CN112015081B - Parameter self-tuning method of SISO (SISO) compact-format model-free controller based on PSO-LSTM (particle swarm optimization-least Square transform) cooperative algorithm - Google Patents

Parameter self-tuning method of SISO (SISO) compact-format model-free controller based on PSO-LSTM (particle swarm optimization-least Square transform) cooperative algorithm Download PDF

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CN112015081B
CN112015081B CN202010558464.XA CN202010558464A CN112015081B CN 112015081 B CN112015081 B CN 112015081B CN 202010558464 A CN202010558464 A CN 202010558464A CN 112015081 B CN112015081 B CN 112015081B
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卢建刚
杨晔
陈晨
陈金水
王文海
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Zhejiang University ZJU
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Abstract

The invention discloses a parameter self-tuning method of a SISO (SISO) compact format model-free controller based on a PSO-LSTM (pseudo-static synchronous compensator) cooperative algorithm, which comprises the steps of firstly optimizing an LSTM initial weight coefficient matrix by utilizing the PSO algorithm, then, the system error data set is used as the input of the LSTM neural network, the LSTM neural network carries out forward calculation and outputs parameters to be set of the SISO tight format model-free controller such as punishment factors, step factors and the like through an output layer, the control input is obtained by calculation of the control algorithm of the SISO tight format model-free controller, aiming at the minimization of the value of the system error function, adopting a gradient descent method, combining control input to respectively aim at the gradient information of each parameter to be set, utilizing a chain type rule to carry out system error back propagation calculation, and updating all weight coefficients to be learned in the LSTM neural network in real time on line, and realizing the parameter self-tuning of the controller based on the PSO-LSTM cooperative algorithm. The method provided by the invention can effectively overcome the difficulty of online setting of the controller parameters and has good control effect on the SISO system.

Description

Parameter self-tuning method of SISO (SISO) compact-format model-free controller based on PSO-LSTM (particle swarm optimization-least Square transform) cooperative algorithm
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a parameter self-tuning method of a SISO (SISO) compact-format model-free controller based on a PSO-LSTM (particle swarm optimization-least Square positioning) cooperative algorithm.
Background
A SISO (Single Input and Single Output) system is widely used in controlled objects such as reactors, rectifying towers, machines, devices, apparatuses, production lines, workshops, factories, and the like in industries such as oil refining, chemical engineering, thermal power, machinery, electricity, petrochemical industry, pharmaceutical industry, food, paper making, water treatment, metallurgy, cement, rubber, and the like. With the continuous improvement of the technological level, industrial devices are increasingly large and complex, so that a plurality of links such as nonlinearity, time variation, large time lag and the like appear in the production process, and the traditional controller represented by PID is often difficult to achieve an ideal control effect when controlling a complex controlled object with characteristics such as nonlinearity, time variation, large time lag and the like. The model-free controller is a novel control model based on data driving, has a good control effect on an unknown nonlinear time-varying system, and therefore has a good application prospect.
Existing implementations of a modeless controller for a SISO system include a SISO compact-format modeless controller. The SISO compact format model-free controller is a novel control method based on data driving, and is characterized in that the analysis and design of the controller are carried out only depending on input and output data measured by a controlled object of a SISO system in real time without depending on any mathematical model information of the controlled object, the realization method is simple, the calculation burden is small, the performance is stable, the unknown nonlinear time-varying SISO system can be well controlled, and the application prospect is very bright. The theoretical basis of the SISO compact-format model-free controller is proposed by Houzhong and Jinshangtai in the 'model-free adaptive control-theory and application' (scientific publishing agency, 2013, page 55) of the Hemo, and the control algorithm is as follows:
Figure GDA0003194687890000011
wherein u (k) is the system control input at time k; e (k) is the system error at time k; phi is ac(k) The estimated value of the pseudo-partial derivative of the SISO system at the moment k; λ is a penalty factor and ρ is a step factor.
However, the SISO compact-format model-less controller has a problem of difficult parameter setting in the use of an actual industrial scene, the numerical values of parameters such as the penalty factor λ and the step factor ρ need to be set in advance according to professional knowledge and industry experience before the controller is put into use, the problem of working condition failure and the like may be caused by wrong parameter value setting, and meanwhile, the online self-setting of the parameters such as the penalty factor λ and the step factor ρ is not realized in the actual application process. The lack of effective setting means of the controller parameters not only causes time and labor consumption in the using and debugging process of the SISO compact-format model-free controller, but also even seriously influences the control effect of the SISO compact-format model-free controller, thereby limiting the wide application of the SISO compact-format model-free controller.
