Research on Inverter Based on DSP and Incremental PI Voltage Loop Control

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Research on Inverter Based on DSP and Incremental PI Voltage Loop Control [Copy link]

Abstract: This paper studies an inverter based on digital control. The scheme adopts voltage instantaneous value loop control to improve output stability while taking into account output dynamic performance. The incremental PI law is used in the feedback circuit, and the PI increment and PI output are limited to avoid output instability caused by false disturbances, further ensuring the stability and dynamic performance of the system. TMS320LF2407A is used to implement the algorithm, and an inverter experiment with a maximum output of 200V and an output power of 500W is carried out.

Keywords: inverter; voltage loop control; incremental PI; DSP control

　

0 Introduction

At present, among the most widely used PWM technologies for inverters, SPWM control has many advantages. Its control technologies mainly include single-loop feedback of voltage instantaneous value, single-loop feedback of current instantaneous value, voltage and current dual-loop feedback loop control and voltage space vector control. The voltage loop makes the system have better stability, and the instantaneous value feedback enhances the dynamic performance of the system [1]. The voltage loop adopts PI control, in which the proportional link promptly reflects the deviation signal of the control system. Once the deviation occurs, the controller immediately takes control action to reduce the deviation; the integral link is mainly used to eliminate static error and improve the system's error-free degree. Compared with position control, incremental control has less impact on false operation, which can be eliminated by logical judgment when necessary; and the impact is small when switching between manual and automatic, which is convenient for achieving disturbance-free switching; at the same time, its formula does not require accumulation, and it is easier to obtain better control effect through weighted processing [2].

Compared with digital control, traditional analog control has exposed many disadvantages: it requires a large number of discrete components and circuit boards, which has a relatively high manufacturing cost; a large number of analog components make the connection between them quite complicated; the aging problem and uncompensable temperature drift problem of analog components, as well as susceptibility to environmental interference, will affect the long-term stability of the control system. With the continuous improvement of the reliability and quality of microprocessors, digital control has occupied a dominant position in inverter control [3]. This paper proposes a solution based on DSP control.

1 Inverter Modeling

The single-phase full-bridge inverter is shown in Figure 1, where E is the input DC voltage, S1 _~ S4 _are switch tubes, L is the filter inductor, r is the inductor equivalent internal resistance, C is the filter capacitor, and R is the load.

Figure 1 Single-phase full-bridge inverter

Let Ls represent the _inductance and 1/ Cs represent the _capacitance , and we can derive the transfer function G ( s ) between the output voltage Vo(s) and the voltage Vi(s) between _points AB as shown in _equation ( 1 ) .

G ( s ) = = (1)

Ignoring the equivalent internal resistance of the inductor, equation (1) can be simplified to

G ( s ) = (2)

In a switching cycle, when S1 _and S4 _are turned on, vi _is -E ; when S2 _and S3 _are turned on, vi is E. Since the switching frequency is 400 times the output frequency, the average value can be used instead of the instantaneous value _in a switching cycle.

v _i = ED +(- E )(1- D )=(2 D -1) E (3)

This solution uses bipolar SPWM, so

D = (4)

Where: v _m is a sinusoidal wave signal, v _m = V _m sin ωt ;

V _tri is the peak value of the triangle carrier.

The modulation ratio M is

M = (5)

Substituting equation (5) into equation (3), we can obtain

vi _≈ (6 )

Transformed into frequency domain,

(7)

From equation (7) and equation (1), we can get equation (8):

(8)

This is the inverter output transfer function, from which the equivalent block diagram of the inverter is shown in Figure 2.

Figure 2 Inverter equivalent block diagram

2 Control scheme design

This system uses voltage loop feedback, and instantaneous value control is used to improve dynamic performance. In the voltage loop control, incremental PI control is used, and its algorithm is optimized to ensure that the output has good stability. The controller uses TI's TMS320LF2407A, whose maximum operating frequency can reach 40MHz, which can well implement the above algorithm.

2.1 Voltage loop design

Ignoring the equivalent internal resistance of the inductor, the equivalent block diagram of the voltage loop is shown in Figure 3.

Figure 3 Voltage loop equivalent block diagram

In the figure: K _pwm is the equivalent gain of the PWM link, and its magnitude is the gain of the modulation wave output to both ends of the inverter AB;

K is the voltage sampling coefficient in the feedback loop.

FIG3 can be simplified to FIG4.

Figure 4 Simplified block diagram of voltage loop

The K _pwm coefficient in the figure has been attributed to the PI module. The inverter switching frequency is 20kHz, and the output is industrial frequency, so the LC filter's corner frequency f _n is 1kHz. Considering the inductor current ripple and voltage drop, L = 1mH, C = 10μF. In this experiment, R = 40Ω at full load .

