Robust digital controller and its designing device
View Patent ↗A robust digital controller is equipped with a high degree of approximation and is able to incorporate a novel two-degree-of-freedom robust digital control system without substantially considering the magnitude of the control inputs and there is provided its designing device. A control compensating means is configured as an integral type control system in which a discrete transfer function W ry (z) between a target value r and a controlled variable y is approximated to a higher-approximate quadratic approximate model transfer function W m (z) and an arithmetic processing can be performed within the digital controller based on the model transfer function W m (z). Further, the designing device automatically calculates parameters constituting the control system. Consequently, a robust digital controller can be easily realized that is equipped with a high degree of approximation as compared with a conventional approximate digital control system for realizing a first-order model and is robust against output noises.
1. A designing device of a robust digital controller, wherein said designing device realizes an integral type control system that is obtained by equivalently converting a system and is connected with a control target satisfying the following state equation 5 when an input h, a controlled variable y, a first equivalent disturbance q v , a second equivalent disturbance q v and a time-lag ξ 1 are given respectively:
x d ( k+ 1)= A d x d ( k )+ B d h ( k )
y ( k )= C d x d ( k )+ q y ( k )
where x d =[xξ] T Equation 5
wherein aid system converted is formed by approximating a transfer function W ry (z) between a target value r and said controlled variable y when a state feedback rule and a feedforward rule are applied to said control target to determine a quadratic approximate model transfer function W m (z) shown in the following equation 6:
W
ry
=
(
1
+
H
1
)
(
1
+
H
2
)
(
1
+
H
3
)
(
z
-
n
1
)
(
z
-
n
2
)
(
z
+
H
4
)
(
1
-
n
1
)
(
1
-
n
2
)
(
z
+
H
1
)
(
z
+
H
2
)
(
z
+
H
3
)
(
z
+
H
4
)
≈
W
m
(
z
)
=
(
1
+
H
1
)
(
z
+
H
1
)
Equation
6
(where z=exp (jωt); n 0 , n 1 , n 2 are zeros; and H 1 , H 2 , H 3 , H 4 are poles.) and then by combining the model transfer function W m (z), an inverse function W m (z) −1 of said model transfer function W m (z) and a dynamic compensator K(z) with characteristics, shown in the equation 7, for realizing the inverse function W m (z) −1 :
k
(
z
)
=
k
z
z
-
1
+
k
z
Equation
7
said integral type control system, further comprising:
a first feedback means configured to output a product of said controlled variable y and parameter k 1 ,
a second feedback means configured to output a product of said controlled variable y and parameter k 2 ,
a third feedback means configured to output a product of a first time-lag output ξ 1 and parameter k 3 ,
a fourth feedback configured to output a product of a second time-lag output ξ 2 and parameter k 4 ,
a fifth feedback means configured to output a product of a third time-lag output ξ 3 and a parameter k 5 ,
a sixth feedback means configured to output a product of said controlled variable y and parameter k 6 ,
a first arithmetic means configured to calculate a difference between said controlled variable y and said target value r,
an integrating means configured to integrate the calculated value from the first arithmetic means to covert the integrated value into a fourth time-lag output ξ 4 ,
a first accumulating means configured to output a product of a fourth time-lag output ξ 4 from said integrating means and parameter k in ,
a first adding means configured to add an output from said first accumulating means, an output from said fifth feedback means and an output from said sixth feedback means,
a first time-lag means configured to output said third time-lag output ξ 3 that has made the added result from said first adding means undergo a sampling time-lag,
a second accumulating means configured to output a product of a third time-lag output ξ 3 and a parameter k i ,
a third accumulating means configured to output a product of a third time-lag output ξ 3 and a parameter k iz ,
