CN100552574C - Machine group loading forecast control method based on flow model - Google Patents

Abstract

A kind of machine group loading forecast control method based on flow model, belong to automatic control, infotech and advanced manufacturing field, be specifically related to before and after have twice bottleneck operation and per pass bottleneck operation and exist in the complicated production manufacture process of many group machine groups, it is characterized in that may further comprise the steps: the timing sampling of machine group load in road, the back bottleneck operation the forecast Control Algorithm of back road each machine group load of bottleneck operation, back road bottleneck operation machine group load expectation value is determined, back road bottleneck operation machine group load d rank predictive control model is set up and preceding road bottleneck operation machine group controlled variable is asked for.The present invention is based on flow model and Adaptive Neuro-fuzzy Inference and set up road, back each machine group load estimation controlling models of bottleneck operation, and the quadratic sum minimum of the difference of road each machine group actual loading of bottleneck operation later on and expectation load is the optimal control target, adopt the Lagrange relaxation method, provide the task output rating of preceding road each machine group of bottleneck operation, to improve production performance.

Description

Machine group loading forecast control method based on flow model

Technical field

The invention belongs to automatic control, infotech and advanced manufacturing field.Be specifically related to a class have before and after twice bottleneck operation and per pass bottleneck operation have in the complicated production manufacture process of many group machine groups method for load predicative control to each machine group of bottleneck operation.

Background technology

Twice bottleneck operation and per pass bottleneck operation exist in the complicated production manufacture process of many group machine groups before and after a class has, owing to exist on a large scale at goods processing flow phenomenon at twice bottleneck inter process, if machine group task output rating in the preceding road bottleneck operation is lacked effectively control, to make back road each machine group load of bottleneck operation can't arrive expectation value, influence production performance.Therefore, in above-mentioned manufacturing process, according to the working ability of forward and backward road each machine group of bottleneck in-process and the expectation load of road each machine group of bottleneck in-process afterwards, road each machine group actual loading of bottleneck operation later on is minimum with the quadratic sum of expectation load difference to be the optimal control target, determine task output rating in preceding road each machine group of bottleneck operation, with road each machine group load of bottleneck operation after controlling, thereby improve production performance.At present, conventional machine loading control method mostly is heuristic control method greatly, as when certain machine group load in road, the front and back bottleneck operation is big, then in preceding road bottleneck operation, reduce the task amount that flows to this machine group, but because twice bottleneck inter process exists the processing of middle non-bottleneck operation to postpone, and above-mentioned heuristic forecast Control Algorithm lacks the effective forecasting mechanism of back road bottleneck operation machine group load, thereby adopts said method to be difficult to realize effective control to back road bottleneck operation machine group load.

Summary of the invention

In order to solve in the above-mentioned complicated production manufacture process deficiency of road, back each machine group load control method of bottleneck operation, the invention provides a kind of have before and after twice bottleneck operation and per pass bottleneck operation have in the complicated production manufacture process of many group machine groups machine group loading forecast control method (abbreviating AFFC as) based on flow model.In the present invention, flow model is mainly used in investigates the charge capacity (being production task summation process time) that each machine group is processed and finished in the unit interval, because the operation of twice bottleneck inter process is non-bottleneck operation (hereinafter referred is middle operation) in the above-mentioned complex process, production task is compared much smaller (can ignore) during through middle operation its stand-by period with process time, so angle from flow model, after production load the past road bottleneck operation (hereinafter referred is a preceding working procedure) flows into middle operation, only need can flow to back road bottleneck operation (hereinafter referred is a later process) (as shown in Figure 2) from middle operation through after certain time delay.The present invention is based on flow model and set up later process machine group load 1 rank predictive control model, adopt ANFIS (Adaptive Neuro-fuzzy Inference) to set up later process machine group load d rank nonlinear prediction controlling models on this basis, it is input as current time preceding working procedure task output rating, be output as the later process machine group load of d after the moment, on above-mentioned predictive control model basis, according to d each machine group load expectation value of later process and each machine group working ability of front and back procedure after the moment, determine the task output rating of each machine group of preceding working procedure, make the quadratic sum minimum of difference of the actual loading of later process machine group and expectation load, thereby improve road, back bottleneck operation production performance.

