A controller parameter setting method based on an improved artificial rabbit algorithm and a controller

Abstract

The application relates to a controller parameter setting method and a controller based on an improved artificial rabbit algorithm and relates to the technical field of intelligent controllers. The application solves the problem that the application of the traditional artificial rabbit algorithm in the prior art cannot meet actual requirements, leading to limited use and the like. The application is realized through the following steps: initializing algorithm parameters; entering an iteration cycle and performing position updating; introducing a dynamic adjustment factor in a detour foraging stage and performing position updating; introducing a Levy flight strategy in a random hiding stage and performing hiding position updating; introducing a boundary control strategy in an energy contraction stage; calculating the fitness of a new population; and outputting optimal parameters of a controller. The application introduces a dynamic adjustment factor, a Levy flight strategy and a boundary control strategy, thereby improving the global search capability and the convergence speed. The method has better robustness and precision, and the controller can produce more excellent control effects.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of intelligent controllers, and particularly relates to a controller parameter setting method based on an improved artificial rabbit algorithm. BACKGROUND

[0002] In the past few decades, swarm intelligence algorithms have been increasingly favored in complex engineering fields because this method is more convenient and efficient than traditional numerical methods. Swarm intelligence algorithms have many advantages. First, their randomness can ensure that the algorithm successfully avoids local optimal solutions. Second, the black box concept, which does not require understanding of the internal structure of the program, only needs to know the input and desired output, 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 development. In the exploration stage, the algorithm tends to find potential global optimal solutions in the search space, and this search process is global and extensive. In the development stage, the algorithm tends to improve the optimal solution found so far by searching in the neighborhood of the solution. Obviously, when development 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 Rabbit Optimization (ARO) is a swarm intelligence algorithm proposed by Wang et al. in 2022. As a new type of swarm intelligence algorithm, the artificial rabbit optimization algorithm (ARO) provides a low-parameter, low-complexity optimization method by simulating the survival strategy of rabbits. However, ARO also has problems such as being prone to local optimization, slow convergence speed, and ineffective boundary processing. Therefore, the present application improves the traditional artificial rabbit algorithm to eliminate the defects and deficiencies of the traditional artificial rabbit algorithm.

[0004] There are several methods for improving the artificial rabbit algorithm at present, including:

[0005] 1. Application No. CN202410272769.2, Patent Name: An Improved Method Based on Self-Adaptive Artificial Rabbit Algorithm, which controls position update through self-adaptive weight, but only uses random number to update position in detour foraging and random hiding stage, lacks dynamic adjustment factor, and cannot effectively balance between global and local search. This method does not introduce Levy flight strategy, resulting in insufficient jumping and being easy to fall into local optimum. In addition, no energy control mechanism is designed, which cannot simulate the influence of energy change in actual system on search behavior, so there is essential difference with this patent.

[0006] 2. Application No. CN202410181740.3, Patent Name: Artificial Rabbit Group Optimization Algorithm Based on Self-Adaptive Adjustment of Weight (IARO), which improves global search ability by initially introducing larger weight, and adjusts weight adaptively according to population distribution in later period for fine search. Although this algorithm dynamically adjusts individual position, it does not combine dynamic adjustment factor, resulting in inflexible global and local search step, and being easy to converge early or lack local search precision.

[0007] 3. Application No. CN202410336356.6, Patent Name: An Improved Algorithm for Battery State of Charge Prediction by Combining Firefly Algorithm and Artificial Rabbit Optimization Algorithm, which optimizes support vector machine model by fusing firefly spiral flight mode and artificial rabbit detour foraging and random hiding, and introducing adaptive weight factor. However, this method does not consider the adaptive control of dynamic adjustment factor on search step in different stages, making the algorithm lack flexibility in global and local search, and does not consider the enhancement of Levy flight strategy on jumping, which limits the ability of the algorithm to jump out of local optimum.

