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Torque ripple control system for switched reluctance motor based on microstepping drive

2026-04-06 06:00:49 · · #1
1 Introduction In recent years, the requirements for various speeds in the field of servo application systems have increased people's interest in switched reluctance motors (SRMs). The main reason is that SRMs have advantages such as simple structure, low cost, reliable operation, large low-speed torque, simple power conversion circuit, flexible control mode and high efficiency. Although SRMs have developed greatly in the past few years, there are still some problems to be studied. For example, compared with general motors, their torque pulsation is more obvious, which limits their application in servo drive systems. In order to enable SRMs to play their inherent advantages in the servo field, it is of great significance to study how to effectively suppress the low-speed torque pulsation of SRMs. In this regard, scholars from various countries have done a lot of research. Some people have proposed to optimize the structural design of the motor according to the static characteristics of generating an approximately sinusoidal torque/angle during saturation operation, and to use a servo motor controller to generate a sinusoidal desired current/angle distribution to weaken the instantaneous torque pulsation. Reference [1] adopts a fuzzy adaptive emerging SRM control scheme, and the fuzzy parameters are adjusted from the initial free selection to the final optimal. Reference [2] uses a local approximation neural network to learn the desired current waveform online, thereby minimizing torque ripple. However, the above method has not been widely applied in practice, mainly because its control scheme is complex and difficult to control in real time. In this paper, by referring to the stepper motor microstepping drive technology and combining the analysis of SRM torque-angle characteristics, the control strategy of this paper is provided with a theoretical basis, and the effectiveness of the control strategy is verified in the experiment, achieving the experimental purpose, effectively reducing torque ripple, and greatly reducing noise. 2 Principle of differential drive In the drive control of stepper motor, the current in the motor winding is subdivided according to each equilibrium position, and the conventional rectangular wave power supply is changed to a stepped wave power supply. The current in the winding rises to the rated value through several steps or falls to zero from the rated value through several steps. After subdivision, the change amplitude of the drive current is greatly reduced. Therefore, the excess energy when the rotor reaches the equilibrium position is also greatly reduced; on the other hand, the frequency of the control signal is increased by N times (subdivision number), so it can be far away from the low frequency resonance frequency of the rotor. Therefore, microstepping not only makes the motor run smoothly, but also reduces or eliminates low-frequency noise caused by oscillations. As can be seen from the above, microstepping in a stepper motor essentially replaces the direct switching of winding currents during current switching between different phases. For a microstepping motor (SRM), its working principle is similar to that of a large-angle stepper motor. The stator magnetomotive force moves in space at a large step angle. Therefore, we consider whether the idea of ​​microstepping in stepper motors can be applied to SRM driving. During commutation, the winding current can be subdivided to make the current through the winding change stepwise. By controlling the magnitude of the current in each phase, the winding torque vector can be kept basically constant at each equilibrium position of the rotor, thus reducing torque ripple. 3. SRM Torque Vector Control Principle In the SRM torque-angle characteristic analysis, if the influence of nonlinear factors in the magnetic circuit is ignored, the electromagnetic torque can be expressed as: Where: L0 and L1 are the amplitudes of the constant component and fundamental component of the self-inductance, respectively, and can be considered constants. Nr is the number of teeth of the SRM rotor. From (1) and (2), we can get: T(θ,i)=-Tmax*sin (Nrθ)……………………(3) Therefore, the fundamental electromagnetic torque generated by each phase winding is a spatial sine wave, and the stable zero position depends on the position of the magnetic pole center line of that phase. The electromagnetic torque is a function of the rotor position θ and the phase current. Therefore, the electromagnetic torque of the A-phase winding can be represented by the spatial vector TA, and its phase is consistent with the magnetic pole center line of the A-phase winding. In the step motion analysis of the switched reluctance motor, the rotating magnetic field torque vector diagram can