A fractional order PID controller parameter automatic tuning method based on MPSO-BP algorithm

Abstract

The application provides a fractional order PID controller parameter automatic setting method based on an MPSO-BP algorithm, and comprises the following steps: initializing basic parameters of a BP neural network; initializing a mutation particle swarm optimization algorithm; calculating weights of the BP neural network through the mutation particle swarm optimization algorithm; inputting output signals of an action object of the fractional order PID controller in a previous sampling period and a current sampling period and an error signal of the current sampling period into the BP neural network with the updated weights; and adopting variation values of proportional coefficients, integral coefficients and differential coefficients of the fractional order PID controller output by the BP neural network and integral order and differential order to adjust parameters of the fractional order PID controller in a next sampling period. The application has stronger robustness and greatly improves control efficiency.

Description

Technical Field

[0001] This invention belongs to the field of intelligent algorithm control technology, specifically relating to an automatic parameter tuning method for a fractional-order PID controller based on the MPSO-BP algorithm. Background Technology

[0002] In recent years, with the increasing applications of fractional calculus in science and engineering, analysis and research have shown that fractional calculus theory, due to its extended order compared to integer calculus theory, results in fractional PID controllers exhibiting superior dynamic and static performance compared to integer PID controllers. While fractional PID controllers significantly expand their adjustment range by incorporating both integral and derivative parameters, their parameter tuning remains a challenging problem. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of the aforementioned background technology and provide an automatic tuning method for fractional-order PID controller parameters based on the MPSO-BP algorithm, which has stronger robustness and greatly improves control efficiency.

[0004] The technical solution adopted in this invention is: initializing the basic parameters of the BP neural network; initializing the mutated particle swarm optimization algorithm;

[0005] Based on the output signals of the fractional-order PID controller in the previous and current sampling periods, the weights of the BP neural network are calculated using the mutated particle swarm optimization algorithm.

[0006] The output signals of the fractional-order PID controller in the previous sampling period and the current sampling period, as well as the error signal in the current sampling period, are input into the BP neural network after the weights are updated; the error signal in the current sampling period is the difference between the output signals of the fractional-order PID controller in the previous sampling period and the current sampling period.

[0007] The parameters of the fractional-order PID controller in the next sampling period are adjusted by using the changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order, and derivative order of the fractional-order PID controller output by the BP neural network.

[0008] In the above technical solution, the input of the BP neural network is the output signal of the fractional-order PID controller in the previous sampling period and the current sampling period, as well as the error signal in the current sampling period. The BP neural network uses the output signal of the fractional-order PID controller to construct performance index parameters, calculates and outputs the changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order and derivative order of the fractional-order PID controller.

[0009] In the above technical solution, the process of initializing the basic parameters of the BP neural network includes determining the structure of the BP neural network and the number of neurons in each layer, and giving the initial weights W from the input layer to the hidden layer. ij and the initial weights W from the hidden layer to the output layer oj Initial values ​​of each parameter of the fractional-order PID controller, learning efficiency η, momentum factor α;

[0010] The BP neural network comprises a three-layer structure: an input layer, a hidden layer, and an output layer. The input layer includes three neurons, which represent the output signal of the fractional-order PID controller for one sampling period and the current sampling period, as well as the error signal for the current sampling period. The output layer includes three neurons, which represent the changes in the proportional coefficient, integral coefficient, and derivative coefficient of the fractional-order PID controller, as well as the changes in the integral order and the derivative order.

[0011] In the above technical solution, the process of initializing the mutated particle swarm optimization algorithm includes: determining the dimension M of the mutated particle swarm, and giving the range of particle swarm inertia weights [W]. min W max Learning factors C1 and C2, velocity range of each particle [v] min ,v max ] and location range [X min ,X max Maximum mutation probability P max and minimum mutation probability P min .

