CN110275441B - PSORBFD (particle swarm optimization-based adaptive feedback) rapid self-adaptive decoupling control method - Google Patents

PSORBFD (particle swarm optimization-based adaptive feedback) rapid self-adaptive decoupling control method Download PDF

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CN110275441B
CN110275441B CN201910590310.6A CN201910590310A CN110275441B CN 110275441 B CN110275441 B CN 110275441B CN 201910590310 A CN201910590310 A CN 201910590310A CN 110275441 B CN110275441 B CN 110275441B
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廖雪超
陈振寰
邓万雄
伍杰平
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Wuhan Yidian Cloud Technology Co.,Ltd.
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Wuhan University of Science and Engineering WUSE
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Abstract

The invention discloses a PSORBFD rapid self-adaptive decoupling control method, which comprises the following steps: s1, system modeling: determining a transfer function matrix model of the system according to the relation between the control quantity and the output quantity; s2, establishing an RBFD decoupling controller: the RBFD decoupling controller comprises an input layer, a hidden layer and an output layer, and the decoupling control process of the RBFD decoupling controller comprises RBF initialization, RBF clustering, RBF model training and RBF testing; s3, establishing a PSORBFD decoupling controller: and (3) improving the RBFD decoupling controller by adopting a PSO particle swarm optimization algorithm, and establishing a PSORBFD decoupling controller. The PSORBFD decoupling controller is applied to a multichannel film thickness control system, so that the problem of film thickness deviation caused by the coupling problem of a BOPP film production line can be effectively solved, and the production quality of the film is ensured. Meanwhile, the method is also suitable for decoupling control of a multi-channel coupling system, the training speed of the RBF model is obviously improved, the training efficiency is greatly improved, and the anti-interference capability is strong.

Description

PSORBFD (particle swarm optimization-based adaptive feedback) rapid self-adaptive decoupling control method
Technical Field
The invention relates to the technical field of decoupling of a coupling system, in particular to a PSORBFD rapid self-adaptive decoupling control method.
Background
The thickness control system of the biaxially oriented polypropylene (BOPP) film is a nonlinear complex multivariable coupling system with Multiple Input Multiple Output (MIMO), and in the actual production process, the heating bolts influence each other, so that the coupling between the thermal expansion bolts cannot be ignored.
Specifically, the flow of the BOPP film production line is shown in fig. 1, and the working process thereof is as follows: the film raw material (plastic particles) is fed from a feeding port, the liquid raw material is sent to a film head by an extruder after being heated and melted, the liquid raw material is extruded out by a thermal expansion bolt at the lip of the film head, the liquid raw material is cooled by a cooling roller to form a solid thick sheet, the thick sheet is transmitted by a synchronous transmission system, the thick sheet is firstly thinned by longitudinal stretching, then the thin film is further thinned and widened by transverse stretching by a transverse stretcher, and finally the finished film is obtained by shaping and rolling. The whole control divides the film to be produced into a plurality of zones, and each zone corresponds to one heating expansion bolt. When the quality of a certain part of the finished film is found to be poor, the heating quantity of the corresponding bolt can be adjusted to change the opening of the lip mouth, so that the extrusion quantity of the liquid raw material is changed, and the purpose of adjusting the thickness of the film is achieved.
The BOPP film thickness control system is an MIMO coupling system, and since the interaction between the loops in the coupling system will destroy the stable control of other independent loops, as shown in fig. 2, the thermal expansion bolts are uniformly distributed on the film head, and if the influence between the heating bolts and other factors are not considered, each thermal expansion bolt can be regarded as an independent control channel. However, in practical situations, the coupling between the thermal expansion bolts is often not negligible, and this coupling relationship can seriously degrade the control quality of the system, so how to eliminate the coupling effect in the film thickness control is a problem to be considered.
The schematic diagram of the thickness control system structure of a single channel is shown in fig. 3, and comprises a thickness controller, n heating bolts, a thickness gauge and the like, wherein the thickness controller controls the heating quantity of the heating bolts, the thickness gauge measures the thickness output by the BOPP film and feeds the measured thickness back to the thickness controller, and the thickness controller adjusts according to a feedback result and finally outputs the required BOPP film.
Considering the model of the single loop of each bolt, the heating temperature of the single bolt controls the opening degree of the corresponding film head lip, and further controls the extrusion amount of the liquid raw material. And the heating temperature between adjacent bolts and the opening degree of the film head lip are influenced mutually, so that the thickness of the film between adjacent channels has a serious coupling relation.
For decoupling control of a coupling system, common decoupling methods mainly include decoupling by a traditional method, a self-adaptive decoupling method, intelligent decoupling control and the like.
The traditional decoupling is represented by a modern frequency domain and is mainly suitable for a deterministic MIMO system, and the basic idea is to design a decoupling network so that a transfer function matrix of the MIMO control system becomes a diagonal matrix and the system is easier to control; the decoupling method requires that the transfer matrix is steady-state nonsingular, has a simple structure and no dynamic characteristic, ensures that the output response of the open-loop system is steady-state and has no deviation, but cannot effectively improve the decoupling adjustment capability of the closed-loop control system.
