Turboshaft engine cascade PID control method based on EPPO algorithm

Abstract

The application provides a kind of EPPO algorithm-based turbo-shaft engine cascade PID control method, belongs to turbo-shaft engine technical field, including constructing turbo-shaft engine model, based on cascade PID controller to control turbo-shaft engine model;The original PPO algorithm is improved to obtain EPPO algorithm, including introducing Sine chaos mapping in initialization stage and introducing tangent flight strategy in cannibalistic behavior;Based on the EPPO algorithm, the control parameters of the cascade PID controller for controlling the turbo-shaft engine model are optimized to obtain the optimal PID parameter combination;Based on the simulation platform, the speed control of the cascade PID controller for the turbo-shaft engine model under the optimal PID parameter combination is simulated and verified. Through the processing scheme of the application, the limitations of traditional artificial experience trial-and-error method are overcome, the response speed and accuracy are improved, and the engine control performance is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of turboshaft engines, and particularly relates to a turboshaft engine cascade PID control method based on an EPPO algorithm. BACKGROUND

[0002] As the core propulsion device of a helicopter, the performance of a turboshaft engine is directly related to the flight quality of the aircraft. The turboshaft engine drives the rotor and tail rotor through a transmission system. Due to the complex characteristics of multiple degrees of freedom and strong coupling, the system is easily disturbed by torsional vibration and time delay and other factors during operation. In order to achieve excellent flight quality, the control system of the turboshaft engine needs to have the characteristics of fast response and high precision to ensure that the absolute error between the engine output speed and the expected speed is always kept within the minimum range.

[0003] Cascade PID (Proportional, Integral, Derivative) control is widely used in the speed control of turboshaft engines due to its simple structure and strong robustness. Through the coordinated action of the inner and outer loops, this control strategy can effectively suppress most disturbances and improve the anti-interference ability of the system. However, the traditional cascade PID controller has significant limitations, and the tuning of its parameters is highly dependent on the experience of engineers and repeated trial and error, which makes it difficult to find the optimal parameter combination under the complex and variable conditions of turboshaft engines.

[0004] More importantly, the traditional cascade PID control lacks predictive ability. In transient conditions such as helicopter climbing, due to the time delay caused by rotor torque measurement and engine dynamic response, the engine cannot timely and accurately track the power demand of the helicopter, resulting in slow response speed and a large absolute error between the output speed and the expected speed. Although existing research has applied nonlinear optimization methods to solve the transient control problem, these methods still face challenges such as convergence and robustness in practical applications, making it difficult to achieve high-quality control effect.

[0005] Therefore, there is an urgent need for an intelligent and adaptive optimization method to solve the problems of slow response speed and poor control precision of the traditional cascade PID controller under complex conditions of turboshaft engines. SUMMARY

[0006] In view of the problems of existing turboshaft engine cascade PID controllers, such as difficult parameter tuning, poor robustness, and inability to adapt to complex and variable conditions, the present application proposes a turboshaft engine cascade PID control method based on an EPPO algorithm. The present application aims to realize the automatic and intelligent tuning of controller parameters through intelligent optimization algorithms, thereby effectively improving the dynamic response performance and steady-state control precision of the engine.

[0007] The embodiment of the application provides a cascade PID control method for turboshaft engines based on an EPPO algorithm, and the method comprises the following steps:

[0008] A turboshaft engine model is constructed, and the turboshaft engine model is controlled based on a cascade PID controller;

[0009] The original PPO algorithm is improved to obtain an EPPO algorithm, and the improvement of the original PPO algorithm comprises the following steps: introducing a Sine chaotic mapping in an initialization stage of the original PPO algorithm and introducing a tangent flight strategy in cannibalism behavior of the original PPO algorithm;

[0010] The control parameters of the cascade PID controller for controlling the turboshaft engine model are optimized based on the EPPO algorithm, and an optimal PID parameter combination is obtained;

[0011] The speed control of the turboshaft engine model by the cascade PID controller under the optimal PID parameter combination is simulated and verified based on a simulation platform.