[0012] In the above technical solution, the process of calculating the weights of the BP neural network using the mutated particle swarm optimization algorithm includes: In the M-dimensional search space, the position of the i-th particle in the M-dimensional space is represented as: X i =(X i1 ,X i2 ,X i3 ,...,X iM The optimal position experienced by the i-th particle is denoted as P. best =(P best1 ,P best2 ,P best3 ,...,P bestM The optimal positions experienced by all particles are denoted as: g best =(g best1 ,g best2 ,g best3 ,...,g bestM );

[0013] The velocity of each particle is v i =(v i1,v i2 ,v i3 ,...,v iM Each particle updates its velocity and position according to the following formula:

[0014] v id (k+1)=Wv id (k)+C1rand(P id -X id )+C2rand(P gd -X id )

[0015] X id (k+1)=X id +v id

[0016] Where d∈[1,M]; k is the current iteration number of the particle; P id For the current particle to experience the optimal position, P gd For all positions that have been reached, W represents the current velocity weight coefficient in the particle swarm optimization algorithm.

[0017] The particle fitness value, particle optimum, and population optimum are updated using the updated particle position and velocity, and a mutation operation is performed. This process is repeated until the maximum number of iterations is reached or the error value is met, at which point the updated BP neural network weighting coefficients W are output. ij and W oj .

[0018] In the above technical solution, the process of performing mutation operation includes: calculating the particle swarm variance and mutation probability based on the particle fitness value, the particle optimal value, and the population optimal value using a mutated particle swarm optimization algorithm;

[0019] Let the variance of particle swarm fitness be σ. 2 The following formula is used for calculation:

[0020]

[0021] Among them, f i f represents the error value of the loss function. max denoted by , where f represents the maximum value of the loss function, and f represents the difference between the maximum and minimum values ​​of the loss function.

[0022] The expression for the loss function E is as follows:

[0023]

[0024] Where r(k) represents the output signal of the fractional-order PID controller in the previous sampling period; y(k) represents the output signal of the fractional-order PID controller in the current sampling period.

[0025] The particle swarm mutation probability p m Designed as an operator k:

[0026]

[0027] σ d 2 This indicates setting the maximum variance value; f gbest The loss function f represents the loss function that allows all particles to experience optimal positions. d Indicates the current loss function;

[0028] Determine the calculated mutation probability p m Is it within the interval [P]? min ,P max If the determination is yes, then the mutation operation is performed based on the particle swarm mutation probability; otherwise, it is determined whether the maximum variance value is greater than the particle swarm fitness variance, and whether the loss function of all particles experiencing the best position is greater than the current loss function error value.

[0029] If one of the conditions is true, then the mutation operation is performed with a fixed mutation probability; otherwise, no mutation operation is performed.

[0030] In the above technical solution, the expressions for the current velocity weight coefficient W, learning factors C1 and C2 in the particle swarm optimization algorithm are as follows:

[0031] W(k)=W max -(W max -W min )k / N

[0032] C1(k)=C 1max -(C 1max -C 1min )k / N

[0033] C2(k)=C 2max +(C 2max -C 2min )k / N

[0034] Where k is the current iteration number of the particle, and N is the maximum iteration number; C 1max This represents the maximum value of the learning factor C1; C 1min This represents the minimum value of the learning factor C1; C 2max This represents the maximum value of the learning factor C2; C 2min This represents the minimum value of the learning factor C2.

[0035] In the above technical solution, the fractional-order PID controller is discretized, and its time-domain expression u(k) is:

[0036]

[0037] Among them, K P K represents the proportional coefficient of a fractional-order PID controller. I K represents the integral coefficient of the fractional-order PID controller. D λ represents the derivative coefficients of the fractional-order PID controller; μ represents the integral order of the fractional-order PID controller; h is the time step; q j and d j The coefficients are binomial coefficients, and their subscript values ​​represent the corresponding numbers; k represents the sampling period number; e() represents the error signal of the corresponding sampling period; i and j both represent the iteration number; q0 and d0 represent the initial binomial coefficients;

[0038]

[0039] The changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order, and derivative order of the fractional-order PID controller output by the BP neural network are calculated using the following formulas:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] Where f1 and f2 are the calculation coefficients, respectively; η represents the learning efficiency.