The self-adaptive decoupling method combines the self-adaptive control and decoupling control technology, and the essence of the method is that coupling signals are taken as interference for processing, and a self-correcting feedforward control method is adopted to perform action and static compensation on coupling; although the feedforward-like decoupling algorithm has a good decoupling effect on the MIMO coupling system, the coupling influence caused by the change of the input signal cannot be completely eliminated.
The intelligent decoupling control has unique advantages in solving the nonlinear aspect, the method can realize online accurate decoupling of the nonlinear system, and solves the problem that the traditional decoupling method is difficult to realize accurate decoupling, so that the intelligent decoupling control has wide attention in the aspect of nonlinear system decoupling control. The neural network decoupling control is a typical method, can realize mapping from multiple inputs to multiple outputs, has a self-learning function, and is suitable for time-varying, nonlinear and unknown-characteristic objects.
The method adopts a RBF neural network decoupling algorithm (RBFD) to perform decoupling control on a film thickness control system, and adopts a particle swarm optimization to optimize the structure of the RBF decoupling system, so that a PSORBFD decoupling controller is designed.
Disclosure of Invention
In order to overcome the defects of the technology, the invention provides a PSORBFD rapid self-adaptive decoupling control method, which obviously improves the speed and decoupling performance of model training.
The technical scheme adopted by the invention for overcoming the technical problems is as follows:
a PSORBFD fast self-adaptive decoupling control method comprises the following steps:
s1, system modeling: determining a transfer function matrix model of the system according to the relation between the control quantity and the output quantity;
s2, establishing an RBFD decoupling controller: the RBFD decoupling controller comprises an input layer, a hidden layer and an output layer, and the decoupling control process of the RBFD decoupling controller comprises RBF initialization, RBF clustering, RBF model training and RBF testing;
s3, establishing a PSORBFD decoupling controller: and (3) improving the RBFD decoupling controller by adopting a PSO particle swarm optimization algorithm, and establishing a PSORBFD decoupling controller.
Further, in step S1, the system modeling specifically includes:
taking the thickness of each channel as a measured value and the temperature of the heating bolt as a control quantity to form a three-input three-output control system, and setting the system control quantity as (u)1，u2，u3) The output quantity is (y)1，y2，y3) Wherein each output quantity yiSubject to a plurality of control quantities u simultaneouslyiTo determine a transfer function matrix model for the three channel thickness system, as follows:
Figure BDA0002115795130000041
further, in step S2, the RBF network initialization is to initialize system data, where the system data includes: input samples X (k), hidden layer RjNumber of clusters, data center CjThe spreading constant σjAnd a hidden layer RjWeight w to output layer iji(ii) a Then extracting M pieces of running data as a training set of the RBF network, and taking all coupling influence correlation factors as system input of the RBF network, wherein the expression is as follows:
Figure BDA0002115795130000042
further, in step S2, the RBF clustering specifically includes the following steps:
1) initializing clusters:
randomly partitioning all data x (k) (k 1.. M) of the dataset into n clusters, Rj(j＝1...n)；
To obtain each RjCenter point C ofj＝avg[X(j)] (X(j)∈Rj)；
2) And (4) cluster updating:
Figure BDA0002115795130000043
recalculate each RjNew center point C ofj＝avg[X(j)] (X(j)∈Rj)；
3) Termination judgment conditions:
if(Cj(T+1)≠Cj(T)) (T is the clustering iteration times), then the step 2) clustering updating is executed again;
after else clustering is finished, turning to the step 4);
4) and (3) outputting a clustering result:
get clusters RjInitial center point C ofj *；
Spreading constant
Figure BDA0002115795130000051
Further, in step S2, the RBF model training employs a gradient descent method by minimizing the objective function Ei(i ═ 1,2,3) implementation for each hidden layer node RjA data center point C of (j 1.. n)jExpansion constant σjAnd the output weight wjiThe adaptive adjustment specifically includes:
1) randomly initializing the weight value:
Figure BDA0002115795130000052
2) training data set:
for k＝1 to M
calculation of RjAnd (3) outputting:
Figure BDA0002115795130000053
calculate all output layer outputs:
Figure BDA0002115795130000054
calculating an output layer error: e.g. of the typei(k)＝0-ymi(k) (i＝1,2,3) (12
Calculating an output layer objective function:
Figure BDA0002115795130000055
using gradient descent method to adjust the regulating quantity Delta Cj，Δσj，ΔwijAnd (3) accumulating:
Figure BDA0002115795130000056
Figure BDA0002115795130000057
Figure BDA0002115795130000058
(