[0012] According to a specific implementation manner of the embodiment of the application, the optimization of the control parameters of the cascade PID controller for controlling the turboshaft engine model based on the EPPO algorithm comprises the following steps:

[0013] Step 31: A Sine chaotic mapping is used to initialize a population of the original PPO algorithm;

[0014] Step 32: The initialized PID parameters are input into the cascade PID controller, the turboshaft engine model is run, and a target function value is calculated based on an output result of the turboshaft engine model;

[0015] Step 33: Based on the target function value, the optimal position of a male spider in the current population is found;

[0016] Step 34: Based on the optimal position of the male spider in the current population, the position of a female spider is updated;

[0017] Step 35: The escape energy of the male spider in the current population and the average distance between all male spiders and female spiders are calculated;

[0018] Step 36: The position of the male spider is updated based on the escape energy of the male spider and the average distance, the ejection escape behavior, the cannibalism behavior based on the tangent flight strategy and the predation recovery behavior;

[0019] Step 37: Based on the updated male spider positions, recalculate the objective function value corresponding to each new position in the entire population, sort the objective function values ​​corresponding to each new position, identify the best position of the male spider in this iteration, and if the best position of the male spider in this iteration is better than the best position of the male spider in the historical record, then update the best position of the male spider in the historical record with the best position of the male spider in this iteration.

[0020] Step 38: Repeat steps 34 to 37 until the loop termination condition is triggered, and output the optimal PID parameter combination.

[0021] According to a specific implementation of an embodiment of this application, updating the male spider's position based on the male spider's escape energy and average distance for ejection escape behavior, sexual cannibalism based on tangential flight strategy, and predation recovery behavior includes:

[0022] Calculate the current Euclidean distance and survival factor between the male and female spiders;

[0023] The first position update for the male spider to launch an escape behavior is based on the male spider's escape energy and Euclidean distance.

[0024] When the Euclidean distance is less than the survival factor, a second position update is performed based on the cannibalistic behavior of sexual intercourse using a tangential flight strategy.

[0025] When the Euclidean distance is greater than or equal to the survival factor, the third position update of the predator recovery behavior is performed.

[0026] According to a specific implementation of an embodiment of this application, the expression for the Sine chaotic mapping is:

[0027] ,

[0028] The initialization expression is:

[0029] ,

[0030] in, Let i be the i-th value in the chaotic sequence generated using the Sine chaotic map. , Let i be the (i+1)th value in the chaotic sequence generated using the Sine chaotic map. Let U be the position of the i-th male spider in the j-th dimension. j Let L be the upper bound of the search in the j-th dimension. j This is the lower bound for the search in the j-th dimension.

[0031] According to a specific implementation of this application, the expression for the objective function value is:

[0032] ,

[0033] Among them, F f The objective function value, e( is a time variable) ) represents the instantaneous error of the system.

[0034] According to a specific implementation of this application, the expression for the escape energy is:

[0035] ,

[0036] Where E is the escape energy, max{F f} represents the maximum value of the objective function in the current population, min{F f} represents the minimum value of the objective function in the current population. It is an infinitesimal positive number.

[0037] According to a specific implementation of an embodiment of this application, the expression for updating the first position is:

[0038] ,

[0039] ,

[0040] in, Let i be the position of the i-th male spider in the j-th dimension at the (t+1)-th iteration. Let v be the position of the i-th female spider in the j-th dimension at the t-th iteration, v be the escape velocity, θ be the escape angle, and E be the escape velocity. i It is the escape energy of the i-th male spider. X is the Euclidean distance between the male and female spiders. i Y represents the position of the i-th male spider. i This indicates the position of the i-th female spider.

[0041] According to a specific implementation of an embodiment of this application, the expression for the survival factor is:

[0042] ,

[0043] ,

[0044] Where σ is the survival factor, t is the t-th iteration, and T max ω is the maximum number of iterations, ω is the average distance between all male and female spiders, and n is the number of male spiders generated, with the number of female spiders being the same as the number of male spiders.

[0045] According to a specific implementation of an embodiment of this application, the expression for updating the second position is:

[0046] ,

[0047] ,

[0048] in, Let i be the position of the i-th female spider in the (t+1)-th iteration. Let r1 be the position of the i-th female spider in the t-th iteration, and r2 be the second random number in the range [0,1]. Let be the position of the i-th male spider in the t-th iteration, tan(·) be the tangent function, and rand(1,d) represent a random vector of dimension d with values ​​between [0,1]. Let represent the position of the i-th male spider in the (t+1)-th iteration, and Levy denotes the step size extracted using the Levy distribution.

[0049] According to a specific implementation of an embodiment of this application, the expression for updating the third position is:

[0050] ,

[0051] in, is the best position of the male spider in the historical record, r3 is the third random number between [0,1], and cos is the (·) cosine function.

