Abstract: This paper first establishes a simulation model of an asynchronous motor vector control system based on rotor field orientation. To further improve the speed regulation performance of the system, a fuzzy adaptive PI controller is constructed based on the fuzzy control principle on the basis of a conventional PI controller. A fuzzy adaptive PI speed controller is designed using the fuzzy logic control toolbox in MATLAB. Simulations of the system using two different speed controllers are performed in the Simulink environment, and the results are compared. Simulation results show that the fuzzy adaptive PI speed controller has the characteristics of fast response and small overshoot. Keywords: asynchronous motor; vector control; fuzzy adaptive speed regulator[b][align=center]The Research of induction Motor Vector Control System Based on Fuzzy Self-adaptive Speed ​​Controller CHEN Shuang, DUAN Guo-yan, SUN Cong-jun[/align][/b] Abstract: This paper build a simulation model of induction motor vector control system which based on the rotor magnetic-chain direction method. In order to improve the performance of the system, a new fuzzy self-adaptive PI speed controller was presented on the basic of the conventional PI speed controller. Also, we designed a fuzzy self-adaptive speed controller using Fuzzy Logic Toolbox in MATLAB, and did a comparison of the performance of the two controllers in the environment of Simulink. The simulation result indicated that, the latter has the high performance of fast response and small over shoot. Keywords: Induction Motor; Vector Control; Fuzzy Self-adaptive Speed ​​Controller 1 Introduction The mathematical model of an AC asynchronous motor is a high-order, multivariable, and strongly coupled nonlinear system. Only with the introduction of vector control algorithms based on coordinate transformation could the speed regulation performance of AC asynchronous motors rival that of DC motors. However, the decoupling effect of coordinate transformation does not change the fundamental nature of the asynchronous motor as a high-order, multivariable, and nonlinear system; vector control based on the motor's mathematical model is still affected by changes in motor parameters. To address the drawback of the controller's over-reliance on the controlled object's parameters, we introduce fuzzy control theory into the motor's speed control. Fuzzy control is characterized by its independence from the precise mathematical model of the controlled object, ease of utilizing expert experience, and strong adaptability and robustness, effectively overcoming changes in the speed regulation system model and environmental parameters. However, pure fuzzy control suffers from steady-state errors and is prone to jitter in steady state. To solve this problem, fuzzy control theory is introduced to tune the parameters of the PI controller online, thus forming a fuzzy adaptive PI regulator. 2. Simulation Model of Asynchronous Motor Vector Control System Oriented by Rotor Magnetic Field By employing the modern control theory concepts of parameter reconstruction and state reconstruction, the excitation component and torque component of the stator current of the asynchronous motor can be decoupled, realizing the equivalent of the control process of an AC motor to that of a DC motor. Based on the basic principles of vector control, we established a simulation model of an asynchronous motor vector control system oriented by rotor magnetic field, the structure of which is shown in Figure 1. [align=center] Figure 1 Simulation Model of Asynchronous Motor Vector Control System Oriented by Rotor Magnetic Field [/align] This system is divided into a speed control subsystem and a flux linkage control subsystem. The speed control subsystem is similar to a DC speed regulation system, adopting a cascade control structure. A speed regulator (ASR) is set in the speed control subsystem, and the speed feedback signal is taken from the speed sensor on the motor shaft. The output Tei of the speed regulator serves as the setpoint for the inner-loop torque regulator ATR. The torque feedback signal is taken from the rotor flux observation. The purpose of setting up a torque closed loop is to reduce or eliminate the inertial coupling between the two channels. Furthermore, from a closed-loop perspective, any change in flux is equivalent to a disturbance