Modern industrial servo drives often employ AC servo systems that drive permanent magnet synchronous motors (PMSMs), with their AC drive units using three-phase full-bridge voltage-source inverters. PWM modulation frequency conversion control technology enables real-time control of the dynamic torque of the AC motor, significantly improving the control performance of the servo system.
However, for PWM inverters, inserting a delay time into the switching signal of the drive power transistor to prevent direct short circuit of the DC bus will lead to a dead time effect, causing distortion of the inverter output waveform and drop in the fundamental voltage, which will affect the further improvement of the servo system performance [1].
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A review of inverter dead-time compensation methods
To compensate for voltage fluctuations caused by time fluctuations (td), researchers have proposed various compensation methods, which can be roughly divided into three categories.
The most common method is to add pulse trains of opposite polarity to the missing pulse trains within the range of current polarity to cancel out their effects. Since one phase of the three-phase current must have opposite polarity to the other two phases, a simple method is to perform double voltage overcompensation on the phase with opposite polarity, so that the effects of the three-phase voltage dead zone cancel each other out, and the line voltage waveform is sinusoidal [1]. Reference [2] analyzes in detail the causes and effects of dead zone generation, and gives hardware circuit compensation methods for dead zone based on analog modulation and digital modulation respectively. Reference [3] proposes a mathematical model of an inverter with dead zone compensation based on the switching state of the full-bridge circuit. The characteristic of this model is that it is composed of a simple hysteresis structure. According to this model, dead zone compensation can be achieved by a calculation formula.
The second type of method is to achieve dead-time compensation based on the principle of invalid devices. At any given time, only one of the two power devices in each arm of the inverter is active. When the upper arm device is turned off, the output voltage is the negative terminal voltage of the DC bus regardless of whether the lower arm device is on or off. At this time, the lower arm device is called "inactive". The method of dead-time compensation is to keep the drive signal of the active device unchanged and change the drive signal of the inactive device to meet the requirements of setting the dead time. Since the on and off of the "inactive" device does not affect the output voltage state, there is no need for a drive signal. Only the drive signal of the active device needs to be sent. Thus, there is no need to add a dead time and there is no problem of dead-time compensation. However, this method will cause distortion due to error at the current zero-crossing point. Therefore, attention should be paid to the handling of the current zero-crossing region when using this method. Some scholars have further proposed improved methods. Reference [4] adds a hysteresis loop at the current zero-crossing point and uses normal switching dead-time protection during the hysteresis time, which can reduce distortion. Due to interference in current sampling and the complexity of current changes, reference [5] suggests providing two drive signals and adding dead time and dead time compensation in the region near the current zero-crossing point. Using the PWM turn-off time to implement switch dead time protection during commutation can eliminate the influence of the switch dead time.
The third type of method is current predictive control. A relatively accurate motor system model is established, the distortion of the current waveform is analyzed, and the current waveform is corrected through predictive control. Reference [6] addresses the dead zone problem in predictive current control by estimating the back EMF to compensate for voltage waveform distortion and current zero-point clamping. Reference [7] establishes the matrix equations of the asynchronous motor model and compensates for the spatial voltage vector based on the prediction of the stator phase current in the SVPWM algorithm. Reference [8] uses the PMSM model in the dq rotating coordinate system to design an observer to observe the voltage loss along the q-axis, converting it into the dead time tc to be compensated, thus achieving online compensation of the dead zone. Reference [9] uses time delay control to estimate the interference voltage caused by the dead zone and feeds it back to the voltage reference setpoint to compensate for the dead zone effect. Current prediction methods are computationally cumbersome, and the compensation effect is directly related to the accuracy of the motor model and the time-varying parameter values, making it difficult to obtain satisfactory results.
The impact of inverter dead time
As can be seen from the basic principle of PWM dead time generation [1], the voltage deviation of the inverter output voltage caused by the deviation pulse within the winding current period t1 can be equivalently represented by a square wave. For ease of analysis, it is assumed that the voltage deviation pulses are evenly spaced in time, then the height of the equivalent square wave is:
As the polarity of the current changes, the direction of the error voltage pulse also changes. Moreover, as the carrier frequency increases, the number of error voltage pulses also increases. Although the dead time is very short, only a few microseconds, the accumulated error voltage within one cycle can still have a significant impact on the fundamental amplitude of the output voltage. The qualitative relationship between the error voltage and the ideal voltage and the actual output voltage is shown in Figure 2.
Fourier analysis of the deviation square wave in Figure 2 yields the following results:
Where ω1 is the fundamental angular frequency of the current; ψ is the phase difference between the desired voltage and the motor current.