[0052] Beneficial effects:

[0053] The cascade PID control method for turboshaft engines based on the EPPO algorithm in this application embodiment is an EPPO algorithm (Enhanced Philoponella Prominens Optimizer) that integrates a tangential flight strategy. This invention addresses the problems of existing metaheuristic algorithms being prone to getting trapped in local optima and having slow convergence speed by making two key improvements to the original PPO algorithm (Philoponella Prominens Optimizer):

[0054] Chaotic initialization: Sine chaotic mapping is introduced in the initialization phase of the PPO algorithm. By using chaotic sequences instead of traditional random number generation, the diversity and quality of the initial population are effectively enhanced, laying a solid foundation for the algorithm's global optimization.

[0055] Tangent Flight Strategy: A tangent flight mechanism is introduced into the "female chases male" strategy of the PPO algorithm. The nonlinear step size generated by the tangent function enhances the search agent's exploration capabilities, enabling it to move in a more random and spontaneous manner. This effectively improves the algorithm's global optimization performance and convergence speed, and helps it escape local optima.

[0056] This invention applies the EPPO algorithm to the cascade PID control system of a turboshaft engine to automatically and intelligently tune the inner and outer loop parameters of the cascade controller. This overcomes the limitations of traditional trial-and-error methods based on manual experience, improves response speed and accuracy, and effectively enhances the engine's control performance under various control modes such as maximum output power, minimum fuel consumption per unit power, or optimal speed stability. Attached Figure Description

[0057] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 This is a flowchart of a cascaded PID control method for a turboshaft engine based on the EPPO algorithm according to an embodiment of the present invention;

[0059] Figure 2 This is a schematic diagram of an equivalent cascaded PID control system according to an embodiment of the present invention;

[0060] Figure 3 This is another flowchart of a cascaded PID control method for a turboshaft engine based on the EPPO algorithm according to an embodiment of the present invention. Detailed Implementation

[0061] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0062] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0063] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0064] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0065] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0066] This application provides a cascaded PID control method for a turboshaft engine based on the EPPO algorithm, which will be described in detail below with reference to the accompanying drawings.

[0067] In one embodiment, refer to Figure 1 This paper provides a cascade PID control method for a turboshaft engine based on the EPPO algorithm, the method comprising:

[0068] Step 1: Construct a turboshaft engine model and control the turboshaft engine model based on a cascade PID controller;

[0069] Step 2: Improve the original PPO algorithm to obtain the EPPO algorithm. The improvement of the original PPO algorithm includes: introducing Sine chaotic mapping in the initialization stage of the original PPO algorithm and introducing tangent flight strategy in the cannibalistic behavior of the original PPO algorithm.

[0070] Step 3: Optimize the control parameters of the turboshaft engine model controlled by the cascade PID controller based on the EPPO algorithm to obtain the optimal combination of PID parameters;

[0071] Step 4: Based on the simulation platform, the speed control of the turboshaft engine model by the cascade PID controller under the optimal PID parameter combination is simulated and verified.

[0072] In this embodiment, an EPPO algorithm integrating a tangent flight strategy is proposed. Addressing the issues of existing metaheuristic algorithms being prone to getting trapped in local optima and having slow convergence speed, two key improvements are made to the original PPO algorithm:

[0073] Chaotic initialization: Sine chaotic mapping is introduced in the initialization phase of the PPO algorithm. By using chaotic sequences instead of traditional random number generation, the diversity and quality of the initial population are effectively enhanced, laying a solid foundation for the algorithm's global optimization.

[0074] Tangent Flight Strategy: A tangent flight mechanism is introduced into the "female chases male" strategy of the PPO algorithm. The nonlinear step size generated by the tangent function enhances the search agent's exploration capabilities, enabling it to move in a more random and spontaneous manner. This effectively improves the algorithm's global optimization performance and convergence speed, and helps it escape local optima.

[0075] Furthermore, the EPPO algorithm is applied to the cascade PID control system of a turboshaft engine to automatically and intelligently tune the inner and outer loop parameters of the cascade controller. The outer loop parameters include K. P1 K I1 K D1 The inner loop parameters include K P2 K I2 K D2 K P1 and K P2 These are the first proportional gain and the second proportional gain, respectively, K I1 and K I2 These are the first integral gain and the second integral gain, respectively, K D1 and K D2 These are the first and second derivative gains, respectively. The proportional gain directly responds to the current error and determines the response speed of the control system; the integral gain eliminates the steady-state error of the system, ensuring that the system can ultimately and accurately reach the target value; and the derivative gain predicts the trend of error changes, helping to suppress overshoot and improve system stability. This method overcomes the limitations of traditional trial-and-error methods based on manual experience, improves response speed and accuracy, and effectively enhances engine control performance under various control modes such as maximum output power, minimum fuel consumption per unit power, or optimal speed stability.

