A fan model predictive control method based on convexification and CPSOGSA optimization

Abstract

The present application relates to model predictive control, swarm intelligence optimization algorithm and wind turbine independent variable pitch control technology, aiming at the problems that the blade load distribution is uneven, the variable pitch actuator is constrained and the traditional control method is difficult to consider load suppression and control feasibility under the conditions of turbulent wind, wind shear and working condition switching of wind turbine, a wind turbine model predictive control method based on convexity and CPSOGSA optimization is proposed, including wind turbine mathematical model establishment, independent variable pitch modeling and convexity processing based on coordinate transformation and constraint reconstruction, CPSOGSA-MPC hierarchical collaborative optimization based on feasible region geometric reconstruction, and unified performance evaluation and structure feedback based on control-prediction dual domain coupling. The present application can realize the collaborative suppression of wind turbine blade root bending moment, tower load and rotor speed error, improve the individual variable pitch control performance under the condition of meeting the physical constraint conditions such as variable pitch angle, reduce the structural fatigue load of wind turbine, and improve the operation safety and control accuracy of the unit.

Description

Technical Field

[0001] This invention belongs to the field of intelligent control technology for wind turbine generator sets, and involves model predictive control, swarm intelligence optimization algorithms and independent pitch control technology for wind turbine generator sets. Specifically, it relates to a wind turbine model predictive control method based on convexity and CPSOGSA optimization. Background Technology

[0002] Among numerous renewable energy sources, wind power has become an important development direction for the current energy structure transformation due to its advantages such as cleanliness, renewability, and gradually decreasing costs. As the core equipment of a wind power system, the operating performance of wind turbines directly affects power generation efficiency and equipment lifespan. In actual operation, wind turbines are typically deployed in areas with complex wind conditions and harsh environments, such as mountainous areas, offshore areas, and deserts. Under conditions such as turbulent winds, wind shear, and switching operating conditions, the loads on the blades exhibit significant uneven distribution, easily leading to structural fatigue and localized damage. Therefore, how to suppress blade load fluctuations and improve system operational stability through effective control strategies has become an important research direction in the field of wind power control. Independent pitch control, as an important advanced control strategy, can effectively suppress cyclic loads by independently adjusting the pitch angle of each blade. Model predictive control methods, due to their ability to explicitly handle system constraints and their good multivariable control capabilities, have been widely used in the pitch control of wind turbines. However, in the practical application of independent pitch model predictive control, several key technical problems still need to be solved.

[0003] First, after performing multi-blade coordinate transformation on the three-blade pitch system, the control variables are mapped from the physical space to the decoupled coordinate system. The original simple boundary constraints are transformed into complex constraints containing periodic variations. These constraints typically manifest as nonlinear inequalities, and their feasible regions exhibit irregular or even non-convex characteristics. This non-convex constraint significantly increases the difficulty of solving model predictive control optimization problems, easily leading to instability or getting trapped in local optima, affecting control performance and real-time performance. Second, existing model predictive control methods typically employ fixed constraint structures, meaning that the feasible region of the control input is determined during the design phase and does not change with operating conditions. This approach struggles to guarantee system control performance under conditions of significant wind variations, limiting the system's adaptive capabilities. Furthermore, in multi-objective control, wind turbine control systems typically need to simultaneously meet multiple performance requirements, including power point tracking, load suppression, and control smoothness. Existing methods often use weighted methods to comprehensively evaluate different performance indicators, but these methods involve independent indicators lacking a unified coupling mechanism, and the weight parameters rely on empirical settings, making it difficult to achieve optimal performance matching under different operating conditions.

[0004] In response to the above problems, scholars at home and abroad have conducted relevant research and proposed a series of improvement methods.

[0005] 1. In their study titled "An MPC approach to individual pitch control of wind turbines using uncertain LIDAR measurements," Mahmood Mirzaei et al. applied model predictive control to the independent pitch control problem of wind turbines. By linearizing the nonlinear model and constructing a predictive model, they achieved effective suppression of blade loads. This method can handle multivariate coupling problems within the predictive framework and improve the problem of uneven load distribution. However, it mainly achieves control through multi-condition linearization and scheduling, and its ability to handle complex constraint structures is limited. The optimization problem remains difficult to solve under complex constraints.

[0006] 2. In the study titled "MPC framework for constrained wind turbine individual pitch control," Vlaho Petrović et al. explicitly introduced control constraints into the MPC framework to address the constraint problem of wind turbine actuators. They pointed out that directly introducing constraints would lead to non-convex characteristics in the optimization problem, and therefore proposed modifying the constraints to ensure the convexity of the problem. This method can solve the solution difficulties caused by constraints to a certain extent and improve control stability. However, its constraint handling method is still based on a fixed structural form, does not consider the dynamic changes of constraints with the operating state, and does not perform parametric modeling of the constraint geometry, thus lacking flexibility.

[0007] 3. In the article titled "Load Predictive Control of Independent Pitch System Based on FFRLS," Jiang Ping, Geng Jinpeng, Zhang Tianyi, and other scholars proposed an independent pitch predictive control method based on online parameter identification. This method uses a recursive least squares algorithm to update system parameters in real time, thereby improving control accuracy and load suppression capabilities. This method can improve model adaptability under time-varying wind speed conditions and alleviate blade unbalanced load problems. However, it mainly focuses on system parameter identification and predictive model optimization, with less attention paid to modeling and optimizing the control constraint structure. Therefore, its adaptability under complex constraint conditions still needs improvement. Summary of the Invention

[0008] To address the technical problems of uneven blade load distribution, constrained pitch actuators, and the difficulty of balancing load suppression and control feasibility in traditional control methods under turbulent wind, wind shear, and operating condition switching conditions in existing wind turbine generators, this invention provides a model predictive control method for wind turbines based on convexity and CPSOGSA optimization. This method can solve the non-convex constraint problem in independent pitch control of wind turbine generators, reduce computational complexity, and achieve multi-objective optimization control.

[0009] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0010] A wind turbine model predictive control method based on convexity and CPSOGSA optimization includes the following steps:

[0011] S1. Establishment of mathematical model for wind turbine:

[0012] The wind turbine is linearized under small disturbances near its rated operating point, transforming the nonlinear system into a linear system. Through Taylor expansion and neglecting higher-order terms, the linear model is discretized, resulting in the linear model shown below:

[0013]

[0014] in, Represents the system state vector. Indicates control input, Indicates system output, The state matrix, For the input matrix, The output matrix is ​​defined as follows: the state vectors are selected as rotor speed, tilting moment, and yaw moment; the output variables are the load signal and speed deviation. The influence of wind speed disturbance on the system is also considered, and a disturbance term is introduced.

