MIMO different-factor compact-form model-free control

A method of MIMO different-factor compact-form model-free control, 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 MIMO different-factor compact-form model-free control method comprising:
• calculating the i-th control input ui(k) at time k as follows:
• u
• i
• ⁡
• (
• k
• )
• =
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• i
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• (
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• +
• ρ
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• ⁢
• ∑
• j
• =
• 1
• n
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• ϕ
• j
• ,
• i
• ⁡
• (
• k
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• e
• j
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• λ
• i
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• 
• Φ
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• (
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• 2
• where k is a positive integer;
• 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, where m is the total number of control inputs in said MIMO system and m is a positive integer greater than 1;
• 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;
• 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;
• Φ(k) is the estimated value of pseudo partitioned Jacobian matrix for said MIMO system at time k, ϕji(k) is the j-th row and the i-th column of matrix Φ(k), ∥Φ(k)∥ is the 2-norm of matrix Φ(k);
• λi is the penalty factor for the i-th control input;
• ρi is the step-size factor for the i-th control input;
• for said MIMO system, calculating a control input vector u(k)=[u1(k), . . . ,um(k)]T, by traversing all values of i in the positive integer interval [1, m];
• said MIMO different-factor compact-form model-free control method has a different-factor characteristic;
• said different-factor characteristic is that at least one of the following two 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 MIMO different-factor compact-form model-free control method:
• λi≠λx;ρi≠ρx;
• 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.