CN100595701C - Robust multivariable predicting control method based on uncertain color model - Google Patents

Abstract

This invention relates to one dye machine module formula multi-variable prediction robust bar H infinity control method, which determines one dye machine mode formula multiple step prediction robust Hinfinity control method through data collection, process resolution, prediction control, robust H infinity control technique; using the control method to reduce uncertain factors color impact.

Description

Robust multivariable predicting control method based on uncertain color model

Technical field

The invention belongs to areas of information technology, relate to automatic technology, particularly relate to a kind of robust H of overflow dyeing machine based on the model algorithm multivariable prediction _∞Control method.

Background technology

The final products of dyeing mainly embody with color, and whether the decision finished color satisfies customer requirement, crucial pre-treatment and dyeing link at grey cloth.At home in the pre-treatment of grey cloth, after grey cloth is handled through each operation, obtain half-finished technological parameter instability, the production control parameter that causes dyeing is also unstable, the repeatability that adds the product in man-hour is poor, same prescription different results occurs with the meeting of production for the second time for the first time with the production control parameter, thereby the technical parameter that causes producing lacks confidence level.Color control at present relies on technician's experience fully, production cost is increased and the production cycle lengthening, and effect is very undesirable.The technical equipment of China's dyeing industry is relatively backward again, and energy consumption height, poor performance, automaticity are low, is difficult to adapt to the requirement of market short run, many kinds, high-quality, fast delivery, also is difficult to reach just-in-time production and a secondary accuracy production.More than all factors cause the instability of the control of color in the textile dyeing.

Summary of the invention

Purpose of the present invention is exactly at the deficiencies in the prior art, and a kind of color control method is provided, and specifically is based on the robust H of the multivariable prediction of model algorithm _∞The on-line correction method of the factory formula of control overflow dyeing machine, pressure, the speed of a motor vehicle, temperature.This method has remedied the deficiency of traditional controller, guarantees the stability of closed-loop system, satisfies H simultaneously _∞Performance makes performance index be no more than given chromatic value.

The present invention forms example to a large amount of overflow dyeing machine production instances, pressure, temperature and the rotating speed experimental knowledge of dyeing slip-stick artist's control overflow dyeing machine production are summarized as rule, obtain original pressure, temperature and the rotating speed that overflow dyeing machine is produced by mixed inference, obtain the factory formula that overflow dyeing machine is produced by data mining to example data (containing the sample prescription) based on example and rule.Then, pressure, temperature, rotating speed and half-finished chromatic value by online acquisition is as the input of robust controller, by robust controller calibrating (base measuring) pressure, temperature and rotating speed,, remove controlled pressure, temperature and rotating speed by configuration software the industrial computer of pressure, temperature and rotating speed input.

The step of the inventive method comprises:

1. determine the initial value of control variable, concrete grammar is: utilize overflow dyeing machine to produce example and the rule of the control overflow dyeing machine is produced in dyeing pressure, temperature and rotating speed, obtain original pressure, temperature and rotating speed that overflow dyeing machine is produced; Obtain the initial dyeing recipe that overflow dyeing machine is produced by processing to example data.

The method that obtains original pressure, temperature and the rotating speed of overflow dyeing machine production realizes that by reasoning algorithm this method is a mature technology, is widely used in fields such as medical treatment, chemical industry.Here reasoning algorithm is applied in the textile dyeing.

Obtaining initial dyeing recipe also adopts reasoning algorithm to realize, concrete grammar is: to obtaining historical duplicate sample prescription, historical datas such as board factory formula are set up data warehouse, produce the satisfied needed factory formula data of producing by data acquisition, mode with decision tree is handled the historical data of overflow dyeing machine production, obtains the initial formulation that overflow dyeing machine is produced.

