CN113947202A - Design method of industrial process multi-state perception prediction controller - Google Patents

Design method of industrial process multi-state perception prediction controller Download PDF

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CN113947202A
CN113947202A CN202111096738.9A CN202111096738A CN113947202A CN 113947202 A CN113947202 A CN 113947202A CN 202111096738 A CN202111096738 A CN 202111096738A CN 113947202 A CN113947202 A CN 113947202A
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于淼
杨博
李宏光
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Beijing University of Chemical Technology
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Abstract

The invention discloses a design method of an industrial process multi-state perception prediction controller, which adopts a method of establishing a multi-state prediction model, trains an ESN neural network through historical data under different working points, establishes prediction model submodels corresponding to the different working points, reflects the characteristics of a controlled process when the working points are switched, solves an optimization algorithm by states according to the multi-characteristic characteristics, and finally obtains a control strategy meeting the process requirements. Compared with single-state optimization, the method adopting multi-state optimization can solve an optimal control strategy better according to different characteristics of a controlled process.

Description

Design method of industrial process multi-state perception prediction controller
Technical Field
The invention relates to a perception prediction controller aiming at multiple states of an industrial process, belongs to the technical field of industrial controllers, and is verified by using an ethanol-water rectifying tower as an example.
Background
The invention is mainly used for controlling the chemical process with multi-state characteristics, and the multi-state characteristics are generally generated by the factors of the intensity of the working load of the controlled process, the disturbance magnitude, different process requirements and the like. For a controlled object with the characteristics, a common prediction controller mostly adopts a method of training a neural network by using historical data to fit a multi-state controlled process, establishes a single prediction model, and designs a corresponding optimization algorithm to solve an optimal control strategy. However, once the operating point of the controlled process changes due to the multi-state factor, the original prediction model cannot accurately predict the future characteristics of the controlled object, so that the final control effect does not meet the process requirement, which is also a main reason why the prediction control is difficult to be implemented in the industrial field. At this time, the safety and the economy of the controlled object need to be fully considered, and a multi-state predictive controller needs to be established to obtain an optimal control strategy.
In order to build a more efficient nonlinear prediction model, a deep learning method is combined with prediction control, which has attracted much attention in recent years. The echo state network is an improved recurrent neural network, has certain advantages in nonlinear time sequence processing and dynamic system prediction, and overcomes the defects of high training difficulty, long running time and the like of the traditional RNN. The hidden layer of the traditional MLP network is a layer-by-layer fully-connected neuron, and the ESN introduces a reserve pool calculation mode to replace the original hidden layer. The network uses a recursive structure with large-scale loose connections as hidden layers, also called dynamic reservoirs, which help to improve the "echo" characteristics of the network. The hidden layer is an important link of information processing, and also a core part of the ESN, and an input layer and an output layer are provided in addition. The ESN neural network is used for establishing a prediction model, and the input and output characteristics of the controlled process at a certain working point can be well reflected.
The existing predictive control technology combined with deep learning generally adopts a predictive control algorithm based on an LSTM neural network, a predictive control algorithm based on an ESN neural network and the like. When the control problem of the multi-state chemical process is processed, the following problems mainly exist:
1. at present, a prediction model based on a single model in a multi-state industrial process cannot well reflect system characteristics, and particularly when a working point changes, model mismatch is serious.
2. In the face of multi-state industrial process characteristics, an optimization algorithm is not considered according to the situation, and a control strategy meeting the requirements cannot be solved well.
3. The control strategy switching of different states often generates larger fluctuation, influences the final control effect and generates larger loss to the controller.
Disclosure of Invention
In order to solve the problems, a design method of a predictive controller for the multi-state chemical process is invented. The invention adopts a method for establishing a multi-state prediction model, trains an ESN neural network through historical data under different working points, establishes prediction model sub-models corresponding to the different working points, reflects the characteristics of a controlled process when the working points are switched, solves an optimization algorithm in different states according to the multi-characteristic characteristics, and finally obtains a control strategy meeting the process requirements.
