Explanation of two dual-loop instantaneous feedback control methods in inverter power supply

　　This paper analyzes two dual-loop instantaneous feedback control methods of the inverter - current-type quasi-PWM control method and three-state DPM current hysteresis tracking control method, introduces their working principles, analyzes and compares their dynamic and static performances, and gives specific implementation circuits and system simulation results.

　　Current-mode dual-loop control technology is widely used in DC/DC converters. It can achieve better dynamic and static performance than single voltage-loop control [3]. The basic idea is to use the output of the outer loop voltage regulator as the inner loop current, detect the inductor (or switch) current and compare it with the inner loop current, and then control the power switch by the output of the comparator, so that the peak current of the inductor and the power switch directly changes with the output of the voltage regulator. The current and voltage dual closed-loop converter system thus constructed has good transient performance and high steady-state accuracy, especially the inherent current limiting capability of the power switch current. The inverter (DC/AC converter) is much more complicated to control than the DC/DC converter due to its AC output. In the early days, the open-loop control method with switch point preset was adopted [1]. In recent years, the transient feedback control method has been widely studied, and a variety of distinctive implementation schemes have been proposed. Among them, the three-state DPM (discrete pulse modulation) current hysteresis tracking control method has excellent performance and is easy to implement. This paper successfully applies the current-mode PWM control method to inverter control, introduces its working principle, compares the dynamic and static performance with the current hysteresis tracking control method, and gives simulation results.

　　Three-state DPM current hysteresis tracking control method

　　There are many implementation forms of current hysteresis tracking control, among which the three-state DPM current hysteresis tracking control has better performance and is easy to implement. Referring to Figure 1, its basic working principle is: detect the filter inductor current iL and generate a current feedback signal if. if is compared with the given current ig, and the difference between the two current instantaneous values ​​is used to determine the conduction status of the four switches of the single-phase inverter bridge in the next switching cycle: when ig-if>h (h is shown in Figure 1, which is the current hysteresis width and can be selected according to the reference [1] P64 formula 5?2), S1 and S4 are turned on, UAB=+E, +1 state; when ig-if-h, S2 and S3 are turned on, UAB=“-”E, -1 state; when |ig-if|h, S1, S3 or S2, S4 are turned on, UAB=“0,” 0 state. The two D flip-flops make the switch state change of S1~S4 only occur at the rising edge of the periodic pulse signal CLK (frequency 2f), that is, the switch point is discrete on the time axis, and the maximum switching frequency is f.

　　Simulation and experiments show that in the positive half cycle of iL, the inverter basically switches between the +1 and 0 states, while in the negative half cycle of iL, the inverter basically switches between the -1 and 0 states. Only near the zero crossing point of U0 are there a small number of state jumps between +1 and -1, thereby reducing the output pulsation.

　　Current-mode quasi-PWM control

Figure 1 Three-state DPM current hysteresis tracking control method

　　Combining the advantages and disadvantages of conventional PWM unipolar and bipolar working modes, and drawing on the hysteresis control technology, the improved current loop control circuit is shown in Figure 2. S3 and S4 basically work in a low-frequency complementary manner, and S1 and S2 work in a high-frequency complementary manner. Its basic working principle:

　　(1) Ig positive half cycle, that is, when Ig>0

　　Comparator CMP1 outputs a high level and S3 is always off.

　　The rising edge of the clock signal CLK sets the trigger RS1 to 1, S1 and S4 are turned on, S2 is turned off, UAB is +E, and iL rises according to formula (1).

　　M1=diL/dt=（E-U0）/L（1）

　　When iL rises to if>ig, RS1 flips, S1 turns off, S2 turns on, UAB is 0, and iL changes according to formula (2)

　　M2=diL/dt=-U0/L（2）

　　If U0>0, iL decreases until the switching cycle ends; if U00, iL continues to increase, and three situations may occur:

　　①If the rising rate of if is less than ig, then if decreases relative to ig until the end of the switching cycle;

　　②If the rising rate of if is slightly greater than ig, if is greater than ig but less than ig+h at the end of the switching cycle, the next switching cycle will still maintain this state (UAB is 0);

　　③ If if rises to ig+h, CMP3 flips to 1, RS3 is cleared, S4 is turned off, the load continues to flow through D2 and D3, UAB is -E, and iL decreases according to formula (3) until the switching cycle ends. The peak value of if is not greater than ig+h

　　M2=diL/dt=-(E+U0)/L(3)

　　(2) In the negative half cycle of ig, that is, the ig comparator CMP1 outputs a low level and S4 is always off.

