Controller optimization method based on improved Seagull algorithm

Abstract

The controller optimization method based on the improved seagull algorithm includes the following steps: determining the migration behavior and predation behavior of seagulls in the seagull optimization algorithm; secondly, initializing the population using the opposition search operator strategy, and recording the current optimal individuals and groups; finally, using the nonlinear change convergence factor to calculate the control factor and mutation operation, eliminating the seagull individuals with poor fitness in the population and continuously updating the optimization, so as to continuously correct and adjust the PI controller parameters. The present invention improves the traditional seagull optimization algorithm through the opposition search operator strategy, the nonlinear change convergence factor and the mutation operation strategy, making up for the shortcomings of the traditional seagull algorithm that converges early and falls into the local optimum; at the same time, the improved seagull algorithm is used to optimize the controller, thereby improving the response speed and real-time online adjustment capability.

Description

Technical Field

[0001] The invention relates to the field of controller optimization, and in particular to a controller optimization method based on an improved Seagull algorithm. Background Art

[0002] Controllers are widely used in chemical, electrical, automatic control and other fields, and the rationality of their parameters is an important factor affecting the performance of controllers. Therefore, with the continuous progress and development of human society, how to improve the response speed of controllers and achieve real-time online adjustment capabilities has become a current research hotspot.

[0003] Regarding controller optimization, the solutions in the prior art are as follows:

[0004] 1) The moth-to-fire algorithm is used to optimize the parameters of the PI controller of the dynamic voltage restorer to achieve rapid recovery of voltage fluctuations. This method imitates the uniqueness of moths' lateral orientation according to flames at night, thereby making an appropriate trade-off between exploration and development and effectively avoiding local optimality, but the search efficiency of this method is relatively low because it only uses a single moth to approach each flame, which is not enough to simulate actual problems.

[0005] 2) Use particle swarm optimization to optimize the controller design and solve the problem of high energy consumption in controller data debugging. This method has a simple model, few control parameters, and is easy to implement. Therefore, it is widely used in the mining of high-utility itemsets. However, when solving combinatorial optimization problems in discrete systems, this method needs to obtain discrete variables through binary coding, which will greatly reduce the running calculation speed.

[0006] 3) Introduce an adaptive weight balancing strategy into the Seagull optimization algorithm to achieve PID parameter optimization and improve controller performance. Due to the mechanism of the Seagull optimization algorithm itself, it has the advantages of wide search range and good robustness. The introduction of an adaptive weight balancing strategy in the algorithm further enhances the original Seagull optimization algorithm's ability to balance global and local searches. However, the adaptive weight coefficient in the adaptive weight balancing strategy is artificially given based on past experience and is not universal for different control objects.

[0007] 4) Siso feedback technology is used to solve the difficulty of PI controller parameter tuning. This method has a wide global search range and high accuracy of the results, but it has disadvantages such as local parameter optimization and the amount of calculation in Matlab.

[0008] Compared with the controller optimization methods in the prior art, it can be found that the Seagull optimization algorithm can perform global and local searches when optimizing parameters. It has the advantages of a wide search range and good robustness. It can quickly correct and optimize the controller parameters according to actual conditions. However, it still has problems such as early convergence and being trapped in local optimal solutions.

[0009] In summary, how to improve the shortcomings of existing swarm intelligence algorithms and optimize the controller parameter setting through improved algorithms has become an urgent problem to be solved. Summary of the invention

[0010] The present invention provides a controller optimization method based on an improved Seagull algorithm, which can solve the problems of the traditional Seagull algorithm, such as easy early convergence and being trapped in a local optimal solution. The improved algorithm can be further used to optimize the controller, improve the response speed of the controller, and realize online setting of control parameters at the same time.

[0011] The technical solution adopted by the present invention is:

[0012] The controller optimization method based on the improved Seagull algorithm includes the following steps:

[0013] First, the migratory and predatory behaviors of seagulls in the seagull optimization algorithm are determined;

[0014] Secondly, the adversarial search operator strategy is used to initialize the population and record the current optimal individuals and groups;

[0015] Finally, the control factor and mutation operation are calculated by using the nonlinear change convergence factor to eliminate the seagull individuals with poor fitness in the population and continuously update the optimization to continuously correct and adjust the PI controller parameters.

[0016] Migration phase: Seagulls maintain their individual flight independence according to certain rules to avoid collisions with each other, which mainly includes three processes: avoiding collisions, optimal position direction, and approaching the optimal position. Predation phase: Seagulls perform spiral movements in the air, constantly changing the attack angle and speed, and attacking prey in a spiral manner.