a second adding means configured to add said second equivalent disturbance q v , an output from said second accumulating means, an output from said first feedback means, an output from said third feedback means and an output from said fourth feedback means,
a second time-lag means configured to output said second time-lag output ξ 2 that has made the added result from said second adding means undergo a sampling time-lag,
a third adding means configured to add an output from said second time-lag means, an output from said third accumulating means and an output from said second feedback means to produce an input h to said control target, wherein each parameter is expressed as equation 8 when said state feedback rule F=[F(1,1) F(1,2) F(1,3) F(1,4)] and said feedforward rule G have been applied:
k
1
=
-
F
(
1
,
1
)
-
F
(
1
,
2
)
FF
(
1
,
1
)
+
(
(
-
F
(
1
,
4
)
-
F
(
1
,
2
)
FF
(
1
,
4
)
)
(
-
F
(
1
,
2
)
/
FF
(
1
,
2
)
)
)
-
(
GH
4
+
GF
z
)
(
(
1
-
n
0
)
k
z
/
(
(
1
+
H
1
)
(
1
+
H
2
)
)
)
k
2
=
-
F
(
1
,
2
)
/
FF
(
1
,
2
)
-
G
(
(
1
-
n
0
)
k
z
/
(
(
1
+
H
1
)
(
1
+
H
2
)
)
)
k
3
=
-
F
(
1
,
3
)
-
F
(
1
,
2
)
(
FF
(
1
,
3
)
)
k
4
=
F
z
k
5
=
n
0
k
6
=
-
(
k
z
(
1
-
n
0
)
(
1
+
H
1
+
H
2
)
+
n
0
(
1
-
n
0
)
k
z
)
/
(
(
1
+
H
1
)
*
(
1
+
H
2
)
)
k
i
=
GH
4
+
GF
z
k
iz
=
G
k
i
n
=
k
z
(
1
-
n
0
)
FF
(
1
,
1
)
=
-
A
d
(
1
,
1
)
/
A
d
(
1
,
2
)
FF
(
1
,
2
)
=
A
d
(
1
,
2
)
FF
(
1
,
3
)
=
-
A
d
(
1
,
3
)
/
A
d
(
1
,
2
)
FF
(
1
,
4
)
=
-
B
d
(
1
,
1
)
/
A
d
(
1
,
2
)
F
z
=
-
F
(
1
,
4
)
-
F
(
1
,
2
)
FF
(
1
,
4
)
Equation
8
wherein said designing device comprises:
a parameter specifying means configured to specify pole values H 1 , H 2 , zero values n 1 , n 2 of said control target in a discrete-time and parameter values p 1 , p 2 , p 3 , k z ,
an undetermined value calculating means configured to calculate each of undetermined values of a zero n 0 and pole H 3 from the following relational equation shown in equation 9 by using each of the pole values specified by said parameter specifying means:
(
-
n
1
(
-
n
0
)
-
n
2
(
-
n
0
)
+
H
3
n
1
n
2
-
n
2
H
3
-
H
3
n
1
+
k
z
(
-
n
0
)
H
3
+
n
1
n
2
(
-
n
0
)
+
k
z
-
1
-
n
1
n
2
+
k
z
(
-
n
0
)
+
H
3
+
n
1
+
n
2
+
k
z
H
3
+
(
-
n
0
)
)
/
(
1
-
n
2
-
n
1
+
n
1
n
2
)
=
-
(
p
1
+
p
3
+
p
2
)
Equation
9
(
-
k
z
n
1
(
-
n
0
)
-
k
z
n
2
(
-
n
0
)
H
3
-
H
3
n
1
n
2
+
(
-
n
0
)
H
3
+
n
1
n
2
(
-
n
0
)
H
3
+
H
3
n
1
-
n
2
(
-
n
0
)
H
3
-
H
3
-
k
z
n
1
H
3
-
k
z
n
2
H
3
-
k
z
n
2
(
-
n
0
)
-
k
z
n
1
-
k
z
n
2
-
n
1
(
-
n
0
)
H
3
-
n
1
n
2
(
-
n
0
)
+
n
2
(
-
n
0
)
+
n
2
H
3
+
n
1
(
-
n
0
)
-
(
-
n
0
)
-
k
z
n
1
(
-
n
0
)
H
3
)
/
(
1
-
n
2
-
n
1
+
n
1
n
2
)
=
p
1
p
3
+
p
1
p
2
+
p
2
p
3
(
k
z
n
1
n
2
(
-
n
0
)
-
(
-
n
0
)
H
3
+
k
z
H
3
n
1
n
2
+
k
z
n
1
n
2
(
-
n
0
)
H
3
+
n
2
(
-
n
0
)
H
3
+
n
1
(
-
n
0
)
H
3
-
n
1
n
2
(
-
n
0
)
H
3
+
k
z
n
1
n
2
)
/
(
1
-
n
2
-
n
1
+
n
1
n
2
)
=
-
p
1
p
2
p
3
a controller parameter determining means configured to calculate each of parameter values k 1 , k 2 , k 3 , k 4 , k 5 , k 6 , k i , k iz , k in that constitute said integral type control system by using each of the undetermined values from said undetermined value calculating means; and
a controller parameter outputting means configured to output each of the parameter values calculated by said controller parameter determining means to said robust digital controller.
2. A designing device of a robust digital controller according to claim 1 , wherein an integral type control system incorporated into said robust digital controller, further comprising:
a first feedforward means configured to output a product of said target value r and parameter k 1r ,
a second feedforward means configured to output a product of said target value r and parameter k 2r ,
a third feedforward means configured to output a product of said target value r and parameter k 3r , wherein
an output of said third feedforward means is further added by the first adding means,
an output of said second feedforward means is further added by the second adding means,
an output of said first feedforward means is further added by the third adding means, wherein
when said parameters are made up so as to satisfy k 1r =G, k 2r =GH 4 +GF z , k 3r =k z , said controller parameter determining means calculates each of parameter values k 1 , k 2 , k 3 , k 4 , k 5 , k 6 , k 1r , k 2r , k 3r , k i , k iz , k in by using each of the undetermined values from said undetermined value calculating means.