[0008] 4. Application No. CN202311356557.4, Patent Name: A Step-by-Step Hydropower Station Dispatching Optimization Method Based on Artificial Rabbit Optimization Algorithm, which optimizes constraint conditions by penalty function, and solves the dispatching model by improved artificial rabbit optimization algorithm to maximize the settlement income of step-by-step hydropower station. However, this method does not consider the adaptive control of dynamic adjustment factor on search step in different stages, making the algorithm lack flexibility in global and local search, and does not introduce Levy flight strategy, which limits the jumping ability of the algorithm in search space and the ability to jump out of local optimal solution. In addition, this method lacks consideration in the design of energy factor, which may affect the fineness and convergence speed of later search.

[0009] In summary, the application provides a controller parameter setting method based on an improved artificial rabbit algorithm, which first introduces a dynamic adjustment factor to adaptively adjust the step size in the iteration process, making the early search range wider and the global search ability stronger, and reducing the step size in the later period to improve the local search precision; secondly, the Levy flight strategy is introduced to enhance the random jumping in the search process and avoid falling into local optimum; finally, an energy factor is added to simulate the energy decreasing process, concentrate on fine search, make the algorithm gradually shrink the search range in the later period, and improve the search precision and convergence speed. The improvement has the advantages of higher global search ability, fast convergence speed, avoidance of local optimum, and adaptation to complex constraint optimization problems. SUMMARY

[0010] The application provides a controller parameter setting method based on an improved artificial rabbit algorithm and a controller to solve the problems in the application process of the traditional artificial rabbit algorithm, such as slow convergence speed, easy falling into local optimum, and ineffective boundary processing, which leads to the fact that the use of the controller cannot meet the actual demand.

[0011] A controller parameter setting method based on an improved artificial rabbit algorithm, which is realized by the following steps:

[0012] Step one, initializing the parameters of the improved artificial rabbit algorithm, and calculating the initial population fitness;

[0013] Step two, setting the number of loop iterations, and requiring the number of iterations to be less than the maximum number of iterations;

[0014] Step three, detour foraging stage: introducing a dynamic adjustment factor, applying the dynamic adjustment factor to the mathematical model of the rabbit exploring in the search space, and realizing position updating; the specific process is as follows:

[0015] Step three one, setting the rabbit to explore in the search space, and the mathematical model is as follows:

[0016]

[0017] In the formula, i, j = 1, ···, n, j ≠ i, is a new position calculated according to 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, r1 is a random number between 0 and 1, round() is a function of rounding to a specified number of digits, and n1 is a random number obeying the standard normal distribution;

[0018] Step three two, introducing a dynamic adjustment factor, which is expressed as follows:

[0019]

[0020] In the formula, alpha (t) is a dynamic adjustment factor of t iterations; alpha min is a minimum adjustment factor; T is a maximum iteration number; alpha max is a maximum adjustment factor;

[0021] Step three, the dynamic adjustment factor is applied to the mathematical model, which is expressed as:

[0022]

[0023] In the formula, Z i (t) and Z best (t) are the current position and the best position found at the tth iteration of the ith individual respectively;

[0024] Step four, the random hiding stage: Levy flight strategy is introduced to update the hiding position;

[0025] Step five, the energy contraction stage: according to the set energy factor, the detour foraging stage or the random hiding stage is executed;

[0026] Step six, the boundary control strategy is introduced to ensure that the position is within the boundary; which is expressed as:

[0027]

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

[0029] Step seven, it is judged whether the iteration number reaches the upper limit, if yes, the iteration is stopped, and the optimal position and the new population fitness value are obtained; otherwise, return to step two until the termination iteration condition is met; the controller parameter setting is realized.

[0030] The application also provides a controller which is set by the above parameter setting method.

[0031] The beneficial effects of the application are:

[0032] 1. The application provides Levy flight strategy on the basis of the traditional artificial rabbit algorithm, increases the exploration depth and breadth of the search space, enhances the global search ability, and avoids early falling into local optimum.