Based on the machine group loading forecast control method of flow model, it is characterized in that described method realizes successively according to the following steps on machine group load estimation control computer:

Step (1): initialization, set following parameter

Sampling time interval provides each machine group task output rating in the preceding working procedure every time interval T, and described machine group is made up of many similar machines of working ability, and sampling instant is then represented with k;

Machine group working ability is summation process time of the processing tasks that can finish in unit interval inner machine group, the working ability u of machine group i in the preceding working procedure _iExpression, i=1 ..., m is expressed in matrix as U=[u ₁, u ₂..., u _m] ^T, the working ability v of machine group j in the later process _jExpression, j=1 ..., n is expressed in matrix as V=[v ₁, v ₂..., v _n] ^T, m and n are respectively the number of machine group in the forward and backward procedure;

Preceding working procedure machine group task output rating, preceding working procedure machine group i constrains in the task that the k sampling instant machines based on production technology and is arranged to the ratio of later process by machine group j processing, uses c _Ij(k) expression is expressed in matrix as:

$C{\left(k\right)}^{n\×m}={[C_1\left(k\right),C_2\left(k\right),...,C_n\left(k\right)]}^T$

$=[C^1\left(k\right),C^2\left(k\right),...,C^m\left(k\right)]$

$=\left[\begin{array}{cccc}{c}_{11}\left(k\right)& c_{21}\left(k\right)& ...& c_{m1}\left(k\right)\\ c_{12}\left(k\right)& c_{22}\left(k\right)& ...& c_{m2}\left(k\right)\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ c_{1n}\left(k\right)& c_{2n}\left(k\right)& ...& c_{\mathrm{mn}}\left(k\right)\end{array}\right]$

0≤c wherein _Ij≤ 1 and $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{c}_{\mathrm{ij}}=1,$ i＝1，…，m；j＝1，…，n；

The load of machine group, summation process time of wait processing tasks before certain machine group in the operation, later process machine group j is shown y at k loading liquifier constantly _j(k), be expressed in matrix as Y (k) ^{N * 1}=[y ₁(k), y ₂(k) ..., y _n(k)] ^T

Machine group j is expressed as y in k machine loading expectation value constantly in the later process _j ^r(k), be expressed in matrix as

$Y^r{\left(k\right)}^{n\×1}={[y_1^r\left(k\right),y_2^r\left(k\right),...y_n^r\left(k\right)]}^T;$

The processing of middle operation represents that it is meant task from the preceding working procedure completion of processing time delay with d, by the processing of middle operation, arrive the used averaging time unit of later process, contains the stand-by period;

Given control cycle T _AllExpression;

Control cycle T _AllThe total load Load of interior later process machine group j _jExpression;

Step (2): gather machine group load real-time information with machine group load information harvester, machine group load information harvester is constituted by a kind of in PLC harvester, embedded system harvester, the DCS system acquisition device or they;

Step (3): the read machine group load real-time information from described harvester of described machine group load estimation control computer, carry out the control of machine group load estimation successively according to the following steps:

Step (3.1): determine each sampling interval each machine group load expectation value y of later process in the time by following formula _j ^r(k),

$y_j^r\left(k\right)=\frac{{\mathrm{Load}}_j}{T_{\mathrm{all}}/T},j=1,...,n$

Step (3.2): set up later process machine group load estimation control problem by following formula:

$J(k+d+1)=\frac{1}{2}[Y(k+d+1)-Y^r(k+d+1){]}^T\·[Y(k+d+1)-Y^r(k+d+1)]$

$+\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{C}^i{\left(k\right)}^T\·C^i\left(k\right)$

Ask control law C (k), make min{J (k+d+1), wherein all i are satisfied AC ⁱ(k)=1, A=[1,1 ..., 1] ^{1 * m}

Step (3.3): set up later process machine group load estimation controlling models by following step

Step (3.3.1): set up later process machine group load 1 rank predictive control model

y _j(k+1)＝max{y _j(k)-v _jT+[c _1j(k-d)u ₁+…+c _mj(k-d)u _m]T，0}

＝max{y _j(k)-Tv _j+TC _j(k-d)U，0}，j＝1，…，n

Step (3.3.2): adopt Adaptive Neuro-fuzzy Inference ANFIS to set up later process machine group load d rank predictive control model with L bar fuzzy rule

That is:

$Y{(k+d+1)}^{n\×1}=X^{n\×1}+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{N}_q^{n\×n}\·[C^1(k-d+q),...,C^m(k-d+q){]}^{n\×m}\·U^{m\×1}$

$=X^{n\×1}+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{N}_q^{n\×n}\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i(k-d+q)$

Wherein: X ^{N * 1}=[E ₁, E ₂..., E _n] ^T, $E_j=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{h}_l\left(k\right)\·[{\mathrm{\α}}^l(y_j\left(k\right)-{\mathrm{Tv}}_j)+{\mathrm{\β}}^l]$

q＝0，1，…，d， $F_{\mathrm{jq}}=T\·\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{h}_l\left(k\right){\mathrm{\γ}}_q^l,$

h _l(k)=f _l(y _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) be that ANFIS is input as y U) _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) excitation values of l bar fuzzy rule during U, f _lBe fuzzy rule excitation values computing function, it is the product of the membership function of the corresponding fuzzy number of each input variable of ANFIS in the l bar fuzzy rule, wherein, the membership function of above-mentioned fuzzy number adopts bell shaped function, parameter in the bell shaped function is former piece parameter undetermined among the ANFIS, and consequent parameter undetermined is α among the ANFIS ^l, γ ₀ ^l, γ ₁ ^l..., γ _d ^l, β ^l