The technical scheme of the invention is as follows: the design method of the prediction controller is based on the combination of a model switching module, a multi-state prediction model, a multi-state optimization algorithm and a disturbance-free switching module. The multi-state prediction model and the multi-state optimization algorithm are trained and designed in advance by using historical data of a controlled process and then put into use together with other modules. When new data is input, the data enters a model switching module firstly, feature extraction is carried out, and models are matched; then entering a corresponding sub-model in the multi-state prediction model to obtain future output data of the controlled object; then, entering a multi-state optimization algorithm to calculate and output an optimal control strategy; finally, the control strategy is input into a non-disturbance switching module, and when model switching occurs, the module enables the output control strategy not to generate large fluctuation due to switching through a corresponding algorithm; the undisturbed switching module inputs the final control strategy into the controlled process, and part of the output of the controlled process is fed back to the model switching module to form a closed loop. The structure of the multi-state model predictive control method is shown in fig. 1.
Further, the model switching module: the module adopts a static CNN convolutional neural network, labels are attached to historical data in different states in an off-line state, and the labels are used for distinguishing the different states. And (3) training a CNN neural network by using the data with the labels, wherein the trained neural network is used as a model switching module. When the controller runs, real-time data enters the CNN neural network, and the CNN neural network can judge which state the current data is in according to the characteristics of the data.
And further, a multi-state prediction model is adopted, when the controlled process has multi-state characteristics, the multi-state model is adopted, historical data of different states of the controlled process are respectively trained to establish sub-models by an ESN neural network, and finally all the sub-models are integrated to establish the multi-state prediction model, so that the future characteristics of the system can be accurately reflected, and the multi-state prediction model can be better served for a prediction controller. The method for establishing the ESN submodel comprises the following steps:
the ESN echo state network structure comprises an input layer, a reserve pool and an output layer in sequence, wherein the reserve pool is a middle part. The connection state of the neurons in the pool is random. The architecture of the echo-stateful network is shown in fig. 2.
Suppose that the echo state network has N intermediate nodes, i.e. the number of neurons in the reserve pool is N, and the number of neurons in the input layer and the output layer are both D. With u (t) e RD,x(t)∈RN,f(t)∈RDRespectively representing the input at the time t, the state and the output of the network state reserve pool; v is an element of RN×D,R∈RN×N,W∈RD×NRespectively representing input weight, intermediate weight and output weight matrix, and tanh (-) is an activation function, wherein R represents a matrix dimension.
The state updating mode of the reserve pool and the output of the network are as follows:
Figure BDA0003269176440000031
the training of the echo state network mainly comprises the following steps:
the initialization operation is performed first, and the size of the reserve pool, i.e. the number of neurons, is determined first. Like the conventional MLP (multi-layer perceptron), the larger the number of nodes, the stronger the fitting ability. Since the ESN neural network linearly fits the output result only by adjusting the output weight, the general ESN neural network needs to be much larger than the node scale of the general neural network.
This is followed by the random generation of a connection matrix, which indicates which neurons have connections between them, and the direction and weight of the connections, and is in fact a matrix representation of a directed graph. The following scaling matrix is in fact a normalization operation, using a scaling factor with which the original randomly generated matrix is multiplied, faster than scaling using eigenvalues. The weight is initialized to between 0-1 (or-1 to 1) for two reasons:
(1) under the influence of the activation function, the distinction degree of sigmoid and tanh activation functions is larger between 0 and 1, but the activation value is not changed greatly after the difference is larger than 1;
(2) when the activation function is derived, it can be seen that when the activation function is greater than 1, the image is relatively flat, and the derivative is close to 0, so that when the gradient is calculated, the gradient is too small, and the update of the weight cannot be smoothly realized. It is mainly a first problem that the ESN does not use gradients to update the weights. And finally, randomly generating an input weight V and an output weight W.