[0033] 2. The application provides a dynamic adjustment factor on the basis of the traditional artificial rabbit algorithm, which is large in the initial stage, is beneficial to global search, and is small in the later stage, is beneficial to local search and fine adjustment.

[0034] 3. The application provides a boundary control strategy on the basis of the traditional artificial rabbit algorithm, and boundary control is performed on the new position after each position update, so that the position is ensured to be within the preset upper and lower boundaries, thereby ensuring the effectiveness of the search space and avoiding generating invalid solutions.

[0035] 4. The method has wide application range: can be applied to complex engineering optimization, power system optimization, control system optimization, signal processing and many other control fields. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 A flowchart of the controller parameter setting method based on the improved artificial rabbit algorithm; DETAILED DESCRIPTION

[0037] In order to make the purpose, technical scheme and advantages of the application clearer and more apparent, the application will be further described in detail below in combination with the drawings and examples. The application takes a liquid crystal spatial light modulator as an example, which is taken as a controlled object. It should be understood that the specific examples described herein are only used to explain the application and do not limit the application.

[0038] The present embodiment takes a liquid crystal spatial light modulator beam deflection control system (LCOPA) as an example, which is taken as a controlled object. The improved artificial rabbit algorithm is used to verify the superiority of the improved artificial rabbit algorithm. The establishment process of the liquid crystal spatial light modulator beam deflection control system model is not described in detail.

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

[0040]

[0041] In the formula, λ=1064nm represents the wavelength of the laser, d=9.8um is the size of a single array element, q=1.6x10 -19 C is the unit charge, C represents the unit of charge, x=9.8um is the thickness of the liquid crystal layer, θ p is the deflection angle of the outgoing light, k1=1.11x10 -12 N is the curvature elastic coefficient of the liquid crystal molecule, N represents the unit of force, k2=1.71x10 -12 N is the curvature elastic coefficient of the liquid crystal molecule, is the phase change of liquid crystal molecules after applying electric field, η1 is the splay viscosity coefficient, η2 is the bend viscosity coefficient, α1 and α2 are the order, j is the fractional charge coefficient, τ is the time delay coefficient, the fractional charge coefficient j and the time delay coefficient τ are unknown parameters, and D represents the fractional calculus operation. In the fractional order model parameters, the splay viscosity coefficient η1, the bend viscosity coefficient η2, the order α1 and α2, the fractional charge coefficient j, and the time delay coefficient τ are unknown parameters. By using the Legendre wavelet basis function expansion and integral operation, the fractional derivative in the model can be converted into a conventional linear system expression, so that the transfer function form of the liquid crystal spatial light modulator beam deflection control system is obtained.

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

[0043]

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

[0045] G m (s)=G0(s)(1-e -τs ) (1)

[0046] Where G0(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 prediction control strategy, the transfer function of the equivalent controlled object is:

[0048] G0(s)=G0(s)e -τs +G0(s)(1-e -τs ) (2)

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

[0050]

[0051] Where R(s) is the reference input signal, Y(s) is the actual output of the system, and the fractional order PI λ D μ controller contains proportional, integral and differential parts, which correspond to proportional gain K p , integral gain K i and differential gain K d , respectively. Unlike the traditional integer order PID controller, the fractional order PI λ D μThe controller adds two adjustable parameters on the basis of integer order: integral order λ and differential order μ. When 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 values of λ and μ, the response characteristics of integral and differential operations can be adjusted, so that the system performs better in dynamic performance and steady-state accuracy.