[0015]

[0016] in, This indicates wind speed disturbance. It represents the disturbance input matrix, which can provide a basis for the model's predictive control to resist disturbances and improve the model's adaptability to actual wind conditions;

[0017] S2. Independent pitch modeling and convexity processing based on coordinate transformation and constraint reconstruction:

[0018] First, a multi-blade coordinate transformation is performed on the three-blade pitch system of the wind turbine, mapping the three independent pitch angle variables in physical space to the collective pitch component and two periodic pitch components in a decoupled coordinate system. This transforms the originally strongly coupled control problem into a structurally separable control problem. Based on this transformation, the control input constraints are further reconstructed, elevating them from simple boundary constraints to geometric constraints with structural coupling. To achieve decoupling of the periodic load, the multi-blade coordinate transformation is introduced as follows:

[0019]

[0020] in, Indicates the collective pitch component. , Indicates the periodic pitch component, Represents the Coleman transformation matrix. The wind turbine azimuth angle changes in real time with the rotor rotation; this transformation converts the periodic signal into low-frequency and DC signals, and transforms the three-channel coupling into orthogonal decoupling control; after multi-blade coordinate transformation, the original simple constraint becomes:

[0021]

[0022] in, Indicates the minimum pitch angle. Indicates the first Pitch angle control law for each blade This represents the maximum pitch angle; the constraint is about , The nonlinear inequalities, after multi-blade coordinate transformation, transform the original linear boundary constraints in the physical coordinate system into nonlinear inequality constraints containing trigonometric functions. Since the blade azimuth angle changes with time, this constraint forms a set of constraint boundaries with directions rotating with time in the control variable space. The superposition of these constraints constitutes an irregular, non-convex feasible region structure. To address this, this invention proposes to reconstruct the non-convex constraints into equivalent conical constraints. The core idea of ​​the geometric constraints of the conical constraints lies in introducing a control capability allocation relationship. That is, the allowable amplitude of the periodic pitch component is no longer a fixed constant, but has a proportional dependence on the collective pitch component, thus forming a conical feasible region structure with the collective control capability as the axial scale. In this structure, the periodic control degrees of freedom are restricted to a conical space that dynamically changes with the collective control capability, thereby ensuring that the periodic load suppression capability and the overall system control capability remain coordinated.

[0023] Based on the geometric meaning of cone constraints, in In a plane, the amplitude is defined as follows:

[0024]

[0025] This amplitude represents the disturbance intensity of the periodic pitch control. The constraint reconfiguration concept is reflected in the fact that the periodic component cannot exceed the collective pitch control capability, that is, periodic control ≤ main control capability. Therefore, the following constraints are constructed:

[0026]

[0027] in, The scaling factor represents the proportion of periodic control; the essence of this constraint is a second-order cone constraint, whose geometry is based on... Let the cone be the axis. Based on this, the original function can be rewritten as:

[0028]

[0029] This function is convex, therefore the feasible region is... Therefore, the solution is also a convex set;

[0030] S3. CPSOGSA-MPC hierarchical collaborative optimization based on feasible region geometry reconstruction:

[0031] To address the problems of fixed control constraint structure, insufficient adaptability, and difficulty in achieving control performance under multiple operating conditions in existing MPC methods, this invention proposes a control method based on feasible domain geometric parameterization and collaborative optimization of the improved CPSOGSA algorithm. This method reconstructs the feasible domain of the control input geometrically and introduces adjustable parameters to describe its structural characteristics, transforming the control problem from a traditional parameter adjustment problem into a constraint structure design problem, thereby realizing the adaptive adjustment capability of the control system under different wind conditions.

[0032] S4. Unified performance evaluation and structural feedback based on control-prediction dual-domain coupling:

[0033] A coupled evaluation structure of control domain and prediction domain is constructed, in which the control domain reflects the optimization performance of MPC in the prediction time domain, the time domain reflects the actual dynamic response behavior of the system, and the structural domain reflects the impact of geometric changes in the feasible domain on system performance. The three together constitute a unified evaluation function.

[0034]

[0035] in, Represents the geometric structure parameters of the feasible region. Indicates the control domain evaluation index. Indicates the evaluation index in the time domain. Indicates the weighting coefficient;

[0036] The unified evaluation function is no longer a traditional weighted objective function, but a structure-sensitive performance mapping function. That is, under different feasible domain structures, the same error has different penalty strengths, and the evaluation function changes with the constraint space. The evaluation function is a performance mapping function that dynamically changes with the geometry of the controllable feasible domain, rather than a static multi-objective function. Its essence is expressed as the following mapping relationship:

[0037]

[0038] Therefore, the following closed-loop optimization mechanism is constructed:

[0039]

[0040] That is, CPSOGSA generates feasible region geometry parameters. Under this architecture, MPC obtains the control sequence, the system calculates the performance indicators in the control domain and time domain, and constructs a unified performance evaluation function. , Then reverse drive CPSOGSA update This forms a closed-loop system: structure generation → control execution → performance feedback → structure re-optimization.

[0041] Furthermore, step S3, CPSOGSA-MPC hierarchical collaborative optimization based on feasible region geometric reconstruction, specifically includes:

[0042] S31. Feasible region geometric modeling:

[0043] First, the control input constraints in Model Predictive Control (MPC) are uniformly modeled and represented as a set of parameterized feasible regions. Specifically, the feasible region of control input is defined as:

[0044]

[0045] in, Indicates the feasible region of the control input. To control the input vector, The geometric parameter vector that describes the structure of the feasible region. For constraint functions;

[0046] To address the coupling characteristics among control variables in an independent pitch control system for wind turbines, the conical feasible region construction method maps the control input from the physical coordinate system to the decoupled coordinate system and represents the control variables as periodic components.

