram, a frequency response diagram and a
time response diagram, respectively, of a band-pass filter which is used
as a non-identity filter in FIG. 2;
FIGS. 7a through 7c are a block diagram, a frequency response diagram and a
time response diagram, respectively, of a constant gain which is used as a
non-identity filter in FIG. 2;
FIGS. 8a through 8c are a block diagram, a frequency response diagram and a
time response diagram, respectively, of combination of a sampler and a
zero-order-holder which is used as a non-identity filter in FIG. 2;
FIGS. 9a through 9c are a block diagram, a frequency response diagram and a
time response diagram, respectively, of combination of a sampler, a
zero-order-holder and a shift operator which is used as a non-identity
filter in FIG. 2;
FIGS. 10a through 10c are a block diagram, a frequency response diagram and
a time response diagram, respectively, of a time-delay circuit which is
used as a non-identity filter in a conventional adaptive control system;
and
FIGS. 11 through 13 are block diagrams of other servo systems embodying the
present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
A servo system of the present invention in FIG. 2 uses a conventional motor
system as a controlled physical plant whose schematic view is shown in
FIG. 1. In FIG. 1, 101 is a motor, 102 is a rotor with a known inertia
"J", 103 is a damper with an unknown damping coefficient "a", 104 is a
spring with an unknown spring coefficient "b", 105 is a friction board
which applies unknown dry friction "u.sub.d ", 106 is a driving circuit,
and 107 is a motor system which consists of elements 101 through 106.
Also, "y" and "u" represent a rotation angle and an applied torque,
respectively, of motor system 107. Dynamic equation of motor system 107 is
simply expressed as the following:
J(d.sup.2 y/dt.sup.2)+a(dy/dt)+b*y=u+u.sub.d (1)
Eq. (1) can be expressed in a state space form as the following:
(d/dt)x(t)=f(x,t)+h(x,t)+B(x,t)u(t)+d(t) (2)
where
x=[y, (dy/dt)].sup.T is a state output,
f=[(dy/dt), 3].sup.T is a known part of the dynamic equation,
h=[0, -(a/J)*(dy/dt)-(b/J)*y].sup.T is an unknown part of the dynamic
equation,
B=[0, (1/J)].sup.T is a known input distribution matrix, and
d=[0, u.sub.d (t)/J].sup.T is an unknown disturbance.
In motor system 107, the input distribution matrix "B" is known and there
are a single effective input "u" and a single independent output "y".
In FIG. 2, state output measurement device 203, which consists of potential
meter 201 and tachometer 202, measures a state output of motor system 107,
"x(t)=[y(t),dy(t)/dt].sup.T ". Known dynamics value production circuit 204
produces known dynamics value "f(x,t)" by substituting the above measured
"x(t)" into "f(x,t)" in Eq. (2). Unknown dynamics value production circuit
205 produces an unknown dynamics value "w(t)" by adding derivative value
of the measured state output "dx(t)/dt", negative quantity of the known
value "f(x,t)", negative quantity of multiplication of input "u" of motor
system 107 and the known input distribution matrix value "B(x,t)". That
is,
w(t)=dx(t)/dt-f(x,t)-B(x,t)u(t) (3)
It is simply confirmed by combining Eqs. (2) and (3), the produced unknown
dynamics value "w(t)" is exactly equal to an unknown dynamics value
"h(x,t)+d(t)". Non-identity filters 206 filter the unknown dynamics value
"w(t)" into a filtered unknown dynamics value "z(t)". That is,
z(t)=G{w(t)} (4)
where "G{ }" represents a transfer function of non-identity filter 206.
It is clear that the filtered unknown dynamics value "z(t)" exactly
represents the actual unknown dynamics value of motor system 107, if the
following condition is satisfied:
G(s)=1, for all frequencies. (5)
Reference model state output circuit 207 produces a state output value of a
reference model, x.sub.m =[y.sub.m,dy.sub.m /dt].sup.T, based on the
following equation:
(d/dt)x.sub.m (t)=A.sub.m x.sub.m (t)+B.sub.m r(t) (6)
where
A.sub.m is a system matrix,
B.sub.m is an input distribution matrix, and
r is an input.
Error value production circuit 208 produces an error value "e(t)" by
subtracting the above measured "x(t)" from the above produced "x.sub.m
(t)". That is,
e(t)=x.sub.m (t)-x(t). (7)
Error dynamics adjustment value production circuit 209 produces an error
dynamics adjustment value "K*e(t)", where "K" is an error dynamics
adjustment matrix.
Reference model dynamics value production circuit 210 produces a reference
model dynamics value "A.sub.m x(t)+B.sub.m r(t)", using the state output
value "x(t)" measured by state output measurement device 203.
Value summation circuit 211 produces a summed value "s(t)", using the above
measured or produced value by known dynamics value production circuit 204,
non-identity filter 206, reference model dynamics value production circuit
210 and error dynamics adjustment value circuit 209. That is,
s(t)=-f(x,t)-z(t)+A.sub.m x(t)+B.sub.m r(t)-K*e(t). (8)
Finally, control input value production circuit 212 produces a control
input value "u(t)" based on the following equation:
u(t)=B.sup.+ (x,t)*s(t) (9)
=B.sup.+ (x,t){-f(x,t)-z(t)+A.sub.m x(t)+B.sub.m r(t)-K*e(t)}
where
B.sup.+ =(B.sup.T B).sup.-1 B.sup.T =[0,J] is a pseudo-inverse matrix of B.
