BLDC variable domain fuzzy PID control method and system based on tent chaotic grey wolf optimization

Abstract

The present application relates to the technical field of brushless direct current motor control, and particularly relates to a BLDC variable universe fuzzy PID control method and system based on Tent chaotic grey wolf optimization, which first establishes a second-order equivalent mathematical model of a brushless direct current motor and designs a variable universe fuzzy PID controller, the universe of which can be dynamically adjusted according to errors. The present application proposes a variable universe fuzzy PID compound control strategy based on Tent chaotic grey wolf optimization (CGWO). The CGWO algorithm improved by integrating Tent chaotic initialization, cosine nonlinear convergence factor and optimal solution chaotic disturbance is deeply combined with the controller to realize global collaborative optimization of PID initial parameters and scaling factors, solve the blindness and inefficiency of artificial trial and error, and reasonably schedule motor transient control reserves to achieve collaborative improvement of system fast response, high-precision steady-state tracking and strong anti-interference capability.

Description

Technical Field

[0001] This invention relates to the field of brushless DC motor control technology, and in particular to a BLDC variable universe fuzzy PID control method and system based on Tent chaotic gray wolf optimization. Background Technology

[0002] Brushless DC motor (BLDC) systems inherently possess nonlinear, multivariable coupling, and time-varying parameter characteristics. Traditional linear PID control struggles to simultaneously achieve fast response and zero overshoot control across all operating conditions. While fuzzy PID (FPID) control improves system robustness, the fixed universe of discourse limits the controller's fine-tuning capability during the steady-state error-to-zero phase. Variable universe of discourse fuzzy PID (VUFPID) control, by introducing a scaling factor to dynamically adjust the universe of discourse, theoretically achieves more precise zero steady-state error control. However, its performance is highly dependent on the selection of the scaling factor and initial PID parameters. These parameters are high-dimensional and strongly coupled, making it extremely difficult to find a globally optimal solution through trial and error based on human experience. This becomes the core bottleneck restricting further performance improvements.

[0003] To overcome the challenges of parameter tuning, existing technologies attempt to introduce intelligent optimization algorithms. The closest existing invention patent (publication number: CN117674641A) discloses a method for optimizing the speed control of a brushless DC motor using a variable universe of discourse (VUFPID) fuzzy PID. While this patent recognizes the necessity of parameter optimization for VUFPID and constructs a corresponding optimization framework, its optimization method itself is relatively traditional and fails to fundamentally solve the fundamental problems of optimization algorithms easily getting trapped in local optima and insufficient optimization accuracy in high-dimensional, multi-peak parameter spaces. This means that its optimization process may still fall into suboptimal solutions, and it cannot reliably achieve global collaborative optimization of up to seven key parameters, including the initial PID parameters and the variable universe of discourse scaling factor, thus limiting the improvement in system performance.

[0004] Furthermore, another related prior art (publication number: CN110829904A) attempts to use the standard Grey Wolf Optimization (GWO) algorithm for motor controller parameter optimization. However, the standard GWO algorithm suffers from drawbacks such as uneven population distribution due to random initialization and the potential for loss of population diversity and local optima in the later stages of iteration due to the linear convergence factor strategy. When dealing with parameter optimization of such complex nonlinear systems, its optimization accuracy and reliability are insufficient. More importantly, both CN117674641A and CN110829904A primarily focus on optimizing error indicators at the mathematical level, lacking proactive and rational utilization of the motor system's "transient control reserve" in terms of physical mechanisms. This makes it difficult for the controller to sensitively break steady-state constraints when facing large step starts or sudden heavy loads, failing to achieve an optimal balance between "anti-disturbance stiffness" and speed, resulting in either slow system response or significant speed drops and recovery times under disturbances.

[0005] Therefore, there is a significant gap in existing technologies: advanced variable universe fuzzy control structures lack a powerful, reliable global optimization engine that can avoid local optima for tuning parameters; while existing optimization algorithms either have inherent flaws or fail to deeply integrate with the controller to achieve intelligent adjustment at the physical level. There is an urgent need for an innovative method that can deeply integrate improved global optimization algorithms with variable universe fuzzy PID control and achieve intelligent scheduling of "transient control reserves" to systematically resolve the engineering contradictions between speed, steady-state accuracy, and strong disturbance rejection capability. Summary of the Invention

[0006] The purpose of this invention is to provide a BLDC variable universe fuzzy PID control method and system based on Tent chaotic gray wolf optimization, aiming to solve the problems mentioned in the background art of the poor robustness of traditional PID control, the limited steady-state accuracy of conventional fuzzy control, the difficulty in achieving global optimum by manually tuning variable universe parameters, and the difficulty of reasonably scheduling transient physical reserves during the transition process in the existing brushless DC motor control technology.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a fuzzy PID control method for brushless DC motors based on Tent chaotic gray wolf optimization, comprising the following steps:

[0008] S1. Establish a second-order equivalent mathematical model of the brushless DC motor and obtain the open-loop transfer function from voltage to speed.