For the echo state network ESN, all its cyclic connections are inside the hidden unit. The weight connection parameters from the input unit to the hidden unit are randomly created according to actual requirements, and cannot be changed once being created, while the weight connection parameters from the hidden unit to the output unit and the weight connection parameters from the input unit to the output unit can be determined only when the echo state network is trained. The prediction model established by the ESN neural network can be written in the form of a state space. Assuming that the ESN neural network has q hidden units at each time step, the model based on the ESN neural network can be written as the following expression;
Figure BDA0003269176440000041
where γ is a linear self-join parameter, representing the number of hidden units x (k-1) to x (k)There is a linear self-connection, such a hidden unit is also called a leaky unitγApproaching 0, information over a long period of time may be remembered by the echo state network whenγWhen approaching 1, the past state information is forgotten. A is an input weight matrix, D is a cyclic connection matrix, E represents weight connection information from a hidden layer to an output layer, and H represents a weight connection matrix from an input unit to an output unit. Wherein the weight matrices a and D are randomly generated by the system and do not change during the training process, while the values of the weight matrices E and H need to be learned during the training of the echo state network. f is a non-linear function for dealing with non-linear problems. T (k) is the future output response of the controlled process, Fd(k) Is an input control variable that affects the output response of the controlled system.
Through the state space expression of the formula (2), on the basis of accurately predicting the future response of the system, the related optimization problem can be conveniently solved, and then the optimal control strategy is solved. And integrating the sub models corresponding to different states to obtain the multi-state model applied to the multi-state model predictive controller.
Further, a multi-state optimization algorithm: in the optimization algorithm, a minimum value of a function is required, and in each iteration, the value of the objective function is required to be decreased. The confidence domain method, as the name implies, starts from an initial point, first assumes a maximum displacement that can be relied on, and then finds an optimal point of an approximate function (quadratic) of the objective function in an area that takes the current point as the center and the radius to obtain the true displacement. After the displacement is obtained, calculating an objective function value, if the reduction of the objective function value meets a certain condition, indicating that the displacement is reliable, and continuing to carry out iterative calculation according to the rule; if the objective function value can not be reduced to meet a certain condition, the range of the confidence domain is reduced, and then the solution is carried out again. The LM algorithm is an optimization algorithm based on a trust domain method.
The main idea of the LM algorithm is: first, a step length r is selected so that the value of x-x is | |kIn the range of | < r (confidence domain), aimThe target function is approximated by an n-dimensional quadratic model, and a search direction s is selected therefromkTaking xk+1＝xk+skThus, the LM algorithm has fast local convergence of Newton's method and also has excellent overall convergence. The specific implementation method for applying the LM algorithm to the predictive control is as follows:
the main challenge problem faced by the prediction control method based on the ESN neural network is how to deal with the nonlinearity of the echo state network thermal model when calculating an optimization problem, and a specific algorithm for solving the problem is as follows: first, at the present time k, the future Nc-step input manipulated variables (unknown variables that need to be calculated) are represented as:
Fd＝[Fd(k+1),Fd(k+2),…,Fd(k+Nc)]T (3)
similarly, the future input dynamic manipulated variable difference trajectory for Nc time steps is represented as:
ΔFd＝[ΔFd(k+1),ΔFd(k+2),…,ΔFd(k+Nc)]T (4)
the future outputs of the system controlled variables at Np future times predicted from the present time k are then expressed as:
T＝[T(k+1|k),T(k+2|k),…,T(k+Np|k)]T (5)
the set points may be expressed as:
Ttg＝[Ttg,Ttg,Ttg,…,Ttg]T (6)
the control objective is to calculate the optimal manipulated variables to make the predicted controlled variables output as close to the set point as possible. This control problem can be translated into the following optimization problem:
min||Ttg-T||2 (7)
for practical purposes, the part r of a variable is adjustedw||ΔFd||2Adding the cost function to the original cost function to form a new adjustable optimization problem, wherein the expression can be written as the following form:
min||Ttg-T||2+rw||ΔFd||2 (8)
wherein r iswIs an adjustment parameter. r isw||ΔFd||2Is used to adjust the size of the input dynamic manipulated variable to prevent the calculated manipulated variable from being too large to be of practical significance. The above formula, in a manner convenient for expression, can be rewritten in the following form:
Figure BDA0003269176440000051
wherein F (F)d) Denotes that F is FdAs a function of (c).
Figure BDA0003269176440000052
Is a diagonal matrix of the grid,
Figure BDA0003269176440000053
is an identity matrix and R represents the dimension of the matrix.