[0047] The beneficial effects of this invention are as follows: It utilizes an improved mutated particle swarm optimization (MPSO) algorithm combined with the control error of the controlled object to optimize and update the hidden layer weights and output layer weights of the BP neural network, thereby providing optimized weights for the BP neural network. Then, it adjusts the proportional coefficient, integral coefficient, derivative coefficient, integral order, and derivative order of the fractional-order PID control, outputting the optimal solution of the system through self-learning. Furthermore, the mutated particle swarm optimization algorithm can solve the problem of traditional artificial neural networks easily getting trapped in local optima during convergence, exhibiting stronger robustness and significantly improving convergence speed and control efficiency. This invention does not require establishing a precise mathematical model, can automatically identify the controlled parameters, and automatically tune the parameters during algorithm iteration. It automatically approximates the optimal solution of the fractional-order PID through neural network self-learning. Moreover, the improved MPSO-BP algorithm overcomes the problems of slow convergence speed and easy trapping in local optima in the traditional PSO algorithm, and also overcomes the problem of slow adjustment of weighting coefficients during backpropagation in traditional BP neural networks, exhibiting stronger robustness and significantly improving control efficiency. Attached Figure Description

[0048] Figure 1 This is a block diagram of the self-tuning PID controller of the present invention;

[0049] Figure 2 This is a schematic diagram of the BP neural network structure of the present invention;

[0050] Figure 3 This is a flowchart of the method of the present invention;

[0051] Figure 4 This is a vector control block diagram of fractional-order PID control based on MPSO-BP neural network in a specific embodiment. Detailed Implementation

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but these descriptions do not constitute a limitation on the present invention.

[0053] like Figure 1-3 As shown, this invention provides an automatic parameter tuning method for a fractional-order PID controller based on the MPSO-BP algorithm, comprising the following steps:

[0054] Initialize the basic parameters of the BP neural network; initialize the mutant particle swarm optimization algorithm;

[0055] Obtain the output signals of the fractional-order PID controller in the previous sampling period and the current sampling period, and calculate the error signal in the current sampling period;

[0056] Based on the output signals of the fractional-order PID controller in the previous and current sampling periods, the weights of the BP neural network are calculated using the mutated particle swarm optimization algorithm.

[0057] The output signals of the fractional-order PID controller in the previous sampling period and the current sampling period, as well as the error signal in the current sampling period, are input into the BP neural network after the weights are updated; the error signal in the current sampling period is the difference between the output signals of the fractional-order PID controller in the previous sampling period and the current sampling period.

[0058] The parameters of the fractional-order PID controller in the next sampling period are adjusted by using the changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order, and derivative order of the fractional-order PID controller output by the BP neural network.

[0059] like Figure 4 As shown, when the method of the present invention is applied to the inverter control of a permanent magnet synchronous motor in a specific embodiment, the following steps are included:

[0060] S1. Initialize the basic parameters of the BP neural network, i.e., determine the network structure and the number of neurons in each layer, and give the initial weights W from the input layer to the hidden layer. ij and the initial weights W from the hidden layer to the output layer oj Initial values ​​of each parameter of the fractional-order PID controller, learning efficiency η, momentum factor α;

[0061] S2. Initialize the mutated particle swarm optimization algorithm, i.e., determine the maximum number of iterations N, the particle swarm dimension M, the learning factors C1 and C2, and the range of the inertia weight W [W]. min W max [Initial velocity v and position x of each particle, maximum mutation probability P] max and minimum mutation probability P min .

[0062] S3. Sample the input given r(k) and the system output y(k) to obtain the system control error e(k); where r(k) represents the speed signal of the permanent magnet synchronous motor in the previous sampling period, and y(k) represents the speed signal of the permanent magnet synchronous motor in the current sampling period; e(k) = y(k) - r(k).

[0063] S4. Determine the input signals of the BP neural network, namely r(k), y(k) and e(k).

[0064] S5. Based on r(k), y(k), and e(k), update the particle fitness value, the optimal particle value, and the optimal population value using the mutation particle swarm optimization algorithm, and determine the probability p of the number of particles in the mutation operation. mThe algorithm performs a mutation operation; once the maximum number of iterations is reached or the error value is met, the updated weighting coefficients W are input into the BP neural network. ij and W oj .