[0009] S2. Design a variable universe of discourse fuzzy PID controller. The controller adopts a two-dimensional fuzzy structure, with the input variables being the speed error e and the error change rate ec, and the output variable being the correction amount of the PID parameters. , , And introduce a time-varying scaling factor. and And a coupled output scaling factor to achieve adaptive expansion and contraction of the fuzzy universe of discourse with the error state;

[0010] S3. A Tent chaotic gray wolf optimization algorithm is proposed. The algorithm initializes the population through Tent chaotic mapping, updates the convergence factor using a nonlinear decreasing strategy based on cosine law, and introduces an optimal solution chaotic perturbation mechanism to improve the standard gray wolf optimization algorithm.

[0011] S4. Using the Tent chaotic gray wolf optimization algorithm, the initial parameters of the PID controller of the variable universe of discourse fuzzy PID controller are... and scaling factor parameters Perform global collaborative optimization to obtain the optimal control parameter set P*;

[0012] S5. Deploy the optimal control parameter group P* to the online controller, collect the motor speed in real time, calculate the speed error e and the error change rate ec, dynamically adjust the fuzzy domain according to the scaling factor, and update the PID parameters online through fuzzy inference by looking up the table, and output the control voltage to drive the brushless DC motor to run.

[0013] Preferably, in step S2, the fuzzy inference of the variable universe fuzzy PID controller adopts the Mamdani type, the defuzzification method adopts the centroid method, and the universes of discourse of the input variables e and ec are respectively... and The dynamic universe of discourse at time t is:

[0014] ;

[0015] Among them, the scaling factor and It satisfies duality, monotony, and coordination.

[0016] Preferably, in step S3, the specific improvements to the Tent chaotic gray wolf optimization algorithm include:

[0017] S31. Use Tent chaotic mapping to generate a uniformly distributed chaotic sequence and map it to the range of values ​​of the parameter to be optimized, as the initial position of the gray wolf population.

[0018] S32. The linearly decreasing convergence factor 'a' in the standard gray wolf optimization algorithm is replaced with a nonlinear decreasing strategy based on the cosine law. The update formula is as follows: , where t is the current iteration number and Tmax is the maximum iteration number;

[0019] S33. Introduce an optimal solution chaotic perturbation mechanism. When the change in the optimal fitness value over multiple consecutive generations is less than a set threshold, apply a chaotic perturbation based on the Tent mapping to the current α wolf position to generate new candidate solutions to help the algorithm escape local optima.

[0020] Preferably, in step S4, the fitness function for global collaborative optimization adopts the time-multiplied absolute error integral criterion, and its expression is: ,in For speed tracking error, For overshoot, To minimize the overshoot penalty weights, the Tent chaotic gray wolf optimization algorithm aims to minimize J.

[0021] Preferably, in step S4, the parameter vector to be optimized is ,in The shrinkage limit parameter is input as the scaling factor. The shrinkage sensitivity parameter is input as the stretch factor. The value range of each parameter is as follows: , , , , .

[0022] A brushless DC motor variable universe fuzzy PID control system based on Tent chaotic gray wolf optimization is proposed. The system employs a two-layer decoupled architecture consisting of an offline parameter optimization layer and an online closed-loop control execution layer, including:

[0023] The controlled object module is built based on a second-order equivalent mathematical model of a brushless DC motor;

[0024] The multi-controller parallel comparison module integrates a traditional PID controller, a conventional fuzzy PID controller, an unoptimized variable universe fuzzy PID controller, and the variable universe fuzzy PID controller based on Tent chaotic gray wolf optimization as described in claim 1.

[0025] The Tent Chaotic Grey Wolf Optimization Algorithm module is used to perform offline global parameter optimization and output the optimal control parameter set P*.

[0026] The online closed-loop control execution module is used to load the optimal control parameter set P* and execute real-time closed-loop control, including speed acquisition, error calculation, domain of discourse adjustment, fuzzy inference, and control output.

