Controller parameter setting method based on improved artificial rabbit algorithm and controller

Abstract

The invention discloses a controller parameter setting method based on an improved artificial rabbit algorithm and a controller, and relates to the technical field of intelligent controllers. The problem that in the prior art, application of a traditional artificial rabbit algorithm cannot meet actual requirements, and consequently use is limited is solved. According to the method, algorithm parameters are initialized; an iterative loop is entered, and position updating is carried out; in the detour foraging stage, a dynamic adjustment factor is introduced, and the position is updated; in the random hiding stage, a Levy flight strategy is introduced, and hiding positions are updated; an energy contraction stage; introducing a boundary control strategy; calculating the fitness of a new population; and outputting optimal parameters of a controller. According to the method, the dynamic adjustment factor, the Levy flight strategy and the boundary control strategy are introduced, so that the global search capability and the convergence speed are improved. The method provided by the invention has better robustness and precision, so that the controller can generate a more excellent control effect.

Description

Technical Field

[0001] The invention relates to the technical field of intelligent controllers, and in particular to a controller parameter setting method based on an improved artificial rabbit algorithm. Background Art

[0002] In the past few decades, swarm intelligence algorithms have become increasingly popular in complex engineering fields because they are simpler and more efficient than traditional numerical methods. Swarm intelligence algorithms have many advantages. The first is their randomness, which ensures that the algorithm successfully avoids local optimal solutions. The second is the black box concept, that is, there is no need to understand the internal structure of the program, only the input and expected output are known, and the operation is simple. Finally, the algorithm has fewer parameters, is easy to implement, and has a simple mathematical model. There are many swarm intelligence algorithms, but they all have one common feature, that is, the optimization process is divided into two stages: exploration and exploitation. In the exploration stage, the algorithm tends to look for potential global optimal solutions in the search space. This search process is global and extensive. In the exploitation stage, the algorithm tends to improve the optimal solution found so far by searching in the neighborhood of the solution. Obviously, when exploitation and exploration are carried out at the same time, they will conflict with each other. Common swarm intelligence algorithms include Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Bat Algorithm (BA), Sparrow Search Algorithm (SSA), Firefly Algorithm (FA), and Wolf Pack Algorithm (WPA).

[0003] Artificial Rabbits Optimization (ARO) is a swarm intelligence algorithm proposed by Wang et al. in 2022. As a new type of swarm intelligence algorithm, the Artificial Rabbits Optimization (ARO) algorithm simulates the survival strategy of rabbits for mathematical modeling, providing a low-parameter, low-complexity optimization method. However, ARO also has problems such as easy to fall into local optimality, slow convergence speed, and ineffective boundary processing. Therefore, the present invention improves the traditional artificial rabbit algorithm to eliminate the defects and shortcomings of the traditional artificial rabbit algorithm.

[0004] There are several methods currently used to improve the Artificial Rabbit algorithm:

[0005] 1. Application number: CN202410272769.2, Patent name: An improved method based on the adaptive artificial rabbit algorithm. This method controls the position update through adaptive weights, but only uses random numbers to update the position during the detour foraging and random hiding stages. It lacks a dynamic adjustment factor and cannot effectively balance between global and local searches. This method does not introduce the Levy flight strategy, resulting in insufficient jumping and easy to fall into local optimality. In addition, the energy control mechanism is not designed, and the impact of energy changes on search behavior in actual systems cannot be simulated, so it is essentially different from this patent.

[0006] 2. Application number CN202410181740.3, patent name: An Artificial Rabbit Swarm Optimization Algorithm (IARO) based on adaptive weight adjustment. This method improves the global search capability by introducing a large weight in the early stage, and then adaptively adjusts the weight according to the population distribution to perform a fine search. Although the algorithm dynamically adjusts the individual position, it does not combine the dynamic adjustment factor, resulting in inflexible global and local search step sizes, easy early convergence or insufficient local search accuracy.