[0017] The adversarial search operator strategy is used to initialize the population and select the relatively optimal individuals and groups; the nonlinear change convergence factor recalculates the auxiliary variables in the collision avoidance process according to the actual situation; the mutation operation eliminates the seagull individuals with poor fitness in the population and continuously updates the optimization to avoid the algorithm from falling into the local optimum.

[0018] The specific steps of improving the Seagull algorithm are:

[0019] Step 1: Set the population size N, use the adversarial search operator strategy to initialize the seagull group, calculate the fitness value of each seagull, and record the current optimal individual and group position;

[0020] Step 2: According to the formula Initialize and calculate the control factor f c Value, update and set the number of iterations, upper and lower limits of iterations, constant v, etc.;

[0021] x i Represents the current individual; Indicates the individual that is opposite to the current individual; Substitute the value obtained by initializing the function for the current individual relative to the individual; f(x i ) represents the value obtained by substituting the current individual into the initialization function;

[0022] Step 3: for i = 1 to N do, start iterative optimization; i represents a number between 1 and N;

[0023] Step 4: According to formula C s (t) = A × P s (t), A=f c -t×(f c / N max ) Update the new position of the seagull after avoiding collision;

[0024] C s (t) indicates the conflict-free position after the seagull is updated; t indicates the number of iterations; P s (t) represents the current K p , K i Position; A represents K p , K i Updated auxiliary variable; f c is the linear correlation between the control factor and A; N max Indicates the maximum number of iterations.

[0025] Step 5: According to formula m s (t) = B × [Z best (t)-P s (t)], B = 2 × A 2 × d Determine the best orientation direction;

[0026] m s (t) represents the relative direction of the optimal individual; Z best (t) represents the optimal individual position of the seagull; B represents a random number, which is used to balance the two behaviors of the seagull and is a random number that obeys a uniform distribution; r d is a random number in [0, 1];

[0027] Step 6: According to formula D S (t)=|C s (t)+m s (t)|Find the best orientation position;

[0028] D S (t) represents the new position of the seagull after its arrival;

[0029] Step 7: According to the formula P S (t) = D S (i)×X×Y×z+Z best (t), combined with the seagull attack behavior, determine the final new position;

[0030] X represents the X-axis component in three-dimensional space; Y represents the Y-axis component in three-dimensional space; r represents the radius of spiral flight motion; α represents a random number that obeys uniform distribution in [0, 2π], that is, the attack angle; u is a time constant in [0, 1]; v is a time constant in [5, 7]; P S (t) is the final attack position of the seagull;

[0031] Step 8: Perform mutation operation on the current optimal individual and calculate the fitness value of individuals in the group.

[0032] Step 9: Update the current optimal individual and position.

[0033] Step 10: End the iteration and output the best position and fitness value of the seagull.

[0034] The improved Seagull optimization algorithm is used to optimize the PI controller parameters, the proportional coefficient K p , integral time coefficient K i It is similar to each seagull, and the overshoot and error absolute value time integral performance indicators are used as the minimum objective function for parameter selection. At the same time, the control input square term is added to the objective function to avoid excessive control amount.

[0035] The invention discloses a controller optimization method based on an improved Seagull algorithm, which has the beneficial effects of: improving a traditional Seagull optimization algorithm through an opposition search operator strategy, a nonlinear change convergence factor and a mutation operation strategy, thereby making up for the shortcomings of the traditional Seagull algorithm of early convergence and falling into a local optimum; and optimizing the controller by using the improved Seagull algorithm, thereby improving the response speed and the real-time online tuning capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of seagulls' migratory hunting behavior.

[0037] Figure 2 Flowchart for improving the Seagull algorithm.

[0038] Figure 3 KP convergence curves of different algorithms.

[0039] Figure 4 Ki convergence curves of different algorithms. DETAILED DESCRIPTION

[0040] The controller optimization method based on the improved seagull algorithm first determines the migration behavior and predation behavior of seagulls in the seagull optimization algorithm. Secondly, the adversarial search operator strategy is used to initialize the population and record the current optimal individuals and groups. Finally, the nonlinear change convergence factor is used to calculate the control factor and the mutation operation is used to eliminate the seagull individuals with poor fitness in the population and continuously update the optimization, so as to continuously correct and adjust the PI controller parameters, improve the controller response speed and parameter adjustment accuracy, and solve the problem that the controller cannot be adjusted online in real time.