Step (3.3.3): the employing following steps are determined former piece parameter and the consequent parameter among the ANFIS;

Step (3.3.3.1): to all j=1,2 ..., n produces C at random _j(k) value, and (3.3.1) described formula calculates y set by step _j(k+1) value, thus some input and output training datasets that are used to train ANFIS produced, wherein, the input data are Y (k), C (k-d) ..., C (k-1), output data is Y (k+d+1);

Step (3.3.3.2): the training dataset and the classical learning algorithm of ANFIS that adopt step (3.3.2.1) to generate, determine former piece parameter undetermined among the ANFIS and consequent parameter;

Step (3.4):, adopt the Lagrange relaxation method to be calculated as follows Optimal Control rate C (k), wherein C according to the later process machine group load d rank predictive control model that step (3.3) obtains ⁱ(k) be:

$C^i\left(k\right)=u_i(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)\·{[I-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2\right)\text{\·}\stackrel{\‾}{N}(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)]}^{\text{-1}}\·[\stackrel{\‾}{X}+\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\right)\·\frac{\stackrel{\‾}{N}{A}^T}{{\mathrm{AA}}^T}]+\frac{A^T}{{\mathrm{AA}}^T},$

Wherein: I is a unit matrix, $\stackrel{\‾}{X}=N_d^T[X+\underset{q=0}{\overset{d-1}{\mathrm{\Σ}}}\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i(k-d+q)\right)-Y^r(k+d+1)],$ $\stackrel{\‾}{N}=N_d^T{N}_d$

According to above-mentioned machine group loading forecast control method based on flow model, the present invention has done a large amount of l-G simulation tests, can find out that from simulation result road bottleneck operation machine group load control has good effect there is the complicated production manufacture process of many group machine groups in the present invention to twice bottleneck operation before and after having and per pass bottleneck operation after.

Description of drawings

Fig. 1: machine group load estimation control hardware system construction drawing, gather machine group load real-time information by machine group load information harvester among the figure, and pass to machine group load estimation control computer.The ANFIS training computer can be trained ANFIS according to the production history data, obtains later process machine group load estimation controlling models parameter.Machine group load estimation control computer receives machine group load estimation controlling models parameter value and machine group load real-time information, adopts the Lagrange relaxation method, tries to achieve preceding working procedure machine group PREDICTIVE CONTROL parameter (task output rating).

Fig. 2: concern synoptic diagram between the front and back procedure inner machine group task stream, wherein m is the machine group sum of preceding working procedure; N is the machine group sum of later process; D is the average processing time delay of middle operation.

Fig. 3: the process flow diagram of forecast Control Algorithm, wherein according to the sampling time that is provided with, software carries out a machine group load estimation control every the sampling time, and adjusts the machine group task output rating of preceding working procedure; Simultaneously,, by training ANFIS machine group load estimation controlling models parameter is revised at regular intervals, made machine group load estimation controlling models more can embody the complex process present situation along with the increase of sample data.

Fig. 4: later process machine group load actual value and the later process machine group load actual value that adopts the HFC method to obtain, wherein y that (a) and (b), (c) are respectively each machine group load expectation value of later process in the experiment 1, adopt the AFFC method to obtain ₁ ^r(k), y ₂ ^r(k) be respectively two machine groups of later process in k load expectation value constantly; y ₁(k), y ₂(k) be respectively employing AFFC and HFC control method and carry out two machine groups of later process of machine group load control in k actual loading value constantly.

Fig. 5: later process machine group load actual value and the later process machine group load actual value that adopts the HFC method to obtain, wherein y that (a) and (b), (c) are respectively each machine group load expectation value of later process in the experiment 2, adopt the AFFC method to obtain ₁ ^r(k) ..., y ₅ ^r(k) be respectively each machine group of later process in k load expectation value constantly; y ₁(k) ..., y ₅(k) be respectively employing AFFC and HFC control method and carry out each machine group of later process of machine group load control in k actual loading value constantly.

Embodiment

Machine group loading forecast control method of the present invention depends on machine group load estimation control hardware system, is realized by machine group load estimation Control Software.Its hardware system is formed (structural drawing is seen Fig. 1) by machine group load information harvester, ANFIS training computer and machine group load estimation control computer.The ANFIS training computer can be trained ANFIS according to the production history data, obtains machine group load estimation controlling models parameter.Machine group load estimation control computer receives the related parameter values (from the ANFIS training computer) and the machine group load real-time information of machine group predictive control model, the machine group loading forecast control method that operation the present invention proposes, and prediction of output controlled variable (each machine group task output rating of preceding working procedure).

Below to above-mentionedly being elaborated that the present invention proposes based on the related step of the machine group loading forecast control method of flow model:

The first step: the timing sampling of each machine group load of later process is measured, and it contains following steps successively:

In the 1.1st step, install machinery group load harvester is gathered each machine group load real-time information.