In order to break the bottleneck restricting the popularization and application of the SISO compact format model-free controller, the SISO compact format model-free controller also needs to solve the problem of online self-tuning parameters in the actual application process.
Disclosure of Invention
In order to solve the problems existing in the background art, the invention aims to provide a parameter self-tuning method of a SISO (SISO) compact format model-free controller based on a PSO-LSTM (pseudo-static synchronous compensator) cooperative algorithm so as to solve the problem of online parameter self-tuning of the SISO compact format model-free controller.
To this end, the above object of the present invention is achieved by the following technical solution, comprising the steps of:
step (1): parameters of the SISO compact format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a SISO (SISO) compact format model-free controller, wherein the parameters to be set of the SISO compact format model-free controller are part or all of the parameters of the SISO compact format model-free controller and comprise any one or combination of a penalty factor lambda and a step factor rho; determining the number of input layer nodes, the number of hidden layer units and the number of output layer nodes of the LSTM neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO compact-format model-free controller; initializing an input gate, a forgetting gate, an input state and a weight coefficient to be trained and learned in an output gate in each hidden layer unit of the LSTM neural network; initializing a weight coefficient to be trained and learned of an LSTM neural network output layer; determining the maximum iteration times and the population scale of the PSO algorithm; initializing a PSO algorithm particle swarm; determining a lower limit value of the fitness value;
step (2): optimizing and calculating weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network in the step (1) by utilizing a PSO algorithm; the fitness value in the PSO algorithm is obtained by calculating a fitness value calculation function, and the independent variable of the fitness value calculation function comprises a system output expected value and a system output actual value; based on the fitness value of each particle in the particle swarm, by comparing the fitness of the particles, the following updating formula is adopted:
V(i)＝wpsoV(i)+c1r1(gbest(i)-pop(i))+c2r2(zbest-pop(i))
pop(i)＝pop(i)+wpsoV(i)
where V (i) is the individual particle velocity to be updated, pop (i) is the individual particle position to be updated, zbest is the current population optimal particle, gbest is the current individual optimal particle, c1And c2Is a non-negative constant, r1And r2Is a random number, w, distributed between 0 and 1psoIs the inertial weight coefficient;
and (3): transposing and cutting the updated particles to generate a temporary weight matrix, transmitting the temporary weight matrix into an LSTM neural network as an initial weight matrix, outputting the value of a parameter to be set by the SISO tight format model-free controller by the LSTM neural network, controlling a controlled object by adopting a control algorithm of the SISO tight format model-free controller to obtain an actual system output value, and calculating the fitness value of the particles in the current PSO algorithm iteration round;
the PSO algorithm is iterated repeatedly until the fitness value is smaller than the lower limit value of the fitness value, the optimal solution of the group is output, or the optimal solution of the group is output by selecting the result with the minimum fitness value when the iteration times reach the maximum iteration times; performing cutting and transposition operations on the group optimal solution to generate a weight matrix, and obtaining weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network;
and (4): recording the current moment as k moment, and calculating by adopting a system error calculation function to obtain a system error of the k moment based on a system output expected value and a system output actual value, and recording as e (k);
and (5): taking any one or any combination of the system error and the function group thereof, the system output expected value and the system output actual value obtained by the calculation in the step (4) as the input of the LSTM neural network;
and (6): based on the input of the LSTM neural network in the step (5) and based on the input gate, the forgetting gate, the input state and the weight coefficient to be trained and learned in the output gate in each hidden layer unit of the LSTM neural network, the LSTM neural network performs forward calculation, firstly, the input at the current moment and the LSTM output at the last moment are spliced to generate a splicing vector, the output of the forgetting gate in the LSTM hidden layer unit is calculated by using the splicing vector, then, the input gate and the input state in the LSTM hidden layer unit are calculated, the state value of the unit in the LSTM hidden layer unit is calculated based on the values of the input gate and the input state, then, the calculation of the output gate in the LSTM hidden layer unit is completed, the final output of the hidden layer unit is updated by using the calculation results of the output gate and the state of the unit, and finally, the LSTM output at the current moment is obtained through the output layer of the LSTM neural network, calculating and determining the value of a parameter to be set of the SISO compact format model-free controller according to the current time LSTM output;
and (7): calculating to obtain a control input u (k) of the SISO compact format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO compact format model-free controller based on the system error e (k) obtained in the step (4) and the value of the parameter to be set of the SISO compact format model-free controller obtained in the step (6);