[0047]

[0048] in, and These represent the periodic components of the pitch control; based on this, the present invention introduces a conical constraint structure to restrict the control input within a second-order conical space, the constraint form of which is:

[0049]

[0050] in, Indicates the collective pitch control quantity. The cone-shaped opening parameter is used to control the allowable amplitude range of the periodic component relative to the collective component;

[0051] To achieve adaptive adjustment of the conical feasible region, the control constraint structure is further parameterized as follows:

[0052]

[0053] Among them, parameters Parameters used to describe the size of the tapered opening Used to adjust the asymmetry of the constraint space, parameters Used to control the degree of shrinkage or expansion of the overall feasible region;

[0054] S32, CPSOGSA optimization mechanisms for the feasible region:

[0055] During the optimization process, each particle represents a set of feasible domain structure parameters, expressed as follows:

[0056]

[0057] By embedding this parameter into the model predictive controller, the MPC is optimized within the corresponding constraint space, and the objective function is:

[0058]

[0059] in, This represents the discrete time step, i.e., the i-th step in the prediction process. Sampling points This indicates the prediction time domain, i.e., how many steps MPC predicts into the future. Indicates in structural parameters Power tracking error under constraints Indicates in structural parameters Structural load response under constraints Indicates in structural parameters Changes in control input under constraints , , Indicates the weighting coefficient;

[0060] Simultaneously satisfy the conical constraint condition:

[0061]

[0062] Based on this, system performance indicators, including power error, structural load, and control smoothness, are obtained through MPC simulation, and a unified fitness function is constructed. After the fitness calculation is completed, the CPSOGSA algorithm updates the particles according to the fitness function to achieve adaptive optimization of the feasible region structural parameters. The velocity update, mass update, and position update are respectively expressed as:

[0063]

[0064]

[0065]

[0066] in, Indicates inertia weight, This represents the optimal position of an individual. Indicates the current particle position. Indicates the globally optimal position. , These represent individual learning factors and social learning factors, respectively. , Represents a random number; Indicates the first The fitness value of each particle. This indicates the worst fitness level in the current group. This indicates the best fitness level in the current population;

[0067] The particle velocity update follows the contraction factor PSO mechanism to maintain global search capability. At the same time, a gravity search mechanism is introduced to simulate the information attraction effect through the mass difference between particles, so that the better structure gradually converges to the global optimum. The particle mass is obtained by mapping the fitness function, so that the feasible domain structure with better performance has a stronger attraction in the search space, thereby driving the system to evolve towards a better control structure.

[0068] Furthermore, the control domain evaluation index in step S4 This reflects the optimal performance of MPC under the current feasible domain structure constraints, and its evaluation function is defined as:

[0069]

[0070] in, This represents the discrete time step, i.e., the i-th step in the prediction process. Sampling points This indicates the prediction time domain, i.e., how many steps MPC predicts into the future. Indicates in structural parameters Power tracking error under constraints Indicates in structural parameters Structural load response under constraints Indicates in structural parameters Changes in control input under constraints , , These represent weighting coefficients; all of the above indicators explicitly depend on structural parameters. This dependency is derived from the structured expression of MPC constraints:

[0071]

[0072] This constraint indicates that the geometry of the controllable input feasible region is determined by structural parameters. Decision, thereby enabling control input It becomes a function of the structure.

[0073] Furthermore, the time-domain evaluation index in step S4 It is used to characterize the actual response process of a system under disturbance conditions, and is defined as follows:

[0074]

[0075] This metric is represented by the time-weighted integral of absolute error, which makes the impact of initial errors greater and the long-term errors continuously penalized. Its essential function is to force the system not only to be well optimized, but also to respond quickly.

[0076] Furthermore, the unified evaluation function in step S4 is not only used for performance evaluation, but also for back-driving the feasible domain geometry parameters. Update, that is:

[0077]

[0078] in, Indicates the first The parameters to be optimized in the next iteration This indicates that the search direction is being updated, and the update direction is determined by the performance evaluation function:

[0079]

[0080] in, This indicates that the update rule function calculates the next search direction based on the current fitness.

[0081] Compared with existing technologies, the wind turbine model predictive control method based on convexity and CPSOGSA optimization provided by this invention has the following advantages and beneficial effects:

[0082] 1) This invention transforms complex irregular constraints into regular structures by geometrically reconstructing the constraints of traditional independent pitch control, thus overcoming the non-convexity bottleneck. It achieves the internal approximation convex reconstruction of the non-convex feasible region of independent pitch control through parameterized second-order cone (SOCP), which mathematically avoids the physical defects of conventional IPC control algorithms that are prone to getting trapped in local optima and unstable in real-time solutions. This significantly improves the stability and feasibility of model predictive control in practical applications.

[0083] 2) This invention proposes a dual-closed-loop hierarchical collaborative optimization architecture with control-prediction dual-domain coupling. The upper-layer slowly varying loop utilizes an improved CPSOGSA algorithm to optimize the three-dimensional geometric parameters. Instead of focusing on specific pitch angles, the lower-level fast-loop control utilizes MPC to perform highly efficient convex optimization matrix programming, drastically reducing computation time. The upper-level slow-optimization boundary constraint and the lower-level fast-execution precise control time-domain separation mechanism leverages the macroscopic adaptive self-organizing capabilities of intelligent algorithms for complex multi-condition scenarios while preserving the extremely high real-time response speed of convex optimization control. This invention balances intelligence and real-time performance, utilizing a hierarchical time-domain decoupled control architecture that combines constraint structure parameterization with high-speed convex optimization execution. This solves the problem that high-dimensional intelligent optimization algorithms cannot meet the millisecond-level response requirements of wind turbine control due to computational delays.

[0084] 3) This invention utilizes a control-prediction-time-structure multi-domain adaptive feedback evaluation function to achieve comprehensive optimization of power point tracking, load suppression, and control smoothness. It overcomes the problem of static weights in traditional multi-objective methods being unable to adapt to environmental changes. When sudden changes in external wind conditions cause the system to exhibit oscillations, overshoot, and divergence, time-domain indicators and power and load errors surge rapidly. This surge signal, through a unified evaluation function, instantly forces the upper-level CPSOGSA algorithm to reconstruct geometric parameters and tighten the conical boundary, enabling the lower-level MPC to converge at the fastest damping speed within a safer and more rational constraint circle. This achieves accurate, rapid, and stable parameter adjustment under all operating conditions. This invention enables the controller to actively evolve constraint boundaries and tighten control degrees of freedom based on sudden changes in wind conditions, improving the system's ability to cope with oscillations and overshoot, and significantly enhancing the accurate convergence speed and system stability of wind turbines under all operating conditions. Attached Figure Description

[0085] Figure 1 This is a schematic diagram of the wind turbine model predictive control method based on convexity and CPSOGSA optimization provided by the present invention.

[0086] Figure 2 This is a comparison diagram of the non-convex feasible region and the cone-constrained feasible region provided by the present invention.

[0087] Figure 3This is the CPSOGSA-MPC hierarchical collaborative optimization and performance feedback closed-loop structure diagram provided by the present invention.