2. set up forecast model, concrete grammar is: at first, with board temperature, pressure, rotating speed is the input data, as output data, sets up the uncertain controlled autoregressive moving average model (CARMA) based on the discrete differential form of least square method with the spectrum chromatic value of online acquisition

$[\hat{A}\left(z^{-1}\right)+\mathrm{\Δ}\hat{A}\left(z^{-1}\right)]y\left(k\right)=[\hat{B}\left(z^{-1}\right)+\mathrm{\Δ}\hat{B}\left(z^{-1}\right)]u\left(k\right)+[\hat{C}\left(z^{-1}\right)+\mathrm{\Δ}\hat{C}\left(z^{-1}\right)]\mathrm{\ζ}\left(k\right)$

Wherein y (k) represents the chromatic value of a certain grey cloth different colours, and a certain grey cloth of u (k) expression is produced the board control variable, and the unknown immesurable error white noise of ζ (k) expression disturbs, With

The known real parameter that expression obtains by identification,

With

The uncertainty of the parameter of expression norm bounded;

Y (k)=[y ₁(k), y ₂(k) ... y _n(k)] ^Ty _i(k) ∈ R ^{N * 1}, i=1 ..., n; U (k)=[u ₁(k), u ₂(k), u ₃(k)] ^T, u ₁(k) ∈ R ^{M * 1}, u ₂(k) ∈ R ^{M * 1}, u ₃(k) ∈ R ^{M * 1}U wherein ₁(k) temperature of board, u are produced in expression ₂(k) pressure of board, u are produced in expression ₃(k) rotating speed of board is produced in expression;

$\hat{A}\left(z^{-1}\right)=1+\underset{i=1}{\overset{n_a}{\mathrm{\Σ}}}{\hat{a}}_i{z}^{-1},$ $\hat{B}\left(z^{-1}\right)=\underset{i=1}{\overset{n_b}{\mathrm{\Σ}}}{\hat{b}}_i{z}^{-1},$ $\hat{C}\left(z^{-1}\right)=\underset{i=1}{\overset{n_c}{\mathrm{\Σ}}}{\hat{c}}_i{z}^{-1},$

$\mathrm{\Δ}\hat{A}\left(z^{-1}\right)=1+\underset{i=1}{\overset{n_a}{\mathrm{\Σ}}}\mathrm{\Δ}{\hat{a}}_i{z}^{-1},$ $\mathrm{\Δ}\hat{B}\left(z^{-1}\right)=\underset{i=1}{\overset{n_b}{\mathrm{\Σ}}}\mathrm{\Δ}{\hat{b}}_i{z}^{-1},$ $\mathrm{\Δ}\hat{C}\left(z^{-1}\right)=\underset{i=1}{\overset{n_c}{\mathrm{\Σ}}}\mathrm{\Δ}{\hat{c}}_i{z}^{-1}$

$\left|\right|\mathrm{\&Delta;}{\hat{a}}_i\left|\right|<{\mathrm{\&omega;}}_{1i}f\left(k\right){\mathrm{\&tau;}}_1,$ $\left|\right|\mathrm{\&Delta;}{\hat{b}}_i\left|\right|<{\mathrm{\&omega;}}_{2i}f\left(k\right){\mathrm{\&tau;}}_2,$ $\left|\right|\mathrm{\&Delta;}{\hat{c}}_i\left|\right|<{\mathrm{\&omega;}}_{3i}f\left(k\right){\mathrm{\&tau;}}_3$

Wherein, ω _1i, ω _2i, ω _3i, τ ₁, τ ₂And τ ₃Be the known real parameter of surveying, f (k) has the uncertainty that Lebesgue can survey unit, satisfies

f ^T(k)f(k)≤1

The parameter minimum model of the dyeing control of setting up is changed into uncertain non-parametric model based on the impulse response transport function, i.e. forecast model

$y_m(k+1)=({\widehat{\mathrm{\&zeta;}}}_1+\mathrm{\&Delta;}{\widehat{\mathrm{\&zeta;}}}_1)u\left(k\right)+({\widehat{\mathrm{\&zeta;}}}_2+{\widehat{\mathrm{\&zeta;}}}_2)u(k-1)+...+({\widehat{\mathrm{\&zeta;}}}_N+\mathrm{\&Delta;}{\widehat{\mathrm{\&zeta;}}}_N)u(k+1-N)$

Wherein $z^{-1}[\hat{g}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{g}\left(z^{-1}\right)]=z^{-1}\frac{\hat{B}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{B}\left(z^{-1}\right)}{\hat{A}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{A}\left(z^{-1}\right)}$

