A method of MIMO different-factor full-form model-free control with parameter self-tuning, executed on a hardware platform for controlling a controlled plant being a multi-input multi-output (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:
- calculating the i-th control input u1(k) at time k as follows:
- under the condition that the control input length constant of linearization Lu>1,
- u
- i
-
- (
- k
- )
- =
- u
- i
-
- (
- k
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- ∑
- j
- =
- 1
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-
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- (
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- ρ
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- =
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- λ
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- Φ
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- 2
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- under the condition that the control input length constant of linearization Lu=1,
- u
- i
-
- (
- k
- )
- =
- u
- i
-
- (
- k
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- 1
- )
- +
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- j
- =
- 1
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- k
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- k
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- 1
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- ∑
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- 1
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- λ
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- Φ
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- γ
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- 1
-
- (
- k
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-
- 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;
- λ1 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, calculating the control input vector u(k)=[u1(k), . . . , um(k)]T by traversing all values of i in the positive integer interval [1, m];
- 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 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);
- and
- obtaining the system outputs from the MIMO system by adjusting the control inputs of the MIMO system based on the calculated control input vector, such that the system outputs of the MIMO system approach desired system outputs to be received by the hardware platform.