[0088] Figure 4 This is a flowchart of performance evaluation and feedback based on a unified evaluation function provided by the present invention. Detailed Implementation

[0089] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below with reference to specific illustrations.

[0090] Please refer to Figure 1 As shown, this invention provides a wind turbine model predictive control method based on convexity and CPSOGSA optimization, comprising the following steps:

[0091] S1. Establishment of mathematical model for wind turbine:

[0092] To achieve precise regulation of wind turbine load and operating status by subsequent model predictive control, a mathematical model of the wind turbine system needs to be established first. The wind turbine is linearized near its rated operating point to construct a discrete state-space model suitable for predictive control. This model provides the foundation for describing the dynamic response characteristics of the wind turbine under pitch control, the future predicted state of MPC (Model Predictive Control), and the optimization evaluation using CPSOGSA (Contraction Factor Particle Swarm Optimization-Gravitational Search Algorithm, a hybrid intelligent optimization algorithm).

[0093] Wind turbines are typical aerodynamic-structural coupled nonlinear systems, and their dynamic equations can be expressed as:

[0094]

[0095] However, in actual wind turbine units, wind speed exhibits randomness and turbulent characteristics, and the aerodynamic forces of the blades change with the pitch angle. Therefore, the system possesses strong nonlinearity and coupling characteristics, making it unsuitable for direct control design and requiring further processing. This invention performs small-disturbance linearization processing on the wind turbine unit near its rated operating point, transforming the nonlinear system into a linear system. Through Taylor expansion and neglecting higher-order terms, the linear model is discretized, resulting in the linearized model shown below:

[0096]

[0097] in, Represents the system state vector. Indicates control input, Indicates system output, The state matrix, For the input matrix, The output matrix is ​​defined as follows: the state vectors are selected as rotor speed, tilting moment, and yaw moment; the output variables are the load signal and speed deviation. The influence of wind speed disturbance on the system is also considered, and a disturbance term is introduced.

[0098]

[0099] in, This indicates wind speed disturbance. This represents the disturbance input matrix, which can provide a basis for the model's predictive control to resist disturbances and improve the model's adaptability to actual wind conditions.

[0100] S2. Independent pitch modeling and convexity processing based on coordinate transformation and constraint reconstruction:

[0101] To address the issues of control variable coupling and constraint non-convexity in traditional independent pitch control, a multi-blade coordinate transformation is first performed on the three-blade pitch system of the wind turbine. This maps the three independent pitch angle variables in physical space to a collective pitch component and two periodic pitch components in a decoupled coordinate system, thus transforming the originally strongly coupled control problem into a structurally separable one. Based on this transformation, the traditional independent constraint form (i.e., box constraints where each pitch angle is independently constrained) is no longer suitable for describing the true dynamic characteristics of the system. Therefore, this invention further reconstructs the control input constraints, elevating them from simple boundary constraints to geometric constraints with structural coupling. To achieve decoupling of periodic loads, the introduced multi-blade coordinate transformation (MBC) is as follows:

[0102]

[0103] in, This represents the collective pitch component (average control quantity). , This represents the periodic pitch component (load suppression core). Represents the Coleman transformation matrix. The wind turbine azimuth angle changes in real time with the rotor rotation; this transformation converts the periodic signal into low-frequency and DC signals, and transforms the three-channel coupling into orthogonal decoupling control; after multi-blade coordinate transformation, the original simple constraint becomes:

[0104]

[0105] in, Indicates the minimum pitch angle. Indicates the first Pitch angle control law for each blade This represents the maximum pitch angle; the constraint is about , The nonlinear inequalities, after multi-blade coordinate transformation, transform the original linear boundary constraints in the physical coordinate system into nonlinear inequality constraints containing trigonometric functions. Since the blade azimuth angle changes with time, this constraint forms a set of time-rotating constraint boundaries in the control variable space. The superposition of these constraints constitutes an irregular, non-convex feasible region structure. Ignoring the non-convexity or directly approximating it may lead to optimization instability, local optima, and poor real-time performance. To address this, this invention proposes to equivalently reconstruct the non-convex constraints into conical constraints. The core idea of ​​the conical constraint's geometric constraints lies in introducing a control capability allocation relationship. That is, the allowable amplitude of the periodic pitch component is no longer a fixed constant but has a proportional dependence on the collective pitch component, thus forming a conical feasible region structure with the collective control capability as the axial scale. In this structure, the periodic control degrees of freedom are confined within a conical space that dynamically changes with the collective control capability, thereby ensuring consistency between the periodic load suppression capability and the overall system control capability.

[0106] Based on the geometric meaning of cone constraints, in In a plane, the amplitude is defined as follows:

[0107]

[0108] This amplitude represents the disturbance intensity of the periodic pitch control. The constraint reconfiguration concept is reflected in the fact that the periodic component cannot exceed the collective pitch control capability, that is, periodic control ≤ main control capability. Therefore, the following constraints are constructed:

[0109]

[0110] in, The scaling factor represents the proportion of periodic control; the essence of this constraint is a second-order cone constraint (SOCP constraint), whose geometry is based on... Let the cone be the axis. Based on this, the original function can be rewritten as:

[0111]

[0112] This function is convex, therefore the feasible region is... Therefore, the solution is also a convex set.

[0113] The feasible region corresponding to the cone constraint is a set of second-order cone constraints, which transforms the original non-convex optimization problem into a convex optimization problem, thereby ensuring the global optimality and numerical stability of the model predictive control solution process. Physically, the cone constraint indicates that the energy of periodic pitch control is limited by the collective pitch capability, thus achieving load suppression while ensuring the safety of the actuator. Simultaneously, the cone constraint is also an internal approximation constraint of the original pitch constraint, used to shrink the non-convex feasible region into a convex feasible region while ensuring that all control inputs satisfy the physical constraints. For example... Figure 2 As shown, after undergoing multi-blade coordinate transformation, the boundary constraints of traditional independent pitch control in its physical space are mapped to strongly nonlinear, time-varying, and nonconvex inequalities containing trigonometric functions. Due to the nonconvexity of the feasible region, conventional optimization algorithms are prone to getting trapped in local minima, and the solutions obtained cannot guarantee overall performance. This invention introduces parameterized second-order cone constraints. As the optimal inner approximation set of the original non-convex boundary, the convex set property of the second-order cone is used to shrink and reconstruct the original non-convex optimization feasible region into a convex feasible region. Inside the convex feasible region, any local optimal solution is the globally unique optimal solution, thus mathematically eliminating the local traps and multi-extreme interference caused by non-convexity in traditional methods.

