introduction
A key conclusion in sampling control theory is that narrow pulses of equal impulse but different shapes, when applied to an inertial circuit, produce essentially the same effect. PWM control technology is based on this conclusion, controlling the on/off state of semiconductor switching devices to produce a series of pulses with equal amplitude but unequal width at the output. These pulses are used to replace sine waves or other desired waveforms. By modulating the width of each pulse according to certain rules, both the output voltage and frequency of the inverter circuit can be changed.
The basic principle of PWM control was proposed long ago, but due to limitations in the development of power electronic devices, it could not be realized until the 1980s. It wasn't until the 1980s, with the emergence and rapid development of fully controllable power electronic devices, that PWM control technology was truly applied. With the development of power electronics, microelectronics, and automatic control technologies, as well as the application of various new theoretical methods, such as modern control theory and nonlinear system control concepts, PWM control technology has achieved unprecedented development. To date, various PWM control techniques have emerged, which can be mainly categorized into the following eight types based on their characteristics.
1-phase voltage control PWM
1.1 Constant Pulse Width PWM Method
Early VVVF (Variable Voltage Variable Frequency) devices used PAM (Pulse Amplitude Modulation) control technology, but their inverters could only output a square wave voltage with adjustable frequency, not voltage. Equal Pulse Width Modulation (PWM) was developed to overcome this limitation of PAM and is the simplest type of PWM. It uses a pulse train with each pulse of equal width as the PWM wave. By changing the period of the pulse train, the frequency can be adjusted; by changing the pulse width or duty cycle, the voltage can be adjusted. With appropriate control methods, the voltage and frequency can be coordinated. Compared to PAM, this method simplifies the circuit structure and improves the power factor at the input, but it also results in a significant amount of harmonic components in the output voltage in addition to the fundamental frequency.
1.2 Random PWM
From the 1970s to the early 1980s, high-power transistors were primarily bipolar Darlington transistors, with carrier frequencies generally not exceeding 5kHz. This led to concerns about electromagnetic noise and harmonic vibrations in motor windings. To address this, the random PWM method emerged. Its principle is to randomly change the switching frequency to approximate the motor's electromagnetic noise as band-limited white noise (where energy distribution is uniform across frequencies in a linear frequency coordinate system). Although the total decibel level of the noise remains unchanged, the intensity of the colored noise characterized by a fixed switching frequency is significantly reduced. Therefore, even today, with the widespread use of IGBTs, random PWM still holds special value in situations where the carrier frequency must be limited to a lower range. Furthermore, it demonstrates that the best way to eliminate mechanical and electromagnetic noise is not to blindly increase the operating frequency; random PWM technology provides a completely new approach to analyzing and solving this problem.
1.3 SPWM Method
SPWM (Sinusoidal PWM) is a relatively mature and widely used PWM method. A key conclusion in the sampling control theory mentioned earlier is that narrow pulses of equal impulse but different shapes applied to an inertial circuit produce essentially the same effect. SPWM is based on this conclusion, using a PWM waveform—the pulse width of which varies sinusoidally and is equivalent to a sine wave—to control the switching of devices in the inverter circuit. This ensures that the area of the output pulse voltage is equal to the area of the desired output sine wave within the corresponding interval. By changing the frequency and amplitude of the modulation wave, the frequency and amplitude of the inverter circuit's output voltage can be adjusted. Several implementation schemes exist for this method.
1.3.1 Equal Area Method
This scheme is essentially a direct explanation of the SPWM method principle. It replaces the sine wave with a sequence of rectangular pulses of equal amplitude but unequal width. The width and interval of each pulse are then calculated and stored in a microcomputer. A PWM signal is generated by looking up a table to control the switching devices, achieving the desired effect. Because this method is based on the fundamental principles of SPWM control, it can accurately calculate the on/off times of each switching device, and the resulting waveform closely approximates a sine wave. However, it suffers from drawbacks such as cumbersome calculations, large memory footprint, and inability to achieve real-time control.
1.3.2 Hardware Modulation Method
Hardware modulation was proposed to address the cumbersome calculations of the equal-area method. Its principle is to use the desired waveform as the modulating signal and the signal to be modulated as the carrier wave, obtaining the desired PWM waveform through carrier modulation. Typically, an isosceles triangular wave is used as the carrier wave. When the modulating signal wave is a sine wave, the resulting waveform is an SPWM waveform. Its implementation is simple; an analog circuit can be used to construct a triangular wave carrier and a sine modulating wave generation circuit, a comparator is used to determine their intersection point, and the switching on and off of the switching devices at the intersection point is controlled to generate the SPWM wave. However, this analog circuit structure is complex and difficult to achieve precise control.