[0027] The operating condition setting module is used to configure the target speed, load torque, and disturbance application time.

[0028] The results visualization module is used to output and display the system's speed, error, control voltage, phase current, and electromagnetic torque signals.

[0029] Preferably, the Tent chaotic gray wolf optimization algorithm module, the online closed-loop control execution module, the controlled object module, the multi-controller parallel comparison module, the operating condition setting module, and the result visualization module are all implemented in the MATLAB / Simulink simulation platform.

[0030] Preferably, in the online closed-loop control execution module, the fuzzy control logic of the variable universe fuzzy PID controller is implemented by a lookup table method, storing the pre-calculated fuzzy rule table as a two-dimensional array, and directly looking up the corresponding output correction value according to the quantized value of the input variable.

[0031] Preferably, in the controlled object module, the transfer function of the second-order equivalent mathematical model of the brushless DC motor is:

[0032] ,

[0033] Where K_T is the torque coefficient, K_e is the back electromotive force coefficient, L_eq is the equivalent inductance, R_eq is the equivalent resistance, J is the moment of inertia, and B is the viscous friction coefficient.

[0034] Compared with the prior art, the beneficial effects of the present invention are:

[0035] 1. Optimal overall dynamic and static performance, effectively balancing speed and stability: Under a 1000 r / min step command, the rise time of this invention reaches 0.0670 s, which is 26.1% shorter than traditional PID, 13.0% shorter than conventional fuzzy PID (FPID), and 1.5% shorter than unoptimized variable universe of discourse fuzzy PID (VUFPID); the settling time reaches 1.2483 s, which is 9.0% shorter than traditional PID, 2.5% shorter than FPID, and 0.6% shorter than VUFPID; the steady-state error is controlled at 0.0042 r / min, which is 96.7% lower than traditional PID and 57.6% lower than VUFPID. Although the overshoot (17.22%) is slightly higher than FPID (15.29%), it outperforms the other three controllers in terms of overall performance in rise time, settling time, and steady-state accuracy, achieving a good balance between fast response and high-precision steady-state locking.

[0036] 2. Significantly enhanced anti-interference stiffness and outstanding load disturbance suppression capability: Under the condition of a sudden 2 N·m load disturbance during stable operation, the speed drop of this invention is only 226.26 r / min, which is 26.7% less than that of traditional PID, 17.8% less than that of FPID, and 10.8% less than that of VUFPID; the recovery time is only 0.2483 s, which is 33.1% shorter than that of traditional PID, 11.4% shorter than that of FPID, and 2.7% shorter than that of VUFPID. It can quickly establish compensation torque after a sudden load change, effectively suppress speed drop and quickly restore stability, significantly enhancing the robustness of the system under complex disturbances.

[0037] 3. The control logic is physically sound and easy to implement in engineering: The Tent chaotic gray wolf optimization algorithm automatically optimizes the seven key parameters of the controller, avoiding the blindness and inefficiency of manual trial and error; the voltage, current and electromagnetic torque curves output by the algorithm are highly consistent with the physical motion equations of the motor, and the large transient control quantities are reasonable energy scheduling rather than system runaway; all algorithm modules can be implemented based on the MATLAB / Simulink standard library without relying on third-party toolboxes, and the optimized parameters can be directly ported to mainstream embedded controllers such as STM32 and DSP, making it suitable for scenarios with high speed regulation performance requirements such as aerospace, industrial robots, and precision servo systems. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the overall simulation process of the system of this invention.

[0039] Figure 2 This is the top-level structure diagram of the Simulink model of this invention;

[0040] Figure 3 This is a full-process speed response diagram of the four controllers of the present invention;

[0041] Figure 4 This is a magnified view of a portion of the load disturbance in this invention;

[0042] Figure 5 This is the rotational speed error response diagram of the present invention;

[0043] Figure 6 This is a control voltage response diagram of the present invention;

[0044] Figure 7 This is the phase current response diagram of the present invention;

[0045] Figure 8 This is the electromagnetic torque response diagram of the present invention. Detailed Implementation

[0046] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] Please see Figure 1-8 This invention provides a technical solution: a variable universe fuzzy PID control method for brushless DC motors based on Tent chaotic gray wolf optimization. It covers the entire process from system simulation architecture construction, motor mathematical modeling, controller design, intelligent optimization algorithm implementation, offline parameter optimization, online closed-loop control, simulation verification, and engineering deployment. All technical aspects are implemented based on MATLAB / Simulink 2025b standard library modules. Specifically, it includes the following steps:

[0048] Step 1: Building the overall system simulation architecture

[0049] This invention employs a pure simulation verification method, building a complete two-layer decoupled simulation architecture based on MATLAB / Simulink 2025b, consisting of an "offline parameter optimization layer + online closed-loop control execution layer," as shown below. Figure 1 As shown, this architecture places the computationally intensive global optimization process offline in a MATLAB script, while only running lightweight Simulink closed-loop control logic in the online stage. This ensures both the global optimality of the parameters and significantly improves simulation efficiency.