To solve the above multi-state optimization algorithm, the LM algorithm is introduced. During each iteration, a search offset Δ ε needs to be calculated, and then the dynamic control variable results are updated using the following formula.
Fd←Δε+Fd (10)
In the above equation, Δ ∈ indicates a search offset to be calculated, and it is necessary to establish that Δ ∈ be calculatedψAnd a Jacobian matrix F of Δ ε1And F2They can be represented as:
Figure BDA0003269176440000061
the offset Δ u in the LM algorithm is then calculated:
Figure BDA0003269176440000062
wherein;
Figure BDA0003269176440000063
τ in the above equation is the non-negative damping coefficient that is adjusted at each iteration. If the value of f is reduced after the iteration, v of τ divided by v is set empirically. If the value of f increases after the iteration, τ is multiplied by ν. The value of the search offset Δ ∈ can be solved using the gaussian elimination method without the need for a true de-calculated value. To calculate the search offset Δ ε using the above formula, the Jacobian matrix F is first calculated1And F2。
For the first Jacobian matrix F1It can be written as follows:
Figure BDA0003269176440000064
using the formula of the ESN, the formula,
Figure BDA0003269176440000065
can be easily calculated using the following method:
(1) when i < j, because the future input does not affect the present output:
Figure BDA0003269176440000066
(2) when i ═ j, can give
Figure BDA0003269176440000071
Wherein
Figure BDA0003269176440000072
z(k+i|k)＝AFd(k+i)+Dx(k+i-1|k) (18)
(3) When i > j is greater than the sum of the values,
Figure BDA0003269176440000077
wherein
Figure BDA0003269176440000073
Because of Δ Fd(k+i+1)＝Fd(k+i+1)-Fd(k + i), a second Jacobian matrix F2Can be calculated by:
(1) when i ═ j, can give
Figure BDA0003269176440000074
(2) When i is j +1, there are
Figure BDA0003269176440000075
(3) In other cases;
Figure BDA0003269176440000076
finally F can be converted into2Written as follows:
Figure BDA0003269176440000081
now, for each iteration, there is a jacobian matrix F1And F2The search offset variable may then be calculated using a formula and the solution for the next iteration updated using the formula. This iteration will continue until the convergence requirement is reached. By iterationCan find an optimized manipulated variable output Fd。
By using the method, the optimization algorithms corresponding to different submodels are respectively established, and the multi-state optimization algorithm can be obtained.
A disturbance-free switching module: when the controller determines that the model switching is required, as shown in fig. 3, in order to enable the controller to be capable of smoothly switching and avoid the large fluctuation of the actuator from affecting the economic and safety benefits, a non-disturbance switching module is required to be added. The specific implementation of the undisturbed handover is as follows:
at time k, regardless of Δ u1Switch to Δ u2Again from Δ u2Switch to Δ u1The final value of Δ u remains unchanged. Adding an offset factor e to the output variable of the switchuAt the instant of switching the switch, to euA correction is made to keep the output variable at its original value. A bumpless switching diagram is shown in fig. 3. From Δ u in steps k-1 to k1To Δ u2By calculating to obtain Δ u1And Δ u2Then, do euCorrection of (2):
eu(k)＝Δu(k-1)-Δu2(k) (24)
then Δ u (k) ═ Δ u2(k)+eu(k)＝Δu2(k)+Δu(k-1)-Δu2(k) The value of Δ u is maintained before and after the handover, so that the handover is undisturbed.
The method adopts a multi-state model modeling method facing the multi-state chemical process, and can better reflect the multi-state characteristics of the controlled process compared with the traditional method adopting a single model. Compared with single-state optimization, the method adopting multi-state optimization can solve an optimal control strategy better according to different characteristics of a controlled process.
Drawings
Fig. 1 is a diagram of a multi-state model predictive control method.
Fig. 2 is a diagram of an echo state network architecture.
Fig. 3 is a schematic diagram of control policy switching.
Fig. 4 is a schematic diagram of undisturbed handover of the control strategy.
FIG. 5 is a schematic diagram of an ethanol-water rectification column.