$\frac{\hat{B}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{B}\left(z^{-1}\right)}{\hat{A}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{A}\left(z^{-1}\right)}={\widehat{\mathrm{\&zeta;}}}_{1\mathrm{\&Delta;}}+{\widehat{\mathrm{\&zeta;}}}_{2\mathrm{\&Delta;}}+...{\widehat{\mathrm{\&zeta;}}}_{\mathrm{N\&Delta;}}$

N is the modeling time domain,

The uncertainty of expression norm bounded; And

3. design the robust H of multivariable prediction based on forecast model _∞Controller.At first draw the predicted value of colourity by the forecast model of setting up, by with the comparison of the chroma reference value of reality, set up the H of prediction of output sum of errors controlled quentity controlled variable weighting _∞Quadratic performance index J (k),

$J\left(k\right)=\underset{i=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{q}_i{[y_p(k+i)-y_r(k+i)]}^2+\underset{j=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j{\left[u(k+j-1)\right]}^2$

y _p＝[y _1p(k)，y _2p(k)，…，y _np(k)] ^T，y _ip(k)∈R ^n×1，i＝1，…，n

Y wherein _pThe predicted value of representing a certain grey cloth colourity; y _rThe reference value (chromatic value of sample) of expression colourity; q _i, λ _jThe weighting coefficient of expression multi-step prediction output error and controlled quentity controlled variable.This moment predicated error e _p(k)=y _p(k)-y _r(k), for specified attenuation degree γ, make

$\min J\left(k\right)={\left|\right|Y_p(k+p)-Y_r(k+p)\left|\right|}_Q^{\&infin;}+{\left|\right|U(k+L-1)\left|\right|}_{\mathrm{\&lambda;}}^{\&infin;}$

Wherein p is the prediction time domain, and L is the control time domain,

Y _p(k+p)＝[y _p(k+1)，y _p(k+2)，…y _p(k+p)] ^T，

Y _r(k+p)＝[y _r(k+1)，y _r(k+2)，…y _r(k+p)] ^T，

Secondly, calculate probabilistic optimum control rate, can obtain according to above-mentioned objective function,

Δu(k+i-1)＝[(Ξ+ΔΞ) ^TQ(Ξ+ΔΞ)+λ] ^-1(Ξ+ΔΞ) ^TQ×[Y _r(k+p)-A ₀U(k+L-1)-he(k)]

E (k)=y wherein _p(k)-y _m(k), the expression error prediction model, and

Q＝diag{q ₁，q ₂，…q _n}，λ＝diag{λ ₁，λ ₂，λ ₃}，

U(k+L-1)＝[u(k-L+1)，u(k-L+2)，…u(k-1)] ^T，

$\mathrm{\&Xi;}+\mathrm{\&Delta;\&Xi;}=\left[\begin{array}{ccccc}{\widehat{\mathrm{\&zeta;}}}_{1\mathrm{\&Delta;}}& 0& ...& 0& 0\\ {\widehat{\mathrm{\&zeta;}}}_{2\mathrm{\&Delta;}}& {\widehat{\mathrm{\&zeta;}}}_{1\mathrm{\&Delta;}}& ...& 0& 0\\ .& .& & .& .\\ .& .& & .& .\\ .& .& & .& .\\ {\widehat{\mathrm{\&zeta;}}}_{\mathrm{L\&Delta;}}& {\widehat{\mathrm{\&zeta;}}}_{(L-1)\mathrm{\&Delta;}}& ...& {\widehat{\mathrm{\&zeta;}}}_{2\mathrm{\&Delta;}}& {\widehat{\mathrm{\&zeta;}}}_{1\mathrm{\&Delta;}}\\ .& .& & .& .\\ .& .& & .& .\\ .& .& & .& .\\ {\widehat{\mathrm{\&zeta;}}}_{\mathrm{M\&Delta;}}& {\widehat{\mathrm{\&zeta;}}}_{(M+1)\mathrm{\&Delta;}}& ...& {\widehat{\mathrm{\&zeta;}}}_{(M-L+2)\mathrm{\&Delta;}}& \underset{i=1}{\overset{M-L+1}{\mathrm{\&Sigma;}}}{\widehat{\mathrm{\&zeta;}}}_{\mathrm{i\&Delta;}}\end{array}\right]$

M finally draws probabilistic robust H for optimizing time domain according to Δ u (k+i-1)=u (k+i-1)-u (k+i-2) _∞Control rate u (k), thus best chromatic value obtained, and colourity has asymptotic stability.