[0050] The core components of the simulation platform include:

[0051] Controlled object model: A simulation module built based on the second-order equivalent mathematical model of a BLDC motor, which fully reproduces the dynamic characteristics of the motor's voltage, current, torque and speed;

[0052] The multi-controller parallel comparison module integrates four controllers: traditional PID, conventional fuzzy PID (FPID), unoptimized variable universe fuzzy PID (VUFPID), and the CGWO-VUFPID proposed in this invention. All controllers are connected to the same motor model to ensure the fairness of the comparison experiment.

[0053] CGWO optimization algorithm module: Implemented through MATLAB scripts, it performs global optimization of key parameters of the controller and automatically transfers the optimal parameters to the Simulink workspace;

[0054] Operating condition setting module: flexibly configures the target speed step value, load torque magnitude, and the timing of applied disturbance;

[0055] Results visualization module: Equipped with a multi-channel Scope oscilloscope, it can output signals such as speed, error, control voltage, phase current, electromagnetic torque and PID online parameters in real time, making it easy to directly observe waveforms and extract performance indicators after operation.

[0056] The sampling period of the simulation system is uniformly set to 1ms, and the total simulation duration is 2s, consistent with the time range of subsequent performance tests. The top-level structure of the model is as follows: Figure 2 As shown, four groups of controllers are connected in parallel to the same BLDC motor equivalent object. The control side is implemented using Simulink standard library modules. Fuzzy control and variable universe logic are completed by combining lookup tables, proportional factors, integrators and saturation elements. The entire process algorithm verification can be completed without additional hardware support.

[0057] Step 2: Construction of the second-order equivalent mathematical model of the BLDC motor

[0058] Before designing the controller, it is necessary to establish an accurate mathematical model of the BLDC motor to provide a theoretical foundation for subsequent control algorithm design and simulation verification. The modeling process is based on reasonable assumptions commonly used in engineering, including complete symmetry of the three-phase stator windings, neglecting magnetic circuit saturation effects, neglecting eddy current losses and cogging effects, and the rotor permanent magnet magnetic field exhibiting a trapezoidal wave distribution. These assumptions have sufficient accuracy under the rated operating conditions of the motor and can significantly simplify the model complexity. Based on the above assumptions, the voltage balance equation of the three-phase stator windings is derived. For a star-connected system without a neutral lead, the sum of the three-phase currents is zero. Therefore, the influence of interphase mutual inductance can be attributed to self-inductance to obtain the equivalent inductance. Equivalent resistance .

[0059] Further derivation of the electromagnetic torque equation and rotor mechanical motion equation reveals that the electromagnetic torque is generated by the interaction between the stator current and the back electromotive force (EMF). Under ideal units, the electromagnetic torque coefficient and the back EMF coefficient are numerically equal. The rotor mechanical motion equation follows Newton's second law, describing the effect of the difference between the electromagnetic torque and the load torque on the rotor angular velocity. A Laplace transform is performed on the voltage and torque equations. Ignoring initial conditions, intermediate current variables are eliminated through algebraic operations, ultimately yielding the open-loop second-order transfer function from voltage to speed.

[0060]

[0061] This model can accurately reflect the dynamic characteristics of BLDC motors during speed regulation.

[0062] The motor simulation parameters used in this embodiment are: rated voltage 24V, stator resistance R=1.5Ω, stator inductance L=0.005H, and moment of inertia J=0.002. The coefficient of viscous friction is 0.001. The back electromotive force coefficient is 0.15. Torque coefficient 0.15 Under a 2 N·m load, the model calculations show that the current required to maintain steady state is approximately 14.03 A and the voltage required is approximately 36.76 V, which is consistent with the actual operating characteristics of the motor.