FIG. 6 is a simulation experiment diagram of an ethanol-water rectifying tower.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description
FIG. 5 is a prototype model of an ethanol-water rectification column, which can be seen to have 8 trays with a feed position between the fourth and fifth trays. The basic control includes:
(1) the feed flow is controlled by a flow regulator FC-01;
(2) the liquid levels of the reflux tank (D-01) and the reboiler at the bottom of the tower are respectively controlled by LC-01 and LC-02;
(3) the liquid temperature on the first tower plate is controlled by adjusting the reflux ratio by TC-01, and the liquid temperature on the eighth tower plate is controlled by the heating power of a TC-02 adjusting heater (H-01).
Note that the reflux drum liquid level and the output of the first stage tray temperature regulator are simultaneously fed to a reflux ratio calculation unit (RFR) which outputs the opening values of the overhead product flow control valve (LV-01) and the reflux flow control valve (TV-01).
Furthermore, an ethanol-water rectification column is assumed and has the following characteristic assumptions:
(1) it is assumed that the overhead condenser (E-01) has sufficient condensing power and the effluent temperature is constant.
(2) The overhead reflux drum is open, i.e. its pressure is atmospheric (0.101325 MPa).
(3) The reboiler at the bottom of the tower is electrically heated, and the maximum heating power is 2 kW.
The control objective of the ethanol-water rectification column is to purify the ethanol from the mixture of ethanol and water, the purified ethanol will flow out of the top of the column, and it is necessary to meet the requirement that the ethanol reaches a certain concentration. In a control system of the ethanol-water rectifying tower, the liquid level is controlled simply by adopting a PID controller. For the controllers TC-01 and TC-02, strong nonlinearity and strong coupling exist in the control of the temperature of the tower plate at the first layer and the temperature of the tower plate at the eighth layer, and the multi-state perception prediction controller designed by the invention is adopted.
The most common multi-state characteristic in the ethanol-water rectifying tower is caused by different feed material components, a single model is mostly adopted to establish a prediction model in the past implementation of prediction control, and once the feed components are changed to cause the change of a control working point, the accuracy of the original prediction model is reduced, and the control effect is poor.
And (3) simulation process:
(1) the feed was 30 ℃ ethanol-water mixture liquid, wherein the mole fractions of ethanol and water in the initial stage were both 50%, the feed flow was 0.0871kmol/h, the mole fractions of ethanol and water at 10000s were changed to 30% and 70%, and the feed flow was 0.0871 kmol/h.
(2) The amount of initial liquid on the reflux drum and each tray was 0.
(3) The reboiler contained 0.06115kmol of a 30 ℃ ethanol-water mixture with mole fractions of ethanol and water of 0.5 each.
(4) The reflux tank liquid level regulator (LC-01), the reboiler liquid level regulator (LC-02) and the layer 8 tower plate liquid temperature regulator (TC-02) are all arranged automatically, and the set points are 50%, 50% and 90 ℃ respectively. The first-stage tray liquid temperature regulator (TC-01) was manually operated, and 12% of the output was set, i.e., the reflux ratio (R) was controlled to 1.2.
The simulation result is shown in the simulation experiment chart of the ethanol-water rectifying tower in FIG. 6. The experimental result shows that the predictive controller designed by the invention can stably and quickly realize the control of the temperature of the first-layer tower plate and the eighth-layer tower plate of the rectifying tower, and even if the components of the input materials are changed, the disturbance has small influence on the volume fraction occupied by the final product ethanol.

Claims (5)

1. A design method of an industrial process multi-state perception prediction controller is characterized by comprising the following steps: the prediction controller for realizing the design method consists of a model switching module, a multi-state prediction model, a multi-state optimization algorithm and a disturbance-free switching module; the multi-state prediction model and the multi-state optimization algorithm are trained and designed in advance by using historical industrial process data of an industrial field controlled object, and then are put into use together with other modules; when new industrial process data are input, the method firstly enters a model switching module to extract the characteristics of the industrial data and match the model; then entering a corresponding sub-model in the multi-state prediction model to obtain future output industrial process data of the controlled object in the industrial field; then, entering a multi-state optimization algorithm to calculate and output an optimal control strategy; finally, the control strategy is input into a non-disturbance switching module, and when model switching occurs, the module enables the output control strategy not to generate large fluctuation due to switching through a corresponding algorithm; and the undisturbed switching module inputs the final control strategy to the industrial field controlled object, and part of the output of the controlled object is fed back to the model switching module to form the whole set of industrial process control system.
