A review of PWM technology implementation methods
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Abstract: This paper summarizes the main implementation methods of PWM technology since its advent, describes their basic working principles, and analyzes their respective advantages and disadvantages. Keywords: PWM; space vector; direct torque control; nonlinear 0 Introduction There is an important conclusion in sampling control theory: when narrow pulses with equal impulses but different shapes are added to a link with inertia, the effect is basically the same. PWM control technology is based on this conclusion, which controls the on and off of semiconductor switching devices so that the output end obtains a series of pulses with equal amplitudes but unequal widths, and uses these pulses to replace sine waves or other required waveforms. By modulating the width of each pulse according to certain rules, the output voltage of the inverter circuit can be changed, and the output frequency can also be changed. The basic principle of PWM control has been proposed for a long time, but it has not been realized before the 1980s due to the limitation of the development level of power electronic devices. It was not until the 1980s that PWM control technology was truly applied with the emergence and rapid development of fully controlled power electronic devices. With the development of power electronics technology, microelectronics technology and automatic control technology and the application of various new theoretical methods, such as modern control theory and nonlinear system control ideas, PWM control technology has achieved unprecedented development. So far, a variety of PWM control technologies have emerged. According to the characteristics of PWM control technology, there are mainly the following 8 types of methods. 1-phase voltage controlled PWM 1.1 Equal Pulse Width PWM Method[1] In the early days, the VVVF (Variable Voltage Variable Frequency) device was implemented using the PAM (Pulse Amplitude Modulation) control technology. Its inverter part could only output a square wave voltage with adjustable frequency but could not adjust the voltage. The equal pulse width PWM method was developed to overcome this shortcoming of the PAM method and is the simplest of the PWM methods. It uses a pulse train with equal width of each pulse as a PWM wave. By changing the period of the pulse train, the frequency can be adjusted, and by changing the width or duty cycle of the pulse, the voltage can be adjusted. By using appropriate control methods, the voltage and frequency can be coordinated. Compared with the PAM method, the advantage of this method is that it simplifies the circuit structure and improves the power factor at the input end, but at the same time, in addition to the fundamental wave, the output voltage also contains a large harmonic component. 1.2 Random PWM From the 1970s to the early 1980s, since high-power transistors were mainly bipolar Darlington transistors and the carrier frequency generally did not exceed 5kHz, the electromagnetic noise of the motor windings and the vibration caused by harmonics attracted people's attention. In order to improve this, the random PWM method came into being. Its principle is to randomly change the switching frequency so that the electromagnetic noise of the motor is approximately limited-band white noise (in the linear frequency coordinate system, the energy distribution of each frequency is uniform). Although the total decibel number of the noise remains unchanged, the intensity of the colored noise characterized by a fixed switching frequency is greatly weakened. Because of this, even today when IGBTs have been widely used, random PWM still has its special value for occasions where the carrier frequency must be limited to a lower frequency; on the other hand, it shows that the best way to eliminate mechanical and electromagnetic noise is not to blindly increase the operating frequency. Random PWM technology provides a new way to analyze and solve this problem. 1.3 SPWM method SPWM (Sinusoidal PWM) is a relatively mature and widely used PWM method. An important conclusion in the sampling control theory mentioned above is that when narrow pulses with equal impulses but different shapes are added to the inertial link, the effect is basically the same. The SPWM method is based on this conclusion. It uses a PWM waveform, which is equivalent to a sine wave and changes in pulse width according to the sine law, to control the on and off of the switching devices in the inverter circuit, so that the area of the pulse voltage output is equal to the area of the desired sine wave in the corresponding interval. By changing the frequency and amplitude of the modulation wave, the frequency and amplitude of the output voltage of the inverter circuit can be adjusted. There are several solutions to implement this method. 