[0063] Step 3: Design and Implementation of a Variable Universe Fuzzy PID Controller Module

[0064] Based on conventional fuzzy PID controllers, a dynamic universe of discourse scaling mechanism is introduced to resolve the inherent contradiction between control accuracy and response speed under a fixed universe of discourse. The controller adopts a two-dimensional fuzzy structure, with input variables being the speed error e and the error change rate ec, where the speed error e is the difference between the target speed r and the actual speed y, and the error change rate ec is the difference between the error at the current moment and the error at the previous moment; the output variable is PI. , , The final PID parameters of the system are formed by superimposing the initial parameters and the fuzzy correction value, that is... , , .

[0065] Fuzzy inference adopts the Mamdani type, and the defuzzification method uses the centroid method, which has low computational cost and high accuracy. The core idea of ​​variable universe of discourse control is to dynamically adjust the size of the universe of discourse based on the state of the input variables. Let... and Let e ​​and ec be the initial universes of discourse for the error and the rate of change of error, respectively. A time-varying scaling factor is introduced. and Then the dynamic universe of discourse at time t is:

[0066]

[0067] To ensure the stability of the control system, the scaling factor must satisfy mathematical axioms such as duality, monotonicity, and coordination. Specifically, when the error approaches zero, the scaling factor should approach a very small positive number (not zero, to avoid infinite control gain), thereby shrinking the universe of discourse, which is equivalent to amplifying the input signal and improving the control sensitivity in steady state. When the error increases, the scaling factor increases, the universe of discourse expands, preventing variable overflow and reducing gain to reduce overshoot. The input and output variables are divided into seven fuzzy subsets: NB (negative large), NM (negative medium), NS (negative small), ZO (zero), PS (positive small), PM (positive medium), and PB (positive large). Based on engineering experience, 49 fuzzy control rules are established (as shown in Table 1). The core control logic is: when the error is large, increase... To speed up the response; when the error is small, appropriately reduce and increase This eliminates steady-state error and prevents overshoot. The variable universe of discourse mechanism, while keeping the physical rules constant, adjusts the scale of the "ruler" to ensure the rules perform optimally across different error ranges. When building the controller in Simulink, all standard library modules are used. The fuzzy control logic is implemented using a lookup table method, storing the pre-calculated fuzzy rule table as a two-dimensional array. The corresponding output correction is directly looked up based on the quantized value of the input variable. The scaling factor is calculated using a combination of mathematical function and multiplication modules, eliminating the need for a fuzzy logic toolbox and facilitating subsequent porting to embedded platforms.

[0068] Table 1 Fuzzy Control Rule Table

[0069]

[0070] Step 4: Improvement and Implementation of the Tent Chaotic Gray Wolf Optimization (CGWO) Algorithm

[0071] To address the difficulties in manually tuning parameters of fuzzy PID controllers with varying universes of discourse and the challenge of obtaining globally optimal solutions, a gray wolf optimization algorithm based on Tent chaotic mapping is designed for global collaborative optimization of seven key controller parameters. The standard gray wolf optimization algorithm simulates the social hierarchy and predation behavior of a gray wolf population, which is divided into four levels: (Optimal solution) (Suboptimal solution) (Third optimal solution) and (For the remaining individuals), the mathematical model is:

[0072]

[0073] Where X(t) is the current position of the gray wolf at time t, X p (t) represents the position of the alpha wolf at time t, D represents the distance between the current gray wolf and the alpha wolf, and A and C are coefficient vectors. Convergence factor The algorithm decays linearly from 2 to 0 with the number of iterations, but it has the drawbacks of uneven population distribution during random initialization and the tendency to fall into local optima in the later stages of iteration due to loss of population diversity. It cannot guarantee the global optimality of the variable universe of discourse fuzzy PID parameters.

[0074] This invention improves the standard GWO algorithm in three aspects: First, it replaces random initialization with Tent chaotic initialization, and the iterative equation for the Tent mapping is:

[0075]

[0076] By using Tent mapping to generate a uniformly distributed chaotic sequence and mapping it to the range of values ​​of the parameters to be optimized as the initial position of the gray wolf population, the population aggregation problem caused by random initialization is avoided, thus improving the quality of the initial solution. Secondly, the linearly decreasing convergence factor 'a' in the standard GWO is replaced with a nonlinear decreasing strategy based on the cosine law. Where t is the current iteration number, To maximize the number of iterations, this strategy maintains a large convergence factor in the early stages of the algorithm, enhancing global search capabilities, while reducing the convergence factor in the later stages to improve local search accuracy. Finally, an optimal solution chaotic perturbation mechanism is introduced, whereby the change in the optimal fitness value over five consecutive generations is less than... When the algorithm is considered to be trapped in a local optimum, a Tent chaotic perturbation is applied to the current position of the α wolf. This generates new candidate solutions near the current optimal solution, and the fitness value is recalculated, retaining the better solutions to help the algorithm escape the local extremum trap. To comprehensively evaluate the dynamic performance and steady-state accuracy of the control system, this paper selects the Time-in-Absolute Error Integral (ITAE) criterion as the fitness function of the optimization algorithm. The ITAE criterion can impose a larger penalty on the error in the later stage of the transient response, which is beneficial to reducing the settling time and steady-state error.

