US 2020/0249642 A1 · MIMO DIFFERENT-FACTOR FULL-FORM MODEL-FREE CONTROL WITH PARAMETER SELF-TUNING

Abstract

The invention discloses a MIMO different-factor full-form model-free control method with parameter self-tuning. 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. Meanwhile, parameter self-tuning is proposed to effectively address the problem of time-consuming and cost-consuming when tuning the penalty factors and/or step-size factors. Compared with the existing method, the inventive method has higher control accuracy, stronger stability and wider applicability.

A method of MIMO different-factor full-form model-free control with parameter self-tuning, 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
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(
k
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=
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(
k
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(
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under the condition that the control input length constant of linearization Lu=1,
u
i
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(
k
)
=
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(
k
-
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1
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λ
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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
during controlling said MIMO system by using said method, performing parameter self-tuning on the parameters to be tuned in said mathematical formula for calculating the control input vector u(k)=[u1(k), . . . , um(k)]T at time k;
said parameters to be tuned comprise at least one of:
penalty factors λi, and step-size factors ρi,1, . . . , ρi,Ly+Lu (i=1, . . . , m).

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Mimo different-factor full-form model-free control with parameter self-tuning

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Mimo different-factor full-form model-free control with parameter self-tuning

Life of this patent

Abstract

Claims9