Figure BDA0002115795130000059
as a learning rate, as a fixed value) (16)
end for
Parameter adjustment: cj(t)＝Cj(t-1)+ΔCj(k) (17)
σj(t)＝σj(t-1)+Δσj(k) (18)
wji(t)＝wji(t-1)+Δwji(k) (19)
Averaging the target function of the output layer:
Figure BDA0002115795130000061
3) determination of termination condition
if(Ji<Jh) Training is finished, go to step 4) (J)hAs an objective function threshold value)
else t ═ t +1, and re-perform step 2), training the dataset;
4) end of training
To obtain each RjFinal center point
Figure BDA0002115795130000062
Weight value
Figure BDA0002115795130000063
Spreading constant
Figure BDA0002115795130000064
Further, in step S2, the RBF test is to substitute new data of the test set into the RBF model according to each RjFinal center point
Figure BDA0002115795130000065
And an extension constant
Figure BDA0002115795130000066
Get the output yh of the hidden layerj(k)：
Figure BDA0002115795130000067
Further according to the weight of each cluster
Figure BDA0002115795130000068
Obtaining three-channel output of the system:
Figure BDA0002115795130000069
further, in step S3, the specific process of improving the RBFD decoupling controller by using the PSO particle swarm optimization algorithm includes:
1) initializing particle swarm parameters:
randomly generating NpParticles constituting a particle set Wp；
Selecting an implicit layer output yhk (j) (j is 1.. n) of a certain input X (k) as an initial training set of the particle swarm optimization;
the current iteration time Times is 1;
2) calculating the fitness of all particles:
for s＝1to Np
Figure BDA0002115795130000071
3) particle data updating:
updating individual extremum P by adopting optimal principlebest(s), individual extremum fitness Fpbest(s)；
And updating the global extremum: gbest＝min[Pbest(s),(s＝1...Np)]
Updating global extreme fitness: fGbest＝min[Fpbest(s),(s＝1...Np)]
Wherein, the Pbest(s) represents a particle Wp(s) the state with the lowest fitness in the iterative update procedure, Fpbest(s) represents a particle Wp(s) minimum fitness in the iterative Process, GbestRepresents Pbest(s) the least adaptive particle, FGbestIs represented by FpbestMinimum value of (1);
4) update the velocity, position and number of iterations of each particle:
Figure BDA0002115795130000072
Wp(s)＝Wp(s)+V(s)
wherein
Figure BDA0002115795130000073
Is an inertia factor, ξ1，ξ2Is an acceleration constant
Speed limiting: l V(s) l < Vmax
Particle updating: wp(s)＝Wp(s)+V(s)
Where v(s) represents the moving speed of the s-th particle (s ═ 1,2,3 … N)p)，Wp(s) represents a single particle, VmaxRepresents a particle maximum velocity threshold;
5) judging training termination conditions:
if(Times＞Mp||Gbest＜Jg) And the algorithm is finished, and the step 6) is carried out;
else Times is equal to Times +1, and the step 2) is returned, and the particles are retrained;
wherein M ispRepresents the maximum number of iterative updates, JgRepresents an error threshold;
6) outputting initial values of the weights:
after the positions of the obtained global extremum particles are normalized, the positions are used as weight initial values for RBFD controller training
Figure BDA0002115795130000081
The invention has the beneficial effects that:
the PSORBFD decoupling controller is applicable to objects with time variation, nonlinearity and unknown characteristics, is applied to a multi-channel film thickness control system, almost completely eliminates the coupling relation among systems, can effectively solve the problem of film thickness deviation caused by the coupling problem of a BOPP film production line, and ensures the film production quality. Meanwhile, the control method is also suitable for decoupling control of the multi-channel coupling system, and can realize accurate decoupling of the multi-channel system. In addition, the PSORBFD method of the invention obviously improves the training speed of the RBF model, greatly improves the training efficiency and has strong anti-interference capability.
Drawings
Fig. 1 is a schematic flow chart of a BOPP film production line.
Fig. 2 is a schematic view of the coupling relationship of a plurality of bolts.
Fig. 3 is a schematic structural diagram of a BOPP film thickness control system.
Fig. 4 is a schematic structural diagram of the RBFD controller.
Fig. 5 is a flow chart of the RBFD algorithm.
FIG. 6 is a flow chart of the PSORBFD algorithm.
FIG. 7 is a graph of training sample data for a film thickness control model transfer function.
Fig. 8 is a graph of RBF clustering results.
Fig. 9 is a diagram of a training process of the RBFD controller, wherein fig. 9(a), 9(b), and 9(c) are output results of the output layers ym1, ym2, ym3, respectively.
Fig. 10 is a diagram of a training process of the PSORBFD controller, where fig. 10(a), fig. 10(b), and fig. 10(c) are output results of the output layers ym1, ym2, ym3, respectively.
FIG. 11 is a graph of the output response results of a PID controller and SFFD controller system.
FIG. 12 is a graph of the output response of the SFFD controller and RBFD controller systems.
FIG. 13 is a graph of the output response of the SFFD controller and the PSORBFD controller system.