[0041] Seagull migratory hunting behavior Figure 1 As shown,

[0042] Migration stage: During the migration process, each seagull continuously changes its flight position through changes in the surrounding environment and information feedback from other seagulls. Corresponding to the global search, the model can be as follows:

[0043] Avoid collision: The initial values ​​of the seagulls should not be the same, and the individual position update is achieved by introducing an additional variable A.

[0044] C s (t) = A × P s (t) (1);

[0045] In the formula, C s (t) indicates the conflict-free position after the seagull is updated; t indicates the number of iterations; P s (t) represents the current K p , K i Position; A represents K p , K i Updated auxiliary variables.

[0046] The calculation process of A is as follows:

[0047] A=f c -t×(f c / N max ) (2);

[0048] In the formula, f c is the control factor linearly related to A; N max Indicates the maximum number of iterations.

[0049] Optimal position direction: While maintaining the distance from other individuals, the seagull will determine its relative direction to the current best individual and move in this direction.

[0050] m s (t) = B × [Z best (t)-P s (t)] (3);

[0051] B = 2 × A 2 × d (4);

[0052] In the formula, m s (t) represents the relative direction of the optimal individual; Z best (t) represents the optimal individual position of the seagull; B represents a random number used to balance the two behaviors of the seagull, and is a random number that obeys a uniform distribution.

[0053] Approaching the optimal position: After the seagull successfully determines the direction of the optimal position of the best individual, it begins to determine the optimal distance between the two and reaches the new position.

[0054] D S (t)=|C s (t)+m s (t)| (5)

[0055] Where D S (t) represents the new position of the seagull after its arrival.

[0056] During the hunting phase, when seagulls find prey, they will perform spiral movements in the air, constantly changing the attack angle and speed. The mathematical model corresponding to their movement behavior is as follows:

[0057]

[0058] Where r represents the radius of the spiral flight motion; α represents a random number that obeys a uniform distribution within [0, 2π] (i.e., the attack angle); u and v represent the time constants that define the spiral shape.

[0059] The mathematical model of attack behavior from movement behavior is as follows:

[0060] P S (t) = D S (t)×X×Y×Z+Z best (t) (7)

[0061] Where P S (t) is the final attack position of the seagull.

[0062] Compared with other intelligent algorithms, the Seagull Optimization Algorithm can perform global and local searches when optimizing parameters due to its own search mechanism, and has the advantages of wide search range and good robustness. However, the traditional Seagull Optimization Algorithm is prone to early convergence, slow convergence, and falling into the local optimal solution.

[0063] In order to solve the problems of early convergence, slow convergence and falling into local optimal solution of the traditional Seagull optimization algorithm, the present invention introduces an opposition search operator, redesigns the control factors and performs mutation operations to improve the traditional Seagull optimization algorithm, and proposes an improved Seagull optimization algorithm (ISOA).

[0064] (1) Opposing search operator strategy:

[0065] The Seagull Optimization Algorithm is similar to other swarm optimization algorithms. Since the specific location of the optimal solution is uncertain, a random method is used to initialize the initial population individuals. However, the initial population generated by the random method cannot guarantee its diversity and cannot effectively cover all the valid information in the search space, which affects the performance of the algorithm's global optimization to a certain extent, and also affects the algorithm's search efficiency. Therefore, the present invention introduces the opposition search operator strategy into the Seagull Optimization Algorithm.

[0066] First, the initial population is optimized using the opposition search operator to generate the current individual and the opposite individual in the interval [L, U], which is defined as:

[0067]

[0068] In the formula, x i Represents the current individual; Indicates the individual that is opposite to the current individual.

[0069] Then according to the above definition, use the following initialization method: set the population size N, compare the current individual with the opposite individual, and select the individual with the best fitness value as the initial population.

[0070] The initialization formula is as follows:

[0071]

[0072] (2) Nonlinear convergence control factor:

[0073] From formula (7), we can see that the Seagull optimization algorithm relies on the control factor f to a certain extent when performing global search and local search. c . Control factor f c The larger the control factor f, the stronger the global search capability, but it is easy to affect the convergence speed of the algorithm; on the contrary, the control factor f cThe smaller the value, the stronger the local search capability is, and the more likely it is to have a local optimum. Therefore, we hope that the SOA algorithm can have a faster convergence speed when performing global search, and can effectively avoid premature convergence when performing local search. Therefore, the present invention controls the factor f c Redesign, expect f c At the beginning of the algorithm, it increases with the number of iterations. When it reaches a certain value, f c It decreases rapidly to a small value, and then increases gradually at a slow speed.