[0052] In this embodiment, the Smith predictor and the fractional order PI λ D μ The controller structure of the controller, according to the Mason gain formula, obtains the closed-loop transfer function of the liquid crystal spatial light modulator beam deflection regulation system as:

[0053]

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

[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, and set the initial values of the energy factor, dynamic adjustment factor, Levy flight parameters, and boundary control strategy. Calculate the fitness of the initial population;

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

[0057] Step 3. Detour foraging stage: introduce a dynamic adjustment factor and update the position; by introducing a dynamic adjustment factor, the moving step of each individual is adjusted, so that in the early iteration stage, a large range of global search can be performed, and in the later stage, it gradually converges, so as to improve the optimization performance of the algorithm;

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

[0059]

[0060] R=L·c(k) (5)

[0061]

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

[0063] where, is the candidate position of the ith rabbit at the t+1th iteration; is the reference position of the ith rabbit at the tth iteration, is the reference position of the jth rabbit at the tth iteration, g is a random permutation from 1 to d generated by using the function randperm(d), which is used to randomly select the updated dimension during the artificial rabbit detour foraging stage, r1, r2, and r3 are random numbers between [0, 1]; n is the population size; d is the problem dimension; T is the maximum number of iterations; R is the running operator; L is the running length; c is 0 or 1, which is used to randomly select individuals for mutation; n1 is a random number following the standard normal distribution. A dynamic adjustment factor is introduced in this stage to control the search range by gradually changing the step size during the iteration process, so that the algorithm has a larger search step in the early stage to enhance the global search ability, and gradually reduces the step size in the later stage to enhance the local search precision. The mathematical model is as follows:

[0064]

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

[0066]

[0067] where, a(t) is the tth dynamic adjustment factor, a min is the minimum adjustment factor, a max is the maximum adjustment factor, t is the current iteration number, T is the maximum iteration number, Z i (t) represents the current position of the ith individual, Z best (t) represents the best position found so far.

[0068] Step 4. Random hiding stage: introduce Levy flight strategy to update the hiding position; increase the jumping ability of the population through Levy flight strategy, further enhance the exploration ability of the search space, and help individuals jump out of 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 upon. The position of the bth hiding hole of the ith rabbit is:

[0070]

[0071] where, b = 1, ···, m

[0072]

[0073] where, represents the hiding hole position randomly selected from k caves; n2 is a random number subject to standard normal distribution; r4 is a random number 0 or 1; H is a hidden parameter.

[0074] When the rabbits are chased, they will hide in a cave at random, and the position update formula of random hiding is:

[0075]

[0076] where, is a cave randomly selected from m caves, f r is a step scaling factor, r4 and r5 are random numbers from 0 to 1. After completing the detour foraging and random hiding, the rabbit position update is:

[0077]

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

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

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

[0081]

[0082] where: The scale factor of step σ u and the calculation formula of σ v is:

[0083]

[0084] σ v = 1 (20)

[0085] λ takes 1.5. Γ is used to calculate the fractional calculus item in the fractional order controller.

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

[0087]

[0088] where s' is the step size generated by Levy distribution, and a is the step size scaling factor used to control the scale of step size. By introducing the Levy flight strategy, the balance between local search and global search can be achieved, and the local optimum can be avoided.

[0089] Step 5. Energy contraction phase; based on the change of iteration process and population fitness, the energy factor is dynamically updated to control the moving range of individuals, ensuring better local search ability in the later iteration;

[0090] The energy contraction phase simulates the behavior of rabbits concentrating on meticulous foraging after discovering food sources, that is, this search mechanism is determined by the energy of rabbits, and the energy of rabbits gradually decreases over time. The energy factor in ARO is defined as follows:

[0091]

[0092] where r is a random number between 0 and 1, and when A(t) > 1, the population individuals execute the detour foraging strategy; otherwise, the population individuals execute the random hiding strategy.

[0093] Step 6. Boundary control strategy: ensure that individuals do not exceed the range of the search space after each position update, and adjust the individuals that exceed the boundary appropriately;

[0094] By adjusting the position of individuals, it is ensured that they move 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] where z min is the minimum boundary value of the search space, and z max is the maximum boundary value of the search space.

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

[0098] Step 8. Determine whether the maximum number of iterations is reached. If yes, the optimal controller parameters are output, including five key parameters, for optimizing the dynamic response performance and control accuracy of the controller. Otherwise, the iteration number is increased by 1, and the process returns to step 2.