and (8): based on the control input u (k) obtained in the step (7), calculating partial derivatives of the control input u (k) at the time k for the parameters to be set of each SISO compact-format model-free controller, wherein the specific calculation formula is as follows:
when the parameters to be set of the SISO compact-format model-free controller comprise a penalty factor lambda, the partial derivative of the control input u (k) at the moment k for the penalty factor lambda is as follows:
Figure GDA0003194687890000041
when the parameter to be set of the SISO compact-format model-free controller contains a step factor rho, the partial derivative of the control input u (k) at the k moment with respect to the step factor rho is as follows:
Figure GDA0003194687890000042
wherein phi (k) is a pseudo gradient estimation value at the k moment;
and (9): taking the value of a minimized system error function as a target, adopting a gradient descent method based on a chain rule to perform LSTM neural network back propagation calculation, and updating weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network for the LSTM neural network to use in forward calculation at the next moment; the gradient descent method formula is as follows:
Figure GDA0003194687890000051
w is a weight coefficient to be trained and learned in the LSTM neural network, J (w) is a system error function related to the weight coefficient w, alpha is a learning rate, and alpha is a real number between 0 and 1; in the back propagation calculation process, when weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network are updated, the control input u (k) obtained in the step (8) is used for respectively aiming at partial derivatives of parameters to be set of each SISO tight-format model-free controller at the moment k;
step (10): and (e) after the control input u (k) acts on the controlled object, obtaining a system output actual value of the controlled object at the later moment, returning to the step (4), and repeating the steps (4) to (10).
The LSTM (Long Short Term Memory) neural network is a time recursive neural network, a hidden layer of the LSTM neural network comprises four important door mechanisms and state quantities which are a forgetting door, an input state and an output door respectively, and the door mechanisms and the state quantities ensure that the LSTM neural network has the learning capacity of the traditional feedforward neural network and the Memory capacity of storing time sequence information. The SISO compact-format model-free controller generates different system control input and output data, system errors and other time sequence information in real time in the using process, the online self-setting of the controller parameters is closely connected with the system variables, and the LSTM neural network can well process the time sequence information and comprises the steps of extracting the characteristics of the time sequence information and iteratively learning the internal connection between the parameters to be set and the time sequence information.
However, in the course of training and learning the LSTM neural network, because of the complex network structure, the number of weight coefficients to be trained is much greater than that of the conventional neural network, and the huge calculation amount and whether to fast converge are the difficult problems faced by such neural network, so the determination of the initial values of the weight coefficients of the LSTM neural network is extremely important, and the appropriate initial values can help the neural network to fast converge to achieve the purpose of parameter learning.
The PSO algorithm is a novel genetic algorithm, has the advantages of few parameters, simple structure and easy engineering realization, has no fussy cross and variation operation compared with the common genetic algorithm, only depends on the speed of particles to complete the search, and has the search speed far faster than other algorithms. In the application range of the PSO algorithm, the optimization of the neural network is a very important application field, the optimization mode is that the weight coefficients to be trained and learned in the neural network are regarded as particles in the particle swarm, the optimal particles are determined through a certain round of search, and the particles can be regarded as the initialized weight coefficients optimized by the PSO algorithm and used for LSTM neural network training. The PSO algorithm can therefore solve the above problem of weight coefficient initialization for LSTM neural networks.
While adopting the above technical scheme, the present invention can also adopt or combine the following further technical schemes:
the independent variables of the system error calculation function in the step (4) comprise a system output expected value and a system output actual value.
The systematic error calculation function in the step (4) adopts e (k) y*(k) -y (k), wherein y*(k) The system output expected value is set for the time k, and y (k) is the system output actual value obtained by sampling at the time k; or using e (k) ═ y*(k +1) -y (k), wherein y*(k +1) is the system output expected value at the moment of k + 1; or using e (k) ═ y (k) — y*(k) (ii) a Or using e (k) ═ y (k) — y*(k+1)。
Said system in said step (5)The systematic error and its function set include the systematic error e (k) at time k, the accumulation of the systematic errors at time k and all previous times
Figure GDA0003194687890000061
Any one or any combination of first order backward differences e (k) -e (k-1) of the k-time systematic error e (k), second order backward differences e (k) -2e (k-1) + e (k-2) of the k-time systematic error e (k), and high order backward differences of the k-time systematic error e (k).