Detailed Description
In order to facilitate a better understanding of the invention for those skilled in the art, the invention will be described in further detail with reference to the accompanying drawings and specific examples, which are given by way of illustration only and do not limit the scope of the invention.
Examples 1,
As shown in fig. 6, a PSORBFD fast adaptive decoupling control method according to this embodiment is specifically an adaptive decoupling control method of a PSORBFD applied to a BOPP film thickness control system, but the decoupling control method is not limited to the BOPP film thickness control system, and may also be applied to decoupling control of other multi-channel coupling systems, and the PSORBFD fast adaptive decoupling control method according to this embodiment includes the following steps:
step S1, modeling the system: and determining a transfer function matrix model of the system according to the relation between the control quantity and the output quantity.
System modeling
Considering a three-channel film thickness control system, taking the thickness of each channel as a measured value and the temperature of a heating bolt as a control quantity to form a three-input three-output control system, and setting the system control quantity as (u)1，u2，u3) The output quantity is (y)1，y2，y3) Wherein each output quantity yiSubject to a plurality of control quantities u simultaneouslyiDetermining a transfer function matrix model of the three-channel thickness system according to the process parameters of the system, as follows:
Figure BDA0002115795130000101
the discretization transfer function model of the three-channel film thickness control system according to the formula (1) is in a discretization form:
Figure BDA0002115795130000102
Figure BDA0002115795130000103
Figure BDA0002115795130000104
due to the processThe flow is complex and changeable, and the flow can not be accurately described only by transfer function, so that the random noise epsilon is added to the output of three systemsi＝rand(0,0.05)(i＝1,2,3)。
(II) analysis of coupling Properties
By calculating the Relative Gain matrix (RGA) of the controlled object, not only the response characteristic of the controlled quantity to the regulating quantity can be determined and used as the basis for designing the control system, but also the degree and type of process correlation and the influence on each loop control system can be pointed out.
For n inputs (u)1，u2，...，un) N outputs (y)1，y2，...，yn) In the multivariable system, the ith loop is selected to make other control quantity uk(k 1, 2., n, k ≠ i) is kept unchanged, i.e. corresponding to other loops being open (not controlled), and only the controlled variable u is changedjIs a Δ ujY obtained byiThe amount of change of (a) and (u)jThe ratio of the amount of change of (a) is called ujTo yiThe open loop gain of the channel. The loop i is selected so that the other control variables remain unchanged, i.e. the other loop yk(k ≠ 1, 2., n, k ≠ i) is closed, varying only the controlled quantity yiObtained yiThe amount of change of (a) and (u)jThe ratio of the amount of change of (a) is called ujTo yiClosed loop gain of the channel. The ratio of open-loop gain to closed-loop gain is defined as the relative gain, i.e.:
Figure BDA0002115795130000111
wherein the relative gain matrix (RGA) has the following properties:
(1) the sum of the element values of each row or each column in the matrix is 1;
(2) the element values of the same row or column in the matrix are the same or close to each other, which indicates that the coupling degree between the channels is strong;
(3) the values of the elements of the matrix are in the interval 0, 1]Inner, indicates the degree of coupling that exists between the process control channelsλijThe closer to 1, the smaller the channel coupling degree is, so that the formed single loop has better control effect;
(4) if the value of an element in the matrix is greater than 1, then there are elements less than 0 in the same row or column, which indicates that the interaction between the channels is very influential.
According to a relative gain matrix (RGA) analysis method, programming and calculating a transfer function matrix model in the formula (1) to obtain a relative gain matrix of the film thickness control system, wherein the relative gain matrix is as follows:
Figure BDA0002115795130000112
as is apparent from equation (6), the film thickness control system is a multivariable system with coupling, and due to the coupling, the control effect is reduced, so that it is necessary to perform a decoupling design.
Step S2, establishing RBFD decoupling controller
An RBF (radial Basis function) neural network, namely a radial Basis function neural network, is a neural network proposed by J.Moody and C.Darken in the end of the 80 th century, is a three-layer forward network, an input layer consists of signal source nodes, only plays a role in transmitting input data, does not transform the input data, and only maps the input data to an implied layer; the second layer is a hidden layer, and the neuron of the hidden layer performs operation on the data input by the input layer; the third layer is an output layer that is responsive to the input signal. The conversion function of the hidden layer adopts a radial basis function which has local sensing characteristics and reflects the nonlinear mapping capability of the RBF network. Based on the network characteristics of the RBF, the following radial Basis Function decoupling RBFD (radial Basis Function decoupling) controller is designed.
Taking channel 1 as an example, y1(k)＝y11(k)+y12(k)+y13(k)：
Wherein: y is11(k) Is the transfer function of its main channel, y12(k),y13(k) Is composed ofAnd in order to realize decoupling, the control targets of the RBF decoupling controller are as follows: y ism1＝y12(k)+y13(k)→0。
The decoupling method for the channel 2 and the channel 3 is similar to that of the channel 1, and the control targets of the RBF decoupling controller are as follows: y ism2＝y21(k)+y23(k)→0，ym3＝y31(k)+y32(k)→0。
The structure of the RBFD decoupling controller described in this embodiment is shown in fig. 4, and the RBFD decoupling controller is composed of an input layer, an implicit layer, and an output layer.