Calculating probabilistic optimum prediction control rate carries out as follows:

1. according to calculating

Bound, get

Upper bound substitution formula

2. calculate predicated error e _p(k), if e _p(k)≤0.01, stop to calculate; If e _p(k)＞0.01,, get half of the upper bound according to search principle by half, repeating step 1., up to searching

Lower bound.

At last, the optimal control law that draws, promptly board is produced best pressure, the speed of a motor vehicle, temperature, pressure, temperature and rotating speed is input to pressure, temperature and the rotating speed of industrial computer control overflow dyeing machine again, finishes the The whole control circulation.

It is low to the present invention is directed in the domestic whole dyeing flow automatization level, has a lot of uncertain factors.In order to keep the stability of chromatic value, chromatic value is controlled in certain accuracy rating, for traditional control method, can not satisfy the requirement of technology such as PID, PLC control.In order to reduce the influence of uncertain factor to color, the present invention proposes the on-line correction method of a factory formula, pressure, the speed of a motor vehicle, temperature based on the overflow dyeing machine of the robust H ∞ control of model algorithm multi-step prediction, this method has remedied the deficiency of traditional controller, guarantee the stability of closed-loop system, satisfy H simultaneously _∞Performance makes performance index be no more than given chromatic value.

The control technology that the present invention proposes can effectively reduce the influence of uncertain factor to color, has remedied the deficiency of traditional controller, has guaranteed the stability of closed-loop system, and the chromatic value of dyed color is no more than designated value simultaneously.

Realize that technical scheme of the present invention is by data acquisition, process identification, PREDICTIVE CONTROL, robust H _∞Control technology has been established a kind of robust H based on the model algorithm multi-step prediction of overflow dyeing machine _∞Control method utilizes this control method to reduce the influence of uncertain factor to color.

Embodiment

Below in conjunction with technical scheme, be described in detail the specific embodiment of the present invention.

With certain dyeing workshop number one dyeing unit dyeing course control system is example:

(1) determines initial dyeing recipe and produce pressure, the speed of a motor vehicle, the temperature of the first trial production of board.

The model that concerns between the duplicate sample prescription of utilization foundation dyeing and board factory formula, according to the data of historical duplicate sample prescription and board factory formula and their data relationship, use the method for data processing directly to obtain initial dyeing recipe by the duplicate sample prescription by reasoning algorithm.

Utilize production board controlled variable (pressure, the speed of a motor vehicle, temperature) model and the reasoning algorithm set up, determine pressure, the speed of a motor vehicle, the temperature of the first trial production of production board.

First step inference system requires user's input to desire the kind (corduroy, plain cloth, yarn card etc.) of dying cloth and expecting, color, striped (thick bar, slice etc.) and dye type (intellectual circle, activity etc.), colorant match method (KNB colorant match, KBF colorant match etc.), these belong to the fundamental type information of cloth; Also require the input dry fastness, fastness to wet rubbing and soaping fastness, these belong to the dyeing quality requirement.

During first step reasoning, inference machine is put into inference machine with the above data of user's input, and the suitable rule of extraction is mated from inference machine.The concrete form of rule

The FRAME reasoning of dyeing

The IF cloth==corduroy

The AND color==coffee AND striped==thick bar

The AND dyestuff==active A ND machine number==1

Pressure=2.2 in THEN lathe left side pressure=1.8AND lathe

The right pressure of the AND lathe=1.9 AND driving speed of a motor vehicle=30

First group of drying room temperature=85.5 of AND

Second group of drying room temperature=95 of AND

SECONDIF coloured light==yellow partially dark

SECONDTHEN ADVICE=step-down, air door is turned down

SECONDIF coloured light==glow partially

SECONDTHEN ADVICE=pressurization, air door is transferred big

POSSIBILITY＝0.95

IF wherein ... THEN partly is the reasoning of the first step, and SECONDIF..SECONDTHEN is that the reasoning in second step is used.POSSIBILITY has represented the confidence level of this rule.Intelligence adjustment can be made to confidence level by system.If a plurality of in practice examples all meet this rule, then confidence level rises.If all being inconsistent, a plurality of examples will not cause confidence level to descend.