[0114] S3. CPSOGSA-MPC hierarchical collaborative optimization based on feasible region geometry reconstruction:

[0115] This invention addresses the problems of fixed control constraint structures, insufficient adaptability, and difficulty in achieving balanced control performance under multiple operating conditions in existing MPC methods. It proposes a control method based on feasible region geometric parameterization and a collaborative optimization of the improved CPSOGSA algorithm. This method geometrically reconstructs the feasible region of the control input and introduces adjustable parameters to describe its structural characteristics, transforming the control problem from a traditional parameter adjustment problem into a constraint structure design problem. This enables the control system to achieve adaptive adjustment capabilities under different wind conditions.

[0116] As a specific embodiment, step S3, CPSOGSA-MPC hierarchical collaborative optimization based on feasible domain geometric reconstruction, specifically includes:

[0117] S31. Feasible region geometric modeling:

[0118] First, the control input constraints in Model Predictive Control (MPC) are uniformly modeled and represented as a set of parameterized feasible regions. Specifically, the feasible region of control input is defined as:

[0119]

[0120] in, Indicates the feasible region of the control input. To control the input vector, The geometric parameter vector that describes the structure of the feasible region. This is a constraint function. Unlike traditional methods that fix upper and lower bound constraints, this invention introduces parameters. This makes the control feasible region a dynamic geometric structure that varies with the parameters, thus providing structural degrees of freedom for subsequent optimization.

[0121] To address the coupling characteristics among control variables in an independent pitch control system for wind turbines, the conical feasible region construction method maps the control input from the physical coordinate system to the decoupled coordinate system and represents the control variables as periodic components.

[0122]

[0123] in, and These represent the periodic components of the pitch control; based on this, the present invention introduces a conical constraint structure to restrict the control input within a second-order conical space, the constraint form of which is:

[0124]

[0125] in, Indicates the collective pitch control quantity. The conical opening parameter is used to control the allowable amplitude range of the periodic component relative to the collective component. The introduction of this conical constraint means that the control input is no longer independently constrained, but rather a coupling relationship is established between periodic control and collective control through geometric structure, thereby achieving a rational allocation of control capability.

[0126] To achieve the adaptive adjustment of the aforementioned conical feasible region, the control constraint structure is further parameterized as follows:

[0127]

[0128] Among them, parameters Parameters used to describe the size of the tapered opening Used to adjust the asymmetry of the constraint space, parameters This is used to control the degree of contraction or expansion of the overall feasible region. Through the above parameterized representation, the control input constraints are no longer fixed in form, but rather a dynamic structure defined by a set of adjustable geometric parameters, enabling the control system to adaptively adjust the constraint space according to changes in operating state.

[0129] S32, CPSOGSA optimization mechanisms for the feasible region:

[0130] This section primarily introduces the embedding mechanism of CPSOGSA with MPC after optimization, as well as the CPSOGSA update mechanism and structural evolution process. During optimization, each particle represents a set of feasible domain structure parameters, expressed as follows:

[0131]

[0132] The parameters correspond to the conical opening, shape offset, and degree of contraction, respectively. By embedding these parameters into the model predictive controller, the MPC is optimized within the corresponding constraint space. The objective function is:

[0133]

[0134] in, This represents the discrete time step, i.e., the i-th step in the prediction process. Sampling points This indicates the prediction time domain, i.e., how many steps MPC predicts into the future. Indicates in structural parameters Power tracking error under constraints Indicates in structural parameters Structural load response under constraints Indicates in structural parameters Changes in control input under constraints , , Indicates the weighting coefficient;

[0135] Simultaneously satisfy the conical constraint condition:

[0136]

[0137] Based on this, system performance indicators, including power error, structural load, and control smoothness, are obtained through MPC simulation, and a unified fitness function is constructed. After the fitness calculation is completed, the CPSOGSA algorithm updates the particles according to the fitness function to achieve adaptive optimization of the feasible region structural parameters; where velocity update, mass update, and position update are respectively expressed as:

[0138]

[0139]

[0140]

[0141] in, Indicates inertia weight, This represents the optimal position of an individual. Indicates the current particle position. Indicates the globally optimal position. , These represent individual learning factors and social learning factors, respectively. , Represents a random number; Indicates the first The fitness value of each particle. This indicates the worst fitness level in the current group. This indicates the best fitness level in the current population;

[0142] The particle velocity update follows the contraction factor PSO mechanism to maintain global search capability. At the same time, a gravity search mechanism is introduced to simulate the information attraction effect through the mass difference between particles, so that the better structure gradually converges to the global optimum. The particle mass is obtained by mapping the fitness function, so that the feasible domain structure with better performance has a stronger attraction in the search space, thereby driving the system to evolve towards a better control structure.

[0143] In this invention, the improved CPSOGSA algorithm is no longer used to optimize the control input, but rather to search for the optimal feasible region structure. Specifically, each particle does not represent a set of controller parameters, but rather a control constraint geometry. The optimization objective of the algorithm is to find a feasible region structure such that, under these constraints, when running MPC, the system can simultaneously satisfy the following three objectives: minimizing power error, minimizing structural load fluctuations, and optimizing the smoothness of control input changes. To achieve this objective, each candidate feasible region structure is embedded into the MPC simulation for evaluation. MPC solves for the optimal control sequence within this constraint space, while CPSOGSA updates the feasible region structure parameters based on the system performance indicators fed back from the control results. Therefore, this method forms a two-layer closed-loop optimization mechanism: the upper layer optimizes the constraint structure, and the lower layer performs control calculations, the entire structure as follows: Figure 3 As shown. Under specific wind and operating conditions, the specific geometric parameters are generated by the upper-level CPSOGSA algorithm based on the current transient characteristics of the system (such as wind speed and load). The control sequence calculated by the lower-level MPC at the boundary possesses deterministic global unique optimality. As the operating conditions drift, the structural parameters of the upper-level feasible region change. (Conical opening parameters) Asymmetric adjustment parameters , contraction and expansion scale The system adaptively reconstructs and evolves, enabling the control input space to dynamically approximate the real physical limits. This collaborative approach of dynamic boundary adjustment and absolute global optimum within the domain ensures that the controller output converges to the globally relatively optimal feasible solution under the current environmental constraints under any complex operating conditions, avoiding conservative control or instability caused by traditional fixed constraints.