The decoupling control process of the RBFD decoupling controller is shown in FIG. 5 and comprises RBF initialization, RBF clustering, RBF model training and RBF testing.
RBF initialization: initializing system data;
RBF clustering: determining each hidden layer RjCenter point C ofjThe spreading constant σj；
RBF model training: adjust the weight wjiThe spreading constant σjCenter point Cj；
RBF test: and obtaining system output according to the training model and the test data.
The RBF decoupling controller has the following principle: initializing the system, and then using clustering algorithm to input sample Xk(k 1.. M) clustering, and determining each hidden layer node R in the RBF networkjData center of (j 1.. n)
Figure BDA0002115795130000135
And according to the distance between the data centers | | | Xk-CjTo determine each R | |jSpreading constant of
Figure BDA0002115795130000134
Then each R is obtainedjOutput yh ofjAnd then adjusting each R by adopting a self-learning algorithmjData center CjExpansion constant σjAnd the output weight wjiAnd finally obtainTo RBF training models
Figure BDA0002115795130000133
And then, substituting the subsequent actual data into the RBF training model for testing to obtain an output result.
Step S21, RBF initialization
The method comprises the following steps of operating in a Matlab simulation environment to sample data by using a film thickness transfer function matrix model of a formula (1), extracting M pieces of operating data to serve as a training set of the RBF network, and taking all relevant factors of coupling influence as system input of the RBF network in order to achieve a control target, wherein the expression is as follows:
Figure BDA0002115795130000131
step S22, RBF clustering
The RBF clustering comprises clustering initialization, clustering updating, termination condition judgment and clustering result output, and the method comprises the following steps:
1) initializing clusters:
randomly partitioning all data x (k) (k 1.. M) of the dataset into n clusters, Rj(j＝1...n)；
To obtain each RjCenter point C ofj＝avg[X(j)] (X(j)∈Rj)；
2) And (4) cluster updating:
Figure BDA0002115795130000132
Figure BDA0002115795130000141
recalculate each RjNew center point C ofj＝avg[X(j)] (X(j)∈Rj)；
3) Termination judgment conditions:
if(Cj(T+1)≠Cj(T)) (T is the number of clustering iterations),re-executing the clustering update of the step 2);
after else clustering is finished, turning to the step 4);
4) and (3) outputting a clustering result:
get clusters RjInitial center point C ofj *；
Spreading constant
Figure BDA0002115795130000142
Step S23, RBF training
The RBF model training adopts a gradient descent method and minimizes an objective function Ei(i ═ 1,2,3) implementation for each hidden layer node RjA data center point C of (j 1.. n)jExpansion constant σjAnd the output weight wjiThe adaptive adjustment of (3). The RBF training comprises the following steps: weight initialization, training data set, termination condition judgment and training result output are as follows:
1) randomly initializing the weight value:
Figure BDA0002115795130000143
2) training data set:
for k＝1 to M
calculation of RjAnd (3) outputting:
Figure BDA0002115795130000144
calculate all output layer outputs:
Figure BDA0002115795130000145
calculating an output layer error: e.g. of the typei(k)＝0-ymi(k) (i＝1,2,3) (12)
Calculating an output layer objective function:
Figure BDA0002115795130000151
using gradient descent method to adjust the regulating quantity Delta Cj，Δσj，ΔwijAnd (3) accumulating:
Figure BDA0002115795130000152
Figure BDA0002115795130000153
Figure BDA00021157951300001511
end for
parameter adjustment: cj(t)＝Cj(t-1)+ΔCj(k) (17)
σj(t)＝σj(t-1)+Δσj(k) (18)
wji(t)＝wji(t-1)+Δwji(k) (19)
Averaging the target function of the output layer:
Figure BDA0002115795130000155
3) determination of termination condition
if(Ji<Jh) Training is finished, go to step 4) (J)hAs an objective function threshold value)
else t ═ t +1, and re-perform step 2), training the dataset;
4) end of training
To obtain each RjFinal center point
Figure BDA0002115795130000156
Weight value
Figure BDA0002115795130000157
Spreading constant
Figure BDA0002115795130000158
Step S24, RBF test
The RBF test is to substitute the new data of the test set into the RBF model according to each RjFinal center point
Figure BDA0002115795130000159
And an extension constant
Figure BDA00021157951300001510
Get the output yh of the hidden layerj(k)：
Figure BDA0002115795130000161
Further according to the weight of each cluster
Figure BDA0002115795130000162
Obtaining three-channel output of the system:
Figure BDA0002115795130000163
step S3, establishing a PSORBFD decoupling controller: and (3) improving the RBFD decoupling controller by adopting a PSO particle swarm optimization algorithm, and establishing a PSORBFD decoupling controller.