make the analysis more intuitive. In the analysis of this paper, the (8/6) four-phase SR motor is taken as an example, as shown in Figure 1. [align=center] Figure 1 SRM rotating magnetic field torque vector[/align] For the (8/6) four-phase SR motor, the stable zero position generated by the A-phase winding and the stable zero position generated by the B-phase winding are offset by a step angle, which is 15 degrees in space geometrically, or 90 degrees in electrical angle. If the rotor is defined as rotating clockwise as forward rotation, then as long as the windings of each phase are supplied in the order of ABCD, the rotor of the switched reluctance motor will rotate forward step by step at a step angle of 15 degrees. Assuming that the mutual inductance of the motor is ignored, the torques are allowed to be vectored together, which yields the rotating magnetic field torque vector shown in Figure 1. Among them, TAB, TBC, TCA and TAD are called derived torque vectors, representing the combined torque of two phases supplied at the same time; TA, TB, TC and TD are called basic torque vectors. Their phases depend on the spatial position of the stator magnetic pole center line, representing the torque when one phase is supplied alone. The two adjacent torques are staggered by a step angle of 3.75 degrees. The relationship between the derived torque and the basic torque can be expressed as the following vector form: Tab=Ta+Tb…………………………(4) The phase of the derived torque vector can be adjusted by controlling the amplitude of the winding current, so that it appears at any phase between the basic torque vectors. By controlling the winding current, the number of steps per revolution of the SRM can be increased, the resolution can be improved, and the torque pulsation can be reduced. As the number of microsteps per revolution of the motor increases, the best discrete current waveform to choose from is a sine function waveform. If the current of each phase winding can be controlled to be a sine wave, then the continuous control of SRM can be realized. 4 Implementation of differential drive in SRM control system From the above analysis of the torque control principle of (8/6) SRM, it can be seen that the core of microstep drive of switched reluctance motor is to realize that the torque vector amplitude is equal, and to control the phase winding current to follow the given current magnitude corresponding to the given speed, so that the real-time speed is kept within the given speed error range, thereby effectively reducing the torque pulsation. The current of the two phase windings that are simultaneously conducting can be expressed as the following formula, where is the current magnitude corresponding to the composite vector: ia=Im*cosθ; ib=Im*sinθ ; ………………………………………(5) Then the composite current vector i (with ia as reference): i is a vector with Im as amplitude and -θ as argument. Thus, as shown in equations (1) and (6), whenever the value of θ changes, the synthesized vector rotates through a corresponding angle while maintaining its magnitude, achieving constant torque subdivision drive. Equation (5) can be used to obtain the subdivision phase current data. Therefore, to control the torque, the current must be controlled, and controlling the current involves using the power switching signal whose output pulse width of the PWM power converter is modulated as the direct control quantity, causing the actual output current to change according to a stepped current pattern. Therefore, the differential drive of the SRM relies on controlling the duty cycle of the PWM. The duty cycle of the PWM signal applied to the conducting phase winding is expressed by the following formula: Ya = Y * cosθ; Yb = Y * sinθ;……………………………………(7) In the above formula: Y is the duty cycle amplitude; Ya and Yb are the components of Y in the energized phase winding, respectively; θ is the torque angle; The duty cycle amplitude Y in formula (7) and the given speed in the speed closed loop are linearly correlated by quantization: Y = k * n; k is the proportional coefficient; Therefore, under the premise of the given speed, the duty cycle amplitude Y remains constant. As can be seen from formula (7), the duty cycle components of each phase PWM pulse width can be controlled by adjusting the torque angle at a specific equilibrium position. According to the correspondence between formula (5) and formula (7), the magnitude of the conducting phase current is controlled by the change in the magnitude of the duty cycle components of each phase. (8/6) The four-phase SRM rotor pole pitch angle (period) is 60 degrees, and the step angle of each phase is 15 degrees. Therefore, the behavior of differential drive is to subdivide the 15-degree step angle and find three torque balance positions within the 15-degree step angle. Since the magnitude of the SRM winding current is controlled by the PWM power converter, adjusting the PWM