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Simulation of a brushless DC motor system based on piecewise current control

2026-04-06 05:13:18 · · #1
Brushless DC motors have been increasingly widely used due to their small size, simple structure, high reliability, large output torque, and good dynamic performance. Due to the torque ripple generated by the characteristics of the BLDCM itself, the accuracy of its control is greatly reduced. At the same time, the application of switching transistors and microprocessors also increases the cost of the BLDCM system. Therefore, people have long been concerned about how to improve the control performance of BLDCM and reduce the system cost, and have tried to achieve a balance between the two in engineering practice. Reference [1] proposes a current model digital control method for BLDCM, which avoids the large amount of calculation of traditional digital control methods, thereby reducing the difficulty and cost of engineering implementation. It is also more suitable for embedding this digital control strategy in large-scale integrated circuits and has a wide application prospect in fields where the control accuracy requirement is not high. Current model digital control regards the BLDCM as a pure digital system. By comparing the actual speed and the given speed, a suitable state is selected to achieve the purpose of controlling the speed or torque. If the speed range is too large, the speed ripple will inevitably increase, and the performance of the system will be affected. By dividing the speed range into n segments and increasing the speed sampling frequency, the speed fluctuation can be effectively reduced, and a better control effect can be achieved. This improved current control, in addition to retaining the advantages of the original control method, also boasts higher control accuracy. Overview of Current Model Digital Control Current model digital control treats the BLDCM as a digital system with only two preset states. State-1 (s-1) and State-2 (s-2) represent the high and low levels of the system, respectively, with the phase current being the system's state variable. The effect of s-1 (corresponding to phase current ih) on the system is the maximum speed ωh, and the effect of s-2 (corresponding to phase current il) on the system is the minimum speed ωl. The actual speed ω is compared with the given speed ω* (compared to ωl<ω*<ωh) and the appropriate state is selected: when ω<ω*, s-1 is selected. When ω>ω*, s-2 is selected. [align=center] Figure 1 Schematic diagram of the current model digital control strategy system[/align] As shown in Figure 1, the digital controller determines the state that the system should be in according to the relationship between the actual speed and the given speed in each sampling period and selects the corresponding phase current value. The current hysteresis controller controls the gate drive signal output according to the value of the state variable (phase current), and then controls the commutation circuit so that the main circuit reaches the corresponding phase current value. The electromagnetic torque of bldcm [2,3] is: (1) Where te is the electromagnetic torque, ea, eb, ec are the back electromotive forces of a, b, c, ia, ib, ic are the phase currents of a, b, c, and kt is the electromagnetic torque constant. When the current model digital controller selects different states, the corresponding bldcm phase current value also changes. As can be seen from equation (1), the electromagnetic torque generated also changes accordingly, and the speed of the motor also changes. The relationship between phase current state switching and speed is shown in Figure 2. [align=center] Figure 2 Schematic diagram of the relationship between phase current state switching and speed[/align] In Figure 2, the speed sampling frequency of the current model digital controller is ω/2π, that is, the motor speed is sampled once for one revolution of bldcm, and the period is t=t1-t0. At time t1, the actual speed ω>ω*, and the digital controller switches the system from state s-1 to state s-2. The phase current changes from ih to il, and the speed begins to decrease. Let: ω=ωmax at t=t1 ω=ω'max at t=t'1 If the speed sampling period becomes t'=t'1-t0, the system state switches at t=t'1. As can be seen from Figure 2, ωmax>ω'max, that is, the speed fluctuation decreases when the speed sampling frequency increases. The kinematic formula for the design and parameter setting of the digital controller bldcm is: te-tl-bω= (2) where te is the electromagnetic torque, tl is the load torque, b is the damping coefficient, ω is the mechanical angular velocity of the motor, and j is the moment of inertia. In steady state, from equation (2), we can get: te-tl-bω=0 (3) From equations (1) and (3), we can get the relationship between the speed and the current as: (4) From equation (4), we can know that when the load torque tl is constant, the steady-state speed generated by different current values ​​is different; when the current is is constant, the steady-state current corresponding to different load torques is also different. When i=ih: (5) When i=il: (6) From equations (5) and (6), we can get: δω=ωh-ωl∝ih-il (7) From equation (7), we can know that the speed range is proportional to the current range. As the speed range increases, the difference between ih and il also increases. As discussed above, increasing the sampling frequency of the current control speed reduces the speed fluctuation. This requires the system to switch from ih to il in a very short time. If the speed range is large, the difference between ih and il will be large. Due to the presence of inductance in the bldcm system, it is difficult to achieve a large phase current switching in a very short time. Therefore, in order to ensure the speed range requirement, segmented current control is adopted [4]. The entire speed range is divided into n segments, so that the difference between inh and inl in the nth speed range is small enough to achieve current switching. Using the speed ω as a variable to represent the current value i, equation (4) can be written as: (8) From equation (8), it can be seen that in the range of ωnl-ωnh, when ω=ωnh and the load torque tl takes the maximum value tlmsx, is takes the maximum value inh in this range. Meanwhile, due to factors such as errors in the bldcm system parameters, a certain margin a is taken, then inh is: (9) Similarly, when ω=ωnl and the load torque tl takes the minimum value tlmin, is takes the minimum value inl: (10) The numerical controller parameters need to be set reasonably according to the design requirements and brushless DC motor system parameters. When the difference between the highest and lowest current values ​​in the nth segment of segmented current control is large, the difference can be adjusted by adjusting the size of the speed segment to meet the design requirements. The specific process is shown in Figure 2: [align=center] Figure 3 Schematic diagram of controller parameter design process[/align] Conclusion Compared with the traditional digital control method, the current model digital control of brushless DC motor reduces the difficulty and cost of engineering implementation, but the speed fluctuation is large, which limits its application range. Segmented current control solves this problem well without increasing its engineering difficulty, and simulation experiments prove that the scheme is effective. However, the load range of segmented current control is too small, which limits its application in a wider range of fields.
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