In step S2, the weight w is initialized due to RBF model trainingji *The RBF algorithm is generated randomly, and if the initial value of the weight is unreasonable, the subsequent training iteration process is increased, so that the efficiency of the RBF algorithm is influenced. Therefore, in the embodiment, a PSO Particle Swarm Optimization algorithm (Particle Swarm Optimization) is adopted to improve the RBFD algorithm aiming at the above problems, a PSORBFD controller is designed, and the decoupling performance and the anti-interference capability are enhanced while the training time of the gradient descent method is reduced.
Based on RBFD control algorithm, constructing the following PSO particle swarm:
Wp: particle Wp＝(Wp(1),Wp(2),...,Wp(Np) Wherein N) ispIs the particle swarm scale;
Wp(s): single particle Wp(s)＝[w11,w12,w13,...,wj1,wj2,wj3,...wn1,wn2,wn3]N is the number of hidden layers, wji( i 1,2,3, j 1, 2.. and n) are weights of 3 output layers of each hidden layer of the RBFD;
Lp: particle set WpDimension of(s), Lp＝n×3；
Mp: maximum iteration updating times;
v(s): moving speed of the s-th particle, (s ═ 1,2,3 … Np)；
Vmax: a particle maximum velocity threshold;
Fp(s): particle fitness;
Jg: an error threshold;
Pbest(s): individual extreme value, particle Wp(s) iteratively updating the state of minimum fitness in the process;
Gbest: global extreme value, Pbest(s) the least suitable particle;
Fpbest(s): fitness of individual extreme value, particle Wp(s) a minimum fitness in an iterative process;
FGbest: global extreme fitness, FpbestMinimum value of (1).
The specific process for improving the RBFD decoupling controller by adopting the PSO particle swarm optimization algorithm comprises the following steps:
1) initializing particle swarm parameters:
randomly generating NpParticles constituting a particle set Wp；
Selecting an implicit layer output yhk (j) (j is 1.. n) of a certain input X (k) as an initial training set of the particle swarm optimization;
the current iteration time Times is 1;
2) calculating the fitness of all particles:
Figure BDA0002115795130000171
3) particle data updating:
updating individual extremum P by adopting optimal principlebest(s), individual extremum fitness Fpbest(s)；
And updating the global extremum: gbest＝min[Pbest(s),(s＝1...Np)]
Updating global extreme fitness: fGbest＝min[Fpbest(s),(s＝1...Np)]
Wherein, the Pbest(s) represents a particle Wp(s) the state with the lowest fitness in the iterative update procedure, Fpbest(s) represents a particle Wp(s) minimum fitness in the iterative Process, GbestRepresents Pbest(s) the least adaptive particle, FGbestIs represented by FpbestMinimum value of (1);
4) update the velocity, position and number of iterations of each particle:
Figure BDA0002115795130000181
Wp(s)＝Wp(s)+V(s)
wherein
Figure BDA0002115795130000182
Is an inertia factor, ξ1，ξ2Is an acceleration constant
Speed limiting: l V(s) l < Vmax
Particle updating: wp(s)＝Wp(s)+V(s)
Where v(s) represents the moving speed of the s-th particle (s ═ 1,2,3 … N)p)，Wp(s) represents a single particle, VmaxRepresents a particle maximum velocity threshold;
5) judging training termination conditions:
if(Times＞Mp||Gbest＜Jg) And the algorithm is finished, and the step 6) is carried out;
else Times is equal to Times +1, and the step 2) is returned, and the particles are retrained;
wherein M ispRepresents the maximum number of iterative updates, JgRepresents an error threshold;
6) outputting initial values of the weights:
after the positions of the obtained global extremum particles are normalized, the positions are used as weight initial values for RBFD controller training
Figure BDA0002115795130000183
。
After the initial weight value is obtained through the algorithm, the adverse effect caused by the random initial weight value can be reduced, and therefore the training speed of the RBF network is effectively improved.
Example 2 Experimental comparative analysis
System experimental environment
In order to verify the effect of the PSORBFD decoupling controller described in embodiment 1 above, in this embodiment, the following four controllers are used to perform experimental simulation on the film thickness control model in the MATLAB environment.
PID: a PID controller;
SFFD: a feedforward-like decoupling controller;
RBFD: an RBF neural network decoupling controller;
PSORBFD: a PSO-based RBF decoupling controller.
The controlled object model of the experiment in this embodiment is a second-order discrete transfer function model described in equations (2), (3), and (4). Setting v based on the model1＝v2＝v3When the system is stable, the data with time 401:1400 is selected as the training sample, as shown in fig. 7.
The initial clustering number of RBFD is set to 20 groups, the clustering result after training is shown in FIG. 8, and since no data belongs to the 1 st and 14 th data centers after iteration, the 2 data centers are deleted and the other 18 data centers are reserved.
Table 1 shows the settings of the various controller parameters during the simulation experiment.