[0076] In specific implementation, refer to Figure 2 The control system used in this embodiment is an equivalent cascade PID control system for a turboshaft engine. This system consists of a main loop controller and a secondary loop controller, used to control the power turbine speed and the gas generator speed, respectively. The optimization targets in this embodiment are six key parameters in these two controllers: K... P1 KI1 K D1 K P2 K I2 K D2 In the optimization algorithm, these six parameters are treated as a position vector of a search agent (i.e., a spider), with a dimension of 6.

[0077] A major advantage of cascaded PID control systems is their ability to effectively handle controlled objects with significant hysteresis and disturbances. It is a system structure where two regulators (a primary regulator and a secondary regulator) work together on a single actuator to achieve setpoint control. The output of the primary regulator serves as the input to the secondary regulator, and the output of the secondary regulator directly affects the actuator. This design ensures that the control system remains stable and achieves precise control even in the face of rapidly changing or unstable conditions.

[0078] Figure 2 The diagram shown is an equivalent cascade control system block diagram, where n pr n represents the desired rotational speed. p n represents the output speed of the turboshaft engine's power turbine. g This refers to the speed of the gas generator. The minus sign "-" in the diagram indicates a subtraction operation. The gas generator controller is the inner loop, and the power turbine controller is the outer loop.

[0079] In one embodiment, optimizing the control parameters of a turboshaft engine model controlled by a cascaded PID controller based on the EPPO algorithm includes:

[0080] Step 31: Use Sine chaotic mapping to initialize the population of the original PPO algorithm;

[0081] Step 32: Input the initialized PID parameters into the cascade PID controller, run the turboshaft engine model, and calculate the objective function value based on the output results of the turboshaft engine model;

[0082] Step 33: Based on the objective function value, find the optimal location for male spiders in the current population;

[0083] Step 34: Update the position of the female spider based on the best position of the male spider in the current population;

[0084] Step 35: Calculate the escape energy of male spiders in the current population and the average distance between all male and female spiders;

[0085] Step 36: Update the male spider's position based on its escape energy and average distance, including ejection escape behavior, cannibalism based on tangential flight strategy, and predation recovery behavior.

[0086] Step 37: Based on the updated male spider positions, recalculate the objective function value corresponding to each new position in the entire population, sort the objective function values ​​corresponding to each new position, identify the best position of the male spider in this iteration, and if the best position of the male spider in this iteration is better than the best position of the male spider in the historical record, then update the best position of the male spider in the historical record with the best position of the male spider in this iteration.

[0087] Step 38: Repeat steps 34 to 37 until the loop termination condition is triggered, and output the optimal PID parameter combination.

[0088] Furthermore, the method of updating the male spider's position based on its escape energy and average distance for ejection escape behavior, its sexual cannibalism based on tangential flight strategy, and its predation recovery behavior includes:

[0089] Calculate the current Euclidean distance and survival factor between the male and female spiders;

[0090] The first position update for the male spider to launch an escape behavior is based on the male spider's escape energy and Euclidean distance.

[0091] When the Euclidean distance is less than the survival factor, a second position update is performed based on the cannibalistic behavior of sexual intercourse using a tangential flight strategy.

[0092] When the Euclidean distance is greater than or equal to the survival factor, the third position update of the predator recovery behavior is performed.

[0093] In practical implementation, to enhance the diversity and global exploration capability of the initial population, this invention introduces a Sine chaotic map to initialize the population of the original PPO algorithm, replacing the traditional random initialization method. The expression for the Sine chaotic map is:

[0094] (1),

[0095] Based on this chaotic sequence, the position X of the i-th search agent (male spider) is... i The initialization expression for (i.e., a set of PID parameters) is:

[0096] (2),

[0097] in, Let i be the i-th value in the chaotic sequence generated using the Sine chaotic map. , Let i be the (i+1)th value in the chaotic sequence generated using the Sine chaotic map. Let be the position of the i-th male spider (search agent) in the j-th dimension. In this embodiment, there are a total of 6 parameter variables that need to be optimized, i.e., dimension d=6, U j Let L be the upper bound of the search in the j-th dimension. j This is the lower bound for the search in the j-th dimension.

[0098] In one embodiment, the expression for the objective function value is:

[0099] (3),

[0100] Among them, F f The objective function value, e( is a time variable) ) represents the instantaneous error of the system.

[0101] In one embodiment, the expression for the escape energy is:

[0102] (4),

[0103] Where E is the escape energy, max{F f} represents the maximum value of the objective function in the current population, min{F f} represents the minimum value of the objective function in the current population. It is an infinitesimal positive number to avoid the denominator being zero.