[0144] This invention utilizes hierarchical time-domain separation to improve control accuracy and real-time performance. Traditional intelligent optimization algorithms directly optimize control inputs, but due to the drastic dynamic changes of wind turbines and the enormous computational load of high-dimensional online optimization, significant control delays and system oscillations are often caused. This invention employs a two-layer collaborative closed-loop optimization architecture. The upper layer (slow-variable loop) utilizes an improved CPSOGSA algorithm to perform intermittent, high-level adaptive self-organizing search only on low-dimensional constraint geometric parameters, fundamentally changing the boundary defense rules of the controller. The lower layer (fast-variable loop), based on the input space being convexized into a second-order cone space by the upper layer, uses online MPC to transform it into a highly mature and efficient convex quadratic programming or interior-point method solution. This time-domain separation mechanism extracts the complex nonlinear intelligent search from the real-time control loop, significantly reducing the single-step computation time of the lower-layer MPC to the millisecond level, ensuring accurate and high-speed output of control actions, perfectly meeting the rapid pitch response requirements of wind turbine actuators.

[0145] S4. Unified performance evaluation and structural feedback based on control-prediction dual-domain coupling:

[0146] Traditional methods for performance evaluation typically suffer from two independent problems: focusing solely on MPC control domain metrics or solely on time response metrics. This leads to steady-state optimization but poor dynamic performance. Furthermore, these metrics are often simply linearly weighted, lacking a physical-level interpretation, causing the optimization process to fail to reflect real system structural changes. To address these issues, this invention no longer treats performance evaluation as a single scalar function. Instead, it constructs a coupled evaluation structure of the control domain and prediction domain. The control domain reflects the optimization performance of MPC in the prediction time domain, the time domain reflects the system's true dynamic response behavior, and the structural domain reflects the impact of feasible domain geometric changes on system performance. These three domains together constitute a unified evaluation function.

[0147]

[0148] in, Represents the geometric structure parameters of the feasible region. Indicates the control domain evaluation index. Indicates the evaluation index in the time domain. This represents the weighting coefficient.

[0149] In the control domain, control domain evaluation indicators This reflects the optimal performance of MPC under the current feasible region structure constraints, and its evaluation function is defined as:

[0150]

[0151] in, This represents the discrete time step, i.e., the i-th step in the prediction process. Sampling points This indicates the prediction time domain, i.e., how many steps MPC predicts into the future. Indicates in structural parameters Power tracking error under constraints Indicates in structural parameters Structural load response under constraints Indicates in structural parameters Changes in control input under constraints , , This represents the weighting coefficients. It is important to emphasize that, unlike traditional methods, all of the above indicators explicitly depend on the structural parameters. This dependency is derived from the structured expression of MPC constraints:

[0152]

[0153] This constraint indicates that the geometry of the controllable input feasible region is determined by structural parameters. Decision, thereby enabling control input It becomes a function of the structure. The evaluation index is not just the sum of squared errors, but a comprehensive consideration of power tracking error, structural load response, and changes in control input, which respectively reflect the ability to achieve control objectives, mechanical safety, and actuator burden. Therefore, the performance of the control domain is no longer a single error, but a comprehensive reflection of the system's internal optimization behavior.

[0154] Control domain metrics alone cannot reflect the dynamic performance of a system; therefore, time domain metrics are introduced. Used to characterize the true response process of a system under disturbance conditions, it is defined as:

[0155]

[0156] This metric is represented by the time-weighted integral of absolute error, which makes the impact of initial errors greater and the long-term errors continuously penalized. Its essential function is to force the system not only to be well optimized, but also to respond quickly.

[0157] The introduction of structural domains is the key innovation of this invention. The unified evaluation function is not only used for performance evaluation, but also for back-driving the geometric structural parameters of the feasible domain. Update, that is:

[0158]

[0159] in, Indicates the first The parameters to be optimized in the next iteration This indicates that the search direction is being updated, and the update direction is determined by the performance evaluation function:

[0160]

[0161] in, This indicates that the update rule function calculates the next search direction based on the current fitness.

[0162] Therefore, the unified evaluation function described in this invention is no longer a traditional weighted objective function, but a structure-sensitive performance mapping function. That is, under different feasible domain structures, the same error has different penalty intensities, and the evaluation function changes with the constraint space. The evaluation function is a performance mapping function that dynamically changes with the geometry of the controllable feasible domain, rather than a static multi-objective function. Its essence is expressed as the following mapping relationship:

[0163]

[0164] Therefore, the following closed-loop optimization mechanism is constructed:

[0165]

[0166] That is, CPSOGSA generates feasible region geometry parameters. Under this architecture, MPC obtains the control sequence, the system calculates the performance indicators in the control domain and time domain, and constructs a unified performance evaluation function. , Then reverse drive CPSOGSA update This forms a closed-loop system: structure generation → control execution → performance feedback → structure re-optimization, such as... Figure 4 As shown. To achieve high disturbance rejection stability of the system, this invention explicitly introduces a time-domain evaluation index into the constructed unified performance evaluation function. This index explicitly weights the error over time (giving high weight to initial dynamic errors and continuously applying integral penalties to long-term steady-state deviations) to constrain and guide the CPSOGSA to adjust the feasible region online. When the wind turbine encounters sudden turbulent winds or changes in operating conditions, if the system exhibits overshoot or oscillation tendencies, the time-domain index will surge. This surge signal immediately drives the upper-level algorithm to tighten or bias the feasible region boundary through mapping relationships, actively limiting the irrational and blind output of periodic pitch. This forces the lower-level MPC to solve for optimal control actions with maximum system damping and minimum control input variation within a safer and more rational convex constraint range. Ultimately, through an adaptive closed loop from structural adaptive generation to high-speed convex optimization control execution to dynamic feedback of time response to precise contraction of the constraint space, bidirectional suppression of power error and structural load fluctuations is achieved, ensuring that the wind turbine can accurately and quickly converge to the steady-state operating point under all operating conditions.

[0167] The weight coefficients in the unified evaluation function and model predictive control objective function described in this invention are pre-set static constant balancing factors. Traditional multi-objective predictive control methods typically require frequent online adjustments of these weight coefficients to adapt to different wind conditions. This not only easily leads to the failure of online quadratic programming (QP) problems due to matrix condition number deterioration, but also lacks clear physical boundary protection. In stark contrast, this invention completely maps the system's adaptive capability to handle full-condition switching to the geometric parameters of the feasible region. The dynamic evolution of the system is addressed by maintaining a constant weighting coefficient during control. When sudden changes in wind conditions cause fluctuations in system load or power, the accumulated error is amplified by the constant weighting, which is directly reflected in the surge of the adaptive feedback evaluation function. The upper-level CPSOGSA algorithm then reverses this to precisely reconstruct the control constraint boundary, thereby forcibly tightening the control degrees of freedom through the active contraction of the physical boundary while maintaining the complete stability of the mathematical structure of the lower-level optimization solution (weights do not drift over time). This decoupled control mechanism, where static weights establish priorities and dynamic boundaries defend against extreme conditions, significantly improves the numerical robustness and operational safety of the controller in engineering applications.