[0007] 3. Application number CN202410336356.6, patent name: An improved algorithm for battery state of charge prediction that combines the moth-to-flame algorithm with the artificial rabbit optimization algorithm. This method optimizes the support vector machine model by integrating the spiral flight mode of moths with the detour foraging and random hiding of artificial rabbits, and introducing an adaptive weight factor. However, this method does not consider the adaptive control of the search step length at different stages by the dynamic adjustment factor, which makes the algorithm lack flexibility in global search and local search, and does not consider the enhancement of jumping by the Levy flight strategy, which limits the ability of the algorithm to jump out of the local optimum.

[0008] 4. Application number CN202311356557.4, patent name: A scheduling optimization method for cascade hydropower stations based on the artificial rabbit optimization algorithm, which optimizes the constraints through penalty functions and uses the improved artificial rabbit optimization algorithm to solve the scheduling model, with the goal of maximizing the settlement income of cascade hydropower stations. However, this method does not consider the adaptive control of the search step size by the dynamic adjustment factor at different stages, which makes the algorithm insufficiently flexible in global and local searches. At the same time, the Levy flight strategy is not introduced, which limits the algorithm's jumping in the search space and its ability to jump out of the local optimal solution. In addition, this method lacks consideration in the design of the energy factor, which may affect the fineness and convergence speed of the later search.

[0009] In summary, the present invention provides a controller parameter setting method based on an improved artificial rabbit algorithm. This method firstly introduces a dynamic adjustment factor to adaptively adjust the step size during the iteration process, so that the early search range is wider, the global search capability is enhanced, and the step size is reduced in the later stage to improve the local search accuracy; secondly, the Levy flight strategy is introduced to enhance the random jumps in the search process and avoid falling into the local optimum; finally, an energy factor is added to simulate the energy decreasing process, and the fine search is concentrated, so that the algorithm gradually shrinks the search range in the later stage, and the search accuracy and convergence speed are improved. This improvement has the advantages of higher global search capability, fast convergence speed, avoiding local optimum, and adapting to complex constrained optimization problems. Summary of the invention

[0010] The present invention provides a controller parameter setting method and a controller based on an improved artificial rabbit algorithm to solve the problems that the traditional artificial rabbit algorithm has slow convergence speed, is easy to fall into local optimum, and has ineffective boundary processing, which leads to the inability of the controller to meet actual needs during application.

[0011] A controller parameter tuning method based on an improved artificial rabbit algorithm is implemented by the following steps:

[0012] Step 1: Initialize the parameters of the improved artificial rabbit algorithm and calculate the initial population fitness;

[0013] Step 2: Set the number of loop iterations, requiring the number of iterations to be less than the maximum number of iterations;

[0014] Step 3, detour foraging stage: introduce a dynamic adjustment factor, apply the dynamic adjustment factor to the mathematical model of the rabbit's exploration in the search space, and realize position update; the specific process is:

[0015] Step 31: Set the rabbit to explore in the search space. The mathematical model is:

[0016]

[0017] Where, i, j = 1, · · ·, n, j ≠ i, It is the new position calculated based on the positions of other individuals and the dynamic adjustment factor. is the reference position of the i-th rabbit at the t-th iteration, is the reference position of the jth rabbit at the tth iteration, t is the current iteration number, R is the running operator, and r 1 is a random number between [0,1], round() is a function that rounds to the specified number of digits, n 1 Random numbers that follow a standard normal distribution;

[0018] Step 32: Introduce a dynamic adjustment factor, expressed as follows:

[0019]

[0020] Where α(t) is the dynamic adjustment factor for the tth iteration; min is the minimum adjustment factor; T is the maximum number of iterations; α max is the maximum adjustment factor;

[0021] Step 33: Apply the dynamic adjustment factor to the mathematical model, expressed as follows:

[0022]

[0023] In the formula, Z i (t) and Z best (t) are the current position of the i-th individual at the t-th iteration and the best position currently found;

[0024] Step 4: Random hiding phase: Introduce the Levy flight strategy to update the hiding position;

[0025] Step 5, energy contraction phase: execute the detour foraging phase or random hiding phase according to the set energy factor;

[0026] Step 6: Introduce boundary control strategy to ensure the position is within the boundary; it can be expressed as follows:

[0027]

[0028] In the formula, z i (t+1) is the updated position of the i-th individual at the t+1th iteration, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space;

[0029] Step 7: Determine whether the number of iterations has reached the upper limit. If so, stop the iteration to obtain the optimal position and the fitness value of the new population; otherwise, return to step 2 until the termination condition is met to achieve the tuning of the controller parameters.