[0077]

[0078] In the formula For speed tracking error, For overshoot, The overshoot penalty weights are used. The goal of the CGWO algorithm is to minimize... The parameter vector to be optimized is: in: These are the initial proportional, integral, and derivative coefficients of the PID controller; The shrinkage limit parameter, which is the input scaling factor, determines the minimum degree of shrinkage of the universe of discourse; The shrinkage sensitivity parameter, which is the input scaling factor, determines the rate at which the universe of discourse changes with error. , , , , Based on the improved CGWO algorithm, offline global optimization is performed on the seven key parameters of the variable universe fuzzy PID controller, and the optimal parameters are deployed to the online controller to achieve closed-loop control.

[0079] Step 5: Controller parameter offline global optimization and online real-time closed-loop control execution process

[0080] The CGWO algorithm is combined with a variable universe fuzzy PID controller to form an "offline-online" two-layer decoupled architecture. First, the CGWO algorithm is executed in MATLAB, with the population size set to 30, the maximum number of iterations to 50, and the chaotic perturbation threshold set. Overshoot penalty weight =0.1

[0081] The Simulink model of the BLDC motor is loaded, and an initial population is generated through Tent chaos. Fitness is calculated iteratively, the social hierarchy of gray wolves is determined, the position is updated by combining the cosine convergence factor, and chaotic perturbation is applied to the α wolves as needed. Finally, the globally optimal parameter set is output. Then Loaded to the controller, the system sequentially performs speed acquisition, error and error change rate calculation, scaling factor and fuzzy universe of discourse dynamic adjustment, fuzzy inference lookup table, PID parameter update, and control voltage output with a 1ms cycle. The core achieves intelligent physical-level adjustment through a variable universe of discourse mechanism. When starting or suddenly adding load, the universe of discourse expands and the PID parameters increase. It actively calls the transient control reserve of peak voltage of 100V and current of 47.50A, which shortens the rise time by 26.1% compared with traditional PID. When approaching steady state, the universe of discourse shrinks exponentially and the control stiffness increases sharply, which is equivalent to "dynamic electronic braking". The steady-state error is as low as 0.0042r / min. When the load changes suddenly, the compensation torque is quickly established and the speed drop is reduced by 26.7% compared with traditional PID. It achieves a balance between high speed, high precision and strong disturbance rejection.

[0082] Step 6: System simulation verification and multi-dimensional performance analysis