The independent variable of the system error function in the step (9) comprises any one or any combination of a system error, a system output expected value and a system output actual value.
The system error function in the step (9) is ae2(k)+bΔu2(k) Where e (k) is the systematic error, Δ u (k) -u (k-1), and a and b are constants greater than or equal to 0.
The controlled object comprises a reactor, a rectifying tower, automation equipment, an industrial device, a workshop production line and a factory.
The hardware platform for operating the SISO compact-format model-free controller comprises any one of a programmable logic controller, a digital signal processing controller, an embedded system controller, a field programmable gate array controller, a chip computer controller, a microprocessor controller, an industrial control computer, a single distributed control system, a field bus control system, an industrial Internet of things control system and an industrial Internet control system
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FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a schematic diagram of a three-tank SISO system;
FIG. 3 is a diagram of the control effect of the output of the SISO system of the three-water-tank system;
FIG. 4 is a control input curve of a three-tank SISO system;
FIG. 5 is a variation curve of penalty factor λ for control input of a three-tank SISO system;
FIG. 6 is a variation curve of step factor ρ inputted by the control of the SISO system of the three-tank SISO system;
FIG. 7 is an evolutionary curve of the PSO algorithm in a three-tank SISO system.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
Fig. 1 shows a schematic block diagram of the present invention. For a SISO system with a single input and a single output, a SISO compact format model-free controller is adopted for control; parameters of the SISO compact format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a SISO (system-in-process) compact-format model-free controller, wherein the parameters to be set of the SISO compact-format model-free controller are part or all of the parameters of the SISO compact-format model-free controller and comprise any one or combination of a punishment factor lambda and a step factor rho; determining the number of input layer nodes, the number of hidden layer units and the number of output layer nodes of the LSTM neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO compact-format model-free controller; initializing an input gate, a forgetting gate, an input state and a weight coefficient to be trained and learned in an output gate in each hidden layer unit of the LSTM neural network; initializing a weight coefficient to be trained and learned of an LSTM neural network output layer; determining the maximum iteration times and the population scale of the PSO algorithm; initializing a PSO algorithm particle swarm; and determining a lower limit value of the adaptability value.
Optimizing and calculating the weight coefficients to be trained and learned in an input gate, a forgetting gate and an input state in each hidden layer unit of the LSTM neural network by using a PSO algorithm; the fitness value in the PSO algorithm is obtained by calculating a fitness value calculation function, and the independent variable of the fitness value calculation function comprises a system output expected value and a system output actual value; and updating the speed and the position of the particles by comparing the fitness of the particles based on the fitness value of each particle in the particle swarm. Transposing and cutting the updated particles to generate a temporary weight matrix, transmitting the temporary weight matrix into an LSTM neural network as an initial weight matrix, outputting the value of a parameter to be set by the SISO tight format model-free controller by the LSTM neural network, controlling a controlled object by adopting a control algorithm of the SISO tight format model-free controller to obtain an actual system output value, and calculating the fitness value of the particles in the current PSO algorithm iteration round;
the PSO algorithm is iterated repeatedly until the fitness value is smaller than the lower limit value of the fitness value, the optimal solution of the group is output, or the optimal solution of the group is output by selecting the result with the minimum fitness value when the iteration times reach the maximum iteration times; performing cutting and transposition operations on the group optimal solution to generate a weight matrix, and obtaining weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network;
recording the current time as k time; will output the expected value y*(k) And outputting the difference between the actual value y (k) and the actual value y (k) as the system error e (k) at the time k, and simultaneously calculating the first-order backward difference e (k) -e (k-1) of the system error at the time k and the sum of historical system errors
Figure GDA0003194687890000081
A reaction product of e (k), e (k) -e (k-1),
Figure GDA0003194687890000082
The combined vector is used as the input of the LSTM neural network, meanwhile, based on the weight coefficients to be trained and learned in the input gate, the forgetting gate, the input state and the output gate in each hidden layer unit of the LSTM neural network, the LSTM neural network carries out forward calculation, firstly, the input at the current moment and the LSTM output at the last moment are spliced to generate a spliced vector, the spliced vector is utilized to calculate the output of the forgetting gate in the LSTM hidden layer unit, then, the calculation of the input gate and the input state in the LSTM hidden layer unit is carried out, the value of the unit state in the LSTM hidden layer unit is calculated based on the values of the input gate and the input state, then completing the calculation of the output gate in the LSTM hidden layer unit, updating the final output of the hidden layer unit by using the calculation results of the output gate and the unit state, finally obtaining the current time LSTM output through the output layer of the LSTM neural network, and calculating and determining the value of the parameter to be set of the SISO compact-format model-free controller according to the current LSTM output. Based on the system error e (k), the value of the parameter to be set of the SISO tight format model-free controller, the SISO tight format model-free controller is adoptedThe control algorithm of (1) is used for calculating to obtain the control input u (k) of the SISO compact-format model-free controller aiming at the controlled object at the time k; and calculating partial derivatives of the parameters to be set of each SISO compact format model-free controller at the time k by using the control input u (k).
