A method of a multi-input multi-output (MIMO) different-factor full-form model-free control, executed on a hardware platform for controlling a controlled plant being a MIMO system, wherein the MIMO system having a predetermined number of control inputs and a predetermined number of system outputs, said controlled plant comprises at least one of:
- a reactor, a distillation column, a machine, a device, a set of equipment, a production line, a workshop, and a factory, said hardware platform comprises at least one of:
- an industrial control computer, a single chip microcomputer controller, a microprocessor controller, a field programmable gate array controller, a digital signal processing controller, an embedded system controller, a programmable logic controller, a distributed control system, a fieldbus control system, an industrial control system based on internet of things, and an industrial internet control system, said method comprising:
- for said MIMO system, calculating a control input vector u(k)=[u1(k), . . . um(k)]T at time k, wherein a i-th control input ui(k) in said control input vector u(k)=[u1(k), . . . , um(k)]T is calculated as follows:
- under a condition that a 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
- f
- +
-
- Φ
- Ly
- +
- 1
-
- (
- k
- )
-
- 2
- +
- ∑
- j
- =
- 1
- n
-
- ϕ
- j
- ,
- i
- ,
- Ly
- +
- 1
-
- (
- k
- )
-
- (
- -
- ∑
- p
- =
- Ly
- +
- 2
- Ly
- +
- Lu
-
- ρ
- i
- ,
- p
-
- (
- ∑
- iu
- =
- 1
- m
-
- ϕ
- j
- ,
- iu
- ,
- p
-
- (
- k
- )
-
- Δ
-
- u
- i
-
- u
-
- (
- k
- +
- L
-
- y
- -
- p
- +
- 1
- )
- )
- )
- λ
- i
- +
-
- Φ
- Ly
- +
- 1
-
- (
- k
- )
-
- 2
- under a condition that a 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
- Ly
- +
- 1
-
- (
- k
- )
-
- 2
- where k is a positive integer;
- m is a total number of control inputs in said MIMO system, m is a positive integer greater than 1;
- n is a total number of system outputs in said MIMO system, n is a positive integer;
- i denotes a i-th of the total number of control inputs in said MIMO system, i is a positive integer, 1≤i≤m;
- j denotes a 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 a j-th error at time k, and a j-th element in error vector e(k)=[e1(k), . . . , en(k)]T;
- Δyjy(k)=yjy(k)−yjy(k−1), yjy(k) is a jy-th actual system output at time k, jy is a positive integer;
- Φ(k) is an estimated value of pseudo partitioned Jacobian matrix for said MIMO system at time k, Φp(k) is a p-th block of Φ(k), ϕj,i,p(k) is a j-th row and a i-th column of matrix Φp(k), ∥ΦLy+1(k)∥ is a 2-norm of matrix ΦLy+1(k);
- p is a positive integer, 1≤p≤Ly+Lu;
- λi is a penalty factor for the i-th control input;
- ρi,p is a p-th step-size factor for the i-th control input;
- Ly is a control output length constant of linearization and Ly is a positive integer;
- Lu is a the control input length constant of linearization and Lu is a positive integer;
- said method has a different-factor characteristic;
- said different-factor characteristic is that at least one of the following inequalities holds true for any two unequal positive integers i and x in a positive integer interval [1, m] during controlling said MIMO system by using said method:
- ρi,1≠ρx,1;
- . . . ;
- ρi,Ly+Lu≠ρx,Ly+Lu;
- λi≠λx;
- where the first inequality is ρi,1≠ρx,1, the (Ly+Lu)-th inequality is ρi,L y+Lu≠ρx,Ly+Lu, and the (Ly+Lu+1)-th inequality is λi≠λx;
- and
- controlling the MIMO system by adjusting the control inputs of the MIMO system based on the calculated control input vector.