[0083] To fully verify the effectiveness of the control strategy of this invention, two sets of comparative experiments under typical operating conditions were conducted on the built Simulink simulation platform. All controllers used the same motor model and operating condition settings to ensure the comparability of the experimental results. The first set was a 1000 r / min step response experiment, in which a speed step command of 1000 r / min was applied at t=0. The full-range speed response curves of the four controllers are shown below. Figure 3As shown in the figure, it can be clearly seen that traditional PID control has the slowest start-up, the largest overshoot, and a maximum speed of 1208.87 r / min, accompanied by obvious oscillations; under the effect of fuzzy parameter tuning, FPID control significantly shortens the rise time and reduces the overshoot, with a maximum speed of 1152.89 r / min; VUFPID control further shortens the rise time, but due to the non-optimal parameters set manually, the overshoot increases slightly; the CGWO-VUFPID control of this invention has the shortest rise time, only 0.0670s. Although the overshoot is 17.22%, slightly higher than FPID's 15.29%, the settling time is the shortest, only 1.2483s, and the steady-state error is controlled at an extremely low level of 0.0042 r / min, achieving the best balance between speed and stability. The second group is a load disturbance experiment. A 2 N·m load disturbance is suddenly applied when the system is running stably for t=1s. The interval after the 1s load disturbance is amplified to obtain... Figure 4 The difference in anti-interference capabilities is clearly visible in the figure. Traditional PID control exhibits the deepest speed drop, reaching 308.74 r / min, with the longest recovery time of 0.3714 s. FPID and VUFPID control show progressively smaller speed drops, at 275.25 r / min and 253.54 r / min respectively, with recovery times of 0.2803 s and 0.2553 s respectively. The CGWO-VUFPID control of this invention demonstrates the strongest anti-interference stiffness, with a speed drop of only 226.26 r / min and a recovery time of only 0.2483 s, enabling rapid recovery and re-locking of the target speed after a sudden load change. Further analysis of the control quantity and parameter change curves provides a deeper understanding of the control mechanism of this invention. The speed error response curve is shown in the figure. Figure 5 As shown, the initial error of all four controllers at startup is approximately 104.72 rad / s (corresponding to a speed difference of 1000 r / min). The CGWO-VUFPID controller exhibits the fastest error convergence speed and the smallest error fluctuation in the steady-state phase. The control voltage response curve is shown below. Figure 6 As shown, the maximum output voltage during the startup phase of traditional PID control is only 43.98V, while the peak control voltage of CGWO-VUFPID reaches 100V, significantly higher than the 36.76V required for steady-state operation. This demonstrates the controller's proactive use of transient control reserves. The phase current response curve is shown below. Figure 7 As shown, consistent with the trend of control voltage changes, the peak current of the CGWO-VUFPID reaches 47.50A, far exceeding the 14.03A required for steady-state operation, providing sufficient power for rapid response; the electromagnetic torque response curve is shown below. Figure 8As shown, the maximum electromagnetic torque of CGWO-VUFPID reaches 7.13 N·m, which is basically in phase with the current curve. It can quickly establish compensation torque after load change and suppress speed drop. The detailed performance index comparison of the four controllers is shown in Table 2. The data shows that the control strategy of this invention is superior to the other three control methods in key indicators such as rise time, settling time, anti-disturbance drop and recovery time, and has the best overall performance.

[0084] Table 2 Comparison of Performance Indicators of Four Controller Groups

[0085]

[0086] Step 7: Simulation Result Analysis and Algorithm Optimization Direction

[0087] Based on the simulation results above, a comprehensive analysis of the performance of the control strategy of this invention is conducted. This invention successfully achieves intelligent scheduling and adaptive virtual stiffness adjustment of the motor's transient control reserve by globally and collaboratively optimizing the key parameters of the variable universe fuzzy PID using the Tent chaotic gray wolf optimization algorithm, effectively solving the problem of the mutual exclusion between speed and stability in traditional control. Furthermore, regarding the issue of slightly higher overshoot than conventional fuzzy PID found in the simulation, this can be addressed by adjusting the overshoot penalty weight in the fitness function. Further optimization, when When the parameters are increased, the algorithm tends to select parameter combinations with smaller overshoot, thereby reducing the overshoot to some extent. However, this may sacrifice some rise time and disturbance rejection performance. A trade-off adjustment can be made based on the specific application requirements. Furthermore, this simulation uses an ideal second-order equivalent motor model. Further nonlinear factors such as magnetic circuit saturation, cogging torque, and time-varying parameters can be introduced to verify the algorithm's robustness under more complex operating conditions.

[0088] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A BLDC variable universe fuzzy PID control method based on Tent chaotic gray wolf optimization, characterized in that, Includes the following steps: S1. Establish a second-order equivalent mathematical model of the brushless DC motor and obtain the open-loop transfer function from voltage to speed. S2. Design a variable universe of discourse fuzzy PID controller. The controller adopts a two-dimensional fuzzy structure, with the input variables being the speed error e and the error change rate ec, and the output variable being the correction amount of the PID parameters. , , And introduce a time-varying scaling factor. and And a coupled output scaling factor to achieve adaptive expansion and contraction of the fuzzy universe of discourse with the error state; S3. A Tent chaotic gray wolf optimization algorithm is proposed. The algorithm initializes the population through Tent chaotic mapping, updates the convergence factor using a nonlinear decreasing strategy based on cosine law, and introduces an optimal solution chaotic perturbation mechanism to improve the standard gray wolf optimization algorithm. S4. Using the Tent chaotic gray wolf optimization algorithm, the initial parameters of the PID controller of the variable universe of discourse fuzzy PID controller are... and scaling factor parameters Perform global collaborative optimization to obtain the optimal control parameter set P*; S5. Deploy the optimal control parameter group P* to the online controller, collect the motor speed in real time, calculate the speed error e and the error change rate ec, dynamically adjust the fuzzy domain according to the scaling factor, and update the PID parameters online through fuzzy inference by looking up the table, and output the control voltage to drive the brushless DC motor to run.