The method is characterized in that the value of a minimized system error function is taken as a target, a gradient descent method based on a chain rule is adopted to carry out back propagation calculation on an LSTM neural network, and weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network are updated for the LSTM neural network to use in forward calculation at the next moment; when updating the weight coefficients to be trained and learned in the input gate, the forgetting gate, the input state and the output gate in each hidden layer unit of the LSTM neural network, respectively aiming at the partial derivatives of the parameters to be set of each SISO (SISO) compact-format model-free controller at the time k by using the control input u (k) obtained in the step (8); taking the current moment as an example, for the weight coefficient to be trained and learned of the output layer of the LSTM neural network, firstly calculating the gradient of the error function about the weight coefficient of the output layer at the current moment, and updating the weight coefficient of the output layer at the current moment by using a gradient descent method; for all weight coefficients to be trained and learned in the hidden layer unit of the LSTM neural network, gradient values of error functions related to forgetting gates, input states and output gates in the hidden layer unit are calculated one by using a chain rule, gradient algebraic expressions of the error functions related to ownership coefficients in the hidden layer are obtained by using a full derivative formula, and the weight coefficients can be updated by using a gradient descent method; and after the control input u (k) acts on the controlled object, obtaining an output actual value of the controlled object at the next moment, repeating the process, and performing an LSTM-based parameter self-tuning process of the SISO compact-format model-free controller at the next moment.
The following is a specific embodiment of the present invention.
The controlled object three-container water tank is a single-input single-output SISO system, is a typical industrial object with complex characteristics of nonlinearity, large inertia and the like, the figure 2 is a schematic diagram of the three-container water tank and is composed of 3 water tanks, wherein the actual output value y of the system is that of the water tank 3The liquid level height (cm) and the control input u is the valve opening (%) of the flow regulating valve into the water tank 1. The initial working conditions of the three-container water tank are as follows: u (0) ═ 40%, y (0) ═ 50 cm. At 20 seconds, the system outputs a desired value y to meet the requirement of industrial field working condition adjustment*(20) Adjusting the length of the sample to be 60cm from 50 cm; subsequently, at 60 seconds, the system outputs the desired value y*(60) From 60cm again, adjust back to 50 cm. And three groups of tests are carried out for comparison and verification aiming at the typical actual working conditions of the industrial field. The hardware platform for operating the control method of the invention adopts an industrial control computer.
First set of experiments (RUN 1): the number of input layer nodes of the LSTM neural network is preset to be 3, the number of hidden layer nodes is preset to be 9, the number of output layer nodes is preset to be 2, and 2 output layer nodes respectively output punishment factors lambda and step factors rho; then, a control algorithm of a SISO compact format model-free controller is adopted to control the SISO system of the three water tanks; the RUN1 curve in fig. 3 is a graph of control effect of output, the RUN1 curve in fig. 4 is a curve of control input, the RUN1 curve in fig. 5 is a curve of penalty factor λ variation of control input, and the RUN1 curve in fig. 6 is a curve of step factor ρ variation of control input; FIG. 7 is a graph of evolution using the PSO algorithm; from the RUN1 curve of fig. 3, it can be found that the system output actual value can quickly track the change of the system output expected value, and meanwhile, the overshoot of the system output actual value is small, so that ideal control performance is realized; from the RUN1 curves shown in fig. 5 and fig. 6, it can be found that the penalty factor λ and the step factor ρ can be self-tuned online in time according to the change of the system error, so that the system can track and output the expected value more quickly, accurately and stably. The method of the invention can realize good control effect by self-setting the penalty factor lambda and the step factor rho at the same time, and can effectively overcome the difficult problem that the penalty factor lambda and the step factor rho need to be time-consuming and labor-consuming to set.
