Abstract Brushless DC motors are multivariable nonlinear control systems, and fuzzy control is widely used in them. To address the shortcomings of online parameter adjustment in fuzzy controllers, this paper proposes a fuzzy controller based on particle swarm optimization (PSO) to globally optimize the fuzzy controller parameters and apply it to the control of brushless DC motors. The system uses dual closed-loop control for current and speed, with the speed loop employing a PSO-optimized fuzzy controller. Simulation experiments demonstrate online parameter adjustment, and the system achieves good adaptive tracking of a given speed reference model, exhibiting advantages such as flexible control, strong adaptability, high control accuracy, and good robustness. Keywords : Brushless DC motor; Fuzzy control system; Particle swarm optimization algorithm [align=center]Study on the Particle Swarm Optimization Fuzzy Controller Logic in Brushless DC Motor System Li Hong, Wang Fang (Department of Computer and Automation Beijing Institute of Machinery, Beijing 100085) [/align] ABSTRACT The Brushless DC motor is a multi-variable and non-linear system, fuzzy control has been used in the field of the BLDCM control. Due to the shortage of parameters' online adjustment in fuzzy logic controller, a fuzzy logic controller based on particle swarm optimization is presented. Particle swarm optimization is used to optimize three proportional parameters of fuzzy logic controlled and this controller is applied in the control of BLDCM. The system includes current and speed closed loops. Simulation results prove the flexibility of the control system in real Time. Excellent flexibility and adaptability as well as high precision and good robustness are obtained by the proposed strategy. KEY WORDS : brushless DC motor; fuzzy control; particle swarm optimization 1 Introduction Brushless Direct Current Motor (BLDCM) is a mechatronic motor that has matured rapidly in recent years with the development of power electronic devices and new permanent magnet materials. It has the advantages of AC motors such as simple structure, reliable operation and convenient maintenance, as well as DC motors with good speed regulation performance and no mechanical commutator. It is now widely used in servo control systems, medical devices, instruments, robots, home appliances and other fields [1]. Fuzzy control technology is an emerging control technology based on fuzzy control theory. It does not rely on precise mathematical models, is not sensitive to parameter changes, has strong adaptability and good robustness. However, in practical applications, for time-varying parameter nonlinear systems, especially for nonlinear systems such as motor speed regulation, the control rules on which conventional fuzzy control relies lack online self-learning ability and the controller parameters lack self-adjustment ability [2], which makes it difficult to meet control needs. Therefore, by combining fuzzy control with other control strategies, various types of fuzzy controllers can be designed, such as parameter self-adjusting fuzzy controllers, fuzzy-variable structure fuzzy controllers, and adaptive fuzzy controllers [3-5], to overcome the limitations of conventional fuzzy control, further improve accuracy, and adapt to more precise control needs. The Particle Swarm Optimization (PSO) algorithm was proposed by Eberhart and Kennedy in 1995 [6-8]. Similar to genetic algorithms, PSO is also a population-based evolutionary computation method. Since the PSO algorithm does not involve crossover and mutation as in genetic algorithms, it is relatively simple, easy to implement, fast, and efficient. PSO has been widely applied in function optimization, neural network training, fuzzy control systems, and control parameter optimization. This paper proposes a particle swarm optimization (PSO) fuzzy controller for the speed control of brushless DC motors. Specifically, the PSO algorithm is used to optimize the three parameters k_a, k_b, and k_u of the fuzzy controller, enabling real-time tracking of parameter changes with environmental and load variations. This improves the robustness and control performance of the fuzzy controller. Simulation examples are provided at the end of the paper, and the effects are compared with PID control and fuzzy control under the same conditions. 2. Mathematical Model of Brushless DC Motor The back electromotive force of a brushless DC motor exhibits a trapezoidal wave. The three-phase stator windings are connected in a star configuration, and the three-phase windings are completely symmetrical. The motor structure is a surface permanent magnet type, as shown in Figure 1. [align=center] Figure 1: Structure Diagram of Brushless DC Motor[/align] A mathematical model of the brushless DC motor is established using a two-phase star-connected three-phase 6-state as an example. Assuming the magnetic circuit is unsaturated, eddy current and hysteresis losses are ignored, and the three-phase windings are completely symmetrical, the voltage balance equation of the three-phase windings is [9] 3 Particle Swarm Optimization Algorithm Particles learn and update continuously, and eventually fly to the position of the optimal value in the solution space. The search process ends, and the final output is the global optimal value. 