TABLE 1 control parameter settings for four decoupled controller simulations
Figure BDA0002115795130000191
(II) RBF training process comparative analysis
Fig. 9 and 10 are comparison of the training process of the RBFD controller and the PSORBFD controller, respectively, where the abscissa is the number of times of training and the ordinate is the output value of the output layer, where fig. 9(a), 9(b), and 9(c) are the output results of the output layers ym1, ym2, ym3 of the RBFD controller, respectively, and fig. 10(a), 10(b), and 10(c) are the output results of the output layers ym1, ym2, ym3 of the PSORBFD controller, respectively. As can be seen from the figure, the number of training iterations of the RBFD is 27, while the PSORBFD only needs 5, and the training speed improvement effect on the RBF model is very obvious.
(III) decoupling performance comparison analysis
In order to verify the effectiveness of the decoupling design model algorithm of the BOPP film thickness control system, 1400 groups of data are selected as test samples, and input signals v1＝v2＝v3At different sampling time points, the system is stable with three input signals v being 31，v2，v3Adding different interfering signals:
for v1Adding a sine wave interference with the duration of 125 and the amplitude of 0.25 at the 50 th sampling time point;
for v2At the 250 th sampling time point, a step signal is added to convert v to2From 3 to 4;
for v3At the 700 th sampling point, a sawtooth disturbance with a duration of 50 and an amplitude of 0.6 is added.
Under the above input signal conditions, fig. 11 is a graph of the system output response result of the thickness control system using the PID controller and the SFFD controller, fig. 12 is a graph of the system output response result of the SFFD controller and the RBFD controller, fig. 13 is a graph of the system output response result of the SFFD controller and the PSORBFD controller, and table 2 is the performance index data of the PID, SFFD, RBFD, and PSORBFD controllers. Therefore, the anti-interference capability of the SFFD controller is obviously improved compared with that of a PID controller, but when an input signal of the system is suddenly changed, a coupling phenomenon to a certain degree still exists, the anti-coupling capability of the RBFD controller is stronger, when an interference signal of a certain channel appears, output signals of other channels basically do not fluctuate, the coupling of the system is basically eliminated, the anti-coupling capability of the PSORBFD controller is equivalent to that of the RBFD controller, and the whole system achieves a good decoupling control effect.
TABLE 2 PID, SFFD, RBFD, PSORBFD controller Performance index data
Figure BDA0002115795130000211
From a combination of FIGS. 9-13 and Table 2, the results of the above experiments can be seen:
(1) by adopting the PID controller, the system has long and unstable adjustment time on the coupling influence, the anti-interference capability is weak, and the influence of the change of one channel on other channels is great.
(2) Compared with a PID (proportion integration differentiation) controller, the SFFD controller is adopted, the adjustment time of the coupling influence of the system is obviously shortened, the anti-interference capability is improved, and the coupling influence on other channels when one channel is changed is obviously reduced.
(3) By adopting the RBFD controller, the main channel of the system is basically not influenced by interference signals of other channels, the decoupling performance of the system is good, but the training time of the RBF model is too long (27 times).
(4) By adopting the PSORBFD controller, compared with the RBFD controller, the convergence speed is accelerated (5 times) in the RBF training process, and the system decoupling performance is equivalent to that of the RBFD controller.
In conclusion, after the film thickness control system adopts the PSORBFD controller provided by the text, the RBF model training efficiency of the system is optimal, the response speed is high, the anti-interference capability is strong, the coupling relation between the systems is almost completely eliminated, and the whole system achieves better control quality.
The foregoing merely illustrates the principles and preferred embodiments of the invention and many variations and modifications may be made by those skilled in the art in light of the foregoing description, which are within the scope of the invention.