Second set of experiments (RUN 2): the penalty factor lambda is fixed, and the value of the penalty factor lambda is the average value of the change curve of the penalty factor lambda in the first group of tests (RUN 1); the step factor rho is fixed and takes the value as the average value of the step factor rho change curve in the first group of experiments (RUN 1); then, a control algorithm of a SISO compact format model-free controller is adopted to control the SISO system of the three water tanks; the RUN2 curve in fig. 3 is a graph of control effect of the output, the RUN2 curve in fig. 4 is a graph of control input, the RUN2 curve in fig. 5 is a penalty factor λ of the control input, and the RUN2 curve in fig. 6 is a step factor ρ of the control input; from the RUN2 curve of fig. 3, it can be seen that the system output actual value can slowly track the change of the system output expected value, and the overshoot of the system output actual value is small; the second set of trials (RUN2) were inferior in terms of the rapidity index of control performance compared to the control performance of the first set of trials (RUN 1).
Third set of experiments (RUN 3): the values of the penalty factor lambda and the step factor rho are both fixed to be common values of 0.5; then, a control algorithm of a SISO compact format model-free controller is adopted to control the SISO system of the three water tanks; the RUN3 curve in fig. 3 is a graph of control effect of output, and the RUN3 curve in fig. 4 is a graph of control input; from the RUN3 curve of fig. 3, it can be seen that the system output actual value can track the change of the system output expected value at the fastest speed, but the overshoot of the system output actual value is large; the third set of tests (RUN3) was inferior in stability index of control performance compared to the control performance of the first set of tests (RUN 1).
The results of the three groups of tests show that the parameter self-tuning method of the SISO compact format model-free controller based on the PSO-LSTM cooperative algorithm adopted in the first group of tests (RUN1) has the optimal control performance comprehensive index.
It should be noted that in the above-described embodiment, the desired value y will be output*(k) The difference from the output actual value y (k) is used as the system error e (k) at time k, i.e. e (k) y*(k) -y (k), only one method of calculating a function for said error; the system at the moment k +1 can also output the expected value y*The difference between (k +1) and the time k output y (k) is taken as the system error e (k), i.e. e (k) y (k)*(k +1) -y (k); the error calculation function may also employ other methods of calculating the output desired value and the output actual value, such as, for example,
Figure GDA0003194687890000111
for the controlled object of the above embodiment, good control effects can be achieved by using the different system error calculation functions.
It should be more particularly noted that, in the above-described embodiment, when the hidden layer weight coefficients and the output layer weight coefficients of the LSTM neural network are updated with the goal of minimizing the value of the systematic error function, the systematic error function employs the square of the systematic error e2(k) Only one of said systematic error functions; for example, the systematic error function can also be ae2(k)+bΔu2(k) Wherein Δ u (k) -u (k-1), a and b are constants greater than or equal to 0; it is clear that the systematic error function only takes into account e when b equals 02(t), indicating that the objective of minimization is to minimize the systematic error, i.e. to pursue high accuracy; and when b is greater than 0, the systematic error function takes e into account2Contribution of (t) and Δ u2The contribution of (t) indicates that the goal of minimization is to pursue small system error and small control input variation, i.e., both high precision and stable steering. For the controlled object of the above embodiment, good control effect can be achieved by adopting the different system error functions; considering only e with the systematic error function2(k) Control effects in contribution to the system error function while considering e2Contribution of (t) and Δ u2The contribution of (t) is that the control precision is slightly reduced and the operation stability is improved.
Finally, it should be particularly noted that the parameters to be set by the SISO compact-format model-less controller include one or all of a penalty factor λ and a step factor ρ; in the above specific embodiment, the penalty factor λ and the step factor ρ realize simultaneous self-tuning during experimental verification; in practical application, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor rho is fixed, and the penalty factor realizes self-setting; in addition, the parameters to be set by the SISO compact-format modeless controller include, but are not limited to, a penalty factor λ and a step factor ρ, and for example, according to the specific situation, the parameters may also include parameters such as an estimation value of pseudo-partial derivative Φ (k) of the SISO system.