[0030] The present invention also provides a controller, which performs parameter setting by the above parameter setting method.

[0031] Beneficial effects of the present invention:

[0032] 1. The present invention provides a Levy flight strategy based on the traditional artificial rabbit algorithm, which increases the exploration depth and breadth of the search space, enhances the global search capability, and avoids falling into the local optimum at an early stage.

[0033] 2. The present invention provides a dynamic adjustment factor on the traditional artificial rabbit algorithm. In the initial stage, the step size is large, which is conducive to global search; in the later stage, the step size is reduced, which is conducive to local search and fine adjustment.

[0034] 3. The present invention provides a boundary control strategy based on the traditional artificial rabbit algorithm. After each position update, the new position is boundary controlled to ensure that the position is within the preset upper and lower boundaries, thereby ensuring the validity of the search space and avoiding the generation of invalid solutions.

[0035] 4. The method of the present invention has a wide range of applications: it can be applied to many control fields such as complex engineering optimization, power system optimization, control system optimization, signal processing, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flow chart of a controller parameter setting method based on an improved artificial rabbit algorithm according to the present invention; DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The present invention takes a liquid crystal spatial light modulator as an example and uses it as a controlled object. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0038] This embodiment takes a liquid crystal spatial light modulator beam deflection control system (LCOPA) as an example and uses it as a controlled object to verify the superiority of the improved artificial rabbit algorithm. The process of establishing the model of the liquid crystal spatial light modulator beam deflection control system is not elaborated in detail.

[0039] The fractional-order model of the liquid crystal spatial light modulator beam deflection control system is:

[0040]

[0041] Where, λ = 1064nm represents the laser wavelength, d = 9.8μm single element size, q = 1.6×10 -19 C is the unit charge, C represents coulomb, which is the unit of charge, x = 9.8 μm is the thickness of the liquid crystal layer, θ p is the deflection angle of the outgoing light, k 1 =1.11×10 -12 N is the elastic coefficient of liquid crystal molecules. N represents the unit of force, i.e. Newton. 2 =1.71×10 -12 N is the bending elastic coefficient of the liquid crystal molecules, is the phase change of the liquid crystal molecules after the electric field is applied, η 1 is the splay viscosity coefficient, η2 is the bending viscosity coefficient, α 1 , α 2 is the order, j is the volume charge fraction coefficient, τ is the time lag coefficient, both the volume charge fraction coefficient j and the time lag coefficient τ are unknown parameters, and D represents the fractional calculus operation. In the fractional model parameters, the splay viscosity coefficient η 1 , bending viscosity coefficient η 2 , order α 1 , α 2 , the volume charge fractional coefficient j, and the time lag coefficient τ are all unknown parameters. By using Legendre wavelet basis function expansion and integral operation, the fractional derivatives in the model can be converted into conventional linear system expressions, thereby obtaining the transfer function form of the liquid crystal spatial light modulator beam deflection control system.

[0042] The fractional-order model of the liquid crystal spatial light modulator beam deflection control system is changed into the transfer function form:

[0043]

[0044] The transfer function of the Smith predictor can be expressed as:

[0045] G m (s) = G 0 (s)(1-e -τs ) (1)

[0046] Among them, G 0 (s) is the delay-free term of the transfer function, e -τs is the delay term, and τ represents the delay time of the system.