Therefore, ignoring the high-frequency noise caused by the power switch, the inverter's output voltage is:
Among them, the modulation index (ma) is the ratio of the amplitude of the modulated sine wave to the amplitude of the triangular wave carrier wave.
As can be seen from the above formula, due to the existence of the inverter dead time, not only does the fundamental frequency of the inverter output voltage change, but the output voltage also contains higher harmonics such as the 3rd, 5th, and 7th.
Switching dead time causes distortion of the inverter output voltage waveform, which in turn causes distortion of the output current waveform, i.e., current crossover distortion.
The longer the dead time, the greater the loss of the inverter's output fundamental voltage and the greater the degree of voltage waveform distortion; the more the load fundamental current amplitude decreases, the more severe the current waveform distortion.
For a given dead time, a decrease in the load power factor will increase the amplitude of the inverter's output fundamental voltage, decrease the voltage waveform distortion rate, decrease the amplitude of the fundamental current, and increase the current waveform distortion rate.
• When the output voltage is low, the amplitude of the space voltage vector is very small, the relative conduction time of the three bridge arms becomes shorter, and the impact of the dead time becomes greater.
Dead zone affects not only the output voltage amplitude but also its phase; the dead zone causes the PWM waveform to become symmetrical about the center, thus causing a deviation in the amplitude of the space voltage vector and a change in its phase.
Location-based dynamic dead zone compensation method
A common feature of various dead-time compensation methods is that they compensate for the voltage signal based on the current waveform. Therefore, it is necessary to detect the actual current value, determine the positive and negative signs of each phase current, and use the zero-crossing point as the switching moment of the compensation voltage signal. The current detection stage consists of a current sensor, a low-pass filter, and an A/D converter; digital filtering is also required in the program to reduce noise. The detected current contains errors caused by device precision and interference, and also has a phase delay. Therefore, it is difficult to accurately compensate for the dead-time effect using the actual detected current signal, and even greater current distortion may occur due to incorrect compensation near the zero-crossing point.
Currently, torque control in PMSMs is mostly achieved through vector control. To accurately control the motor current, its current loop response frequency is very high, reaching over 1kHz, allowing the actual current to precisely track the current command signal. In high-precision AC servo systems, high-resolution position sensors, typically 16 or 17 bits, are required to achieve high-precision position servo control. However, high-speed, high-precision A/D devices are relatively expensive, with resolutions generally limited to 10 or 12 bits. Since the current vector is related to the rotor position, if the position signal is used to determine the current's sign, and a voltage dead-zone compensation signal is applied, the compensation accuracy can be higher than that of the actual current signal used, and it is unaffected by interference signals.
As can be seen from the PMSM vector diagram, the current vector of the field-oriented control forms a 90° (electrical angle) with the rotor magnetic poles and rotates synchronously with the rotor. The position of the rotor magnetic poles can be determined by a high-resolution encoder. After rotor field-oriented control, the electrical angle of the current changing over time coincides with the spatial rotation angle of the magnetic poles, thus obtaining the spatial position of the current vector. Based on the spatial position of the current vector, the zero-crossing point of each phase current can be determined.
The position angle of the magnetic poles has a fixed relationship with the phase of the current. After analysis, we perform voltage compensation according to the following position change law:
• When the angle 0 < θ < π, ia > 0, phase a compensates for the forward voltage; otherwise, it compensates for the reverse voltage.
• When the angle 2π/3 < θ < 5π/3, ib > 0, and phase b compensates for the forward voltage; otherwise, it compensates for the reverse voltage.
When the angle -2π/3 < θ < π/3, ic > 0, and phase c compensates for the forward voltage; otherwise, it compensates for the reverse voltage.
The formula for calculating the amplitude of the compensation voltage is:
Where factor is the adjustment coefficient, which is usually taken as 0.7.
Figures 4 and 5 compare the experimental results with and without dead-time compensation. The current waveforms show that the current without dead-time compensation is distorted at the zero-crossing point.
There are flat steps. After adding the dead-zone compensation method mentioned above, the actual current in Figure 5 tracks the given current, resulting in a sine waveform with excellent performance.
The switching dead-time effect of inverters has a significant impact on the performance of AC servo systems, therefore, dead-time correction and compensation are necessary. This paper, based on an analysis of various dead-time compensation methods, proposes a dynamic compensation method based on position detection signals. This method utilizes a high-resolution encoder to improve the accuracy of current direction determination, and experiments demonstrate its good compensation effect.