The above-described embodiments are intended to illustrate the present invention, but not to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit of the present invention and the scope of the claims fall within the scope of the present invention.

Claims (8)

  1. A parameter self-tuning method of a SISO compact format model-free controller based on a PSO-LSTM cooperative algorithm is characterized by comprising the following steps:
    step (1): parameters of the SISO compact format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a SISO (SISO) compact format model-free controller, wherein the parameters to be set of the SISO compact format model-free controller are part or all of the parameters of the SISO compact format model-free controller and comprise any one or combination of a penalty factor lambda and a step factor rho; determining the number of input layer nodes, the number of hidden layer units and the number of output layer nodes of the LSTM neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO compact-format model-free controller; initializing an input gate, a forgetting gate, an input state and a weight coefficient to be trained and learned in an output gate in each hidden layer unit of the LSTM neural network; initializing a weight coefficient to be trained and learned of an LSTM neural network output layer; determining the maximum iteration times and the population scale of the PSO algorithm; initializing a PSO algorithm particle swarm; determining a lower limit value of the fitness value;
    step (2): optimizing and calculating weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network in the step (1) by utilizing a PSO algorithm; the fitness value in the PSO algorithm is obtained by calculating a fitness value calculation function, and the independent variable of the fitness value calculation function comprises a system output expected value and a system output actual value; based on the fitness value of each particle in the particle swarm, by comparing the fitness of the particles, the following updating formula is adopted:
    V(i)＝wpsoV(i)+c1r1(gbest(i)-pop(i))+c2r2(zbest-pop(i))
    pop(i)＝pop(i)+wpsoV(i)
    where V (i) is the individual particle velocity to be updated, pop (i) is the individual particle position to be updated, zbest is the current population optimal particle, gbest is the current individual optimal particle, c1And c2Is a non-negative constant, r1And r2Is a random number, w, distributed between 0 and 1psoIs the inertial weight coefficient;
    and (3): transposing and cutting the updated particles to generate a temporary weight matrix, transmitting the temporary weight matrix into an LSTM neural network as an initial weight matrix, outputting the value of a parameter to be set by the SISO tight format model-free controller by the LSTM neural network, controlling a controlled object by adopting a control algorithm of the SISO tight format model-free controller to obtain an actual system output value, and calculating the fitness value of the particles in the current PSO algorithm iteration round;
    the PSO algorithm is iterated repeatedly until the fitness value is smaller than the lower limit value of the fitness value, the optimal solution of the group is output, or the optimal solution of the group is output by selecting the result with the minimum fitness value when the iteration times reach the maximum iteration times; performing cutting and transposition operations on the group optimal solution to generate a weight matrix, and obtaining weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network;
    and (4): recording the current moment as k moment, and calculating by adopting a system error calculation function to obtain a system error of the k moment based on a system output expected value and a system output actual value, and recording as e (k);
    and (5): taking any one or any combination of the system error and the function group thereof, the system output expected value and the system output actual value obtained by the calculation in the step (4) as the input of the LSTM neural network;
    and (6): based on the input of the LSTM neural network in the step (5) and based on the input gate, the forgetting gate, the input state and the weight coefficient to be trained and learned in the output gate in each hidden layer unit of the LSTM neural network, the LSTM neural network performs forward calculation, firstly, the input at the current moment and the LSTM output at the last moment are spliced to generate a splicing vector, the output of the forgetting gate in the LSTM hidden layer unit is calculated by using the splicing vector, then, the input gate and the input state in the LSTM hidden layer unit are calculated, the state value of the unit in the LSTM hidden layer unit is calculated based on the values of the input gate and the input state, then, the calculation of the output gate in the LSTM hidden layer unit is completed, the final output of the hidden layer unit is updated by using the calculation results of the output gate and the state of the unit, and finally, the LSTM output at the current moment is obtained through the output layer of the LSTM neural network, calculating and determining the value of a parameter to be set of the SISO compact format model-free controller according to the current time LSTM output;
    and (7): calculating to obtain a control input u (k) of the SISO compact format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO compact format model-free controller based on the system error e (k) obtained in the step (4) and the value of the parameter to be set of the SISO compact format model-free controller obtained in the step (6);