　　The rising edge of the clock signal CLK clears the flip-flop RS2 to 0, S2 and S3 are turned on, S1 is turned off, UAB is -E, and iL decreases according to formula (3).

　　When iL drops to if, RS2 flips, S2 turns off, S1 turns on, UAB is 0, and iL changes according to formula (2): if U0, iL rises until the end of the switching cycle; if U0>0, iL continues to decrease. At this time, three situations may occur:

　　①If the falling rate of if is less than ig, then if rises relative to ig until the end of the switching cycle;

　　②If the rate of if decreases is slightly greater than ig, if is less than ig but greater than ig-h at the end of the switching cycle, then the next switching cycle will still maintain this state (UAB is 0);

　　③ If if drops to ig-h, CMP4 flips to 1, RS3 is cleared, S3 is turned off, the load continues to flow through D1 and D4, UAB is +E, and iL rises according to formula (1) until the end of the switching cycle. The peak value of |if| is not greater than |ig-h|, that is, |ig|+h.

　　It can be seen that this is also a three-state working mode: when iL and U0 are in phase, the inverter works in PWM mode, switching between state 1 and state 0 (or state -1 and state 0); when the two are in anti-phase, the hysteresis loop takes effect, which makes the inverter switch between the three states of 1, 0 and -1.

Figure 2 Current-mode quasi-PWM

　　Comparison of static performance

　　Taking a certain inverter as an example, the dynamic and static performances under the above two control modes are analyzed and compared. Circuit parameters: E=180VDC, L=1mH, C=20μF; modulation frequency is f; output: U0=115VAC, fo=400Hz; rated load: 1kVA, current and voltage feedback coefficients are 0.4167 and 0.25 respectively; voltage regulator is PI type: amplification factor Ap=13?5, time constant τ1=0.27ms;

　　Table 1 shows the static error between U0 and the reference voltage Ur and the THD of U0 under different loads and different modulation frequencies.

　　Table 1 Comparison of steady-state performance under different control modes

Figure 3 Dynamic response process of starting and sudden load increase or decrease

　　(a) Three-state DPM current hysteresis tracking control method

　　(b) Current-type quasi-PWM control method

　　Analyzing Table 1 and the simulation waveform (omitted), we find that:

　　(1) When the modulation frequency f is low, the current-type quasi-PWM waveform is more severely distorted, but its THD decreases rapidly as f increases.

　　(2) The average switching frequency of the power switch tube in the current-mode PWM mode is higher than that in the hysteresis mode, which means that the switching loss of the former is larger.

　　(3) Under the current-type PWM mode, the harmonic components are concentrated near the modulation frequency and its integer multiples, while under the current hysteresis tracking control mode, the harmonics of UAB are more evenly distributed in a wider range, and it is easy to generate larger noise when the modulation frequency is low.

　　(4) The output voltage static error is basically not affected by the current tracking method and modulation frequency, but mainly depends on the voltage regulator parameters and is also affected by the main circuit parameters.

　　Comparison of dynamic performance

　　Due to the discreteness of the switch point, the DPM current tracking control method introduces an equivalent pure hysteresis link with a time constant of 1/f in the control circuit, which has an adverse effect on the stability and dynamic performance of the closed-loop system. Figure 3 shows the simulated waveforms of the inductor current iL and the output voltage U0 under the two control methods during startup and load changes. It can be seen that the dynamic performance under the PWM method is better, especially when the modulation frequency is low, the difference is more obvious. However, as the modulation frequency increases, the hysteresis time constant decreases, and the dynamic performance of the hysteresis loop method is significantly improved, close to the PWM method.

　　Changing the parameters of the PI voltage regulator (reducing the gain or increasing the integral time constant) can improve the stability of the dynamic response and reduce the dynamic voltage drop, but it will increase the static error, that is, the voltage drop under heavy load, and extend the adjustment time. In other words, under the premise of achieving the same dynamic performance, the current-type PWM control method allows a larger gain or a smaller integral time constant, thereby obtaining better static performance.

　　Conclusion

　　The three-state DPM current hysteresis tracking control method is simple to implement, with low switching loss and distortion. The current-type quasi-PWM control method can obtain better dynamic performance, especially system stability and smaller output voltage drop. The circuit implementation is relatively complex. It is suitable for situations where the modulation frequency is low or the inverter output filter inductor L and capacitor C are small. When the modulation frequency is high, the three-state DPM current hysteresis tracking is a simple and high-performance control method.