[0104] In practical implementation, the initialized PID parameters are input into the cascade PID controller, the turboshaft engine model is run, and the results are output to calculate the optimization objective function, thereby sorting the fitness (objective function value) of the input PID parameter set. In this embodiment, the EPPO algorithm uses minimizing the time-weighted absolute error integral (ITAE) as the optimization objective function to calculate the fitness, and the specific expression is shown in equation (3). By minimizing the ITAE index, the dynamic response speed of the control system can be effectively improved and the steady-state error can be reduced.

[0105] In the EPPO algorithm, the objective function value is further processed, and the escape energy E of the male spider is used to measure the quality of the solution. This energy is inversely proportional to the objective function value, F. f The smaller the value, the larger E is, and the better the location of the solution. See equation (4) for the expression.

[0106] In one embodiment, the core optimization process of the PPO algorithm simulates the special behavior of male spiders after mating, mainly including three strategies: ejection escape, sexual cannibalism, and predation recovery. This embodiment makes a key improvement to the sexual cannibalism strategy by introducing a tangential flight strategy to enhance the algorithm's global optimization capability.

[0107] Ejection escape behavior is the act of male spiders immediately ejecting after mating to avoid being eaten by the female. This behavior is modeled as a projectile motion, causing the male spiders to rapidly converge near the female for a local search. The expression for the first position update of this behavior is:

[0108] (5),

[0109] (6),

[0110] in, Let i be the position of the i-th male spider in the j-th dimension at the (t+1)-th iteration. Let v be the position of the i-th female spider in the j-th dimension during the t-th iteration, v be the escape velocity, θ be the escape angle (θ is a random number vector of dimension d (d=6), with values ​​ranging from 0 to π), and E be the escape velocity. i It is the escape energy of the i-th male spider. The Euclidean distance D between the male and female spiders. i X i Y represents the position of the i-th male spider. i This indicates the position of the i-th female spider.

[0111] In one embodiment, the survival factor is expressed as:

[0112] ,

[0113] ,

[0114] Where σ is the survival factor, t is the t-th iteration, and T max ω is the maximum number of iterations, ω is the average distance between all male and female spiders, and n is the number of male spiders generated, with the number of female spiders being the same as the number of male spiders.

[0115] In one embodiment, sexual cannibalism manifests as follows: if the male spider is less than the survival factor σ after being ejected from the female spider, the male is eaten, and the female lays new spiderlings. Before being eaten, the female chases the male. This invention improves the position update formula during this chase by introducing a tangential flight strategy.

[0116] The formula for updating the female's position in the primitive chasing behavior is:

[0117] (7),

[0118] Based on the above formula (7), this embodiment introduces a tangent flight strategy. The improved formula is the expression for the second position update, specifically:

[0119] (8),

[0120] (9),

[0121] in, Let i be the position of the i-th female spider in the (t+1)-th iteration. Let r1 be the position of the i-th female spider in the t-th iteration, and r2 be the second random number in the range [0,1]. Let be the position of the i-th male spider in the t-th iteration, tan(·) be the tangent function, and rand(1,d) represent a random vector of dimension d with values ​​between [0,1]. Let represent the position of the i-th male spider in the (t+1)-th iteration, and Levy denotes the step size extracted using the Levy distribution.

[0122] This tangent flight strategy is a movement mechanism embedded in the specific behavioral stage of "sexual cannibalism," specifically designed to update the female spider's position vector. Its core principle lies in utilizing the tangent function tan(·) to the drastic nonlinear response to random inputs within the [0,1] interval. When the random input value approaches a specific point within its period, the tangent function exhibits a sharp, large jump in value. This is modeled as a long-distance, sudden "flight" of the female spider in the search space, aiming to significantly enhance the algorithm's global exploration capability by introducing powerful random perturbations and providing crucial mutation opportunities for the algorithm to escape local optimum traps. Therefore, the nonlinear step size generated by the tangent function designed in this embodiment effectively enhances the search agent's exploration capability, enabling it to move in a more random and sudden manner, thereby effectively improving the algorithm's global optimization performance and convergence speed. In other input ranges, however, it exhibits a smooth, small-step movement, failing to produce random and sudden movement and thus not improving the algorithm's global optimization performance and convergence speed. After the female spider updates its position, the new male spider will... For the generation and location formula of the male spider, please refer to equation (9).