[0047] According to the Smith predictive control strategy, the transfer function of the equivalent controlled object is:

[0048] G 0 (s) = G 0 (s)e -τs +G 0 (s)(1-e -τs ) (2)

[0049] Fractional PI λ D μ The mathematical model of the controller is:

[0050]

[0051] Where R(s) is the reference input signal, Y(s) is the actual output of the system, and fractional-order PI λ D μ The controller consists of three parts: proportional, integral and differential, corresponding to the proportional gain Kp , integral gain K i and differential gain K d , unlike the traditional integer-order PID controller, the fractional-order PI λ D μ The controller adds two adjustable parameters on the basis of integer order: integral order λ and differential order μ. When the values ​​of λ and μ are 1, the fractional order PI λ D μ The controller is equivalent to an integer-order PID controller. However, in actual design, by selecting different λ and μ values, the response characteristics of the integral and differential operations can be adjusted, so that the system can perform better in terms of dynamic performance and steady-state accuracy.

[0052] In this implementation, the Smith predictor and fractional-order PI are integrated. λ D μ The controller structure of the controller, according to the Mason gain formula, the closed-loop transfer function of the liquid crystal spatial light modulator beam deflection control system is:

[0053]

[0054] in, represents the fractional integral term, λ is the integral order; K d s μ represents the fractional differential term, μ is the differential order. Fractional PI λ D μ Controller parameter K p , K i , K d , λ, and μ are all unknown. Therefore, the improved artificial rabbit algorithm is used to adjust the parameters of the controller. The specific process is:

[0055] Step 1. Initialize the algorithm parameters, determine the population size, set the maximum number of iterations, initialize the upper and lower bounds of the controller parameters, set the initial values ​​for the energy factor, dynamic adjustment factor, Levy flight parameters and boundary control strategy, and calculate the initial population fitness;

[0056] Step 2. Enter the iteration loop and update the position; set the number of iterations < the maximum number of iterations;

[0057] Step 3. Detour foraging stage: introduce dynamic adjustment factors and update positions; by introducing dynamic adjustment factors to adjust the individual moving step length, a larger global search can be performed in the early iteration stage, and gradually converge in the later stage to improve the optimization performance of the algorithm;

[0058] The detour foraging stage simulates the exploratory behavior of rabbits when looking for food. In this stage, the rabbit searches for possible food sources by conducting extensive exploration in the search space. The mathematical model is:

[0059]

[0060] R=L·c(k) (5)

[0061]

[0062] g = randpern(d) (8)

[0063] in, is the candidate position of the i-th rabbit at the t+1th iteration; is the reference position of the i-th rabbit at the t-th iteration, is the reference position of the jth rabbit at the tth iteration, g is a random permutation from 1 to d generated by a function, which is used to randomly select the updated dimension during the artificial rabbit foraging phase, and r 1 、r 2 and r 3 is a random number between [0,1]; n is the population size; d is the problem dimension; T is the maximum number of iterations; R is the run operator; L is the run length; c is 0 or 1, used to randomly select individuals for mutation; n 1 A random number that obeys a standard normal distribution. A dynamic adjustment factor is introduced at this stage. By gradually changing the step size during the iteration process, the search range is controlled so that the algorithm has a larger search step size in the early stage to enhance the global search capability, and gradually reduces the step size in the later stage to enhance the local search accuracy. Its mathematical model is as follows:

[0064]

[0065] Apply the formula to equation (4):

[0066]

[0067] Among them, α(t) is the dynamic adjustment factor of generation t, α min is the minimum adjustment factor, α max is the maximum adjustment factor, t is the current number of iterations, T is the maximum number of iterations, and Z i (t) represents the current position of the i-th individual, Z best (t) represents the best position currently found.

[0068] Step 4. Random hiding stage: Introduce the Levy flight strategy and update the hiding position; increase the jumping nature of the population through the Levy flight strategy, further enhance the exploration ability of the search space, and help individuals jump out of the local optimal solution;

[0069] The random hiding stage simulates the random hiding behavior of rabbits in the natural environment to avoid predators. In each iteration, the rabbit will generate m holes around itself along the dimension of the search space to reduce the probability of being preyed on. The location of the bth hiding hole of the i-th rabbit is:

[0070]

[0071] Where b=1,···,m

[0072]

[0073] in, represents the location of the hiding hole randomly selected from k holes; n 2 is a random number that follows a standard normal distribution; r 4 is a random number 0 or 1; H is a hidden parameter.