[0168] Compared with existing technologies, the wind turbine model predictive control method based on convexity and CPSOGSA optimization provided by this invention has the following advantages and beneficial effects:

[0169] 1) This invention transforms complex irregular constraints into regular structures by geometrically reconstructing the constraints of traditional independent pitch control, thus overcoming the non-convexity bottleneck. It achieves the internal approximation convex reconstruction of the non-convex feasible region of independent pitch control through parameterized second-order cone (SOCP), which mathematically avoids the physical defects of conventional IPC control algorithms that are prone to getting trapped in local optima and unstable in real-time solutions. This significantly improves the stability and feasibility of model predictive control in practical applications.

[0170] 2) This invention proposes a dual-closed-loop hierarchical collaborative optimization architecture with control-prediction dual-domain coupling. The upper-layer slowly varying loop utilizes an improved CPSOGSA algorithm to optimize the three-dimensional geometric parameters. Instead of focusing on specific pitch angles, the lower-level fast-loop control utilizes MPC to perform highly efficient convex optimization matrix programming, drastically reducing computation time. The upper-level slow-optimization boundary constraint and the lower-level fast-execution precise control time-domain separation mechanism leverages the macroscopic adaptive self-organizing capabilities of intelligent algorithms for complex multi-condition scenarios while preserving the extremely high real-time response speed of convex optimization control. This invention balances intelligence and real-time performance, utilizing a hierarchical time-domain decoupled control architecture that combines constraint structure parameterization with high-speed convex optimization execution. This solves the problem that high-dimensional intelligent optimization algorithms cannot meet the millisecond-level response requirements of wind turbine control due to computational delays.

[0171] 3) This invention utilizes a control-prediction-time-structure multi-domain adaptive feedback evaluation function to achieve comprehensive optimization of power point tracking, load suppression, and control smoothness. It overcomes the problem of static weights in traditional multi-objective methods being unable to adapt to environmental changes. When sudden changes in external wind conditions cause the system to exhibit oscillations, overshoot, and divergence, time-domain indicators and power and load errors surge rapidly. This surge signal, through a unified evaluation function, instantly forces the upper-level CPSOGSA algorithm to reconstruct geometric parameters and tighten the conical boundary, enabling the lower-level MPC to converge at the fastest damping speed within a safer and more rational constraint circle. This achieves accurate, rapid, and stable parameter adjustment under all operating conditions. This invention enables the controller to actively evolve constraint boundaries and tighten control degrees of freedom based on sudden changes in wind conditions, improving the system's ability to cope with oscillations and overshoot, and significantly enhancing the accurate convergence speed and system stability of wind turbines under all operating conditions.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A fan model predictive control method based on convexification and CPSOGSA optimization, characterized in that, Includes the following steps: S1. Establishment of mathematical model for wind turbine: The wind turbine is linearized under small disturbances near its rated operating point, transforming the nonlinear system into a linear system. Through Taylor expansion and neglecting higher-order terms, the linear model is discretized, resulting in the linear model shown below: in, Represents the system state vector. Indicates control input, Indicates system output, The state matrix, For the input matrix, The output matrix is ​​defined as follows: the state vectors are selected as rotor speed, tilting moment, and yaw moment; the output variables are the load signal and speed deviation. The influence of wind speed disturbance on the system is also considered, and a disturbance term is introduced. in, This indicates wind speed disturbance. It represents the disturbance input matrix, which can provide a basis for the model's predictive control to resist disturbances and improve the model's adaptability to actual wind conditions; S2. Independent pitch modeling and convexity processing based on coordinate transformation and constraint reconstruction: First, a multi-blade coordinate transformation is performed on the three-blade pitch system of the wind turbine, mapping the three independent pitch angle variables in physical space to the collective pitch component and two periodic pitch components in a decoupled coordinate system. This transforms the originally strongly coupled control problem into a structurally separable control problem. Based on this transformation, the control input constraints are further reconstructed, elevating them from simple boundary constraints to geometric constraints with structural coupling. To achieve decoupling of the periodic load, the multi-blade coordinate transformation is introduced as follows: in, Indicates the collective pitch component. , Indicates the periodic pitch component, Represents the Coleman transformation matrix. The wind turbine azimuth angle changes in real time with the rotor rotation; this transformation converts the periodic signal into low-frequency and DC signals, and transforms the three-channel coupling into orthogonal decoupling control; after multi-blade coordinate transformation, the original simple constraint becomes: in, Indicates the minimum pitch angle. Indicates the first Pitch angle control law for each blade This represents the maximum pitch angle; the constraint is about , The nonlinear inequalities, after multi-blade coordinate transformation, transform the original linear boundary constraints in the physical coordinate system into nonlinear inequality constraints containing trigonometric functions. Since the blade azimuth angle changes with time, this constraint forms a set of constraint boundaries with directions rotating with time in the control variable space. The superposition of these constraints constitutes an irregular, non-convex feasible region structure. To address this, this invention proposes to reconstruct the non-convex constraints into equivalent conical constraints. The core idea of ​​the geometric constraints of the conical constraints lies in introducing a control capability allocation relationship. That is, the allowable amplitude of the periodic pitch component is no longer a fixed constant, but has a proportional dependence on the collective pitch component, thus forming a conical feasible region structure with the collective control capability as the axial scale. In this structure, the periodic control degrees of freedom are restricted to a conical space that dynamically changes with the collective control capability, thereby ensuring that the periodic load suppression capability and the overall system control capability remain coordinated. Based on the geometric meaning of cone constraints, in In a plane, the amplitude is defined as follows: This amplitude represents the disturbance intensity of the periodic pitch control. The constraint reconfiguration concept is reflected in the fact that the periodic component cannot exceed the collective pitch control capability, that is, periodic control ≤ main control capability. Therefore, the following constraints are constructed: in, The scaling factor represents the proportion of periodic control; the essence of this constraint is a second-order cone constraint, whose geometry is based on... Let the cone be the axis. Based on this, the original function can be rewritten as: This function is convex, therefore the feasible region is... Therefore, the solution is also a convex set; S3. CPSOGSA-MPC hierarchical collaborative optimization based on feasible region geometry reconstruction: To address the problems of fixed control constraint structure, insufficient adaptability, and difficulty in achieving control performance under multiple operating conditions in existing MPC methods, this invention proposes a control method based on feasible domain geometric parameterization and collaborative optimization of the improved CPSOGSA algorithm. This method reconstructs the feasible domain of the control input geometrically and introduces adjustable parameters to describe its structural characteristics, transforming the control problem from a traditional parameter adjustment problem into a constraint structure design problem, thereby realizing the adaptive adjustment capability of the control system under different wind conditions. S4. Unified performance evaluation and structural feedback based on control-prediction dual-domain coupling: A coupled evaluation structure of control domain and prediction domain is constructed, in which the control domain reflects the optimization performance of MPC in the prediction time domain, the time domain reflects the actual dynamic response behavior of the system, and the structural domain reflects the impact of geometric changes in the feasible domain on system performance. The three together constitute a unified evaluation function. in, Represents the geometric structure parameters of the feasible region. Indicates the control domain evaluation index. Indicates the evaluation index in the time domain. Indicates the weighting coefficient; The unified evaluation function is no longer a traditional weighted objective function, but a structure-sensitive performance mapping function. That is, under different feasible domain structures, the same error has different penalty strengths, and the evaluation function changes with the constraint space. The evaluation function is a performance mapping function that dynamically changes with the geometry of the controllable feasible domain, rather than a static multi-objective function. Its essence is expressed as the following mapping relationship: Therefore, the following closed-loop optimization mechanism is constructed: That is, CPSOGSA generates feasible region geometry parameters. Under this architecture, MPC obtains the control sequence, the system calculates the performance indicators in the control domain and time domain, and constructs a unified performance evaluation function. , Then reverse drive CPSOGSA update This forms a closed-loop system: structure generation → control execution → performance feedback → structure re-optimization.