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

[0100] Specific implementation two, the controller of the embodiment is parameterized by the parameter setting method of the improved artificial rabbit algorithm-based controller in specific implementation one. The set controller parameters in the embodiment are applied to the LCOPA system, which significantly improves the dynamic response performance of the system, reduces the overshoot and response time, enhances the tracking accuracy of beam deflection, ensures stable operation of the system in complex environments, optimizes the robustness of the system, and enables the system to maintain high precision and reliability under external disturbances and uncertainty. In addition, the set parameters effectively deal with the nonlinear time delay problem in LCOPA, and provide precise and stable beam control capability for high-demand industrial applications such as optical regulation, laser processing and optical communication.

[0101] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described, but as long as the combinations of the technical features do not contradict, they should be considered as within the scope of the present disclosure.

[0102] The above-described embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it should not be understood as limiting the scope of the patent. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the scope of protection of the present application should be subject to the appended claims.

Claims

1. A controller parameter setting method based on an improved artificial rabbit algorithm, characterized in that: The method is realized by the following steps: Step one, initialize the parameters of the improved artificial rabbit algorithm, calculate the initial population fitness; Step two, set the number of iterations, and require the number of iterations < maximum number of iterations; Step three, detour foraging stage: introduce a dynamic adjustment factor, apply the dynamic adjustment factor to the mathematical model of the rabbit exploring in the search space, realize position update; the specific process is: Step three one, set the rabbit to explore in the search space, the mathematical model is: where i, j = 1, ···, n, j≠i, is a new position calculated from the positions of other individuals and a dynamic adjustment factor, is the reference position of the ith rabbit at the tth 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 of rounding to the specified number of digits, and n1 is a random number following a standard normal distribution; Step three two, introduce a dynamic adjustment factor, which is expressed by: In the formula, a(t) is a dynamic adjustment factor of tth iteration; a min is a minimum adjustment factor; T is a maximum iteration number; a max is a maximum adjustment factor; Step three three, apply the dynamic adjustment factor to the mathematical model, which is expressed by: wherein Z i (t) and Z best (t) are the current position of the i-th individual and the best position found so far at the t-th iteration, respectively. Step four, random hiding stage: introduce Levy flight strategy, perform hiding position update; Step five, energy contraction stage: according to the set energy factor, execute the detour foraging stage or the random hiding stage; Step six, introduce boundary control strategy to ensure that the position is within the boundary; it is expressed by: wherein z i (t+1) is the updated position of the i-th individual at the t+1 iteration, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space; Step seven, judge whether the number of iterations reaches the upper limit, if yes, stop iteration, obtain the optimal position and new population fitness value; otherwise, return to step two until the termination iteration condition is met; realize the controller parameter setting.

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

3. The controller parameter tuning method based on the improved artificial rabbit algorithm according to claim 1, characterized in that: The specific process of step four is: when the rabbit is chased, it will randomly hide in a cave, and the formula of random hiding position is as follows: wherein, is a new position calculated from the positions of other individuals and a dynamic adjustment factor, is the reference position of the ith rabbit at the tth 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 r4 is a random number between [0, 1]; is a randomly selected cave from m caves; After random hiding, the rabbit position update formula is as follows: where f(w i f(t+1) is the fitness value at iteration t+1; f(t) is the fitness value at iteration t; Apply Levy flight strategy to the random hiding position update formula, and the position update formula is as follows: Where s' is the step length generated by Levy distribution, and α is the step length scaling factor, which is used to control the scale of step length.

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

5. The controller parameter tuning method based on the improved artificial rabbit algorithm according to claim 1, characterized in that: In step five, the formula of 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 population individual executes the detour foraging stage; otherwise, the population individual executes the random hiding stage.

6. A controller characterized by: The controller is parameterized by the parameter setting method of any one of claims 1-5.

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