[0123] In one embodiment, predation-recovery behavior refers to the male spider successfully escaping and recovering its strength by preying on prey if the distance between it and the female spider is greater than or equal to the survival factor. This behavior is modeled as a local search near the optimal position to enhance the utilization of known optimal solutions. The expression for the third position update is:

[0124] (10)

[0125] in, is the best position of the male spider in the historical record, r3 is the third random number between [0,1], and cos is the (·) cosine function.

[0126] This predation recovery behavior allows successful male spiders to consolidate their dominance and conduct more refined searches around optimal locations.

[0127] In one embodiment, a detailed cascade PID control method for a turboshaft engine based on the EPPO algorithm is provided, referring to... Figure 3 This includes the following steps:

[0128] The Sine chaotic mapping is introduced by initializing formula (2) according to formula (1);

[0129] Fitness calculation of PID parameters: The initialized parameters are input into the cascade PID controller, the turboshaft engine model is run, and the optimization objective function is calculated according to formula (3);

[0130] Find the optimal location X for male spiders in the current population. opt ;

[0131] Update the position Y of the female spider;

[0132] Calculate the male spider's energy E and the tie distance ω between the male and female spiders;

[0133] Perform ejection escape behavior and update the position of the i-th male spider according to formulas (5) and (6);

[0134] Calculate the Euclidean distance D between the i-th male spider and the female spider. i ;

[0135] Calculate a survival factor σ;

[0136] Judge D i If σ is true, then the position of the female spider is updated according to formula (8) and the correct flight strategy is introduced. Then the cannibalistic behavior is performed, the male spider is eaten, but the female spider will lay offspring. The position of the offspring is updated by formula (9); if not, the predation recovery behavior is performed, and the position of the male spider is updated according to formula (10).

[0137] Determine if the number of iterations t < T max If the condition is not met, return the optimal PID parameters; if it is met, perform t+1 iterations to recalculate the fitness of the PID parameters and update the position.

[0138] In one embodiment, for iterative loops and parameter updates, when optimizing PID parameters, a core iterative loop process is used to gradually converge to the optimal solution. After completing parameter initialization, calculating the initial fitness, and sorting, the algorithm enters the main loop, and its flow and parameter update logic are as follows:

[0139] 1. Position Update: In each iteration, the algorithm first performs a catapult escape behavior. The positions of all search agents (i.e., male spiders) are updated according to the mathematical model of this behavior. Subsequently, the algorithm updates the positions based on the Euclidean distance D between the male and female spiders. i The comparison results with the survival factor σ will determine the subsequent strategy;

[0140] 2. Strategy Execution: If D i If D < σ, then the cannibalistic behavior is performed and updated; otherwise, if D < σ, then the cannibalistic behavior is performed and updated. i If ≥σ, then execute the predation recovery behavior and update;

[0141] 3. Fitness Re-evaluation: After all search agent positions have been updated, the algorithm recalculates the fitness value (objective function value) for each new position in the entire population. This step evaluates the effectiveness of the position update in this iteration and provides the latest fitness ranking for subsequent sorting and optimization.

[0142] 4. Optimal Solution Update: After recalculating fitness, the algorithm sorts all fitness values ​​in the current population and identifies the optimal solution in this iteration. If the newly found optimal solution is different from the best solution in the historical record... If it's better, then update. The value;

[0143] 5. Loop Termination Condition: The algorithm will continue to perform the above-described cycle of "position update - fitness re-evaluation - optimal solution update" until a preset termination condition is met. In this embodiment, the termination condition is reaching the maximum number of iterations T. max When the current iteration number t is greater than or equal to T max The main loop terminates.

[0144] 6. Optimal Solution Output: Once the loop terminates, the algorithm will return the best combination of PID parameters found during all iterations. This is the final output of the optimized control method proposed in this invention.

[0145] In one embodiment, to verify the effectiveness and superiority of the method proposed in this invention, a simulation experiment of cascade PID speed control of a turboshaft engine was conducted on a simulation platform. The experimental results compared the method proposed in this invention with existing technologies, fully demonstrating its significant effect in performance optimization, specifically including the following:

[0146] (1) Experimental environment and parameters

[0147] The simulation experiment in this embodiment was conducted on a nonlinear model of a turboshaft engine built in the MATLAB / Simulink environment. To simulate real-world operating scenarios, the engine model incorporates complex factors such as component dynamics, transmission system inertia, and gas flow characteristics.

[0148] The parameters for the EPPO algorithm are configured as follows:

[0149] Population Size: 50

[0150] Maximum number of iterations: 100

[0151] Optimization variables: Six parameters of a cascade PID controller (K) P1 K I1 K D1 K P2 K I2 K D2 Its search range (i.e., upper and lower bounds) is set based on actual engineering needs and experience to ensure that the search space is physically feasible.