1.3.1 Equal Area Method This scheme is actually a direct explanation of the principle of SPWM method. It uses the same number of equal-amplitude but unequal-width rectangular pulse sequences to replace the sine wave, and then calculates the width and interval of each pulse, and stores these data in the microcomputer. By looking up the table, a PWM signal is generated to control the on and off of the switching device to achieve the desired purpose. Since this method is based on the basic principle of SPWM control, it can accurately calculate the on and off time of each switching device, and the waveform obtained is very close to the sine wave, but it has the disadvantages of cumbersome calculation, large memory usage of data, and inability to control in real time. 1.3.2 Hardware Modulation The hardware modulation method is proposed to solve the shortcoming of the equal area method that the calculation is cumbersome. Its principle is to use the desired waveform as the modulation signal and the modulated signal as the carrier, and obtain the desired PWM waveform by modulating the carrier. Usually, an isosceles triangle wave is used as the carrier. When the modulation signal wave is a sine wave, the SPWM waveform is obtained. Its implementation method is simple. The triangle wave carrier and the sine modulation wave generation circuit can be constructed with an analog circuit, and a comparator is used to determine their intersection. At the intersection, the on and off of the switch device can be controlled to generate an SPWM wave. However, this analog circuit has a complex structure and it is difficult to achieve precise control. 1.3.3 Software Generation Method The development of microcomputer technology makes it easier to generate SPWM waveforms with software, so the software generation method comes into being. The software generation method is actually a method of using software to achieve modulation. There are two basic algorithms, namely the natural sampling method and the regular sampling method. 1.3.3.1 Natural sampling method[2] The natural sampling method uses a sine wave as the modulating wave and an isosceles triangle wave as the carrier wave for comparison, and controls the on and off of the switch device at the natural intersection of the two waveforms. Its advantage is that the resulting SPWM waveform is closest to a sine wave, but because the intersection of the triangle wave and the sine wave is arbitrary, the pulse centers are not equidistant within a cycle, so the pulse width expression is a transcendental equation, which is cumbersome to calculate and difficult to control in real time. 1.3.3.2 Regular sampling method[3] The regular sampling method is a widely used engineering practical method, which generally uses a triangular wave as a carrier. The principle is to use a triangular wave to sample a sine wave to obtain a step wave, and then control the on and off of the switching device at the intersection of the step wave and the triangular wave, thereby realizing the SPWM method. When the triangular wave samples the sine wave only at its apex (or bottom point), the pulse width determined by the intersection of the step wave and the triangular wave is symmetrical in position within a carrier cycle (i.e., the sampling period). This method is called symmetrical regular sampling. When the triangular wave samples the sine wave at both its apex and bottom point, the pulse width determined by the intersection of the step wave and the triangular wave is generally not symmetrical in position within a carrier cycle (twice the sampling period at this time). This method is called asymmetrical regular sampling. The regular sampling method is an improvement on the natural sampling method. Its main advantage is that it is simple to calculate and convenient for online real-time operation. The asymmetric regular sampling method is closer to sine due to its large number of orders. Its disadvantage is that the DC voltage utilization rate is low and the linear control range is small. The above two methods are only applicable to synchronous modulation mode. 1.3.4 Low-order harmonic elimination method[2] The low-order harmonic elimination method is a method for eliminating some major low-order harmonics in the PWM waveform. The principle is to expand the output voltage waveform according to the Fourier series, expressed as u ( ωt ) =  a n sinn ωt . First, determine the value of the fundamental component a1 , and then set two different a n = 0 , then you can establish three equations, and solve them together to get a1 , a2 and a3 , so that the harmonics of the two frequencies can be eliminated. Although this method can effectively eliminate the specified low-order harmonics, the amplitude of the remaining uneliminated lower-order harmonics may be quite large, and it also has the disadvantage of complex calculation. This method is also only applicable to synchronous modulation. 