[0065] S6. Based on the comparison between the loss function of the BP neural network and the target value, adjust the proportional coefficient K of the fractional-order PID controller using the gradient descent method. P Integral coefficient K I Differential coefficient K D And the integral order λ and the differential order μ.

[0066] S8. Calculate the output u(k) of the fractional-order PID controller using its time-domain form; u(k) represents the quadrature-axis current reference signal. Perform PI regulation on the permanent magnet synchronous motor based on the quadrature-axis current reference signal.

[0067] S9. Let k = k + 1, and perform the next sampling control, where k represents time.

[0068] Specifically, the specific structure of the BP neural network is as follows:

[0069] like Figure 2 As shown, the BP neural network has a three-layer structure: input layer, hidden layer, and output layer; j represents an input layer node, i represents a hidden layer node, and l represents an output layer node;

[0070] The activation function for each neuron in each layer is the Sigmoid function:

[0071]

[0072] Then the input quantity of input layer j is:

[0073] Q j =x(j)j=1,2,3 The input of hidden layer i is:

[0074] i = 1, 2, L, Q

[0075] The input to output layer l is:

[0076]

[0077] The output of output layer l is then:

[0078]

[0079] The above describes the forward propagation process in a BP neural network, the purpose of which is to obtain the model's prediction results. During the backward propagation process, a mutated particle swarm optimization algorithm is used to correct the weighting coefficients.

[0080] In step S2, the mutated particle swarm optimization algorithm is initialized, the dimension M of the mutated particle swarm is determined, and the range of particle swarm inertia weights [W] is given. min W max Learning factors C1 and C2, velocity range of each particle [v] min ,v max ] and location range [X min ,X max Maximum mutation probability P max and minimum mutation probability P min .

[0081] In step S5, the position of the i-th particle in the M-dimensional search space is represented as: X i =(X i1 ,X i2 ,X i3 ,...,X iM The optimal position experienced by the i-th particle is denoted as P. best =(P best1 ,P best2 ,P best3 ,...,P bestM The optimal positions experienced by all particles are denoted as: g best =(g best1 ,g best2 ,g best3 ,...,g bestM The velocity of each particle is v. i =(v i1 ,v i2 ,v i3 ,...,v iM Each particle updates its velocity and position according to the following formula:

[0082] v id (k+1)=Wv id (k)+C1rand(P id -X id )+C2rand(P gd -X id )

[0083] X id (k+1)=X id +v id

[0084] Where d∈[1,M]; k is the current iteration number of the particle; P id For the current particle to experience the optimal position, P gd is the optimal position for all experiences; W is the current velocity weight coefficient in the particle swarm algorithm.

[0085] like Figure 3 As shown, the particle fitness value, particle optimum, and population optimum are updated using the updated particle position and velocity, and a mutation operation is performed. This process is repeated until the maximum number of iterations of the mutated particle swarm optimization algorithm is reached or the error value is satisfied, at which point the updated weighting coefficient W is output. ij and W oj .

[0086] Since the weights W and learning factors C1 and C2 are constants in the traditional algorithm, the expressions for the weights W and learning factors C1 and C2 in the improved algorithm are as follows:

[0087] W(k)=W max -(W max -W min )k / N

[0088] C1(k)=C 1max -(C 1max -C 1min )k / N

[0089] C2(k)=C 2max +(C 2max -C 2min )k / N

[0090] Where k is the current iteration number of the particle, and N is the maximum iteration number; C 1max This represents the maximum value of the learning factor C1; C 1min This represents the minimum value of the learning factor C1; C 2max This represents the maximum value of the learning factor C2; C 2min This represents the minimum value of the learning factor C2.

[0091] Let the variance of particle swarm fitness be σ. 2 :

[0092]

[0093] Among them, f i f represents the error value of the loss function. max denoted by , where f represents the maximum value of the loss function, and f represents the difference between the maximum and minimum values ​​of the loss function.