Assume that the PI link transfer function is

G ( s ) = K _p + (9)

The open-loop transfer function of the system is

G ( s ) = K (10)

The PI compensation frequency is 500Hz, and the system crossover frequency is 1kHz. Then, from equation (10), we can get

=2π×500（11）

=1(12)

Where: K is the sampling coefficient, which is designed to be 0.014 in the experiment.

Combining equations (11) and (12), we can get

k _p =39 k _i =124416

Its Bode diagram is shown in Figure 5.

Figure 5 Voltage loop Bode plot

It can be seen from Figure 5 that the system phase margin is 60°, which meets the stability requirement. Figure 6 is the output waveform obtained by simulation.

As can be seen from Figure 6, the output waveform is a sine wave with an amplitude of 200V and a frequency of 50Hz, which is consistent with the design value.

Figure 6 Inverter output waveform

2.2 Incremental PI algorithm and its optimization

The transfer function of the PI link is equation (9), and its corresponding time domain equation is

y ( t )= _kp ( 13)

Where: y ( t ) is the PI output;

e ( t ) is the PI differential input;

Ti is the integration time constant _;

kp is _the proportionality coefficient.

Discretize equation (13) to get

y _k = k _p（14）

Where: Ts _is the sampling time.

This is position PI control. If incremental PI control is used, false operation can be avoided. At the same time, the calculation does not need accumulation, which is particularly convenient for digital control. From formula (14), we can get

y _k－1 = k _p（15）

From equations (14) and (15), we can get

y _k = y _{k- 1} + k _p e _k k _p · e _{k 1} (16)

Formula (16) is a general incremental PI algorithm. However, in actual control, many unstable factors can easily cause the increment to be larger, even larger than the output, which in turn causes the output waveform to be unstable. Therefore, the incremental PI algorithm must be optimized. This scheme adopts the saturation zone judgment rule, that is, the increment

Δ y _k = k p e _k k _p · e _{k 1} (17)

When the absolute value exceeds a certain upper limit Δ Y _lim , that is, enters the saturation zone, Δ Y _lim is assigned an absolute value. However, even after the increment is judged in the saturation zone, its output may be very large due to the accumulation result, and even exceed the carrier amplitude. Therefore, the PI output must also be limited. At this time, the modulation wave amplitude can be used as the limit value, or the carrier amplitude can be simply used as the limit value. After stabilization, this amplitude will not exceed the modulation wave amplitude.

2.3 Implementation of DSP control algorithm

TI's TMS320LF2407A has a maximum operating frequency of 40MHz and a Harvard storage structure. The addressing area of data, program and I/O space can be up to 64k and are independent of each other. There is 32k flash space on the chip. At the same time, the chip has an A/D module with a resolution of 10 bits. It also has a PWM output port that can realize in-phase and inverted output, and can also add dead zone control, which can better implement the voltage loop control algorithm [4].

The program uses a maximum operating frequency of 40MHz and a switching frequency of 20kHz. The timer's periodic interrupt is used to generate a symmetrical triangular carrier using a continuous increase or decrease mode. Set the comparison output enable, use the values of the comparison registers CMPR1 and CMPR2 to control the outputs of PWM1 to PWM4, generate two in-phase and inverted PWM signals, and control the on and off of the switch tube. At the same time, in order to avoid the upper and lower bridge arms being turned on at the same time, a 0.5μs dead zone control is added to the program. The calculation of CMPR1 and CMPR2 is given by each periodic interrupt. During the periodic interrupt, the duty cycle D is generated by sampling the voltage feedback value and after optimized PI incremental control. The values of CMPR1 and CMPR2 can be obtained by D and the timing period. Figure 7 is a program flow chart for periodic interrupts.

Figure 7 Cycle interrupt flow chart

3 Experimental Results

The main circuit of the experiment is a single-phase full-bridge circuit, as shown in Figure 1. The switch tube uses a 20N60S MOS tube, the filter inductor is 1mH, the filter capacitor is 10μF, the load R is 40Ω, the input DC voltage is 250V, and the switching frequency is 20kHz. The proportional coefficient in the PI algorithm is 39, and the integral time constant is (1/3140)s.

FIG8 is an output voltage waveform. It can be seen from FIG8 that the output voltage peak is 200V, the frequency is 50Hz, the THD is very small, and the output waveform is stable.

Figure 8 Inverter output waveform

Figure 9 shows the change of the output waveform when the load is full and then half loaded. It can be seen from Figure 9 that the output immediately returns to stability after a slight disturbance, indicating that the dynamic performance is relatively good.

Figure 9 Output voltage waveform when full load is cut to half load

4 Conclusion

The inverter scheme proposed in this paper adopts voltage instantaneous value control, the feedback loop adopts incremental PI control, and limits the PI increment and PI output to ensure the stability and accuracy of the output, while avoiding false disturbances and having good dynamic performance. The controller is implemented using TI's TMS320LF2407A, which completes the control algorithm well.