2. The design method of the industrial process multi-state perception prediction controller according to claim 1, characterized in that: the model switching module adopts a static CNN convolutional neural network, labels are attached to industrial process historical data in different states in an offline state, and the labels are used for distinguishing the different states; training a CNN neural network by using the industrial process data with the labels, wherein the trained neural network is used as a model switching module; when the controller runs, real-time industrial data enters the CNN neural network, and the current data is judged to be in which state according to the characteristics of the data.
3. The design method of the industrial process multi-state perception prediction controller according to claim 1, characterized in that: multi-state prediction model: when the controlled process has multi-state characteristics, respectively training the historical data of the industrial process of different states of the controlled object by adopting a multi-state model to establish a sub-model by an ESN neural network, and finally integrating all the sub-models to establish a multi-state prediction model;
the method for establishing the sub-model comprises the following steps: the ESN echo state network structure comprises an input layer, a reserve pool and an output layer in sequence, wherein the reserve pool is a middle part; the connection state of neurons in the reservoir is random; suppose the echo state network has N intermediate nodes, namely N neurons in the reserve pool, outputThe number of neurons in the input layer and the output layer is D; with u (t) e RD,x(t)∈RN,f(t)∈RDRespectively representing the input at the time t, the state and the output of the network state reserve pool; v is an element of RN×D,R∈RN×N,W∈RD×NRespectively representing an input weight matrix, an intermediate weight matrix and an output weight matrix, and tanh (-) is an activation function, wherein R represents a matrix dimension;
the state updating mode of the reserve pool and the output of the network are as follows:
Figure FDA0003269176430000021
where x (t) represents reservoir status, f (t) represents neural network output;
obtaining a state space form through a prediction model established by an ESN neural network; assuming that the ESN neural network has q hidden units in each time step, the model based on the ESN neural network is written into the following expression;
Figure FDA0003269176430000022
where γ is a linear self-join parameter indicating that there is a linear self-join from the hidden unit x (k-1) to x (k); a is an input weight matrix, D is a cyclic connection matrix, E represents weight connection information from a hidden layer to an output layer, and H represents a weight connection matrix from an input unit to an output unit; wherein, the weight matrixes A and D are generated randomly by the system and do not change in the training process, and the values of the weight matrixes E and H need to be learned in the process of training the echo state network; f is a non-linear function for dealing with non-linear problems; t (k) is the future output response of the controlled object, Fd(k) An input control variable affecting an output response of a controlled system;
and integrating the submodels corresponding to different states through the state space expression of the formula (2) to obtain the multi-state model applied to the multi-state model predictive controller.