In the 1.2nd step, from machine group load harvester, read corresponding machine group by machine group load estimation Control Software

The load real-time information.

Second step: the determining of each machine group load expectation value of later process

Keep in balance for each machine group is loaded in the whole given control cycle, the total load mean allocation of each machine group in given control cycle arrived each sampling interval in the time, that is:

$y_j^r\left(k\right)=\frac{{\mathrm{Load}}_j}{T_{\mathrm{all}}/T},j=1,...,n;$

Also can be according to the later process machine group load expectation value of producing each sampling instant in the direct in advance given control cycle of needs.

The 3rd step: the foundation of later process machine group load flow model.

Later process machine group load Fuzzy Predictive Control problem can be described as:

Order $J(k+d+1)=\frac{1}{2}[Y(k+d+1)-Y^r(k+d+1){]}^T\·[Y(k+d+1)-Y^r(k+d+1)]$

$+\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{C}^i{\left(k\right)}^T\·C^i\left(k\right)---\left(1\right)$

Ask control law C (k), make min{J (k+d+1), wherein all i are satisfied AC ⁱ(k)=1, A=[1,1 ..., 1] ^{1 * m}Promptly satisfying under the prerequisite of related constraint, determining the task output rating C (k) of preceding working procedure machine group, making at k+d+1 later process machine group load Y (k+d+1) constantly and its load expectation value Y ^rThe quadratic sum minimum of difference (k+d+1) also makes simultaneously C ⁱ(k) variation minimum.

The 4th step: the foundation of later process machine group load d rank predictive control model;

According to Little ' s theorem,, can set up the following flow model (machine group load 1 rank predictive control model) that is used for later process machine group load estimation based on later process working ability, preceding working procedure working ability and preceding working procedure task output rating etc.:

y _j(k+1)＝max{y _j(k)-v _jT+[c _1j(k-d)u ₁+…+c _mj(k-d)u _m]T，0}

＝max{y _j(k)-Tv _j+TC _j(k-d)U，0}，j＝1，…，n (2)

Because formula (2) is a nonlinear model, is difficult to try to achieve y _j(k+d+1) analytical expression, the present invention adopts ANFIS to obtain the Nonlinear Mapping relation of Y (k+d+1) and Y (k) and C (k).ANFIS introduces the self-adaptation node in the basic framework of fuzzy inference system, the multilayer feedforward neural network of formation, and the parameter sets of ANFIS is the summation of parameter sets in its each node.

If L bar rule is arranged among the ANFIS, then can be expressed as follows for rule 1:

If y _j(k)-Tv _jBe

And TC _j(k-d) U is

And TC _j(k-d+1) U is

, and TC _j(k-1) U is

So

$y_j^l(k+d+1)={\mathrm{\α}}^l(y\left(k\right)-{\mathrm{Tv}}_j)+T[{\mathrm{\γ}}_0^l{C}_j(k-d)+{\mathrm{\γ}}_1^l{C}_j(k-d+1)+...+{\mathrm{\γ}}_d^l{C}_j\left(k\right)]U+{\mathrm{\β}}^l---\left(3\right)$

Wherein

Be the pairing fuzzy number of each ANFIS input variable in the 1st fuzzy rule, its membership function adopts bell shaped function, that is:

${\mathrm{\μ}}_{{\underset{~}{A}}_{\mathrm{lj}}}\left(x\right)=\frac{b_{\mathrm{lj}}}{1+{\left|\frac{x-c_{\mathrm{lj}}}{a_{\mathrm{lj}}}\right|}^2},j=\mathrm{1,2},...,d+1,$

Parameter a in the bell shaped function _Lj, b _Lj, c _Lj, j=1,2 ..., d+1 is the 1st the former piece parameter in the fuzzy rule, and α ^l, γ ₀ ^l, γ ₁ ^l..., γ _d ^l, β ^lBe the 1st the consequent parameter in the fuzzy rule.

Article 1, the output of fuzzy rule can be write as

$y_j^l(k+d+1)={\mathrm{\α}}^l(y_j\left(k\right)-{\mathrm{Tv}}_j)+T\left(\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{\mathrm{\γ}}_q^l{C}_j(k-d+q)\right)U+{\mathrm{\β}}^l---\left(4\right)$

Make h _l(k)=f _l(y _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) U) be input as y for ANFIS _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) excitation values of l bar fuzzy rule, wherein f during U _lBe fuzzy rule excitation values computing function $f_l(x_1,x_2,...{,x}_{d+1})=\underset{j=1}{\overset{d+1}{\mathrm{\Π}}}{\mathrm{\μ}}_{{\underset{\‾}{A}}_{\mathrm{lj}}}\left(x_j\right),$ Comprehensively being output as of L bar fuzzy rule then:

$y_j(k+d+1)$

$=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{h}_l\left(k\right)\·y_j^l(k+d+1)$

$=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{h}_l\left(k\right)\·[{\mathrm{\α}}^l(y_j\left(k\right)-{\mathrm{Tv}}_j)+{\mathrm{\β}}^l]+\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{h}_l\left(k\right)\·\left[T\left(\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{\mathrm{\γ}}_q^l{C}_j(k-d+q)\right)U\right]$

So have: $y_j(k+d+1)=E_j+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{F}_{\mathrm{jq}}{C}_j(d-d+q)U,j=1,...,n---\left(6\right)$

Make X ^{N * 1}=[E ₁, E ₂..., E _n] ^T,

Then have:

$Y{(k+d+1)}^{n\×1}=X^{n\×1}+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{N}_q^{n\×n}\·C{(k-d+q)}^{n\×m}\·U^{m\×1}---\left(7\right)$

That is:

$Y{(k+d+1)}^{n\×1}=X^{n\×1}+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{N}_q^{n\×n}\·[C^1(k-d+q),...,C^m(k-d+q){]}^{n\×m}\·U^{m\×1}$

$=X^{n\×1}+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{N}_q^{n\×n}\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i(k-d+q)---\left(8\right)$

Formula (8) promptly is the d rank predictive control model expression formula of Y (k), U wherein, and V is a constant matrices, d, T are constant.

Adopt following method to determine former piece parameter and the consequent parameter among the ANFIS in the formula (8):

To all j=1,2 ..., n produces C at random _j(k) value, and calculate y by formula (2) _j(k+1) value, thus some input and output training datasets that are used to train ANFIS produced, the input data are Y (k), C (k-d) ..., C (k-1), output data is Y (k+d+1).Based on above-mentioned training dataset, use the classical learning algorithm of ANFIS (promptly to adopt BP back propagation learning method that the former piece parameter among the ANFIS is learnt, adopt least square method that the consequent parameter among the ANFIS is upgraded again), this classics learning algorithm can use the ANFIS training software bag among the MATLAB 6.0 to realize), determine ANFIS former piece parameter and consequent parameter in the formula (8), thereby finally obtain the d rank predictive control model of Y (k).

The 5th step: preceding working procedure machine group C (k) asks for.

D rank predictive control model according to the 4th Y (k) that obtain of step adopts the Lagrange relaxation method, finds the solution the machine group load estimation control problem that the 3rd step described, and tries to achieve best controlled variable C (k).

1) adopt Lagrange (Lagrange) relaxation method that the constraint in the problems referred to above is lax.For formula (1), will retrain and can get after lax:

$\stackrel{\‾}{J}(k+d+1)=\frac{1}{2}[Y(k+d+1)-Y^r(k+d+1){]}^T\·[Y(k+d+1)-Y^r(k+d+1)]$

$+\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{C}^i{\left(k\right)}^T\·C^i\left(k\right)+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\λ}}_i(A{C}^i\left(k\right)-1)---\left(9\right)$

λ wherein _i, i=1,2 ..., m is the Lagrangian that is used for loose constraint.

2) for the formula (9) after lax, ask C about given i ⁱ(k) partial derivative also makes that partial derivative is 0, has:

$\frac{\∂\stackrel{\‾}{J}(k+d+1)}{\∂C^i\left(k\right)}=\frac{{\∂(Y(k+d+1)-Y^r(k+d+1))}^T}{{\∂C}^i\left(k\right)}(Y(k+d+1)-Y^r(k+d+1))$

$-C^i\left(k\right)+{\mathrm{\λ}}_i{A}^T=0,i=1,...,m---\left(10\right)$

With formula (8) substitution formula (10), abbreviation can get:

$\frac{\∂\stackrel{\‾}{J}(k+d+1)}{{\∂C}^i\left(k\right)}=u_i{N}_d^T[X+N_d\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i\left(k\right)\right)+\underset{q=0}{\overset{d-1}{\mathrm{\Σ}}}{N}_q\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i(k-d+q)\right)-Y^r(k+d+1)]$

$+C^i\left(k\right)+{\mathrm{\λ}}_i{A}^T=0,i=1,...,m---\left(11\right)$

3) for the formula (9) after lax, ask about λ _iPartial derivative and make that partial derivative is 0, have:

AC ⁱ(k)＝1，i＝1，…，m (12)

4) order $\stackrel{\‾}{X}=N_d^T[X+\underset{q=0}{\overset{d-1}{\mathrm{\Σ}}}\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i(k-d+q)\right)-Y^r(k+d+1)],\stackrel{\‾}{N}=N_d^T{N}_d,$

$S=\stackrel{\‾}{X}+\stackrel{\‾}{N}\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i\left(k\right)\right)---\left(13\right)$

Then formula (11) can be expressed as:

u _iS+C ⁱ(k)+λ _iA ^T＝0，i＝1，…，m (14)