[0152] (2) Optimization objectives and simulation protocols

[0153] The objective function of this embodiment is to minimize the time-weighted absolute error integral, in order to comprehensively measure the response speed and steady-state accuracy of the control system. Its mathematical expression is:

[0154] ,

[0155] In this embodiment, e( Specifically, this refers to the speed tracking error. For time.

[0156] To verify the performance of the method of this invention, a speed step response experiment was designed in the simulation. The experiment was conducted in a standard sea-level environment, with the desired speed stepping from 90% to 100%. The optimization process was performed offline, and the optimal parameters were finally found and embedded into the controller. The method of this invention was compared with the following two methods:

[0157] 1. Traditional PID controller: The parameters are set using commonly used empirical values ​​in the industry.

[0158] 2. Original Spider Optimizer: Uses the original PPO algorithm without any modifications.

[0159] (3) Results and performance analysis

[0160] The method proposed in this invention exhibits superior performance during the optimization process. Compared with the comparative methods, the method of this invention achieves the following significant effects in the speed step response experiment:

[0161] Dynamic response performance: The controller optimized by the method of this invention has a settling time that is reduced by about 25% compared to the traditional PID and by about 10% compared to the original PPO algorithm. This shows that the method of this invention can effectively overcome system inertia and time delay, and achieve a faster dynamic response.

[0162] Steady-state control accuracy: In the steady-state phase, the method of the present invention reduces the absolute error between the speed output and the desired speed by about 35%, verifying its excellent ability to suppress steady-state error.

[0163] Optimization efficiency and robustness: The convergence curve of the EPPO algorithm of this invention tends to stabilize after the 60th iteration. Compared with the original PPO algorithm, it has a faster convergence speed and higher optimization accuracy. This proves that the introduction of the tangent flight mechanism significantly improves the algorithm's optimization efficiency and global optimization capability, effectively avoiding getting trapped in local optima.

[0164] Based on the above simulation results, the method of the present invention shows significantly better performance than the prior art in terms of improving the response speed and accuracy of speed control and enhancing the robustness of the controller.

[0165] The embodiments provided by this invention, through innovation in the algorithm and effective application in the control system, achieve the following significant technical effects:

[0166] 1. Achieving high-precision, fast-response speed control. This invention employs EPPO (Electronic Power Proportioning) and ITAE (Integrated Time Effect) as the optimization target to achieve automated global optimization of the six PID parameters of the turboshaft engine speed controller. Compared with traditional empirical tuning methods, the controller parameters obtained by this method significantly improve the dynamic response performance of the system. Simulation results show that under transient acceleration and deceleration conditions, this invention can shorten the speed settling time by approximately 20% and reduce the steady-state absolute error between the output speed and the desired speed by approximately 35%, thus effectively solving the problems of slow response and low accuracy of existing controllers under complex operating conditions.

[0167] 2. Significantly improves the algorithm's optimization performance and convergence speed. This invention introduces a Sine chaotic mapping for initialization, effectively enhancing the diversity and quality of the initial population. Simultaneously, a tangent flight strategy is incorporated into the "sex-cannibalism" behavior of the PPO algorithm. This strategy, through a nonlinear step-size update mechanism, enhances the algorithm's global exploration capability and avoids getting trapped in local optima. Multiple comparative simulations verify that the improved algorithm proposed in this invention achieves an average convergence speed approximately 15% higher than the original algorithm, significantly reducing computation time while ensuring optimization accuracy.

[0168] 3. The invention endows the controller with strong adaptability and robustness. The optimization method proposed in this invention can automatically find and update the optimal PID parameters according to different engine operating points and performance requirements (such as minimum fuel consumption per unit power or maximum output power). For example, in the minimum fuel consumption control mode, simulation results show that the controller optimized by the method of this invention can reduce the engine's fuel consumption per unit power by about 5% without sacrificing thrust. This fully demonstrates that the method of this invention can enable the controller to have strong adaptability and robustness to cope with complex and ever-changing flight missions and environments.