    and (8): based on the control input u (k) obtained in the step (7), calculating partial derivatives of the control input u (k) at the time k for the parameters to be set of each SISO compact-format model-free controller, wherein the specific calculation formula is as follows:
    when the parameters to be set of the SISO compact-format model-free controller comprise a penalty factor lambda, the partial derivative of the control input u (k) at the moment k for the penalty factor lambda is as follows:
    Figure FDA0003194687880000031
    when the parameter to be set of the SISO compact-format model-free controller contains a step factor rho, the partial derivative of the control input u (k) at the k moment with respect to the step factor rho is as follows:
    Figure FDA0003194687880000032
    wherein phi (k) is a pseudo gradient estimation value at the k moment;
    and (9): taking the value of a minimized system error function as a target, adopting a gradient descent method based on a chain rule to perform LSTM neural network back propagation calculation, and updating weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network for the LSTM neural network to use in forward calculation at the next moment; the gradient descent method formula is as follows:
    Figure FDA0003194687880000033
    w is a weight coefficient to be trained and learned in the LSTM neural network, J (w) is a system error function related to the weight coefficient w, alpha is a learning rate, and alpha is a real number between 0 and 1; in the back propagation calculation process, when weight coefficients to be trained and learned in an input gate, a forgetting gate, an input state and an output gate in each hidden layer unit of the LSTM neural network are updated, the control input u (k) obtained in the step (8) is used for respectively aiming at partial derivatives of parameters to be set of each SISO tight-format model-free controller at the moment k;
    step (10): and (e) after the control input u (k) acts on the controlled object, obtaining a system output actual value of the controlled object at the later moment, returning to the step (4), and repeating the steps (4) to (10).
  2. 2. The parameter self-tuning method of the SISO compact format model-less controller based on the PSO-LSTM cooperative algorithm of claim 1, wherein the arguments of the system error calculation function in the step (4) comprise a system output expected value and a system output actual value.
  3. 3. The SISO compact format model-less controller parameter self-tuning method based on PSO-LSTM cooperative algorithm of claim 2, wherein the system error calculation function employs e (k) -y*(k) -y (k), wherein y*(k)The system output expected value is set for the time k, and y (k) is the system output actual value obtained by sampling at the time k; or using e (k) ═ y*(k +1) -y (k), wherein y*(k +1) is the system output expected value at the moment of k + 1; or using e (k) ═ y (k) — y*(k) (ii) a Or using e (k) ═ y (k) — y*(k+1)。
  4. 4. The parameter self-tuning method of the SISO compact format model-less controller based on the PSO-LSTM cooperative algorithm as claimed in claim 1, wherein the system error and its function set in the step (5) comprises the system error e (k) at time k, and the accumulation of the system errors at time k and all previous times
    Figure FDA0003194687880000041
    Any one or any combination of first order backward differences e (k) -e (k-1) of the k-time systematic error e (k), second order backward differences e (k) -2e (k-1) + e (k-2) of the k-time systematic error e (k), and high order backward differences of the k-time systematic error e (k).
  5. 5. The parameter self-tuning method of the SISO compact format model-less controller based on the PSO-LSTM collaborative algorithm according to claim 1, wherein the argument of the systematic error function in the step (9) comprises any one or any combination of systematic error, systematic output expected value, and systematic output actual value.
  6. 6. The parameter self-tuning method of SISO compact format model-less controller based on PSO-LSTM cooperative algorithm of claim 5, wherein the system error function is ae2(k)+bΔu2(k) Where e (k) is the systematic error, Δ u (k) -u (k-1), and a and b are constants greater than or equal to 0.
  7. 7. The parameter self-tuning method of the SISO compact format model-less controller based on the PSO-LSTM cooperative algorithm according to claim 1, characterized in that: the controlled object comprises a reactor, a rectifying tower, automation equipment, an industrial device, a workshop production line and a factory.
  8. 8. The parameter self-tuning method of the SISO compact format model-less controller based on the PSO-LSTM cooperative algorithm according to claim 1, characterized in that: the hardware platform for operating the SISO compact-format model-free controller comprises any one or any combination of a programmable logic controller, a digital signal processing controller, an embedded system controller, a field programmable gate array controller, a chip computer controller, a microprocessor controller, an industrial control computer, a single distributed control system, a field bus control system, an industrial Internet of things control system and an industrial Internet control system.
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