4. The design method of the industrial process multi-state perception prediction controller according to claim 1, characterized in that: in the multi-state optimization algorithm, an LM algorithm is adopted, and the specific implementation method is as follows:
first, at the present time k, the future Nc-step input manipulated variable is represented as:
Fd＝[Fd(k+1),Fd(k+2),…,Fd(k+Nc)]T (3)
similarly, the future input dynamic manipulated variable difference trajectory for Nc time steps is represented as:
ΔFd＝[ΔFd(k+1),ΔFd(k+2),…,ΔFd(k+Nc)]T (4)
the future outputs of the system controlled variables at Np future times predicted from the present time k are then expressed as:
T＝[T(k+1|k),T(k+2|k),…,T(k+Np|k)]T (5)
the set points are expressed as:
Ttg＝[Ttg,Ttg,Ttg,…,Ttg]T (6)
the control problem is translated into the following optimization problem:
min||Ttg-T||2 (7)
that is, the output of the controlled variable is close to the target value as much as possible; part r for regulating a variablew||ΔFd||2Adding the cost function to the original cost function to form a new adjustable optimization problem, wherein the expression of the new adjustable optimization problem is written in the following form:
min||Ttg-T||2+rw||ΔFd||2 (8)
wherein r iswIs a tuning parameter; r isw||ΔFd||2The method is used for adjusting the size of the input dynamic manipulated variable and preventing the calculated manipulated variable from being too large and having no practical industrial physical significance; will be provided withThe above formula is replaced by a convenient expression, rewritten in the form of:
Figure FDA0003269176430000031
wherein F (F)d) Denotes that F is FdA function of (a);
Figure FDA0003269176430000032
is a diagonal matrix of the grid,
Figure FDA0003269176430000033
is an identity matrix, R represents the dimension of the matrix;
an LM algorithm is introduced to solve a multi-state optimization algorithm, in each iteration process, a search offset delta epsilon needs to be calculated, and then a dynamic control variable result is updated by using the following formula;
Fd←Δε+Fd (10)
in the above equation,. DELTA.epsilon.represents the search offset to be calculated, and a jacobian matrix F of ψ and. DELTA.epsilon.must be established in order to calculate. DELTA.epsilon1And F2Expressed as:
Figure FDA0003269176430000034
the offset Δ ε in the LM algorithm is then calculated:
Figure FDA0003269176430000035
wherein;
Figure FDA0003269176430000036
τ is the non-negative damping coefficient that is adjusted at each iteration; if the value of fAfter iteration, decreasing, and setting v in the v divided by tau according to an empirical value; multiplying τ by ν if the value of f increases after the iteration; searching for the value of the offset delta epsilon, solving by using a Gaussian elimination method without a true de-calculated value; the above formula is used to calculate the search offset delta epsilon, and the Jacobian matrix F is calculated first1And F2；
For the first Jacobian matrix F1It is written as follows:
Figure FDA0003269176430000041
using the formula of the ESN, the formula,
Figure FDA0003269176430000042
is easily calculated using the following method:
(1) when i < j, because the future input does not affect the present output:
Figure FDA0003269176430000043
(2) when i is equal to j, obtain
Figure FDA0003269176430000044
Wherein
Figure FDA0003269176430000045
z(k+i|k)＝AFd(k+i)+Dx(k+i-1|k) (18)
(3) When i > j is greater than the sum of the values,
Figure FDA0003269176430000046
wherein
Figure FDA0003269176430000047
Because of Δ Fd(k+i+1)＝Fd(k+i+1)-Fd(k + i), a second Jacobian matrix F2Calculated by the following way:
(1) when i is equal to j, obtain
Figure FDA0003269176430000051
(2) When i is j +1, there are
Figure FDA0003269176430000052
(3) In other cases;
Figure FDA0003269176430000053
finally F2Written as follows:
Figure FDA0003269176430000054
for each iteration, there is a jacobian matrix F1And F2Then, calculating a search offset variable by using a formula, and updating a solution of the next iteration by using the formula; this iteration will continue until the convergence requirement is reached; obtaining an optimized manipulated variable output F by an iterative methodd(ii) a And respectively establishing optimization algorithms corresponding to different sub-models to obtain a multi-state optimization algorithm.
5. According to claim1, the design method of the industrial process multi-state perception prediction controller is characterized in that: in the undisturbed switching module, when the controller judges that the model switching is required, the specific implementation mode of the undisturbed switching is as follows: at time k, regardless of Δ u1Switch to Δ u2Again from Δ u2Switch to Δ u1The final value of Δ u remains unchanged; adding an offset factor e to the output variable of the switchuAt the instant of switching the switch, to euMaking a correction to keep the output variable at the original value; from Δ u in steps k-1 to k1To Δ u2By calculating to obtain Δ u1And Δ u2Then, do euCorrection of (2):
eu(k)＝Δu(k-1)-Δu2(k) (25)
then Δ u (k) ═ Δ u2(k)+eu(k)＝Δu2(k)+Δu(k-1)-Δu2(k) The value of Δ u remains unchanged before and after switching.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023226236A1 (en) * 2022-05-26 2023-11-30 福建龙氟新材料有限公司 Energy management control system for electronic grade hydrofluoric acid preparation and control method therefor

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