1.3.3 Software Generation Method
The development of microcomputer technology has made it easier to generate SPWM waveforms using software, thus giving rise to software generation methods. Software generation methods essentially use software to implement modulation, and they have two basic algorithms: natural sampling and regular sampling.
1.3.3.1 Natural Sampling Method
Using a sine wave as the modulation wave and an isosceles triangular wave as the carrier wave for comparison, the switching device is controlled at the natural intersection point of the two waveforms. This is the natural sampling method. Its advantage is that the resulting SPWM waveform is closest to a sine wave. However, because the intersection point of the triangular wave and the sine wave is arbitrary, and the pulse center is not equidistant within a cycle, the pulse width expression is a transcendental equation, which is cumbersome to calculate and difficult to control in real time.
1.3.3.2 Rule-based sampling method
Regular sampling is a widely used engineering practice that typically uses a triangular wave as the carrier wave. Its principle is to sample a sine wave with a triangular wave to obtain a stepped wave, and then control the switching on/off state of the switching device at the intersection of the stepped wave and the triangular wave, thus realizing the SPWM method. When the triangular wave samples the sine wave only at its apex (or apex), the pulse width determined by the intersection of the stepped wave and the triangular wave is symmetrical within one 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 apex, the pulse width determined by the intersection of the stepped wave and the triangular wave is generally not symmetrical within one carrier cycle (twice the sampling period). This method is called asymmetric regular sampling.
Regular sampling is an improvement on natural sampling. Its main advantages are its simple calculation and ease of online real-time operation. Among them, the asymmetric regular sampling method is closer to sinusoidal due to its higher order. Its disadvantages are lower DC voltage utilization and a smaller linear control range.
Both of the above methods are only applicable to synchronous modulation.
1.3.4 Low-order harmonic elimination method
The low-order harmonic elimination method aims to eliminate certain major low-order harmonics in a PWM waveform. Its principle is to expand the output voltage waveform using a Fourier series, expressed as u(ωt) = ansinnωt. First, determine the value of the fundamental component a1. Then, set two different an=0 values to establish three equations. Solving these equations simultaneously yields a1, a2, and a3, thus eliminating harmonics at two frequencies.
While this method can effectively eliminate the specified lower harmonics, the amplitude of the remaining uneliminated lower harmonics can be quite large, and it also suffers from computational complexity. This method is also only applicable to synchronous modulation schemes.
1.4 Comparison Method of Trapezoidal Waves and Triangular Waves
The methods described above primarily aim to make the output waveform as close to a sine wave as possible, thus neglecting the utilization rate of DC voltage. For example, the SPWM method has a DC voltage utilization rate of only 86.6%. Therefore, to improve DC voltage utilization, a new method—the trapezoidal wave and triangular wave comparison method—is proposed. This method uses a trapezoidal wave as the modulation signal and a triangular wave as the carrier wave, ensuring that the amplitudes of the two waves are equal. The switching of the switching device is controlled at the intersection of the two waves to achieve PWM control.
When the amplitudes of the trapezoidal wave and the triangular wave are equal, the amplitude of the fundamental component contained in the trapezoidal wave exceeds that of the triangular wave, thus effectively improving the DC voltage utilization rate. However, since the trapezoidal wave itself contains low-order harmonics, the output waveform contains low-order harmonics such as the 5th and 7th orders.
2-line voltage controlled PWM
The various PWM control methods introduced above, when applied to three-phase inverter circuits, control the three-phase output phase voltages individually to make the output approach a sine wave. However, for three-phase symmetrical loads without a neutral line, such as three-phase asynchronous motors, the inverter output does not need to pursue a near-sine phase voltage; instead, the focus can be on making the line voltage approach a sine wave. Therefore, line voltage control PWM is proposed, mainly through the following two methods.
2.1 Comparison Method between Saddle-Shaped Waves and Triangular Waves
The comparison method between saddle-shaped wave and triangular wave is also known as harmonic injection PWM (HIPWM). Its principle is to add a certain proportion of third harmonic to the sine wave, so that the modulation signal will take the shape of a saddle and the amplitude will be significantly reduced. Thus, if the amplitude of the modulation signal does not exceed the amplitude of the carrier wave, the amplitude of the fundamental wave can exceed the amplitude of the triangular wave, 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].