to the inner torque loop, which will inevitably be suppressed by the torque closed loop, thereby reducing or avoiding the impact of sudden flux changes on torque. In the flux control subsystem, a flux regulator is included; its input is externally provided, and the flux feedback signal comes from the flux observation. Fuzzy Adaptive PI Controller 1) Structure of Fuzzy Adaptive PI Controller The fuzzy adaptive PI controller takes error e and error change ec as input, and Kp and Ki or their increments ΔKp and ΔKi as output. It uses fuzzy control rules to adjust the PI parameters online. Its structure is shown in the figure: [align=center] Figure 2 Structure of Fuzzy Adaptive PI Controller[/align] 2) Control Rules of Fuzzy Adaptive PI Controller The function of the fuzzy adaptive PI controller is to find the fuzzy relationship between Kp, Ki and e and ec. By continuously detecting e and ec, Kp and Ki are adjusted according to the fuzzy control principle, so that the controlled object has good dynamic and static performance. Considering the stability, response speed, overshoot and steady-state accuracy of the system, the functions of Kp and Ki are as follows: (1) The function of proportional coefficient Kp is to speed up the response speed of the system and improve the adjustment accuracy of the system. The larger Kp is, the faster the system response speed and the higher the adjustment accuracy, but it is easy to generate overshoot. If the value of Kp is too small, the adjustment accuracy will be reduced, the response speed will be slow, and the adjustment time will be prolonged. (2) The integral coefficient Ki is used to eliminate the steady-state error of the system. The larger Ki is, the faster the steady-state error of the system is eliminated. However, an excessively large Ki will cause integral saturation in the early stage of the response, resulting in a large overshoot in the response process. If Ki is too small, the static error will be difficult to eliminate, affecting the adjustment accuracy of the system. In order to compare with the conventional PI controller, the increments of the PI controller parameters ΔKp and ΔKi are selected as the outputs of the fuzzy controller. Let the error e and the error change ec, as well as the fuzzy subsets of ΔKp and ΔKi, be {NB, NM, NS, ZO, PS, PM, PB}, where the elements represent negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively. Let the universe of discourse of the fuzzy subsets be {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}. Based on practical experience and expert knowledge, establish fuzzy rule tables between ΔKp, ΔKi, e, and ec, as shown in Tables 1 and 2: [align=center]Table 1: Fuzzy rule table for ΔKp Table 2: Fuzzy rule table for ΔKi[/align] 3) Determination of quantization factor and scaling factor The input error e, error change ec, and output control quantity u of the fuzzy controller are all continuously changing precise quantities, so they are first discretized. If the actual range of the precise quantity is [-x, x], and the universe of discourse of the fuzzy subset is [-n, n], then the quantization factor of the error Ke = n/x, the quantization factor of the error change Kc = n/x, and the scaling factor of the output control quantity Ku = x/n. In this system, the given speed wr* is 100 rad/s. The control task is to control the motor speed near the given value, with an allowable error range of no more than 3%. Therefore, the fundamental universe of discourse for the error is [-3, 3], and the quantization factor of the error e is Ke = 6/3 = 2. Assuming the allowable range for the rate of change of error is no more than 5% of the error, the fundamental universe of discourse for the error change ec is [-0.15, 0.15], and its quantization factor Kec = 6/0.15 = 40. We want the adjustment range of ΔKp and ΔKi to be no more than 5% of the tuned parameters. Therefore, the fundamental universe of discourse for ΔKp is [-0.2, 0.2], and its scaling factor Kup = 0.2/6 = 1/30; the fundamental universe of discourse for ΔKi is [-1, 1], and its scaling factor Kui = 1/6. 