2. The BLDC variable universe fuzzy PID control method based on Tent chaotic gray wolf optimization according to claim 1, characterized in that, In step S2, the fuzzy inference of the variable universe of discourse fuzzy PID controller adopts the Mamdani type, and the centroid method is used for defuzzification. The universes of discourse of the input variables e and ec are respectively... and The dynamic universe of discourse at time t is: ； Among them, the scaling factor and It satisfies duality, monotony, and coordination.

3. The BLDC variable universe fuzzy PID control method based on Tent chaotic gray wolf optimization according to claim 1, characterized in that, In step S3, the specific improvements to the Tent chaotic gray wolf optimization algorithm include: S31. Use Tent chaotic mapping to generate a uniformly distributed chaotic sequence and map it to the range of values ​​of the parameter to be optimized, as the initial position of the gray wolf population. S32. The linearly decreasing convergence factor 'a' in the standard gray wolf optimization algorithm is replaced with a nonlinear decreasing strategy based on the cosine law. The update formula is as follows: , where t is the current iteration number and Tmax is the maximum iteration number; S33. Introduce an optimal solution chaotic perturbation mechanism. When the change in the optimal fitness value over multiple consecutive generations is less than a set threshold, apply a chaotic perturbation based on the Tent mapping to the current α wolf position to generate new candidate solutions to help the algorithm escape local optima.

4. The BLDC variable universe fuzzy PID control method based on Tent chaotic gray wolf optimization according to claim 1, characterized in that, In step S4, the fitness function for global collaborative optimization adopts the time-multiplied absolute error integral criterion, and its expression is: ,in For speed tracking error, For overshoot, To minimize the overshoot penalty weights, the Tent chaotic gray wolf optimization algorithm aims to minimize J.

5. The BLDC variable universe fuzzy PID control method based on Tent chaotic gray wolf optimization according to claim 1, characterized in that, In step S4, the parameter vector to be optimized is ,in The shrinkage limit parameter is input as the scaling factor. The shrinkage sensitivity parameter is input as the stretch factor. The value range of each parameter is as follows: , , , , .

6. A BLDC variable universe fuzzy PID control system based on Tent chaotic gray wolf optimization, as described in any one of claims 1-5, characterized in that... The system adopts a two-layer decoupled architecture consisting of an offline parameter optimization layer and an online closed-loop control execution layer, including: The controlled object module is built based on a second-order equivalent mathematical model of a brushless DC motor; The multi-controller parallel comparison module integrates a traditional PID controller, a conventional fuzzy PID controller, an unoptimized variable universe fuzzy PID controller, and the variable universe fuzzy PID controller based on Tent chaotic gray wolf optimization as described in claim 1. The Tent Chaotic Grey Wolf Optimization Algorithm module is used to perform offline global parameter optimization and output the optimal control parameter set P*. The online closed-loop control execution module is used to load the optimal control parameter set P* and execute real-time closed-loop control, including speed acquisition, error calculation, domain of discourse adjustment, fuzzy inference, and control output. The operating condition setting module is used to configure the target speed, load torque, and disturbance application time. The results visualization module is used to output and display the system's speed, error, control voltage, phase current, and electromagnetic torque signals.

7. The BLDC variable universe fuzzy PID control system based on Tent chaotic gray wolf optimization according to claim 6, characterized in that, The Tent chaotic gray wolf optimization algorithm module, the online closed-loop control execution module, the controlled object module, the multi-controller parallel comparison module, the operating condition setting module, and the result visualization module are all implemented in the MATLAB / Simulink simulation platform.

8. The BLDC variable universe fuzzy PID control system based on Tent chaotic gray wolf optimization according to claim 6, characterized in that, In the online closed-loop control execution module, the fuzzy control logic of the variable universe fuzzy PID controller is implemented by a lookup table method. The pre-calculated fuzzy rule table is stored as a two-dimensional array, and the corresponding output correction value is directly looked up based on the quantized value of the input variable.

9. The BLDC variable universe fuzzy PID control system based on Tent chaotic gray wolf optimization according to claim 6, characterized in that, In the controlled object module, the transfer function of the second-order equivalent mathematical model of the brushless DC motor is: ， Where K_T is the torque coefficient, K_e is the back electromotive force coefficient, L_eq is the equivalent inductance, R_eq is the equivalent resistance, J is the moment of inertia, and B is the viscous friction coefficient.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the brushless DC motor variable universe fuzzy PID control method based on Tent chaotic gray wolf optimization as described in any one of claims 1 to 5.

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