[0074] Based on this, the control factor f c The update formula is as follows:

[0075]

[0076] Where: f ci represents the control factor f c Starting value; f cf represents the control factor f c final value; η represents the adjustment coefficient; t represents the current number of iterations; t max Indicates the maximum number of iterations.

[0077] (3) Mutation operation:

[0078] In order to achieve online adjustment and setting of controller parameters, the present invention performs mutation operation on individual seagulls in the following manner:

[0079] With probability 1 / d, from the seagull individual x j =(x j1 , x j2 …x jd ), randomly select an element x k (k=1,2,3…d), in the lower bound l j and upper bound u j Generate a random number in the range to replace the seagull individual x j The elements in the final result are new individuals.

[0080] The variability operation formula is:

[0081]

[0082] In order to obtain satisfactory dynamic characteristics, the algorithm proposed in the present invention takes the error absolute value time integral performance index as the minimum objective function for parameter selection, and adds the control input square term to the objective function to avoid excessive control quantity.

[0083]

[0084] At the same time, in order to avoid overshoot, the overshoot is used as one of the optimal objective functions. The objective function is as follows:

[0085] J(t)=J(t)+100|e(t)|ife(t)<0 (18)

[0086] Where: ω1ω2ω3 are weight coefficients, ω1 is usually set to 0.999; ω2 is set to 0.001.

[0087] The specific steps of improving the Seagull algorithm are as follows Figure 2 shown.

[0088] In order to verify the effectiveness of the DSGWO algorithm proposed in this paper, five typical function optimization problems were selected, among which Sphere and Quartic are unimodal functions, and Rastrigin, Ackley and Griewank are multimodal functions, to test the performance of the improved Seagull algorithm in different types of function optimization problems, and compare it with the particle swarm optimization algorithm (PSO), the whale optimization algorithm (WOA) and the seagull optimization algorithm (SOA). Table 1 lists the basic information of the five test functions, including the test function name, dimension and search space.

[0089] Table 1 Basic information of 5 test functions

[0090]

[0091] MATLAB 2020b was used for simulation verification, and the operating environment was AMD-R7-5800H processor and 16GB memory. For the same test function, each function was run independently 50 times, and the statistical optimal values, means, and variances of the 5 test functions of the 5 algorithms were compared. Table 2 shows the statistical optimal values, means, standard deviations, and time consumption of 50 independent runs of the 5 test functions in the 5 algorithms.

[0092] Table 2 Comparison of standard function optimization results

[0093]

[0094]

[0095] From the data in Table 2, it can be seen intuitively that for the two unimodal functions (Sphere and Quartic), ISOA performs very well in terms of solution accuracy. Except that the optimal value and average value of the Quartic test function are slightly lower than those of the standard ISOA algorithm, the other optimization accuracies are better than those of other comparison algorithms. For the three multimodal functions (Rastrigin, Ackley, and Griewank), the algorithm solution accuracy is slightly lower than that of the unimodal function, mainly due to the increase in dimension, which increases the difficulty of the algorithm solution. However, when solving the multimodal functions Rastrigin and Griewank, the ISOA algorithm reaches the theoretical optimal value. The ISOA algorithm is better than other algorithms in solving other functions, indicating that the performance of the algorithm is improved by adding nonlinear convergence control factors and mutation operations. In summary, it can be found that the ISOA algorithm has obvious advantages in solving unimodal and multimodal test functions.

[0096] In order to further verify the effect of the improved seagull optimization algorithm proposed in the present invention on the controller, this embodiment continues to compare the proposed improved seagull algorithm with three algorithms, namely the ordinary seagull algorithm, the particle swarm algorithm, and the whale algorithm, to set the controller parameters, and verify the superiority of the ISOA algorithm. The experimental simulation software is MATLAB 2020b, Windows 64-bit operating system. The simulation parameters are set as follows: population size N = 50, the maximum number of iterations is 100 times, and the spiral time constants u and v are random numbers between [0, 2].

[0097] The controller parameters are compared by optimizing with four different algorithms.

[0098] Table 3 KP convergence curve optimization data comparison

[0099]

[0100] Table 4 Ki convergence curve optimization data comparison

[0101]

[0102] Depend on Figure 3 , Figure 4 From Table 3 and Table 4, it can be seen that in terms of the number of iterations, the algorithm proposed in the present invention can complete the optimization of control parameters with fewer iterations, indicating that the addition of the opposing search operator strategy improves the performance of the algorithm. Compared with other algorithms, the screening of relatively optimal individuals is completed at the beginning of the iteration, which greatly reduces the number of subsequent iterations. The whale algorithm has a slower convergence speed and the highest number of iterations due to its search mechanism. The convergence speed of the traditional seagull algorithm is almost the same as the number of iterations of this algorithm because it is easy to fall into the local optimum and terminate the optimization early.

