FIELD OF THE INVENTION

The present invention relates to the field of automatic control, and more particularly to MIMO different-factor full-form model-free control.

BACKGROUND OF THE INVENTION

In the fields of oil refining, petrochemical, chemical, pharmaceutical, food, paper, water treatment, thermal power, metallurgy, cement, rubber, machinery, and electrical industry, most of the controlled plants, such as reactors, distillation columns, machines, devices, equipment, production lines, workshops and factories, are essentially MIMO systems (multi-input multi-output systems). Realizing the control of MIMO systems with high accuracy, strong stability and wide applicability is of great significance to energy saving, consumption reduction, quality improvement and efficiency enhancement in industries. However, the control problems of MIMO systems, especially of those with strong nonlinearities, have always been a major challenge in the field of automatic control.

MIMO full-form model-free control method is one of the existing control methods for MIMO systems. MIMO full-form model-free control method is a data-driven control method, which is used to analyze and design the controller depending only on the online measured input data and output data instead of any mathematical model information of the MIMO controlled plant, and has good application prospects with concise implementation, low computational burden and strong robustness. The theoretical basis of MIMO full-form model-free control method is proposed by Hou and Jin inModel Free Adaptive Control: Theory and Applications(Science Press, Beijing, China, 2013, p. 116), the control scheme is given as follows:

u⁡(k)=u⁡(k-1)+ΦL⁢y+1T⁡(k)⁢(ρLy+1⁢e⁡(k)-∑p=1L⁢y⁢ρp⁢Φp⁡(k)⁢Δ⁢y⁡(k-p+1))λ+ΦL⁢y+1⁡(k)2-ΦL⁢y+1T⁢(k)⁢∑p=Ly+2L⁢y+L⁢u⁢ρp⁢Φp⁡(k)⁢Δ⁢u⁡(k+L⁢y-p+1)λ+ΦL⁢y+1⁡(k)2

where u(k) is the control input vector at time k, u(k)=[u1(k), . . . , um(k)]T, m is the total number of control inputs (m is a positive integer greater than 1), Δu(k)=u(k)−u(k−1); e(k) is the error vector at time k, e(k)=[e1(k), . . . , en(k)]T, n is the total number of system outputs (n is a positive integer); Δy(k)=y(k)−y(k−1), y(k) is the actual system output vector at time k, y(k)=[y1(k), . . . , yn(k)]T; Φ(k) is the estimated value of pseudo partitioned Jacobian matrix for MIMO system at time k, Φp(k) is the p-th block of Φ(k) (p is a positive integer, 1≤p≤Ly+Lu), ∥ΦLy+1(k)∥ is the 2-norm of matrix ΦLy+1(k); λ is the penalty factor; ρ1, . . . , ρLy+Luare the step-size factors; 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.

The above-mentioned existing MIMO full-form model-free control method adopts the same-factor structure, namely, at time k, different control inputs u1(k), . . . , um(k) in the control input vector u(k) can only use the same value of penalty factor λ, the same value of step-size factor ρ1, . . . , and the same value of step-size factor ρLy+Lu. However, when applied to complex plants, such as strongly nonlinear MIMO systems with different characteristics between control channels, the existing MIMO full-form model-free control method with the same-factor structure is difficult to achieve ideal control performance, which restricts the popularization and application of MIMO full-form model-free control method.

Therefore, in order to break the bottleneck of the existing MIMO full-form model-free control method with the same-factor structure, the present invention proposes a method of MIMO different-factor full-form model-free control.

SUMMARY OF THE INVENTION

The present invention addresses the problems cited above, and provides 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,

ui⁡(k)=ui⁡(k-1)+∑j=1n⁢ϕj,i,Ly+1⁡(k)(ρi,Ly+1⁢ej⁡(k)-∑p=1Ly⁢ρi,p⁡(∑jy=1n⁢ϕj,jy,p⁡(k)⁢Δ⁢⁢yjy⁡(k-p+1)))λi+ΦL⁢y+1⁡(k)2+∑j=1n⁢ϕj,i,Ly+1⁡(k)⁢(-∑p=Ly+2L⁢y+L⁢u⁢ρi,p⁡(∑iu=1m⁢ϕj,iu,p⁡(k)⁢Δ⁢⁢uiu⁡(k+L⁢y-p+1)))λi+ΦL⁢y+1⁡(k)2

under the condition that the control input length constant of linearization Lu=1,

ui⁡(k)=ui⁡(k-1)+∑j=1n⁢ϕj,i,Ly+1⁡(k)(ρi,Ly+1⁢ej⁡(k)-∑p=1Ly⁢ρi,p⁡(∑jy=1n⁢ϕj,jy,p⁡(k)⁢Δ⁢⁢yjy⁡(k-p+1)))λi+ΦL⁢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; uj(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, Φ(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; λiis the penalty factor for the i-th control input; ρi,pis 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)]Tat 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

While adopting the above-mentioned technical scheme, the invention may adopt or combine the following further technical schemes:

Said j-th error ej(k) at time k is calculated by the j-th error function; independent variables of said j-th error function comprise the j-th desired system output and the j-th actual system output.

Said j-th error function adopts at least one of: ej(k)=yj*(k)−yj(k), ej(k)=yj*(k+1)−yj(k), ej(k)=yj(k)−yj*(k), and ej(k)=yj(k)−yj*(k+1), where yj*(k) is the j-th desired system output at time k, yj*(k+1) is the j-th desired system output at time k+1, and yj(k) is the j-th actual system output at time k.

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.

The hardware platform for running said method 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.

The inventive MIMO different-factor full-form model-free control method uses different penalty factors or step-size factors for different control inputs in the control input vector, 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 MIMO full-form model-free control method with the same-factor structure, the inventive MIMO different-factor full-form model-free control method has higher control accuracy, stronger stability and wider applicability.