output pulse width can make the actual output current change in a stepped current pattern as shown in Figure 2. The energizing sequence of each phase is as follows: When the motor rotates forward: A-AB1-AB2-AB3-B-BC1-BC2-BC3-C-CD1-CD2-CD3-D-DA1-DA2-DA3-A When rotating in reverse: A-AD1-AD2-AD3-D-DC1-DC2-DC3-C-CB1-CB2-CB3-B-BA1-BA2-BA3-A [align=center] Figure 2 (8/6) Ideal current waveform of SRM subdivision winding[/align] In SRM rotor position detection, a photoelectric rotary encoder detects the rotor position and generates a high-resolution digital signal. If the rotor generates N signals per revolution (360 degrees), this is called Np/r (pulses per revolution). These N pulse signals are subdivided, and the phase winding current is adjusted every N/96 pulses, subdividing a large step angle of the rotor into four smaller step angles. This allows the current to replace the commutation point with the commutation zone; that is, during commutation, the current in the off-phase phase does not immediately turn off to zero, but decreases in steps; similarly, the current in the conducting phase does not immediately turn on, but gradually turns on in steps. The width of the step, i.e., the PWM pulse width duty cycle, is determined by the time taken for 32 pulses to complete. The control system principle is shown in Figure 3. The deviation signal generated by comparing the actual speed with the given speed is processed by the regulator through PID calculation to generate the PWM pulse width duty cycle Y corresponding to the given speed. Simultaneously, based on the rotor position pulse, the sine and cosine values ​​corresponding to the torque angle θ at the equilibrium position are looked up in a table. Arithmetic calculations are then performed to obtain the real-time PWM duty cycle amplitudes Ya and Yb of the energized phase, thus controlling the effective current through the SRM winding. 5. Experiments and Conclusions In the specific implementation stage of the differential drive SRM control strategy discussed in this paper, the Microchip PIC18F2331 high-end eight-bit microcontroller was selected. This chip integrates rich peripheral resources, including a power control PWM module, a CCP module, an A/D module, and a photoelectric encoder interface (QEI), which facilitate SRM control. Using the CCP module's capture mode, when the rotor position information pulse meets the set conditions (rising or falling edge), the interrupt flag CCP1IF is automatically set by the hardware, generating a CCP1 capture interrupt. The count value of TMR1 is transferred to the CCPR1 register. The motor speed can be calculated based on the count value. The PIC18F2331 power control PWM module supports three PWM generators and six output channels. In this system, the power conversion section uses a half-bridge circuit, with each phase completely independent. Each phase requires an IGBT as the main switching device, so only two PWM generators and four output channels are needed to meet the motor drive control requirements. The A/D module is a 10-bit high-speed converter, and the chip's operating voltage can be set via a register as the reference voltage for A/D conversion (i.e., using VCC as the reference voltage). The input range of the analog signal is then 0 to VREF. Hall current sensors are used to sample the phase current signal. The Hall current sensor itself has a built-in filter circuit, and its output can be directly provided to the microcontroller's A/D module. An optical encoder is used in this control system to measure the rotor position as feedback for closed-loop control. The PIC18F2331 provides the interface circuit for this encoder. The encoded pulse is input to the chip via two pins, QEA and INDX, as the input clock. The clock signal increments the position counter register (POSCNT). The operating mode of this register determines that it increments on the QEA input edge. If the POSCNT register is matched, the register is reset. If position counter interrupts are enabled, an interrupt will be generated when POSCNT is reset. Because this system uses a PIC microcontroller with high peripheral resource integration, the hardware circuit is relatively simple. The system block diagram is as follows: [align=center] Figure 4 System Block Diagram[/align] Experimental verification shows that this differential drive control method allows the SRM to operate smoothly at a minimum speed of 20 r/min, significantly reducing torque ripple at low speeds and effectively improving noise during rotation. However, under inductive load conditions, the rise or fall of current in the motor is not instantaneous. Especially when the SRM is running at high speed, the current in the windings has only a very short time to track the given value. Therefore, the number of microsteps and the speed are limited to a certain extent, and infinite microstepping is not possible.
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