[0094] The expression for the loss function E is as follows:

[0095]

[0096] Where r(k) represents the output signal of the fractional-order PID controller in the previous sampling period; y(k) represents the output signal of the fractional-order PID controller in the current sampling period.

[0097] The particle swarm mutation probability pm Designed as an operator k:

[0098]

[0099] σ d 2 This indicates setting the maximum variance value; f gbest The loss function f represents the loss function that allows all particles to experience optimal positions. d Indicates the current loss function;

[0100] Determine the calculated mutation probability p m Is it within the interval [P]? min ,P max If the determination is yes, then the mutation operation is performed based on the particle swarm mutation probability; otherwise, it is determined whether the maximum variance value is greater than the particle swarm fitness variance, and whether the loss function of all particles experiencing the best position is greater than the current loss function error value.

[0101] If one of the conditions is true, then the mutation operation is performed with a fixed mutation probability; otherwise, no mutation operation is performed.

[0102] In step S6, the performance index function of the fractional-order PID output of the BP neural network is taken as follows:

[0103]

[0104] The conventional time-domain expression for a fractional-order PID controller is:

[0105]

[0106] The fractional derivative and integral, as defined by Grunwald-Letnikov, can be directly calculated using the following formula:

[0107]

[0108] in,

[0109]

[0110] In this invention, the fractional-order PID controller is discretized:

[0111]

[0112] In the formula: K P K represents the proportional coefficient of a fractional-order PID controller. I K represents the integral coefficient of the fractional-order PID controller. Dλ represents the derivative coefficients of the fractional-order PID controller; μ represents the integral order of the fractional-order PID controller; h is the time step; q j and d j The coefficients are binomial coefficients, and their subscript values ​​represent the corresponding numbers; k represents the sampling period number; e() represents the error signal of the corresponding sampling period; i and j both represent the iteration number; q0 and d0 represent the initial binomial coefficients.

[0113]

[0114] K P ,K I ,K D The adjustment of λ and μ using the gradient descent method can yield the change value ΔK of the proportional coefficient using the k-th fractional-period PID controller. p Change in integral coefficient ΔK t , Change in differential coefficient ΔK D The values ​​of change in integral order Δλ and differential order Δμ are:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] The parameters of the fractional-order PID controller in the next sampling period are adjusted by using the changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order, and derivative order of the fractional-order PID controller output by the BP neural network.

[0122] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. An automatic parameter tuning method for a fractional-order PID controller based on the MPSO-BP algorithm, characterized in that: Includes the following steps: Initialize the basic parameters of the BP neural network; initialize the mutant particle swarm optimization algorithm; Based on the output signals of the fractional-order PID controller in the previous and current sampling periods, the weights of the BP neural network are calculated using the mutated particle swarm optimization algorithm. The output signals of the fractional-order PID controller in the previous sampling period and the current sampling period, as well as the error signal in the current sampling period, are input into the BP neural network after the weights are updated; the error signal in the current sampling period is the difference between the output signals of the fractional-order PID controller in the previous sampling period and the current sampling period. The parameters of the fractional-order PID controller in the next sampling period are adjusted by using the changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order, and derivative order of the fractional-order PID controller output by the BP neural network. The process of performing mutation includes: calculating the particle swarm variance and mutation probability based on the particle fitness value, the particle optimal value, and the population optimal value using a mutated particle swarm optimization algorithm; Let the variance of the particle swarm fitness be . The following formula is used for calculation: ； Among them, f i f represents the error value of the loss function. max denoted by , where f represents the maximum value of the loss function, and f represents the difference between the maximum and minimum values ​​of the loss function. The expression for the loss function E is as follows: ； Where r(k) represents the output signal of the fractional-order PID controller in the previous sampling period; y(k) represents the output signal of the fractional-order PID controller in the current sampling period. The particle swarm mutation probability p m Designed as an operator k: σ d 2 This indicates setting the maximum variance value; f gbest The loss function f represents the loss function that allows all particles to experience optimal positions. d Indicates the current loss function; Determine the calculated mutation probability p m Is it within the interval [P]? min ,P max If the determination is yes, then the mutation operation is performed based on the particle swarm mutation probability; otherwise, it is determined whether the maximum variance value is greater than the particle swarm fitness variance, and whether the loss function of all particles experiencing the best position is greater than the current loss function error value. If one of the conditions is true, then the mutation operation is performed with a fixed mutation probability; otherwise, no mutation operation is performed.