After the rule-based reasoning, inference machine provides the general parameters value that dyeing needs, and these parameters comprise: first group of drying room temperature, second group of drying room temperature, the driving speed of a motor vehicle, board left side pressure, the right pressure of pressure and board in the board.

After the general parameters value produced, inference machine can call the case-based reasoning module, and this general parameters value is tested, and the purpose of check is the example that whether does not meet this result in the dyeing practice of finding in the past, and quantity and ratio.According to this result the general parameters value is adjusted, obtain the net result of first step reasoning.The concrete form of example

PROPERTY cloth corduroy

The thick bar of PROPERTY striped

PROPERTY color coffee

The PROPERTY dye activity

PROPERTY machine number 1

PROPERTY colorant match method KNB colorant match

PROPERTY board left side pressure 1.8

Pressure 2.2 in the PROPERTY board

The right pressure 1.9 of PROPERTY board

First group of drying room temperature 85.5 of PROPERTY

Second group of drying room temperature 95 of PROPERTY

The PROPERTY driving speed of a motor vehicle 30

The dried moisture capacity non-scald on hand of PROPERTY

Aberration is normal in the PROPERTY limit

PROPERTY coloured light is yellow partially dark

It is even that PROPERTY gets color uniformity

The second step inference system can require to import cloth through after the rough handling, and through the result who detects, the content of detection comprises dried moisture capacity, aberration in the limit, and coloured light gets color uniformity, color plumpness, fastness.System will utilize these data to carry out the secondary reasoning, and the PRELIMINARY RESULTS that had before provided is revised, and provide the control method of each parameter.

(2) utilize the robust H of the multivariable prediction of forecast model design _∞Factory formula, pressure, the speed of a motor vehicle, temperature that board is produced in controller control.

Board is produced according to initial dyeing recipe, temperature, pressure, rotating speed, if the online chromatic value that records does not reach requirement, according to the aberration of half-finished left, center, right, oven dry back, the aberration that speed of a motor vehicle direction is continuous batch is by the robust H based on forecast model _∞Prescription, temperature, pressure, rotating speed that the online correction board of control method is produced are adjusted board factory formula and pressure, the speed of a motor vehicle, temperature.

The forecast model of setting up according to the step 2 of the inventive method and the multivariable prediction robust H of step 3 design _∞Controller, by to dyeing course based on process identification method and dyeing experience, carry out parameter estimation, obtain its parameter matrix and be described below:

i＝1，...，n _a，

i＝1，...，n _b，

i＝1，...，n _c，g _1i＝1，i＝1，...，n _a，g _2i＝0.5，i＝1，...，n _b，

g _3i＝0.4，i＝1，...，n _c，τ _1i＝0.5i ²-i+1，i＝1，2，...，n _a，

τ _2i＝0.01i-0.76，i＝1，2，...，n _b，τ _3i＝0.045，i＝1，2，...n _c，

y _r(k)＝0.3e ^k-2，

Get Q=diag{0.1,0.2 ..., n * 10 ^-1,

$\mathrm{\&lambda;}=\left[\begin{array}{ccccc}0.2& 0.4& 0.8& ...& 2^m\&times;{10}^{-1}\\ 0& 0.4& 0& ...& 0\\ 0& 0& 0.8& ...& 0\end{array}\right]$

According to the step of calculating probabilistic optimum prediction control rate, draw the optimum control rate and be

$u\left(k\right)=\left[\begin{array}{c}{0.15e}^{k-1}-0.26{(k-1)}^2+1\\ 0.24k+0.36e^{k-1}\\ 50\end{array}\right]$

Wherein, u _1k: the Optimal Temperature of production; u _2k: the optimum pressure of production; u _3k: the optimized rotating speed of production.