4 Fuzzy Control System Based on Particle Swarm Optimization 4.1 Conventional Fuzzy Control System for Brushless DC Motors Although the traditional PID speed control system has advantages such as stability and simple structure, the PID parameters cannot be changed when the parameters of the controlled object change or are affected by nonlinear factors, which cannot meet the requirements of high performance and high precision. This paper uses a dual closed-loop brushless DC motor control system, in which the current loop adopts hysteresis control and the speed loop adopts a fuzzy controller, which can obtain a faster dynamic response than PID control and improve the control performance of the system. A two-dimensional fuzzy controller is designed. The input variables are the error and error change between the motor speed feedback value and the given value. The fuzzy quantity is obtained by fuzzification, and the accurate output quantity is obtained through fuzzy inference, fuzzy decision and defuzzification. Take the speed error and the speed error change rate as input linguistic variables, and the control quantity as output linguistic variables. Quantize both input and output to the interval [-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6], and the corresponding fuzzy subsets are (NB, NM, NS, ZO, PS, PM, PB), and their membership functions all follow a normal distribution. Based on control experience, establish a suitable fuzzy control rule base [9], which can be described by the following 49 fuzzy condition statements: (1) if E=NB and Ec=NB then U=NB (2) if E=NB and Ec=NM then U=NB (3) if E=NB and Ec=NS then U=NM … (49) if E=PB and Ec=PB then U=PB. Perform reasoning operations based on the above fuzzy rules, and use the area bisector method to solve the fuzziness to obtain u. Compared with PID controller, fuzzy control can effectively reduce system error and improve system control performance. It has a good effect on solving the problem that traditional control methods are difficult to make corresponding adjustments quickly when system parameters are time-varying, nonlinear and load changes. 4.2 Fuzzy control system based on particle swarm optimization Conventional fuzzy control technology is widely used in motor control. However, in practical applications, due to the nonlinear system with time-varying parameters, the control rules on which fuzzy control depends are insufficient and the controller parameters lack self-adjustment capability. This requires that the fuzzy control rules or parameters can be automatically adjusted, modified and improved during operation. This paper proposes to use particle swarm optimization algorithm to dynamically adjust the quantization factors k[sub]a[/sub], k[sub]b[/sub] and proportional factor k[sub]u[/sub] of the fuzzy controller to obtain the best control effect. Figure 2 shows the structure of the adaptive fuzzy controller based on particle swarm optimization. During the transient process of motor operation, PSO can update and optimize the three parameters of the fuzzy controller in time. Moreover, the program is simple, with few statements and short running time. The specific process of the algorithm is as follows[11]: The main purpose of using the fitness function is to improve the transient response of the system and reduce overshoot[12]. (3) Particle update: Update the velocity and position of each particle according to equations (7) to (8). (4) End: The number of iterations in the text is 50 generations, with 30 particles per generation. The iteration stops when the maximum number of generations is reached, and the optimal solution is output. Otherwise, go to (2) and continue to search for the optimal solution. [align=center] Figure 2 Adaptive fuzzy control structure based on particle swarm optimization[/align] 4.3 Simulation experiment Simulation experiments were conducted on the system under PID control, conventional fuzzy control and adaptive fuzzy control based on particle swarm optimization. The speed response curves shown in Figure 4 are obtained. Curves 1, 2 and 3 in the figure correspond to PID control, conventional fuzzy control and adaptive fuzzy control, respectively. Figures 5 to 7 correspond to the torque response curves under the three control actions. Figure 8 reflects the process of the fitness value decreasing with the number of search generations during the particle swarm optimization process. Table 1 is a comparison of the performance parameters of the speed response curves under the three control actions. Table 1 Performance parameters of speed response under three control actions Figure 4 Speed ​​response curve at a given speed of 800 RPM Figure 5 Torque response curve under conventional PID control Figure 6 Torque response curve under fuzzy control Figure 7 Torque response curve under particle swarm optimization fuzzy control Figure 8 Curve of fitness value decreasing with search algebra[/align] As can be seen from Table 1 and Figure 4, compared with PID control and basic fuzzy control, the steady-state error of speed response is significantly reduced under the action of adaptive fuzzy control based on particle swarm optimization, the system's settling time is greatly shortened, and the overshoot of starting torque can be effectively suppressed. 5 Conclusion To address the lack of self-adjustment capability of parameters caused by PID and basic fuzzy control strategies, this paper proposes a new brushless DC motor control strategy, namely, using particle swarm optimization to globally optimize the three parameters k[sub]a[/sub], k[sub]b[/sub], and k[sub]u[/sub] of the fuzzy controller, giving full play to the robustness of the fuzzy controller. Simulation experiments were conducted using Matlab tools to test torque and speed variations. The results show that the particle swarm optimization algorithm can automatically optimize and adjust the parameters of the fuzzy controller, greatly shortening the system response time and exhibiting strong robustness. This paper attempts to use the PSO algorithm for parameter optimization of the fuzzy controller. As a new evolutionary calculation method, the PSO algorithm also provides a new approach for the optimization of a large number of nonlinear, nondifferentiable, and multi-peak complex problems. References [1] Zhang Chen. Principles and Applications of DC Brushless Motors [M]. Beijing: Machinery Industry Press, 2004 [2] Kuang Yaocheng, YingYu Tzou. Fuzzy optimization techniques applied to the design of a digital BLDC Servo drive [C]. IEEE Power Electronics Specialists Conference, Australia, 2002 [3] Yang Wenfeng, Sun Shaoyuan. 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