To formula (14) both sides premultiplication A, can get:

u _iAS+AC ⁱ(k)+λ _iAA ^T＝0，i＝1，…，m (15)

With formula (12) substitution formula (15), existing:

${\mathrm{\λ}}_i=\frac{-1}{{\mathrm{AA}}^T}(u_i\mathrm{AS}+1),i=1,...,m---\left(16\right)$

Again with formula (16) substitution formula (13), then:

$u_{i}S+C^i\left(k\right)+\frac{{-A}^T}{{\mathrm{AA}}^T}(u_i\mathrm{AS}+1)=0,i=1,...,m$

Thereby:

$C^i\left(k\right)=u_i(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)S+\frac{A^T}{{\mathrm{AA}}^T}---\left(17\right)$

Wherein I is m rank unit matrixs.

With formula (17) substitution formula (13), have:

$S=\stackrel{\‾}{X}+\stackrel{\‾}{N}\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i\left(k\right)\right)=\stackrel{\‾}{X}+\stackrel{\‾}{N}[\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)S+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\frac{A^T}{{\mathrm{AA}}^T}]$

$=\stackrel{\‾}{X}+\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2\right)\·\stackrel{\‾}{N}(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)S+\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\right)\·\frac{\stackrel{\‾}{N}{A}^T}{{\mathrm{AA}}^T}$

That is: $[I-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2\right)\·\stackrel{\‾}{N}(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)]S=\stackrel{\‾}{X}+\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\right)\·\frac{\stackrel{\‾}{N}{A}^T}{{\mathrm{AA}}^T}$

$S=[I-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2\right)\·\stackrel{\‾}{N}(\frac{A^{T}A}{{\mathrm{AA}}^T}-I){]}^{-1}\·[\stackrel{\‾}{X}+\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\right)\·\frac{\stackrel{\‾}{N}{A}^T}{{\mathrm{AA}}^T}]---\left(18\right)$

At last, with formula (18) substitution formula (17), can try to achieve the control law C (k) that makes machine group load estimation control problem controlled target minimum:

$C^i\left(k\right)=u_i(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)\·[I-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2\right)\·\stackrel{\‾}{N}(\frac{A^{T}A}{{\mathrm{AA}}^T}-I){]}^{-1}\·[\stackrel{\‾}{X}+\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\right)\·\frac{\stackrel{\‾}{N}{A}^T}{{\mathrm{AA}}^T}]+\frac{A^T}{{\mathrm{AA}}^T},$

i＝1，…，m。

The present invention propose based on the machine group loading forecast control method process flow diagram of flow model as shown in Figure 3.

According to the above-mentioned machine group loading forecast control method that proposes based on flow model, the present invention has done a large amount of l-G simulation tests, because length is limit, adopt the validity of the experiment of following two more difficult PREDICTIVE CONTROL in order to the machine group loading forecast control method of checking the present invention proposition, experiment parameter sees Table 1:

Table 1 emulation experiment parameter

The present invention has designed and has been used for the heuristic (HFC:Heuristic Flow Control) of comparing with the AFFC method, and this method can be described below: with poor Diff (k)=[Y between current time later process machine group load and the load expectation value ^r(k)-Y (k)]=[π ₁, π ₂..., π _n] ^TRegulate C (k), if i.e. π _jGreater than zero, then increase C _j(k) value of each element in; Otherwise, if π _jLess than zero, then reduce C _j(k) value of each element in, thus Y can be reduced ^r(k) poor with Y (k), but increasing and reducing C _j(k) time, should satisfy constraint AC (k)=A.Concrete grammar is: the element among the Diff (k) is rearranged from big to small.If π _jBe one of preceding n/2 big element, then C _j(k)=C _j(k-1)+0.1I; Otherwise, if π _jBe one of n/2 big element in back, then C _j(k)=C _j(k-1)-0.1I.

In numerical simulation, use AFFC and HFC method that C (k) is regulated respectively.Fig. 4 and Fig. 5 represent the numerical simulation result of above-mentioned two experiments respectively.

Y (k) among Fig. 4 (b) and 5 (b) has followed the tracks of expectation value Y among Fig. 4 (a) and 5 (a) preferably ^r(k) variation (maximum error is respectively 5% and 1.79%), and be convergent.And the Y (k) among Fig. 4 (c) and 5 (c) is though can reflect Fig. 4 (a) and the middle Y of 5 (a) ^r(k) variation tendency, but and Y ^r(k) error increasing with the increase in control time (curve is not restrained).As seen the AFFC of the present invention's proposition is effective to following the tracks of later process machine group load expectation value.The shortcoming of HFC method is the forecasting mechanism of not introducing the load of later process machine group, and only according to later process machine group load current state C (k) is regulated, and control method is simpler, makes tracking error bigger.

In numerical simulation, use AFFC and HFC method that C (k) is regulated respectively.Fig. 4 and Fig. 5 have represented the numerical simulation result of above-mentioned two experiments respectively.