Besides injecting the third harmonic, other waveforms with frequencies three times that of a sine wave can also be injected without affecting the line voltage. This is because the phase voltage output by the inverter circuit after PWM modulation will inevitably contain corresponding harmonics with frequencies three times that of a sine wave. However, when synthesizing the line voltage, these harmonics in each phase voltage will cancel each other out, thus ensuring that the line voltage remains a sine wave.
2.2 Unit Pulse Width Modulation Method
Because the three-phase symmetrical line voltages have the relationship Uuv + Uvw + Uwu = 0, at any given moment, a certain line voltage is equal to the sum of the negative values of the other two line voltages. Now, divide one cycle into six equal intervals, each 60°. For a certain line voltage, such as Uuv, the two 60° intervals on either side of half a cycle are represented by Uuv itself, and the middle 60° interval is represented by -(Uvw + Uwu). When Uvw and Uwu are treated in the same way, the three-phase line voltage waveform can be obtained with only two waveform shapes in the two 60° intervals on either side of half a cycle, and both positive and negative. Using such a voltage waveform as the reference signal for pulse width modulation, with the carrier wave still being a triangular wave, and approximating the curves of each interval with straight lines (practice shows that this causes little error and is entirely feasible), the pulse waveform of the line voltage can be obtained. This waveform is completely symmetrical and highly regular; the negative half-cycle is the inverse of the corresponding pulse train of the positive half-cycle. Therefore, once the pulse trains in the two 60° intervals on either side of half a cycle are determined, the modulation 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 operating 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 range. It also brings the convenience of microcomputer control. However, this method is only applicable to asynchronous motors and has a limited range of applications.
3. Current-controlled PWM
The basic idea of current-controlled 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/off state of each switching device is determined, so that the actual output changes with the command signal. There are three main implementation schemes.
3.1 Hysteresis Comparison Method
This is a PWM control method with feedback. The current from each phase is fed back and compared with the current setpoint via a hysteresis comparator to determine the switching state of the corresponding bridge arm switching device, allowing the actual current to track changes in the setpoint current. The advantages of this method are its simple circuitry, good dynamic performance, and output voltage free of harmonic components of specific frequencies. Its disadvantages include a variable switching frequency, resulting in significant noise, and compared to other methods, the output current contains more harmonics at the same switching frequency.
3.2 Triangular Wave Comparison Method
This method differs from the triangular wave comparison method in SPWM. Here, the command current is compared with the actual output current to calculate the deviation current. This deviation current is then amplified and compared with the triangular wave to generate the PWM wave. In this case, the switching frequency is constant, thus overcoming the frequency instability of the hysteresis comparison method. However, the current response of this method is not as fast as that of the hysteresis comparison method.
3.3 Predictive Current Control Method
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 inevitably reduce the predicted error. The advantage of this method is that if the regulator is given more information than just the error, a faster and more accurate response can be obtained. Currently, the limitations of this type of regulator are its response speed and the accuracy of the process model coefficients.
4. Space Vector Control (PWM)
Space Vector Pulse Width Modulation (SVPWM), also known as Flux Sine Pulse Width Modulation, is based on the overall generation effect of three-phase waveforms. Its aim is to approximate the trajectory of an ideal circular rotating magnetic field in the motor's air gap. It uses the actual magnetic flux generated by different switching modes of the inverter to approximate a reference circular magnetic flux, and the comparison result determines the inverter's switching, forming the PWM waveform. This method treats the inverter and motor as a whole from the perspective of the motor, controlling them by approximating a circle with an inscribed polygon, thus enabling the motor to obtain a circular magnetic field (sine flux) with a constant amplitude.
Specific methods are further divided into open-loop and closed-loop flux methods. The open-loop method synthesizes an equivalent voltage vector using two non-zero vectors and one zero vector. If the sampling time is sufficiently small, any voltage vector can be synthesized. This method increases the output voltage by 15% compared to sinusoidal modulation, and the sum of the effective values of harmonic currents is close to minimum. The closed-loop flux method introduces flux feedback to control the magnitude and rate of change of the flux. After comparing the estimated flux with the given flux, the error determines the generation of the next voltage vector, forming a PWM waveform. This method overcomes the shortcomings of the open-loop method, solving the problem of large stator resistance influence at low motor speeds and reducing motor pulsation and noise. However, since torque regulation is not introduced, the system performance is not fundamentally improved.