[0074] When rabbits are being hunted, they will randomly hide in a cave, and the formula for updating the random hiding position is:

[0075]

[0076] in, is a cave randomly selected from m caves, f r is the step size scaling factor, r 4 and r 5 is a random number from 0 to 1. After completing the detour foraging and random hiding, the rabbit's position is updated:

[0077]

[0078] in, Represents the fitness value at time t+1 (current solution); Represents the fitness value at time t (previous solution).

[0079] The Levy flight strategy is introduced at this stage. The Levy flight strategy is a random walk strategy based on Levy distribution.

[0080] The step length formula of the Levy flight strategy is as follows:

[0081]

[0082] in: The step size factor σ u and σ v The calculation formula is:

[0083]

[0084] σ v =1 (20)

[0085] λ is taken as 1.5. Γ is used to calculate the fractional-order calculus term in the fractional-order controller.

[0086] The levy flight strategy is introduced into the optimal position of the artificial rabbit in formula (14). The improved ARO greatly reduces the risk of the artificial rabbit falling into the local optimum and can fully perform local search. The improved formula is as follows:

[0087]

[0088] Among them, s' is the step size generated by Levy distribution, and α is the step size scaling factor, which is used to control the scale of the step size. By introducing the Levy flight strategy, local search and global search can be balanced to avoid falling into the local optimum.

[0089] Step 5. Energy contraction phase: Based on the iteration process and the changes in population fitness, the energy factor is dynamically updated to control the movement range of individuals and ensure better local search capabilities in later iterations;

[0090] The energy contraction phase simulates the rabbit's behavior of concentrating its energy on careful foraging after finding a food source, i.e., this search mechanism is determined by the rabbit's energy, which gradually decreases over time. The energy factor in ARO is defined as follows:

[0091]

[0092] Among them, r is a random number between 0 and 1. When A(t)>1, the individuals in the population implement a detour foraging strategy; otherwise, the individuals in the population implement a random hiding strategy.

[0093] Step 6. Boundary control strategy: ensure that individuals do not exceed the scope of the search space after each position update, and make appropriate adjustments to individuals that exceed the boundary;

[0094] By adjusting the individual positions, we can ensure that they are active within the effective search range, thereby improving the stability and effectiveness of the algorithm. In the existing artificial rabbit optimization algorithm, the boundary control strategy needs to be added to the position update formula, that is, formula (17). The improved formula is as follows:

[0095]

[0096] Among them, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space.

[0097] Step 7. Calculate the fitness of the updated population and find the best individual in the current iteration;

[0098] Step 8. Determine whether the maximum number of iterations has been reached. If so, the algorithm outputs the optimal controller parameters, including five key parameters, to optimize the dynamic response performance and control accuracy of the controller. Otherwise, the number of iterations is increased by 1 and returns to step 2.

[0099] In this embodiment, the improved artificial rabbit algorithm outputs the optimal controller parameters, including five key parameters, which are used to optimize the dynamic response performance and control accuracy of the controller. Figure 1 , set the number of iterations to 20. The optimized artificial rabbit algorithm is used to tune the parameters of the fractional-order composite controller. The parameters of the tuned controller are K p =40.7324,K i =42.5622,K d =79.5144, λ=0.98, μ=0.2653.

[0100] Specific implementation method 2: The controller of this implementation method is parameterized by a controller parameter tuning method based on an improved artificial rabbit algorithm as described in specific implementation method 1. The tuned controller parameters described in this implementation method are applied to the LCOPA system, which significantly improves the dynamic response performance of the system, reduces overshoot and response time; enhances the tracking accuracy of beam deflection, and ensures that the system can still operate stably in complex environments; and optimizes the robustness of the system, so that it can still maintain high accuracy and reliability under external disturbances and uncertain conditions. In addition, the tuned parameters effectively address the nonlinear time lag problem in LCOPA, providing accurate and stable beam control capabilities for high-demand industrial applications such as optical control, laser processing, and optical communications.