2. The wind turbine model predictive control method based on convexity and CPSOGSA optimization according to claim 1, characterized in that, Step S3, CPSOGSA-MPC hierarchical collaborative optimization based on feasible region geometric reconstruction, specifically includes: S31. Feasible region geometric modeling: First, the control input constraints in Model Predictive Control (MPC) are uniformly modeled and represented as a set of parameterized feasible regions. Specifically, the feasible region of control input is defined as: in, Indicates the feasible region of the control input. To control the input vector, The geometric parameter vector that describes the structure of the feasible region. For constraint functions; To address the coupling characteristics among control variables in an independent pitch control system for wind turbines, the conical feasible region construction method maps the control input from the physical coordinate system to the decoupled coordinate system and represents the control variables as periodic components. in, and These represent the periodic components of the pitch control; based on this, the present invention introduces a conical constraint structure to restrict the control input within a second-order conical space, the constraint form of which is: in, Indicates the collective pitch control quantity. The cone-shaped opening parameter is used to control the allowable amplitude range of the periodic component relative to the collective component; To achieve adaptive adjustment of the conical feasible region, the control constraint structure is further parameterized as follows: Among them, parameters Parameters used to describe the size of the tapered opening Used to adjust the asymmetry of the constraint space, parameters Used to control the degree of shrinkage or expansion of the overall feasible region; S32, CPSOGSA optimization mechanisms for the feasible region: During the optimization process, each particle represents a set of feasible domain structure parameters, expressed as follows: By embedding this parameter into the model predictive controller, the MPC is optimized within the corresponding constraint space, and the objective function is: in, This represents the discrete time step, i.e., the i-th step in the prediction process. Sampling points This indicates the prediction time domain, i.e., how many steps MPC predicts into the future. Indicates in structural parameters Power tracking error under constraints Indicates in structural parameters Structural load response under constraints Indicates in structural parameters Changes in control input under constraints , , Indicates the weighting coefficient; Simultaneously satisfy the conical constraint condition: Based on this, system performance indicators, including power error, structural load, and control smoothness, are obtained through MPC simulation, and a unified fitness function is constructed. After the fitness calculation is completed, the CPSOGSA algorithm updates the particles according to the fitness function to achieve adaptive optimization of the feasible region structural parameters. The velocity update, mass update, and position update are respectively expressed as: in, Indicates inertia weight, This represents the optimal position of an individual. Indicates the current particle position. Indicates the globally optimal position. , These represent individual learning factors and social learning factors, respectively. , Represents a random number; Indicates the first The fitness value of each particle. This indicates the worst fitness level in the current group. This indicates the best fitness level in the current population; The particle velocity update follows the contraction factor PSO mechanism to maintain global search capability. At the same time, a gravity search mechanism is introduced to simulate the information attraction effect through the mass difference between particles, so that the better structure gradually converges to the global optimum. The particle mass is obtained by mapping the fitness function, so that the feasible domain structure with better performance has a stronger attraction in the search space, thereby driving the system to evolve towards a better control structure.

3. The wind turbine model predictive control method based on convexity and CPSOGSA optimization according to claim 1, characterized in that, Control domain evaluation index in step S4 This reflects the optimal performance of MPC under the current feasible domain structure constraints, and its evaluation function is defined as: in, This represents the discrete time step, i.e., the i-th step in the prediction process. Sampling points This indicates the prediction time domain, i.e., how many steps MPC predicts into the future. Indicates in structural parameters Power tracking error under constraints Indicates in structural parameters Structural load response under constraints Indicates in structural parameters Changes in control input under constraints , , These represent weighting coefficients; all of the above indicators explicitly depend on structural parameters. This dependency is derived from the structured expression of MPC constraints: This constraint indicates that the geometry of the controllable input feasible region is determined by structural parameters. Decision, thereby enabling control input It becomes a function of the structure.

4. The wind turbine model predictive control method based on convexity and CPSOGSA optimization according to claim 1, characterized in that, The time-domain evaluation index in step S4 It is used to characterize the actual response process of a system under disturbance conditions, and is defined as follows: This metric is represented by the time-weighted integral of absolute error, which makes the impact of initial errors greater and the long-term errors continuously penalized. Its essential function is to force the system not only to be well optimized, but also to respond quickly.

5. The wind turbine model predictive control method based on convexity and CPSOGSA optimization according to claim 1, characterized in that, The unified evaluation function in step S4 is used not only for performance evaluation, but also for back-driving the feasible domain geometry parameters. Update, that is: in, Indicates the first The parameters to be optimized in the next iteration This indicates that the search direction is being updated, and the update direction is determined by the performance evaluation function: in, This indicates that the update rule function calculates the next search direction based on the current fitness.

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