1.4 Comparison between trapezoidal wave and triangular wave[2] The various methods introduced above are mainly aimed at making the output waveform as close to the sine wave as possible, thus ignoring the utilization rate of the DC voltage. For example, the utilization rate of the DC voltage of the SPWM method is only 86.6%. Therefore, in order to improve the utilization rate of the DC voltage, a new method is proposed - the trapezoidal wave and triangular wave comparison method. This method uses the trapezoidal wave as the modulation signal and the triangular wave as the carrier wave, and makes the amplitudes of the two waves equal, and controls the on and off of the switching device at the intersection of the two waves to realize PWM control. When the amplitude of the trapezoidal wave is equal to that of the triangular wave, the amplitude of the fundamental wave component contained in it has exceeded that of the triangular wave, which can effectively improve the utilization rate of the DC voltage. However, since the trapezoidal wave itself contains low-order harmonics, the output waveform contains low-order harmonics such as the 5th and 7th order. 2-line voltage controlled PWM When the various PWM control methods introduced above are used in three-phase inverter circuits, the three-phase output phase voltages are controlled separately to make the output close to a sine wave. However, for three-phase non-neutral symmetrical loads such as three-phase asynchronous motors, the inverter output does not need to pursue phase voltage close to a sine wave, but can focus on making the line voltage tend to a sine wave. Therefore, line voltage control PWM is proposed, mainly in the following two methods. 2.1 Comparison between saddle wave and triangle wave The saddle wave and triangle wave comparison method is also known as the harmonic injection PWM method (HIPWM). Its principle is to add a certain proportion of the third harmonic to the sine wave, so that the modulated signal presents a saddle shape and the amplitude is significantly reduced. Therefore, when the amplitude of the modulated signal does not exceed the carrier amplitude, the fundamental wave amplitude can exceed the triangle wave amplitude, thereby improving the DC voltage utilization rate. In a three-phase system without a neutral line, since the third harmonic current has no path, the three line voltages and line currents do not contain the third harmonic [4]. In addition to injecting the third harmonic, other waveforms that are three times the frequency of the sine wave signal can also be injected, and these signals will not affect the line voltage. This is because the phase voltage output by the inverter circuit after PWM modulation must also contain the corresponding harmonics that are three times the frequency of the sine wave signal, but when synthesizing the line voltage, these harmonics in each phase voltage will cancel each other out, so that the line voltage is still a sine wave. 2.2 Unit Pulse Width Modulation Method[5] Because the three-phase symmetrical line voltage has the relationship of U uv + U vw + U wu = 0, so the voltage of a certain line is equal to the sum of the negative values of the other two line voltages at any time. Now divide a cycle into 6 intervals, each interval is 60°. For a certain line voltage, such as U uv , the 60° intervals on both sides of the half cycle are represented by U uv itself, and the middle 60° interval is represented by -( U vw + U wu ). When U vw and U wu are treated in the same way, the three-phase line voltage waveform can be obtained. There are only two waveform shapes of the 60° intervals on both sides of the half cycle, and there are positive and negative ones. By using such a voltage waveform as the reference signal for pulse width modulation, the carrier wave is still a triangle wave, and the curves of each interval are approximated by a straight line (practice shows that this method does not cause much error and is completely feasible), the pulse waveform of the line voltage can be obtained. The waveform is completely symmetrical and has a strong regularity. The negative half cycle is the inverse of the corresponding pulse train of the positive half cycle. Therefore, as long as the pulse train of the 60° interval on both sides of the half cycle is determined, the modulated pulse waveform of the line voltage is uniquely determined. This pulse is not the driving pulse signal of the switching device, but since the pulse working mode of the three-phase line voltage is known, the driving pulse signal of the switching device can be determined. This method can not only suppress more low-order harmonics, but also reduce switching losses and widen the linear control area, while also bringing the convenience of microcomputer control. However, this method is only applicable to asynchronous motors and has a small application range. 3 Current Control PWM The basic idea of current control PWM is to use the desired output current waveform as the command signal and the actual current waveform as the feedback signal. By comparing the instantaneous values of the two, the on and off of each switch device is determined, so that the actual output changes with the change of the command signal. There are three main implementation schemes. 