[0101] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0102] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A controller parameter tuning method based on an improved artificial rabbit algorithm, characterized in that: The method is implemented by the following steps: Step 1: Initialize the parameters of the improved artificial rabbit algorithm and calculate the initial population fitness; Step 2: Set the number of loop iterations, requiring the number of iterations to be less than the maximum number of iterations; Step 3, detour foraging stage: introduce a dynamic adjustment factor, apply the dynamic adjustment factor to the mathematical model of the rabbit's exploration in the search space, and realize position update; the specific process is: Step 31: Set the rabbit to explore in the search space. The mathematical model is: Where, i, j = 1, · · ·, n, j ≠ i, It is the new position calculated based on the positions of other individuals and the dynamic adjustment factor. is the reference position of the i-th rabbit at the t-th iteration, is the reference position of the jth rabbit at the tth iteration, t is the current iteration number, R is the running operator, r1 is a random number between [0,1], round() is a function that rounds to a specified number of digits, and n1 is a random number that follows a standard normal distribution; Step 32: Introduce a dynamic adjustment factor, expressed as follows: Where α(t) is the dynamic adjustment factor for the tth iteration; min is the minimum adjustment factor; T is the maximum number of iterations; α max is the maximum adjustment factor; Step 33: Apply the dynamic adjustment factor to the mathematical model, expressed as follows: In the formula, Z i (t) and Z best (t) are the current position of the i-th individual at the t-th iteration and the best position currently found; Step 4: Random hiding phase: Introduce the Levy flight strategy to update the hiding position; Step 5, energy contraction phase: execute the detour foraging phase or random hiding phase according to the set energy factor; Step 6: Introduce boundary control strategy to ensure the position is within the boundary; it can be expressed as follows: In the formula, z i (t+1) is the updated position of the i-th individual at the t+1th iteration, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space; Step 7: Determine whether the number of iterations has reached the upper limit. If so, stop the iteration to obtain the optimal position and the fitness value of the new population; otherwise, return to step 2 until the termination condition is met to achieve the tuning of the controller parameters.

2. The controller parameter setting method based on the improved artificial rabbit algorithm according to claim 1, characterized in that: In step 1, the parameters initialized include: determining the population size, setting the maximum number of iterations, initializing the upper and lower bounds of the controller parameters, and setting initial values ​​for the energy factor, dynamic adjustment factor, Levy flight parameters, and boundary control strategy.

3. The controller parameter setting method based on the improved artificial rabbit algorithm according to claim 1, characterized in that: The specific process of step 4 is: when being chased, the rabbit will randomly hide in a cave. The formula for the random hiding position is as follows: In the formula, It is the new position calculated based on the positions of other individuals and the dynamic adjustment factor. is the reference position of the i-th rabbit at the t-th iteration, is the reference position of the j-th rabbit at the t-th iteration, t is the current iteration number, R is the running operator, and r4 is a random number between [0,1]; is a cave randomly selected from m caves; After randomly hiding, the rabbit's position update formula is as follows: In the formula, f(w i (t+1)) is the fitness value at the t+1 iteration; is the fitness value at t iterations; Applying the Levy flight strategy to the random hiding position update formula, the position update formula is as follows: Among them, s' is the step size generated by Levy distribution, and α is the step size scaling factor, which is used to control the scale of the step size.

4. The controller parameter setting method based on the improved artificial rabbit algorithm according to claim 3 is characterized in that: The step length formula for setting the Levy flight strategy is as follows: in: The step size factor σ u and σ v The calculation formula is: s v =1 Where λ is taken as 1.5, and Γ is used to calculate the fractional-order differential and integral terms in the fractional-order controller.

5. The controller parameter setting method based on the improved artificial rabbit algorithm according to claim 1, characterized in that: In step 5, the formula for setting the energy factor A(t) is as follows: Where r is a random number between 0 and 1, and T is the maximum number of iterations. When A(t)>1, the individuals in the population execute the detour foraging phase; otherwise, the individuals in the population execute the random hiding phase.

6. A controller, characterized in that: The controller performs parameter tuning by the parameter tuning method according to any one of claims 1 to 5.

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