Case study on implementation of the present invention is knitted manufacturing enterprise for certain large-scale look, the production of this enterprise mainly comprises loose yarn, compound plate, dyeing, winder, warping, sizing, gaits, plugs in reed and nine procedures such as weave cotton cloth, and wherein the dyeing process and the operation of weaving cotton cloth are the bottleneck operations in this enterprise production process.Winder, warping, sizing are arranged, gait and plug in reed operation in the dyeing and the inter process of weaving cotton cloth, the productive capacity of above-mentioned operation is all bigger, and production task only need can be passed through these operations through certain time-delay (processes time).As seen, this look is knitted production run and is met the complex process situation that the present invention describes, and can control the processing load of each machine group in the operation of weaving cotton cloth by the output rating of control dyeing process task.

At first according to the requirement of this instructions in the operation install machinery group load estimation control hardware system of weaving cotton cloth.

Secondly, read nearest 1 month production data from this look is knitted the production management system of production, the method that provides according to this instructions is set up the training data of ANFIS, amounts to 10000.And use these training datas that ANFIS is trained, set up the d rank model of the operation machine group load estimation control of weaving cotton cloth.When determining the sampling period, knit the practical condition of manufacturing enterprise according to this look, determine sampling period T=2 hour, simultaneously because dyeing and weave cotton cloth between processing time delay of middle operation substantially about 10 hours, so the exponent number d=5 of this predictive control model.

Afterwards, according to the working ability of 23 machine groups in the operation of weaving cotton cloth, the machine group load expectation value of using this instructions to provide determines that method determines the processing load expectation value of above-mentioned 23 machine groups.

At last, the task output rating acquiring method of each machine group on the basis that obtains each the machine group load real-time information of operation of weaving cotton cloth, provides the task output rating of each machine group of dyeing process automatically in the dyeing process that PREDICTIVE CONTROL software provides according to this instructions.

Machine group loading forecast control method based on flow model can be controlled the operation machine group load of weaving cotton cloth well.

Claims (1)

1. Based on the machine group loading forecast control method of flow model, it is characterized in that 1, described method realizes successively according to the following steps on machine group load estimation control computer:

   Step (1): initialization, set following parameter

   Sampling time interval provides each machine group task output rating in the preceding working procedure every time interval T, and described machine group is made up of many similar machines of working ability, and sampling instant is then represented with k;

   Machine group working ability is summation process time of the processing tasks that can finish in unit interval inner machine group, the working ability u of machine group i in the preceding working procedure _iExpression, i=1 ..., m is expressed in matrix as U=[u ₁, u ₂..., u _m] ^T, the working ability v of machine group j in the later process _jExpression, j=1 ..., n is expressed in matrix as V=[v ₁, v ₂..., v _n] ^T, m and n are respectively the number of machine group in the forward and backward procedure;

   Preceding working procedure machine group task output rating, preceding working procedure machine group i constrains in the task that the k sampling instant machines based on production technology and is arranged to the ratio of later process by machine group j processing, uses c _Ij(k) expression is expressed in matrix as:

   $C{\left(k\right)}^{n\×m}={[C_1\left(k\right),C_2\left(k\right),\·\·\·,C_n\left(k\right)]}^T$

   $=[C^1\left(k\right),C^2\left(k\right),\·\·\·,C^m\left(k\right)]$

   $=\left[\begin{array}{cccccc}{c}_{11}\left(k\right)& & c_{21}\left(k\right)& & \·\·\·& c_{m1}\left(k\right)\\ c_{12}\left(k\right)& & c_{22}\left(k\right)& & \·\·\·& c_{m2}\left(k\right)\\ \·& \·& & \·& & \\ \·& \·& \·\·\·& \·& & \\ \·& \·& & \·& & \\ c_{1n}\left(k\right)& & c_{2n}\left(k\right)& & \·\·\·& c_{\mathrm{mn}}\left(k\right)\end{array}\right]$

   0≤c wherein _Ij≤ 1 and $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{c}_{\mathrm{ij}}=1,$ i＝1，…，m；j＝1，…，n；

   The load of machine group, summation process time of wait processing tasks before certain machine group in the operation, later process machine group j is shown y at k loading liquifier constantly _j(k), be expressed in matrix as Y (k) ^{N * 1}=[y ₁(k), y ₂(k) ..., y _n(k)] ^T

   Machine group j is expressed as y in k machine loading expectation value constantly in the later process _j ^r(k), be expressed in matrix as $Y^r{\left(k\right)}^{n\×1}={[y_1^r\left(k\right),y_2^r\left(k\right),\·\·\·,y_n^r\left(k\right)]}^T;$

   The processing of middle operation represents that it is meant task from the preceding working procedure completion of processing time delay with d, by the processing of middle operation, arrive the used averaging time unit of later process, contains the stand-by period;