3.1 Hysteresis comparison method[4] This is a PWM control method with feedback, that is, the current of each phase is fed back and compared with the current given value through the hysteresis comparator to obtain the switching state of the corresponding bridge arm switch device, so that the actual current tracks the change of the given current. The advantages of this method are simple circuit, good dynamic performance, and the output voltage does not contain harmonic components of a specific frequency. Its disadvantage is that the switching frequency is not fixed, causing more serious noise. Compared with other methods, the output current contains more harmonics at the same switching frequency. 3.2 Triangle wave comparison method[2] This method is different from the triangle wave comparison method in the SPWM method. Here, the command current is compared with the actual output current to obtain the deviation current, which is amplified by the amplifier and then compared with the triangle wave to generate a PWM wave. At this time, the switching frequency is constant, thus overcoming the disadvantage of the hysteresis comparison method that the frequency is not fixed. However, the current response of this method is not as fast as the hysteresis comparison method. 3.3 Predictive current control method[6] Predictive current control predicts the current error vector trend at the beginning of each regulation cycle based on the actual current error, load parameters and other load variables. Therefore, the voltage vector generated by PWM in the next regulation cycle will reduce the predicted error. The advantage of this method is that if the regulator is given more information besides the error, a faster and more accurate response can be obtained. At present, the limitations of this type of regulator are the response speed and the accuracy of the process model coefficient parameters. 4 Space voltage vector control PWM[7] Space voltage vector control PWM (SVPWM) is also called flux sinusoidal PWM method. It takes the overall generation effect of three-phase waveform as the premise, aims to approximate the ideal circular rotating magnetic field trajectory of the motor air gap, uses the actual magnetic flux generated by different switching modes of the inverter to approximate the reference circular magnetic flux, and determines the switching of the inverter by their comparison results to form a PWM waveform. Starting from the perspective of the motor, this method regards the inverter and the motor as a whole, and controls them in the way of inscribed polygon approximating a circle, so that the motor obtains a circular magnetic field (sinusoidal magnetic flux) with a constant amplitude. The specific methods are divided into flux open-loop and flux closed-loop. The flux open-loop method uses two non-zero vectors and a zero vector to synthesize an equivalent voltage vector. If the sampling time is small enough, any voltage vector can be synthesized. The output voltage of this method is 15% higher than that of sinusoidal wave modulation, and the sum of the effective values of harmonic currents is close to the minimum. The flux closed-loop method introduces flux feedback to control the size and speed of flux change. After comparing the estimated flux with the given flux, the next voltage vector is generated based on the error to form a PWM waveform. This method overcomes the shortcomings of the flux open-loop method, solves the problem of the large influence of stator resistance when the motor is at low speed, and reduces the pulsation and noise of the motor. However, due to the lack of torque regulation, the system performance has not been fundamentally improved. 5 Vector Control PWM[8] Vector control is also called field-oriented control. Its principle is to convert the stator currents Ia, Ib and Ic of the asynchronous motor in the three-phase coordinate system into AC currents Ia1 and Ib1 in the two -phase stationary coordinate system through three-phase/two-phase transformation , and then convert them into DC currents Im1 and It1 in the synchronous rotating coordinate system through rotor magnetic field oriented rotation transformation ( Im1 is equivalent to the excitation current of the DC motor; It1 is equivalent to the armature current proportional to the torque), and then imitate the control method of the DC motor to achieve the control of the AC motor. Its essence is to convert the AC motor into a DC motor and independently control the speed and magnetic field components. By controlling the rotor flux, the stator current is decomposed to obtain the torque and magnetic field components, and the orthogonal or decoupling control is achieved through coordinate transformation. However, due to the difficulty in accurately observing the rotor flux and the complexity of vector transformation, the actual control effect is often difficult to achieve the effect of theoretical analysis, which is the deficiency of vector control technology in practice. In addition, it must directly or indirectly obtain the position of the rotor flux in space to achieve stator current decoupling control. In this vector control system, rotor position or speed sensors need to be configured, which obviously brings inconvenience to many applications. 