2. The method according to claim 1, characterized in that: The input to the BP neural network is the output signal of the fractional-order PID controller in the previous sampling period and the current sampling period, as well as the error signal in the current sampling period. The BP neural network uses the output signal of the fractional-order PID controller to construct performance index parameters, calculates and outputs the changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order and derivative order of the fractional-order PID controller.

3. The method according to claim 2, characterized in that: The process of initializing the basic parameters of a backpropagation (BP) neural network includes determining the BP neural network structure and the number of neurons in each layer, and giving the initial weights from the input layer to the hidden layers. and the initial weights from the hidden layer to the output layer Initial values ​​of parameters for the fractional-order PID controller, and learning efficiency. Momentum factor ; The BP neural network comprises a three-layer structure: an input layer, a hidden layer, and an output layer. The input layer includes three neurons, which represent the output signal of the fractional-order PID controller for one sampling period and the current sampling period, as well as the error signal for the current sampling period. The output layer includes three neurons, which represent the changes in the proportional coefficient, integral coefficient, and derivative coefficient of the fractional-order PID controller, as well as the changes in the integral order and the derivative order.

4. The method according to claim 3, characterized in that: The process of initializing the mutated particle swarm optimization algorithm includes: determining the dimension M of the mutated particle swarm, and giving the range of particle swarm inertia weights. Learning factor and The velocity range of each particle [ ] and location range [ Maximum mutation probability P max and minimum mutation probability P min .

5. A method according to claim 4, characterized in that: The process of calculating the weights of a BP neural network using the mutant particle swarm optimization algorithm includes: in the M-dimensional search space, the weights of the first... i The positions of the particles in M-dimensional space are represented as follows: , No. i The optimal position experienced by each particle is denoted as: The optimal positions experienced by all particles are denoted as: ; The speed of each particle is Each particle updates its velocity and position according to the following formula: Where d∈[1,M]; k is the current iteration number of the particle; P id For the current particle to experience the optimal position, P gd For all positions that have been reached, W represents the current velocity weight coefficient in the particle swarm optimization algorithm. The particle fitness value, particle optimum, and population optimum are updated using the updated particle position and velocity, and a mutation operation is performed. This process is repeated until the maximum number of iterations is reached or the error value is met, at which point the updated BP neural network weighting coefficients are output. and .

6. A method according to claim 5, characterized in that: The expressions for the current velocity weight coefficient W, learning factors C1 and C2 in the particle swarm optimization algorithm are: Where k is the current iteration number of the particle, and N is the maximum iteration number; C 1max This represents the maximum value of the learning factor C1; C 1min This represents the minimum value of the learning factor C1; C 2max This represents the maximum value of the learning factor C2; C 2min This represents the minimum value of the learning factor C2.

7. A method according to claim 6, characterized in that: Discretize the fractional-order PID controller; its time-domain expression is u(k): in, This represents the proportional gain of a fractional-order PID controller. Represents the integral coefficient of a fractional-order PID controller; Represents the derivative coefficients of a fractional-order PID controller; Indicates the integral order of the fractional-order PID controller; The derivative order of the fractional PID controller is indicated by h; h is the time step. and The coefficients are binomial coefficients, and their subscript values ​​represent the corresponding numbers; k represents the sampling period number; e() represents the error signal of the corresponding sampling period; i and j both represent the iteration number; q0 and d0 represent the initial binomial coefficients; The changes in the proportional coefficient, integral coefficient, derivative coefficient, integral order, and derivative order of the fractional-order PID controller output by the BP neural network are calculated using the following formulas: ； Where f1 and f2 are the calculation coefficients, respectively; η represents the learning efficiency.

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