   Given control cycle T _AllExpression;

   Control cycle T _AllThe total load Load of interior later process machine group j _jExpression;

   Step (2): gather machine group load real-time information with machine group load information harvester, machine group load information harvester is constituted by a kind of in PLC harvester, embedded system harvester, the DCS system acquisition device or they;

   Step (3): the read machine group load real-time information from described harvester of described machine group load estimation control computer, carry out the control of machine group load estimation successively according to the following steps:

   Step (3.1): determine each sampling interval each machine group load expectation value y of later process in the time by following formula _j ^r(k),

   $y_j^r\left(k\right)=\frac{{\mathrm{Load}}_j}{T_{\mathrm{all}}/T},$ j＝1，…，n

   Step (3.2): set up later process machine group load estimation control problem by following formula:

   $J(k+d+1)=\frac{1}{2}{[Y(k+d+1)-Y^r(k+d+1)]}^T\·\left]\right[Y(k+d+1)-Y^r(k+d+1)]$

   $+\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{C}^i{\left(k\right)}^T\·C^i\left(k\right)$

   Ask control law C (k), make min{J (k+d+1), wherein all i are satisfied AC ⁱ(k)=1, A=[1,1 ..., 1] ^{1 * m}

   Step (3.3): set up later process machine group load estimation controlling models by following step

   Step (3.3.1): set up later process machine group load 1 rank predictive control model

   y _j(k+1)＝max{y _j(k)-v _jT+[c _1j(k-d)u ₁+…+c _mj(k-d)u _m]T，0}

   ＝max{y _j(k)-Tv _j+TC _j(k-d)U，0}，j＝1，…，n ，

   Step (3.3.2): adopt Adaptive Neuro-fuzzy Inference ANFIS to set up later process machine group load d rank predictive control model with L bar fuzzy rule

   That is:

   $Y{(k+d+1)}^{n\×1}=X^{n\×1}+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{N}_q^{n\×n}\·{[C^1(k-d+q),\·\·\·,C^m(k-d+q)]}^{n\×m}\·U^{m\×1}$

   $=X^{n\×1}+\underset{q=0}{\overset{d}{\mathrm{\Σ}}}{N}_q^{n\×n}\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i(k-d+q)$

   Wherein: X ^{N * 1}=[E ₁, E ₂..., E _n] ^T, $E_j=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{h}_l\left(k\right)\·[{\mathrm{\α}}^l(y_j\left(k\right)-{\mathrm{Tv}}_j)+{\mathrm{\β}}^l]$

   

   q＝0，1，…，d， $F_{\mathrm{jq}}=T\·\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{h}_l\left(k\right){\mathrm{\γ}}_q^l,$

   h _l(k)=f _l(y _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) be that ANFIS is input as U),

   y _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) excitation values of l bar fuzzy rule during U, f _lBe fuzzy rule excitation values computing function, it is the product of the membership function of the corresponding fuzzy number of each input variable of ANFIS in the l bar fuzzy rule, wherein, the membership function of above-mentioned fuzzy number adopts bell shaped function, parameter in the bell shaped function is former piece parameter undetermined among the ANFIS, and consequent parameter undetermined is α among the ANFIS ^l, γ ₀ ^l, γ ₁ ^l..., γ _d ^l, β ^l

   Step (3.3.3): the employing following steps are determined former piece parameter and the consequent parameter among the ANFIS;

   Step (3.3.3.1): to all j=1,2 ..., n produces C at random _j(k) value, and (3.3.1) described formula calculates y set by step _j(k+1) value, thus some input and output training datasets that are used to train ANFIS produced, wherein, the input data are Y (k), C (k-d) ..., C (k-1), output data is Y (k+d+1);

   Step (3.3.3.2): the training dataset and the classical learning algorithm of ANFIS that adopt step (3.3.2.1) to generate, determine former piece parameter undetermined among the ANFIS and consequent parameter;

   Step (3.4):, adopt the Lagrange relaxation method to be calculated as follows Optimal Control rate C (k), wherein C according to the later process machine group load d rank predictive control model that step (3.3) obtains ⁱ(k) be:

   $C^i\left(k\right)=u_i(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)\·{[I-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2\right)\·\stackrel{\‾}{N}(\frac{A^{T}A}{{\mathrm{AA}}^T}-I)]}^{-1}\·[\stackrel{\‾}{X}+\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\right)\·\frac{\stackrel{\‾}{N}{A}^T}{{\mathrm{AA}}^T}]+\frac{A^T}{{\mathrm{AA}}^T},$

   Wherein: I is a unit matrix, $\stackrel{\‾}{X}=N_d^T[X+\underset{q=0}{\overset{d-1}{\mathrm{\Σ}}}\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{C}^i(k-d+q)\right)-Y^r(k+d+1)],$ $\stackrel{\‾}{N}=N_d^T{N}_d.$

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