6 Direct Torque Control PWM[8] In 1985, Professor Depenbrock of Ruhr University in Germany first proposed the theory of direct torque control (DTC for short). Direct torque control is different from vector control. It does not indirectly control torque by controlling current, flux and other quantities, but directly controls torque as the controlled quantity. It does not need to decouple the motor model, but calculates the actual value of motor flux and torque in a static coordinate system. Then, the PWM signal is generated through the Band-Band control of flux and torque to optimally control the switching state of the inverter, thus solving the above-mentioned shortcomings of vector control to a large extent, and can easily realize speed sensorless, with fast torque response speed and high speed and torque control accuracy. It has been rapidly developed with novel control ideas, concise and clear system structure, and excellent dynamic and static performance. However, direct torque control also has disadvantages, such as the limitation on increasing the inverter switching frequency. 7 Nonlinear Control PWM The single-cycle control method [7], also known as the integration reset control (IRC), is a new type of nonlinear control technology. Its basic idea is to control the switch duty cycle so that the average value of the switch variable is equal to or proportional to the control reference voltage in each cycle. This technology has the dual nature of modulation and control. It achieves the purpose of tracking the command signal through the reset switch, integrator, trigger circuit, and comparator. The single-cycle controller consists of a controller, a comparator, an integrator, and a clock. The controller can be an RS trigger. Its control principle is shown in Figure 1. In the figure, K can be any physical switch or other abstract signal that can be converted into a switch variable. 
Figure 1 Schematic diagram of single-cycle control Single-cycle control does not require error synthesis in the control circuit. It can automatically eliminate steady-state and transient errors within one cycle, so that the error of the previous cycle will not be carried over to the next cycle. Although the hardware circuit is more complex, it overcomes the shortcomings of the traditional PWM control method and is suitable for various pulse width modulation soft switching inverters. It has the advantages of fast response, constant switching frequency, and strong robustness. In addition, single-cycle control can also optimize system response, reduce distortion and suppress power supply interference. It is a very promising control method. 8 Resonant soft switching PWM In traditional PWM inverter circuits, the hard switching working mode of power electronic switching devices, large switching voltage and current stress, and high du / dt and di / dt limit the increase in the operating frequency of the switching devices. High frequency is one of the main development trends of power electronics. It can reduce the size and weight of the converter, reduce costs, and improve performance. Especially when the switching frequency is above 18kHz, the noise will exceed the human hearing range, making noise-free transmission systems possible. The basic idea of resonant soft switching PWM is to add a resonant network based on the conventional PWM converter topology. The resonant network is generally composed of a resonant inductor, a resonant capacitor and a power switch. During the switch conversion, the resonant network works to enable the power electronic device to realize a soft switching process at the switch point. The resonance process is extremely short and basically does not affect the implementation of PWM technology. In this way, the characteristics of PWM technology are maintained and soft switching technology is realized. However, the presence of the resonant network in the circuit will inevitably produce resonant losses and make the circuit affected by inherent problems, which limits the application of this method. 9 Conclusion This article summarizes the principles of various PWM control methods in detail and briefly explains the advantages and disadvantages of various methods. PWM control technology has become the most widely used control method in power electronics technology due to its advantages of simple control, flexibility and good dynamic response, and is also a hot topic of research. As the development of science and technology today has no boundaries between disciplines, combining modern control theory or realizing non-resonant soft switching technology will become one of the main directions of PWM control technology development. About the Author Li Xu (1979-), male, master's degree student, majoring in power electronics and power transmission. His research direction is power conversion technology and application.
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