Claims (1)

1. A PSORBFD fast self-adaptive decoupling control method is characterized by comprising the following steps:
s1, system modeling: determining a transfer function matrix model of the system according to the relation between the control quantity and the output quantity;
the system modeling specifically comprises the following steps:
taking the thickness of each channel as a measured value and the temperature of the heating bolt as a control quantity to form a three-input three-output control system, and setting the system control quantity as (u)1，u2，u3) The output quantity is (y)1，y2，y3) Wherein each output quantity yiSubject to a plurality of control quantities u simultaneouslyiTo determine a transfer function matrix model for the three channel thickness system, as follows:
Figure FDA0003514060410000011
s2, establishing an RBFD decoupling controller: the RBFD decoupling controller comprises an input layer, a hidden layer and an output layer, and the decoupling control process of the RBFD decoupling controller comprises RBF initialization, RBF clustering, RBF model training and RBF testing;
the RBF initialization is to initialize system data, and the system data comprises: input samples X (k), hidden layer RjNumber of clusters, data center CjThe spreading constant σjAnd a hidden layer RjWeight w to output layer iji(ii) a Then extracting M pieces of running data as a training set of the RBF network, and taking all coupling influence correlation factors as system input of the RBF network, wherein the expression is as follows:
Figure FDA0003514060410000012
the RBF clustering specifically comprises the following steps:
1) initializing clusters:
randomly dividing all data x (k), k 1.. M of the dataset into n clusters, Rj，j＝1...n；
To obtain each RjCenter point C ofj＝avg[X(j)]，X(j)∈Rj；
2) And (4) cluster updating:
Figure FDA0003514060410000021
recalculate each RjNew center point C ofj＝avg[X(j)]，X(j)∈Rj；
3) Termination judgment conditions:
if(Cj(T+1)≠Cj(T)), if T is the clustering iteration frequency, re-executing the clustering update in the step 2);
after else clustering is finished, turning to the step 4);
4) and (3) outputting a clustering result:
get clusters RjInitial center point C ofj *；
Spreading constant
Figure FDA0003514060410000022
The RBF model training adopts a gradient descent method and minimizes an objective function EiI-1, 2,3 implementation for each hidden layer node RjN, j ═ 1.. njExpansion constant σjAnd the output weight wjiThe adaptive adjustment specifically includes:
1) randomly initializing the weight value:
Figure FDA0003514060410000023
2) training data set:
for k＝1 to M
calculation of RjAnd (3) outputting:
Figure FDA0003514060410000024
calculate all output layer outputs:
Figure FDA0003514060410000031
calculating an output layer error: e.g. of the typei(k)＝0-ymi(k)，i＝1,2,3(12)
Calculating an output layer objective function:
Figure FDA0003514060410000032
using gradient descent method to adjust the regulating quantity Delta Cj，Δσj，ΔwijAnd (3) accumulating:
Figure FDA0003514060410000033
Figure FDA0003514060410000034
Figure FDA0003514060410000035
end for
parameter adjustment: cj(t)＝Cj(t-1)+ΔCj(k) (17)
σj(t)＝σj(t-1)+Δσj(k) (18)
wji(t)＝wji(t-1)+Δwji(k) (19)
Averaging the target function of the output layer:
Figure FDA0003514060410000036
3) determination of termination condition
if(Ji<Jh) Training is finished, go to step 4), JhIs an objective function threshold;
else t ═ t +1, and re-perform step 2), training the dataset;
4) end of training
To obtain each RjFinal center point
Figure FDA0003514060410000037
Weight value
Figure FDA0003514060410000038
Spreading constant
Figure FDA0003514060410000039
The RBF test is to substitute the new data of the test set into the RBF model according to each RjFinal center point
Figure FDA00035140604100000310
And an extension constant
Figure FDA00035140604100000311
Get the output yh of the hidden layerj(k)：
Figure FDA00035140604100000312
Further according to the weight of each cluster
Figure FDA00035140604100000313
Obtaining three-channel output of the system:
Figure FDA0003514060410000041
s3, establishing a PSORBFD decoupling controller: improving the RBFD decoupling controller by adopting a PSO particle swarm optimization algorithm, and establishing a PSORBFD decoupling controller;
the specific process for improving the RBFD decoupling controller by adopting the PSO particle swarm optimization algorithm comprises the following steps:
1) initializing particle swarm parameters:
randomly generating NpParticles constituting a particle set Wp；
Selecting an implicit layer output yhk (j) of a certain input X (k), wherein j is 1.. n, and the implicit layer output yhk (j) is used as an initial training set of the particle swarm optimization;
the current iteration time Times is 1;
2) calculating the fitness of all particles:
Figure FDA0003514060410000042
3) particle data updating:
updating individual extremum P by adopting optimal principlebest(s), individual extremum fitness Fpbest(s)；
And updating the global extremum: gbest＝min[Pbest(s),(s＝1...Np)]
Updating global extreme fitness: fGbest＝min[Fpbest(s),(s＝1...Np)]
Wherein, the Pbest(s) represents a particle Wp(s) the state with the lowest fitness in the iterative update procedure, Fpbest(s) represents a particle Wp(s) minimum fitness in the iterative Process, GbestRepresents Pbest(s) the least adaptive particle, FGbestIs represented by FpbestMinimum value of (1);
4) update the velocity, position and number of iterations of each particle:
Figure FDA0003514060410000051
Wp(s)＝Wp(s)+V(s)
wherein
Figure FDA0003514060410000052
Is an inertia factor, ξ1，ξ2Is an acceleration constant
Speed limiting: l V(s) l < Vmax
Particle updating: wp(s)＝Wp(s)+V(s)
Where v(s) represents the moving speed of the s-th particle, and s is 1,2,3 … Np，Wp(s) represents a single particle, VmaxRepresents a particle maximum velocity threshold;
5) judging training termination conditions:
if(Times＞Mp||Gbest＜Jg) And the algorithm is finished, and the step 6) is carried out;
else Times is equal to Times +1, and the step 2) is returned, and the particles are retrained;
wherein M ispRepresents the maximum number of iterative updates, JgRepresents an error threshold;
6) outputting initial values of the weights:
after the positions of the obtained global extremum particles are normalized, the positions are used as weight initial values for RBFD controller training
Figure FDA0003514060410000053
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