5 Vector Control PWM
Vector control, also known as field-oriented control, works by converting the stator currents Ia, Ib, and Ic of an asynchronous motor in a three-phase coordinate system into equivalent AC currents Ia1 and Ib1 in a two-phase stationary coordinate system through a three-phase/two-phase transformation. Then, through a rotor field-oriented rotational transformation, these are equivalent to DC currents Im1 and It1 in a synchronous rotating coordinate system (Im1 is equivalent to the excitation current of a DC motor; It1 is equivalent to the armature current proportional to the torque). The control method for a DC motor is then used to control an AC motor. Essentially, it equates an AC motor to a DC motor, independently controlling the speed and magnetic field components. By controlling the rotor flux linkage and decomposing the stator current to obtain the torque and magnetic field components, orthogonal or decoupled control is achieved through coordinate transformation.
However, due to the difficulty in accurately observing rotor flux linkage and the complexity of vector transformation, the actual control effect often falls short of the theoretical analysis, which is a practical limitation of vector control technology. Furthermore, it requires direct or indirect knowledge of the rotor flux linkage's spatial position to achieve stator current decoupling control. This necessitates the configuration of rotor position or speed sensors in such vector control systems, which obviously causes inconvenience in many applications.
6. Direct Torque Control (PWM)
In 1985, Professor Depenbrock of Ruhr University in Germany first proposed the theory of Direct Torque Control (DTC). Unlike vector control, DTC does not indirectly control torque by controlling quantities such as current and flux linkage. Instead, it directly controls torque as the controlled variable. It also does not require decoupling the motor model; instead, it calculates the actual values of motor flux and torque in a stationary coordinate system. Then, a PWM signal is generated through band-band control of flux linkage and torque to optimally control the switching state of the inverter. This largely solves the shortcomings of vector control, easily achieving sensorless operation, providing fast torque response, and high speed and torque control accuracy. With its novel control concept, simple and clear system structure, and excellent dynamic and static performance, DTC has rapidly developed.
However, direct torque control also has its drawbacks, such as limitations on increasing the inverter switching frequency.
7. Nonlinear control PWM
Single-cycle control [7], also known as Integration Reset Control (IRC), is a new type of nonlinear control technology. Its basic idea is to control the duty cycle of the switch 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 both modulation and control properties. It achieves the purpose of tracking the command signal through a reset switch, integrator, trigger circuit, and comparator. The single-cycle controller consists of a controller, comparator, integrator, and clock. The controller can be an RS flip-flop. Its control principle is shown in Figure 1. In the figure, K can be any physical switch or other abstract signals that can be converted into switch variables.
Single-cycle control does not require error synthesis in the control circuit. It can automatically eliminate steady-state and transient errors within one cycle, preventing errors from the previous cycle from being carried over to the next. Although the hardware circuit is more complex, it overcomes the shortcomings of traditional PWM control methods. It is suitable for various pulse width modulation soft-switching inverters and has advantages such as fast response, constant switching frequency, and strong robustness. In addition, single-cycle control can optimize system response, reduce distortion, and suppress power supply interference, making it a very promising control method.
8 Resonant Soft Switching PWM
In traditional PWM inverter circuits, the hard-switching operation of power electronic switching devices, the large switching voltage and current stress, and the high du/dt and di/dt limit the increase of the operating frequency of the switching devices. However, high frequency is one of the main development trends of power electronics. It can reduce the size, weight, cost, and performance of the converter. In particular, when the switching frequency is above 18kHz, the noise will exceed the range of human hearing, making noiseless drive systems possible.
The basic idea of resonant soft-switching PWM is to add a resonant network to the conventional PWM converter topology. This resonant network typically consists of a resonant inductor, a resonant capacitor, and a power switch. During switching, the resonant network enables the power electronic devices to achieve a soft-switching process at the switching point. This resonant process is extremely short and has virtually no impact on the implementation of PWM technology. Thus, it retains the characteristics of PWM technology while achieving soft-switching. However, the presence of the resonant network in the circuit inevitably generates resonant losses and exposes the circuit to inherent problems, thereby limiting the application of this method.
9 Conclusion
This article summarizes the principles of various PWM control methods in detail and briefly explains their advantages and disadvantages. PWM control technology, with its advantages of simple control, flexibility, and good dynamic response, has become the most widely used control method in power electronics technology and is also a hot research topic. Since the boundaries between disciplines have blurred in today's scientific and technological development, combining modern control theory or realizing resonant-free soft-switching technology will become one of the main directions for the development of PWM control technology.