4) Establishing a Fuzzy Controller: Matlab provides a rich toolbox, including the Fuzzy Logic Toolbox for establishing fuzzy controllers. Typing the `fuzzy` command in the Matlab command window will enter the fuzzy controller editing window. Establish a two-dimensional fuzzy controller with inputs `e` and `ec`, and outputs `ΔKp` and `ΔKi`. Based on the analysis above, input the quantization intervals for `e`, `ec`, `ΔKp`, and `ΔKi`, and select appropriate membership functions. Various options are available, including triangular, trapezoidal, Z-shaped, and S-shaped functions, none of which significantly affect the results. Here, a symmetrical triangular function is chosen. Input the fuzzy control rules according to the fuzzy control rule table, using the `if…then…` format. Rule 1: If (e is NB) and (ec is NB) then (ΔKp is PB) (ΔKi is NB) Rule 2: If (e is NB) and (ec is NM) then (ΔKp is PB) (ΔKi is NB) ┋ Rule 49: If (e is PB) and (ec is PB) then (ΔKp is NB) (ΔKi is PB) Select the controller type as Mamdani, the AND method as min, the OR method as max, the Iimplication method as min, the Aggregatin method as max, and the Defuzzification method as centroid. After the fuzzy controller design is completed, save it as a safc.fis file. 3. Establishment and comparison of two speed regulators 1) Conventional PI speed regulator model In the previous simulation system, we established a PI speed regulator with a speed setpoint of 100 rad/s. The given value of the output torque is obtained by PI regulation of the speed error signal. Through repeated adjustments, when Kp=4 and Ki=20, the asynchronous motor exhibits good dynamic and static performance. The model of the conventional PI speed regulator is shown in Figure 3: [align=center] Figure 3 Conventional PI Speed ​​Regulator[/align] 2) Fuzzy Adaptive PI Regulator Model According to the previous analysis, the parameters of the tuned fuzzy adaptive PI speed regulator are obtained by the following formula: Kp=Kp'+ΔKp Ki=Ki'+ΔKi Where Kp' and Ki' are the parameters of the tuned conventional PI regulator, and Kp and Ki are the parameters of the fuzzy adaptive PI regulator, which will directly act on the controlled object. In the Simulink menu, select the Fuzzy logic controller module in the Fuzzy Logic Toolbox and build the fuzzy adaptive PI speed regulator in Simulink according to the method analyzed above and the determined parameters, as shown in Figure 4. In the MATLAB command window, enter the command `matrix=readfis('safc.fis')` to obtain the information of the fuzzy controller. Double-click the Fuzzy Logic Controller module and enter `matrix` to establish the connection between the fuzzy controller and Simulink. [align=center] Figure 4 Fuzzy Adaptive PI Speed ​​Regulator[/align] 4 Simulation Results The asynchronous motor vector control system shown in Figure 1 was simulated and compared using a conventional PI speed regulator and an adaptive fuzzy PI speed regulator. The parameters of the simulated motor were: Pe=3.7kW, Rs=1.5Ω, Rr=2Ω, Ls=20mH, Lr=30mH, Lm=0.85H, J=0.1kg.m2, np=2. Figure 5 shows the speed and torque response curves at a given speed of 100rad/s. The simulation results show that the system using the fuzzy adaptive PI speed regulator has significant advantages such as fast response speed and small overshoot. [align=center]Figure 5 Comparison of simulation results when wr*=100rad/s[/align] 5 Conclusion This paper tunes the parameters of a conventional PI speed regulator, resulting in superior dynamic and static performance. To further improve the system's response speed and steady-state accuracy, a fuzzy adaptive PI speed regulator is introduced into the asynchronous motor vector control system. The parameters of the PI speed regulator are adjusted online in real time based on the speed error and the rate of change of the speed error. Simulation results show that the fuzzy adaptive PI speed regulator enhances the adaptive capability of the system's speed regulation, has a small overshoot, and a fast response speed, significantly improving the system's dynamic and static performance. References [1] Zhang Jing et al. Application of MATLAB in Control Systems [M]. Beijing: Electronic Industry Press, 2007. [2] Li Shiyong. Fuzzy Control - Neural Control and Intelligent Control Theory [M]. Harbin: Harbin Institute of Technology Press, 1998. [3] Li Huade. AC Speed ​​Control System [M]. Beijing: Electronic Industry Press, 2003. [4] Rajani K. Mudi, Nikhil R. Pal. A self-tuning fuzzy PI controller [J], Fuzzy Sets and Systems (2000) 327-338. [5] Zhou Zhen, Wan Shuyun et al. Application of fuzzy control in sensorless AC speed control system [J]. Ordnance Automation, 1999, 20(2), 1-4.