Claims (2)

1,, it is characterized in that the step of this method comprises based on the robust multivariable predicting control method of uncertain color model:

(1) determine the initial value of control variable, concrete grammar is: utilize overflow dyeing machine to produce example and the rule of the control overflow dyeing machine is produced in dyeing pressure, temperature and rotating speed, obtain original pressure, temperature and rotating speed that overflow dyeing machine is produced; Obtain the initial dyeing recipe that overflow dyeing machine is produced by processing to example data;

(2) set up forecast model, concrete grammar is: at first, with board temperature, pressure, rotating speed is the input data, as output data, sets up the uncertain controlled autoregressive moving average model based on the discrete differential form of least square method with the spectrum chromatic value of online acquisition

$[\hat{A}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{A}\left(z^{-1}\right)]y\left(k\right)=[\hat{B}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{B}\left(z^{-1}\right)]u\left(k\right)+[\hat{C}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{C}\left(z^{-1}\right)]\mathrm{\&zeta;}\left(k\right)$

Wherein y (k) represents the chromatic value of a certain grey cloth different colours, and a certain grey cloth of u (k) expression is produced the board control variable, and the unknown immesurable error white noise of ζ (k) expression disturbs, With

The known real parameter that expression obtains by identification,

With

The uncertainty of the parameter of expression norm bounded;

Y (k)=[y ₁(k), y ₂(k) ... y _n(k)] ^Ty _i(k) ∈ R ^{M * 1}, i=1 ..., n; U (k)=[u ₁(k), u ₂(k), u ₃(k)] ^T, u ₁(k) ∈ R ^{M * 1}, u ₂(k) ∈ R ^{M * 1}, u ₃(k) ∈ R ^{M * 1}U wherein ₁(k) temperature of board, u are produced in expression ₂(k) pressure of board, u are produced in expression ₃(k) rotating speed of board is produced in expression;

$\hat{A}\left(z^{-1}\right)=1+\underset{i=1}{\overset{n_a}{\mathrm{\&Sigma;}}}{\hat{a}}_i{z}^{-1},\hat{B}\left(z^{-1}\right)=\underset{i=1}{\overset{n_b}{\mathrm{\&Sigma;}}}{\hat{b}}_i{z}^{-1},\hat{C}\left(z^{-1}\right)=\underset{i=1}{\overset{n_c}{\mathrm{\&Sigma;}}}{\hat{c}}_i{z}^{-1},$

$\mathrm{\&Delta;}\hat{A}\left(z^{-1}\right)=1+\underset{i=1}{\overset{n_a}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;}\hat{a}}_i{z}^{-1},\mathrm{\&Delta;}\hat{B}\left(z^{-1}\right)=\underset{i=1}{\overset{n_b}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{\hat{b}}_i{z}^{-1},\mathrm{\&Delta;}\hat{C}\left(z^{-1}\right)=\underset{i=1}{\overset{n_c}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{\hat{c}}_i{z}^{-1},$

$\left|\right|\mathrm{\&Delta;}{\hat{a}}_i\left|\right|<{\mathrm{\&omega;}}_{1i}f\left(k\right){\mathrm{\&tau;}}_1,$ $\left|\right|\mathrm{\&Delta;}{\hat{b}}_i\left|\right|<{\mathrm{\&omega;}}_{2i}f\left(k\right){\mathrm{\&tau;}}_2,$ $\left|\right|\mathrm{\&Delta;}{\hat{c}}_i\left|\right|<{\mathrm{\&omega;}}_{3i}f\left(k\right){\mathrm{\&tau;}}_3$

Wherein, ω _1i, ω _2i, ω _3i, τ ₁, τ ₂And τ ₃Be the known real parameter of surveying, f (k) has the uncertainty that Lebesgue can survey unit, satisfies

f ^T(k)f(k)≤1

The parameter minimum model of the dyeing control of setting up is changed into uncertain non-parametric model based on the impulse response transport function, i.e. forecast model