[0169] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A cascade PID control method for a turboshaft engine based on the EPPO algorithm, characterized in that, The method includes: A turboshaft engine model was constructed, and the turboshaft engine model was controlled based on a cascade PID controller; The original PPO algorithm is improved to obtain the EPPO algorithm. The improvement of the original PPO algorithm includes: introducing Sine chaotic mapping in the initialization stage of the original PPO algorithm and introducing tangent flight strategy in the cannibalistic behavior of the original PPO algorithm. The control parameters of a turboshaft engine model controlled by a cascade PID controller are optimized based on the EPPO algorithm to obtain the optimal combination of PID parameters. The optimization of the control parameters of the turboshaft engine model controlled by the cascade PID controller based on the EPPO algorithm includes: Step 31: Use Sine chaotic mapping to initialize the population of the original PPO algorithm; Step 32: Input the initialized PID parameters into the cascade PID controller, run the turboshaft engine model, and calculate the objective function value based on the output results of the turboshaft engine model; Step 33: Based on the objective function value, find the optimal location for male spiders in the current population; Step 34: Update the position of the female spider based on the best position of the male spider in the current population; Step 35: Calculate the escape energy of male spiders in the current population and the average distance between all male and female spiders; Step 36: Update the male spider's position based on its escape energy and average distance, including ejection escape behavior, cannibalism based on tangential flight strategy, and predation recovery behavior. Step 37: Based on the updated male spider positions, recalculate the objective function value corresponding to each new position in the entire population, sort the objective function values ​​corresponding to each new position, identify the best position of the male spider in this iteration, and if the best position of the male spider in this iteration is better than the best position of the male spider in the historical record, then update the best position of the male spider in the historical record with the best position of the male spider in this iteration. Step 38: Repeat steps 34 to 37 until the loop termination condition is triggered, and output the optimal PID parameter combination; The speed control of a turboshaft engine model was simulated and verified using a cascaded PID controller under the optimal PID parameter combination based on a simulation platform.

2. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 1, characterized in that, The method of updating the male spider's position based on ejection escape behavior based on the male spider's escape energy and average distance, sexual cannibalism based on tangential flight strategy, and predation recovery behavior includes: Calculate the current Euclidean distance and survival factor between the male and female spiders; The first position update for the male spider to launch an escape behavior is based on the male spider's escape energy and Euclidean distance. When the Euclidean distance is less than the survival factor, a second position update is performed based on the cannibalistic behavior of sexual intercourse using a tangential flight strategy. When the Euclidean distance is greater than or equal to the survival factor, the third position update of the predator recovery behavior is performed.

3. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 1, characterized in that, The expression for the Sine chaotic mapping is: ， The initialization expression is: ， in, Let i be the i-th value in the chaotic sequence generated using the Sine chaotic map. , This refers to the (i+1)th value in the chaotic sequence generated using the Sine chaotic map. Let U be the position of the i-th male spider in the j-th dimension. j Let L be the upper bound of the search in the j-th dimension. j This is the lower bound for the search in the j-th dimension.

4. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 1, characterized in that, The expression for the objective function value is: ， Among them, F f The objective function value, e( is a time variable) ) represents the instantaneous error of the system.

5. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 4, characterized in that, The expression for the escape energy is: ， Where E is the escape energy, max{F f } represents the maximum value of the objective function in the current population, min{F f } represents the minimum value of the objective function in the current population. It is an infinitesimal positive number.

6. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 2, characterized in that, The expression for updating the first position is: ， ， in, Let i be the position of the i-th male spider in the j-th dimension at the (t+1)-th iteration. Let v be the position of the i-th female spider in the j-th dimension at the t-th iteration, v be the escape velocity, θ be the escape angle, and E be the escape velocity. i It is the escape energy of the i-th male spider. X is the Euclidean distance between the male and female spiders. i Y represents the position of the i-th male spider. i This indicates the position of the i-th female spider.

7. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 6, characterized in that, The expression for the survival factor is: ， ， Where σ is the survival factor, t is the t-th iteration, and T max ω is the maximum number of iterations, ω is the average distance between all male and female spiders, and n is the number of male spiders generated, with the number of female spiders being the same as the number of male spiders.

8. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 7, characterized in that, The expression for updating the second position is: ， ， in, Let i be the position of the i-th female spider in the (t+1)-th iteration. Let r1 be the position of the i-th female spider in the t-th iteration, and r2 be the second random number in the range [0,1]. Let be the position of the i-th male spider in the t-th iteration, tan(·) be the tangent function, and rand(1,d) represent a random vector of dimension d with values ​​between [0,1]. Let represent the position of the i-th male spider in the (t+1)-th iteration, and Levy denotes the step size extracted using the Levy distribution.

9. The cascade PID control method for a turboshaft engine based on the EPPO algorithm according to claim 8, characterized in that, The expression for updating the third position is: ， in, is the best position of the male spider in the historical record, r3 is the third random number between [0,1], and cos is the (·) cosine function.

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