US 2020/0249641 A1 · MIMO DIFFERENT-FACTOR FULL-FORM MODEL-FREE CONTROL

Abstract

The invention discloses a MIMO different-factor full-form model-free control method. In view of the limitations of the existing MIMO full-form model-free control method with the same-factor structure, namely, at time k, different control inputs in the control input vector can only use the same values of penalty factor and step-size factors, the invention proposes a MIMO full-form model-free control method with the different-factor structure, namely, at time k, different control inputs in the control input vector can use different values of penalty factors and/or step-size factors, which can solve control problems of strongly nonlinear MIMO systems with different characteristics between control channels widely existing in complex plants. Compared with the existing control method, the inventive method has higher control accuracy, stronger stability and wider applicability.

A method of MIMO different-factor full-form model-free control, the method comprising:

when a controlled plant is a MIMO system, namely a multi-input multi-output system, a mathematical formula for calculating the i-th control input ui(k) at time k using said method is as follows:
under the condition that the control input length constant of linearization Lu>1,
u
i

(
k
)
=
u
i

(
k
-
1
)
+
∑
j
=
1
n

φ
j
,
i
,
Ly
+
1

(
k
)
(
ρ
i
,
Ly
+
1
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e
j

(
k
)
-
∑
p
=
1
Ly

ρ
i
,
p
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(
∑
jy
=
1
n

φ
j
,
jy
,
p
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(
k
)

Δ


y
jy
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(
k
-
p
+
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)
)
)
λ
i
+

Φ
L

y
+
1

(
k
)

2
+
∑
j
=
1
n
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φ
j
,
i
,
Ly
+
1
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(
k
)
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(
-
∑
p
=
Ly
+
2
L

y
+
L
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u
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ρ
i
,
p
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(
∑
iu
=
1
m
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φ
j
,
iu
,
p
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(
k
)
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Δ

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u
iu
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(
k
+
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)
λ
i
+

Φ
L
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y
+
1
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(
k
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
2
under the condition that the control input length constant of linearization Lu=1,
u
i

(
k
)
=
u
i

(
k
-
1
)
+
∑
j
=
1
n

φ
j
,
i
,
Ly
+
1

(
k
)
(
ρ
i
,
Ly
+
1

e
j

(
k
)
-
∑
p
=
1
Ly

ρ
i
,
p

(
∑
jy
=
1
n

φ
j
,
jy
,
p

(
k
)

Δ


y
jy

(
k
-
p
+
1
)
)
)
λ
i
+

Φ
L

y
+
1

(
k
)

2
where k is a positive integer;
m is the total number of control inputs in said MIMO system, m is a positive integer greater than 1;
n is the total number of system outputs in said MIMO system, n is a positive integer;
i denotes the i-th of the total number of control inputs in said MIMO system, i is a positive integer, 1≤i≤m;
j denotes the j-th of the total number of system outputs in said MIMO system, j is a positive integer, 1≤j≤n;
ui(k) is the i-th control input at time k;
Δuiu(k)=uiu(k)−uiu(k−1), iu is a positive integer;
ej(k) is the j-th error at time k, namely the j-th element in the error vector e(k)=[e1(k), . . . ,en(k)]T;
Δyjy(k)=yjy(k)−yjy(k−1), yjy(k) is the jy-th actual system output at time k, jy is a positive integer;
Φ(k) is the estimated value of pseudo partitioned Jacobian matrix for said MIMO system at time k, Φp(k) is the p-th block of Φ(k), ϕj,i,p(k) is the j-th row and the i-th column of matrix Φp(k), ∥ΦLy+1(k)∥ is the 2-norm of matrix ΦLy+1(k);
p is a positive integer, 1≤p≤Ly+Lu;
λi is the penalty factor for the i-th control input;
ρi,p is the p-th step-size factor for the i-th control input;
Ly is the control output length constant of linearization and Ly is a positive integer;
Lu is the control input length constant of linearization and Lu is a positive integer;
for said MIMO system, traversing all values of i in the positive integer interval [1, m], and calculating the control input vector u(k)=[u1(k), . . . , um(k)]T at time k using said method;
said method has a different-factor characteristic;
said different-factor characteristic is that at least one of the following Ly+Lu+1 inequalities holds true for any two unequal positive integers i and x in the positive integer interval [1, m] during controlling said MIMO system by using said method:
λi≠λx;
ρi,1≠ρx,1;
ρi,Ly+Lu≠ρx,Ly+Lu

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Mimo different-factor full-form model-free control

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Mimo different-factor full-form model-free control

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Abstract

Claims5