3. A designing device of a robust digital controller according to claim 1 , wherein said designing device further comprises:
a characteristic judgment means configured to judge whether each of the parameter values calculated in said controller parameter determining means has been incorporated into said robust digital controller to judge whether desired characteristics can be obtained or not when said control target is controlled by the robust digital controller,
a parameter respecifying means configured to trigger said parameter specifying means to specify different parameter values p 1 , p 2 , p 3 , k z , when said characteristic judgment means has judged that no desired characteristic could be obtained and then making said controller parameter determining means calculate again the parameter values.
4. A designing device of a robust digital controller according to claim 3 , further comprising a controller parameter outputting means configured to output each of parameter values calculated in said controller parameter determining means to said robust digital controller when said characteristic judgment means has judged that desired characteristics have been obtained.
5. A designing device of a robust digital controller wherein said designing device realizes an integral type control system that is obtained by equivalently converting a system and is connected with a control target satisfying state equation 10 when an input h, a controlled variable y, a first equivalent disturbance q y , a second equivalent disturbance q v and a time-lag ξ 1 are given respectively:
x d ( k+ 1)= A d x d ( k )+ B d h ( k )
y ( k )= C d x d ( k )+ q y ( k )
wherein x d =[xξ] T Equation 10
wherein said system converted is formed by approximating a transfer function W ry (z) between a target value r and said controlled variable y when a state feedback rule and a feedforward rule are applied to said control target to determine a quadratic approximate model transfer function W m (z) shown in following equation 11,
W
ry
=
(
1
+
H
1
)
(
1
+
H
2
)
(
1
+
H
3
)
(
z
-
n
1
)
(
z
-
n
2
)
(
z
+
H
4
)
(
1
-
n
1
)
(
1
-
n
2
)
(
z
+
H
1
)
(
z
+
H
2
)
(
z
+
H
3
)
(
z
+
H
4
)
≈
W
m
=
(
1
+
H
1
)
(
1
+
H
2
)
(
z
-
n
0
)
(
z
+
H
1
)
(
z
+
H
2
)
(
1
-
n
0
)
Equation
11
(where z=exp (jωt); n 0 , n 1 , are zeros; and H 1 , H 2 , H 3 , H 4 are poles.)
and then by combining the model transfer function W m (z), an inverse function W m (z) −1 of said model transfer function W m (z) and a dynamic compensator K(z) that has characteristics, shown in equation 12, for realizing the inverse function W m (z) −1 ,
k
(
z
)
=
k
z
z
-
1
+
k
z
Equation
12
said integral type control system, further comprising:
a first feedback means configured to output a product of said controlled variable y and parameter k 1 ,
a second feedback means configured to output a product of said controlled variable y and parameter k 2 ,
a third feedback means configured to output a product of a first time-lag output ξ 1 and parameter k 3 ,
a fourth feedback means configured to output a product of a second time-lag output ξ 2 and parameter k 4 ,
a fifth feedback means configured to output a product of said controlled variable y and 1/g (g denotes a steady-state gain between a target value r and a controlled variable y),
a first calculating means configured to calculate a difference between said controlled variable y and an output of the fifth feedback means,
an integrating means configured to integrate the calculated value from the first calculating means to covert the calculated value into an integrated output,
a first accumulating means for outputting a product of an output from said integrating means and an output of parameter k i1 ,
a second accumulating means configured to output a product of an output from said integrating means and an output of parameter k i2 ,
a first adding means configured to add said second equivalent disturbance q v , an output from said second accumulating means, an output from said first feedback means, an output from said third feedback means and an output from said fourth feedback means,
a time-lag means configured to sample an added result from said first adding means into said second time-lag output ξ 2 ,
a second adding means configured to add an output from said time-lag means, an output from said first accumulating means and an output from said second feedback means to produce an input η to said control target,