$y_m(k+1)=({\widehat{\mathrm{\&zeta;}}}_1+\mathrm{\&Delta;}{\widehat{\mathrm{\&zeta;}}}_1)u\left(k\right)+({\widehat{\mathrm{\&zeta;}}}_2+\mathrm{\&Delta;}{\widehat{\mathrm{\&zeta;}}}_2)u(k-1)+...+({\widehat{\mathrm{\&zeta;}}}_N+\mathrm{\&Delta;}{\widehat{\mathrm{\&zeta;}}}_N)u(k+1-N)$

Wherein $z^{-1}[\hat{g}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{g}\left(z^{-1}\right)]=z^{-1}\frac{\hat{B}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{B}\left(z^{-1}\right)}{\hat{A}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{A}\left(z^{-1}\right)}$

$\frac{\hat{B}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{B}\left(z^{-1}\right)}{\hat{A}\left(z^{-1}\right)+\mathrm{\&Delta;}\hat{A}\left(z^{-1}\right)}={\widehat{\mathrm{\&zeta;}}}_{1\mathrm{\&Delta;}}+{\widehat{\mathrm{\&zeta;}}}_{2\mathrm{\&Delta;}}+...{\widehat{\mathrm{\&zeta;}}}_{\mathrm{N\&Delta;}}$

I=1 ..., N, N are the modeling time domain,

The uncertainty of expression norm bounded,, and

(3) based on the robust H of forecast model design multivariable prediction _∞Controller at first draws the predicted value of colourity by the forecast model of setting up, by with the comparison of the chroma reference value of reality, set up the H of prediction of output sum of errors controlled quentity controlled variable weighting _∞Quadratic performance index J (k),

$J\left(k\right)=\underset{i=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{q}_i{[y_p(k+i)-y_r(k+i)]}^2+\underset{j=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j{\left[u(k+j-1)\right]}^2,$

y _p＝[y _1p(k)，y _2p(k)，…，y _np(k)] ^T，y _ip(k)∈R ^n×1，i＝1，…，n

Y wherein _pThe predicted value of representing a certain grey cloth colourity; y _rThe reference value of expression colourity; q _i, λ _jThe weighting coefficient of expression multi-step prediction output error and controlled quentity controlled variable, predicated error at this moment

e _p(k)=y _p(k)-y _r(k), for specified attenuation degree γ, make

$\min J\left(k\right)={\left|\right|Y_p(k+p)-Y_r(k+p)\left|\right|}_Q^{\&infin;}+{\left|\right|U(k+L-1)\left|\right|}_{\mathrm{\&lambda;}}^{\&infin;}$

Wherein p is the prediction time domain, and L is the control time domain,

Y _p(k+p)＝[y _p(k+1)，y _p(k+2)，…y _p(k+p)] ^T，

Y _r(k+p)＝[y _r(k+1)，y _r(k+2)，…y _r(k+p)] ^T，

Secondly, calculate probabilistic optimum control rate, obtain according to above-mentioned objective function,

Δu(k+i-1)＝[(Ξ+ΔΞ) ^TQ(Ξ+ΔΞ)+λ] ^-1(Ξ+ΔΞ) ^TQ

×[Y _r(k+p)-A ₀U(k+L-1)-he(k)]

E (k)=y wherein _p(k)-y _m(k), the expression error prediction model, and

Q＝diag{q ₁，q ₂，…q _n}，λ＝diag{λ ₁，λ ₂，λ ₃}，

U(k+L-1)＝[u(k-L+1)，u(k-L+2)，…u(k-1)] ^T，

M is for optimizing time domain; Finally draw probabilistic robust H according to Δ u (k+i-1)=u (k+i-1)-u (k+i-2) _∞Control rate u (k).

2, the robust multivariable predicting control method based on uncertain color model as claimed in claim 1 is characterized in that the probabilistic optimum prediction control rate of described calculating carries out as follows:

1. according to calculating

Bound, get

Upper bound substitution formula

$\frac{\&PartialD;J\left(k\right)}{\&PartialD;U(k+L-1)}=0$

2. calculate predicated error e _p(k), if e _p(k)≤0.01, stop to calculate; If e _p(k)＞0.01,, get half of the upper bound according to search principle by half, repeating step 1., up to searching

Lower bound.