US 2024/0219869 A1 · DYNAMIC DECOUPLING CONTROL METHOD FOR MULTI-DEGREE-OF-FREEDOM PRECISION MOTION STAGE

Abstract

A dynamic decoupling control method for a multi-degree-of-freedom precision comprises defining a dynamic decoupling controller and parameterizing elements in the form of a finite impulse response (FIR) filter, applying a nominal decoupling control method to measure an actual position signal of an actual system and an output of a nominal decoupling controller, calculating a virtual control quantity, and optimizing an indicator function to obtain an estimated value of a coefficient to be optimized of the dynamic decoupling controller. Decoupling at medium and high frequency bands can be effectively realized with improved accuracy of decoupling, and an algorithm flow is simplified. The method is prone to engineering implementation.

A dynamic decoupling control method for a multi-degree-of-freedom precision motion stage, comprising the following steps:

defining a dynamic decoupling controller K(z):
K
⁡
(
z
)
=
[
K
11
⁢
(
z
)
K
12
⁢
(
z
)
…
K
1
⁢
n
⁢
(
z
)
K
21
⁢
(
z
)
K
22
⁢
(
z
)
…
K
2
⁢
n
⁢
(
z
)
⋮
⋮
⋱
⋮
K
n
⁢
1
⁢
(
z
)
K
n
⁢
2
⁢
(
z
)
…
K
nn
⁢
(
z
)
]
wherein z represents a time shift-forward operator, and for a discrete signal x(t), zx(t)=x(t+1), t represents a sampling time, and n represents a number of degrees of freedom of a motion stage;
parameterizing elements in the dynamic decoupling controller in a form of a finite impulse response (FIR) filter:
K
ij
(
z
)
=
θ
ij
,
0
+
θ
ij
,
1
⁢
z
-
1
+
…
+
θ
ij
,
m
⁢
z
-
m
=
Ψ
⁢
θ
ij
wherein m represents an order of the dynamic decoupling controller;
Ψ=[1, z−1, . . . , z−m] is a basis function;
θij=[θij,0, θij,1, . . . , θij,m]T∈Rm+1 is a coefficient to be optimized;
and R represents a real number field;
applying a nominal decoupling control method to measure an actual position signal y=[y1, y2, . . . , yn]T of an actual system and an output d=[d1, d2, . . . , dn]T of a nominal decoupling controller, and calculating a virtual control quantity ũ:
u
~
(
t
)
=
M
-
1
⁢
Ly
=
[
u
~
1
,
u
~
2
,
…
⁢
u
~
n
]
T
wherein M represents an expected diagonal model, and L represents a filter;
applying the virtual control quantity ũ to the dynamic decoupling controller K(z), guaranteeing that an output from the dynamic decoupling controller is equal to a measured output d from the nominal decoupling controller, and enabling the dynamic decoupling controller K(z) to decouple the actual system in the form of the expected diagonal model M;
defining an indicator function:
J
=
∑
t
=
1
N
∑
i
=
1
n
(
d
i
(
t
)
-
∑
j
=
1
n
u
_
j
(
t
)
⁢
θ
ij
)
2
wherein N represents a number of sampling points, and di represents an i-th element in the output from the nominal decoupling controller, ūj(t) represents an information vector, ūj(t)=Ψũj(t)=[ũj(t),ũj(t−1), . . . , ũj(t−m)]∈R1x(m+1), and ũj represents a j-th element in the virtual control quantity;
the indicator function is minimized to obtain an estimated value of the coefficient to be optimized of the dynamic decoupling controller;
and the following parameters are defined in order to simplify an algorithm flow:
D
i
=
[
d
i
(
1
)
,
d
i
(
2
)
,
…
,
d
i
(
N
)
]
T
τ
i
=
[
θ
i
⁢
1
T
,
θ
i
⁢
2
T
,
…
,
θ
i
⁢
n
T
]
T
ϕ
⁢
(
t
)
=
[
u
_
1
(
t
)
,
u
_
2
(
t
)
,
…
,
u
_
n
(
t
)
]
Φ
=
[
φ
⁢
(
1
)
T
,
φ
⁢
(
2
)
T
,
…
,
φ
⁢
(
N
)
T
]
T
decomposing an optimization problem of the indicator function into n optimization subproblems:
J
=
∑
t
=
1
N
∑
i
=
1
n
(
d
i
(
t
)
-
∑
j
=
1
n
u
_
j
(
t
)
⁢
θ
ij
)
2
=
∑
t
=
1
N
∑
i
=
1
n
(
d
i
(
t
)
-
ϕ
⁢
(
t
)
⁢
τ
i
)
2
=
∑
i
=
1
n
(
D
i
-
Φ
⁢
τ
i
)
T
⁢
(
D
i
-
Φ
⁢
τ
i
)
=
∑
i
=
1
n

D
i
-
Φ
⁢
τ
i

2
letting Ji=∥Di−Φτi∥2, and minimizing Ji, i=1, 2, . . . n to obtain an estimated value {circumflex over (τ)}i of parameter τi:
τ
^
i
(
Φ
T
)
-
1
T
D
i
=
[
θ
^
i
⁢
1
T
,
⁢
θ
^
i
⁢
2
T
,
…
,
θ
^
i
⁢
n
T
]
T
thereby obtaining an estimated value {circumflex over (θ)}ij of the coefficient θij to be optimized of element Kij(z) in the i-th row and the j-th column in the dynamic decoupling controller K(z), thus realizing dynamic decoupling control.

440 more elements

Dynamic decoupling control method for multi-degree-of-freedom precision motion stage

Life of this patent

Dynamic decoupling control method for multi-degree-of-freedom precision motion stage

Life of this patent

Abstract

Claims3