wherein each parameter is expressed as equation 13 when said state feedback rule F=[F(1,1) F(1,2) F(1,3) F(1,4)] and said feedforward rule G have been applied:
k
1
=
F
(
1
,
1
)
-
F
(
1
,
2
)
A
d
(
1
,
1
)
/
A
d
(
1
,
2
)
+
(
-
F
(
1
,
4
)
+
F
(
1
,
2
)
B
d
(
1
,
1
)
/
A
d
(
1
,
2
)
)
F
(
1
,
2
)
/
A
d
(
1
,
2
)
+
(
GH
4
+
G
(
-
F
(
1
,
4
)
+
F
(
1
,
2
)
B
d
(
1
,
1
)
/
A
d
(
1
,
2
)
)
)
k
z
/
(
1
+
H
2
)
k
2
=
F
(
1
,
2
)
/
A
d
(
1
,
2
)
+
Gk
z
/
(
1
+
H
2
)
k
3
=
F
(
1
,
3
)
-
F
(
1
,
2
)
A
d
(
1
,
3
)
/
A
d
(
1
,
2
)
k
4
=
F
(
1
,
4
)
-
F
(
1
,
2
)
B
d
(
1
,
1
)
/
A
d
(
1
,
2
)
k
i
1
=
gGk
z
k
i
2
=
g
(
GH
4
+
G
(
-
F
(
1
,
4
)
+
F
(
1
,
2
)
B
d
(
1
,
1
)
/
A
d
(
1
,
2
)
)
)
k
z
Equation
13
wherein said designing device comprises:
a parameter specifying means configured to specify pole values H 1 , H 4 , zero values n 1 , n 2 of said control target in a discrete-time and parameter values p 1 , p 2 , p 3 , k z ,
an undetermined value calculating means configured to calculate each of undetermined values of H 2 =x+yi, H 3 =x−yi from the following relational equation shown in equation 14, by using each of the values specified by said parameter specifying means:
(
k
z
x
2
+
(
2
k
z
-
2
n
2
+
2
n
1
n
2
-
2
n
1
+
2
)
x
+
k
z
y
2
+
(
-
1
+
n
2
+
k
z
-
n
1
n
2
+
n
1
)
)
/
(
1
-
n
2
-
n
1
+
n
1
n
2
)
=
-
p
1
-
p
3
-
p
2
(
(
-
k
z
n
1
+
n
1
n
2
-
n
2
+
1
-
n
1
-
k
z
n
2
)
x
2
+
(
2
n
2
+
2
n
1
-
2
k
z
n
2
-
2
n
1
n
2
-
2
k
z
n
1
-
2
)
x
+
(
-
k
z
n
1
+
n
1
n
2
-
n
2
+
1
-
n
1
-
k
z
n
2
)
y
2
-
k
z
n
2
-
k
z
n
1
)
/
(
1
-
n
2
-
n
1
+
n
1
n
2
)
=
p
1
p
3
+
p
1
p
2
+
p
2
p
3
(
(
-
1
+
n
2
+
k
z
n
1
n
2
-
n
1
n
2
+
n
1
)
x
2
+
2
k
z
n
1
n
2
x
+
(
-
1
+
n
2
+
k
z
n
1
n
2
-
n
1
n
2
+
n
1
)
y
2
+
k
z
n
1
n
2
)
(
1
-
n
2
-
n
1
+
n
1
n
2
)
=
-
p
1
p
2
p
3
Equation
14
a controller parameter determining means configured to calculate each of parameter values k 1 , k 2 , k 3 , k 4 , k i1 , k i2 that constitute said integral type control system by using each of the undetermined values from said undetermined value calculating means; and
a controller parameter outputting means configured to output each of the parameter values calculated by said controller parameter determining means to said robust digital controller.
6. A designing device of a robust digital controller according to claim 5 , wherein said integral type control system incorporated into said robust digital controller, comprising:
a first feedforward means configured to output a product of said target value r and parameter k r1 ,
a second feedforward means configured to output a product of said target value r and parameter k r2 , wherein
an output of said second feedforward means are added by the first adding means,
an output of said first feedforward means are added by the second adding means,
when said parameters are made up so as to satisfy k r1 =gG, k r2 =g(GH 4 +G(−F(1,4)+F(1,2)B d (1,1)/A d (1,2))),
said controller parameter determining means is configured to calculate each of said parameter values k 1 , k 2 , k 3 , k 4 , k r1 , k r2 , k i1 , k i2 , by using each of undetermined values from said undetermined value calculating means.
7. A designing device of a robust digital controller according to claim 5 , wherein said designing device is further equipped with:
a characteristic judgment means configured to judge whether each of the parameter values calculated in said controller parameter determining means has been incorporated into said robust digital controller to judge whether desired characteristics can be obtained or not when said control target is controlled by the robust digital controller,
a parameter respecifying means configured to trigger said parameter specifying means specify different parameter values p 1 , p 2 , p 3 , k z , when said characteristic judgment means has judged that no desired characteristic could be obtained and then making said controller parameter determining means calculate again the parameter values.
8. A designing device of a robust digital controller according to claim 7 , further comprising a controller parameter outputting means configured to output each of parameter values calculated in said controller parameter determining means to said robust digital controller when said characteristic judgment means has judged that desired characteristics have been obtained.