Unknown dynamics value production circuit 205 consists of addition,
multiplication and differentiation. Reference model state output circuit
207 consists of addition, multiplication and integration. Error value
production circuit 208 consists of addition. Error dynamics adjustment
value production circuit 209 consists of multiplication. Reference model
dynamics value production circuit 210 consists of addition and
multiplication. Value summation circuit 211 consists of addition. Control
input value production circuit 212 consists of multiplication. Therefore,
all these elements 205 and 207 through 212 can be implemented by using
operational amplifiers, digital circuits and/or computer program.
In Eq. (9), which represents adaptive control law of the present invention,
each term has the following function:
"B.sup.+ ", which appears due to control input value production circuit
212, cancels an input distribution matrix "B" of motor system 107;
"-f", which appears due to known dynamics value production circuit 204,
cancels undesired known dynamics;
"-z", which appears due to non-identity filter 206, tries to cancel
undesired known dynamics and disturbance;
"A.sub.m x+B.sub.m r", which appears due to reference model dynamics value
production circuit 210, inserts desired dynamics of a reference model; and
"-K*e", which appears error dynamics adjustment value production circuit
209, adjusts error dynamics into the following desired dynamic equation:
de(t)/dt=A.sub.e *e(t) (10)
where A.sub.e =A.sub.m +K is a system matrix of desired error dynamics.
Eq. (10) can be obtained by substitution of Eq. (9) into Eq. (2) followed
by straight forward algebraic manipulation using Eqs. (3) through (7).
In the above explanation, it was shown that a transfer function "G{ }" of
non-identity filter 206 should satisfy Eq. (5) for precise estimation.
However, it is not clarified yet whether or not it is able to implement an
adaptive control system using the filtered unknown dynamics value "z(t)"
produced by non-identity filter 206.
FIGS. 3a and 3b show feedback loops which have connection with non-identity
filter 206 in FIG. 2. In FIGS. 3a and 3b, "H" represents a transfer
function of motor system 107. FIGS. 3a and 3b can be simplified as FIGS.
4a and 4b, respectively. From FIGS. 4a and 4b, conditions can be derived
as the following, respectively, for an adaptive control system to be able
to implemented.
1-s.sup.2 *J*G(s)*H(s).noteq.0, for a certain frequency (11)
1-G(s).noteq.0, for a certain frequency (12)
Eq. (11) contain "H", a transfer function of motor system 107 and there is
almost no possibility that the left hand side of the equation is exactly
zero for all frequencies. Therefore, it is rational that Eq. (11) are
always satisfied and that Eq. (12) is a single condition in order for the
adaptive control system to be able to be implemented. The following
equation can be simply derived from Eq. (12).
G(s).noteq.1, for a certain frequency. (13)
It is clear that Eq.(13), the condition for implementation and Eq.(5), the
condition for precise estimation can not be simultaneously satisfied.
Therefore, the following practical condition can be obtained by relaxing
the condition of Eq.(5).
G(s).apprxeq.1, for all certain necessary frequencies, and
G(s).noteq.1, for a certain unnecessary frequency. (14)
A filter "G" in Eq.(20) produces an output which is close to, but not
exactly the same to an input, and there are many such filters as shown in
FIGS. 5 through 9.
FIGS. 5a through 5c show a block diagram, frequency response and time
response of low-pass filter 206a which embodies non-identity filter 206 in
FIG. 2. In many practical situations, unknown dynamics and disturbances
exist in low frequencies and low pass filter 206a is an appropriate
embodiment for such cases.
FIGS. 6a through 6c show a block diagram, frequency response and time
response of band-pass filter 206b which embodies non-identity filter 206
in FIG. 2. In some practical situations, an amplitude of disturbance is
not known, but its frequency is known. For such cases, band-pass filter
206b is an appropriate embodiment.
FIGS. 7a through 7c show a block diagram, frequency response and time
response of non-unity-gain filter 206c which embodies non-identity filter
206 in FIG. 2. In some practical situations, unknown dynamics and
disturbances changes very quickly, therefore it is more important that
canceling the uncertainties in respect of its phase than its amplitude.
Non-unity-gain filter 206c is an appropriate embodiment for such cases.
FIGS. 8a through 8c show a block diagram, frequency response and time
response of a combination 206d of a sampler 801 and a zero-order-holder
(ZOH) 802 which combination embodies non-identity filter 206 in FIG. 2. In
many practical situations, an adaptive controller of this invention is
implemented using digital circuits because of its high reliability. Since
a combination 206d of a sampler 801 and a ZOH holder 802 is a standard
element of digital circuits, it is an appropriate embodiment for such
cases.
FIGS. 9a through 9c show a block diagram, frequency response and time
response of a combination 206e of a sampler 801, a ZOH holder 802 and a
shift operator 901 which combination embodies non-identity filter 206 in
FIG. 2. By using computer program, it makes much easier to implement an
adaptive controller of this invention because the adaptive control law of
Eq.(9) can be directly written. However, in this case, time of the
estimation and time of applying the control input signal have to be
separated by an amount of a sampling time in order the computer program to
finish its calculation. Therefore, element 206e is an appropriate
embodiment for such cases.
In contrast with the above explained an adaptive control system of the
present invention, the conventional adaptive control system, which was
proposed in the above referred paper by YOUCEF-TOUMI and ITO, did not
clarify condition of Eq.(14) and gave an only single embodiment--a time
delay circuit--as shown in FIGS. 10a through 10c, thus making difficult to
implement an adaptive control system.
FIG. 11 shows another embodiment of an adaptive control system of the
present invention. In FIG. 11, state output detection device 203 measures
a state output of motor system 107, "x(t)=[y(t),dy(t)/dt]T". Non-identity
filter produces a filtered plant input value which is close to but is not
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