[0103] In terms of optimization accuracy, the algorithm proposed in this invention calculates the control factor according to the actual situation, and adopts the mutation operation strategy to continuously update the optimal individual of the seagull to achieve the highest optimization accuracy. P , K i The convergence curve can jump out of the local optimum when iterating to 11 and 19 times, overcoming the defects of the traditional Seagull algorithm.

[0104] In terms of control error, the improved Seagull optimization algorithm is used in K P When Ki and Ki are adjusted online, there are only 0.26% and 0.21% minimum steady-state errors respectively, and the stabilization time is the shortest.

[0105] In summary, considering the above aspects, the algorithm proposed in the present invention can achieve faster convergence speed, higher convergence accuracy, higher control accuracy, and better overall control performance.

Claims

1. The controller optimization method based on the improved Seagull algorithm is characterized by The following steps are involved: First, the migratory and predatory behaviors of seagulls in the seagull optimization algorithm are determined; Secondly, the adversarial search operator strategy is used to initialize the population and record the current optimal individuals and groups; Finally, the control factor and mutation operation are calculated by using the nonlinear change convergence factor, the seagull individuals with poor fitness in the population are eliminated and the optimization is continuously updated to continuously correct and adjust the PI controller parameters. The improved Seagull algorithm includes the following steps: Step 1: Set the population size N, use the adversarial search operator strategy to initialize the seagull group, calculate the fitness value of each seagull, and record the current optimal individual and group position; Step 2: According to the formula Initialize and calculate the control factor f c Value, update and set the number of iterations, upper and lower limits of iterations, and constant v; x i Represents the current individual; Indicates the individual that is opposite to the current individual; Substitute the value obtained by initializing the function for the current individual relative to the individual; f(x i ) represents the value obtained by substituting the current individual into the initialization function; Step 3: for i = 1 to N do, start iterative optimization, where i represents a number between 1 and N; Step 4: According to formula C s (t) = A × P s (t), A=f c -t×(f c / N max ) Update the new position of the seagull after avoiding collision; C s (t) indicates the conflict-free position after the seagull is updated; t indicates the number of iterations; P s (t) represents the current K p , K i Position; A represents K p , K i Updated auxiliary variable; f c is the control factor linearly related to A; N max Indicates the maximum number of iterations; Step 5: According to formula m s (t) = B × [Z best (t)-P s (t)], B = 2 × A 2 × d Determine the best orientation direction; m s (t) represents the relative direction of the optimal individual; Z best (t) represents the optimal individual position of the seagull; B represents a random number, which is used to balance the two behaviors of the seagull and is a random number that obeys a uniform distribution; r d is a random number in [0,1]; Step 6: According to formula D S (t)=|C s (t)+m s (t)|Find the best orientation position; D S (t) indicates the new position of the seagull after its arrival; Step 7: According to the formula P S (t) = D S (t)×X×Y×Z+Z best (t), combined with the seagull attack behavior, determine the final new position; X represents the X-axis component in three-dimensional space; Y represents the Y-axis component in three-dimensional space; r represents the radius of spiral flight motion; α represents a random number that follows uniform distribution in [0, 2π]; u is a time constant in [0, 1]; v is a time constant in [5, 7]; P S (t) is the final attack position of the seagull; Step 8: Perform mutation operation on the current optimal individual and calculate the fitness value of individuals in the group; Step 9: Update the current optimal individual and position; Step 10: End the iteration and output the best position and fitness value of the seagull.

2. The controller optimization method based on the improved Seagull algorithm according to claim 1, characterized in that: The adversarial search operator strategy is used to initialize the population and select the relatively optimal individuals and groups; the nonlinear change convergence factor recalculates the auxiliary variables in the collision avoidance process according to the actual situation; the mutation operation eliminates the seagull individuals with poor fitness in the population and continuously updates the optimization.

3. The controller optimization method based on the improved Seagull algorithm according to claim 1 is characterized in that: The improved Seagull optimization algorithm is used to optimize the PI controller parameters, the proportional coefficient K p , integral time coefficient K i It is similar to each seagull, and the overshoot and error absolute value time integral performance indicators are used as the minimum objective function for parameter selection. At the same time, the control input square term is added to the objective function to avoid excessive control amount.

Images