Research on Waveform Control Technology of CVCF Inverter-EEWORLD

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1 Introduction

In power electronic devices, UPS with CVCF inverter as the core has been widely used. The main technical requirements for its output waveform include low steady-state total harmonic distortion (THD) and fast dynamic response. Due to the influence of factors such as nonlinear load, dead zone in PWM modulation process and weak damping of the inverter system itself, the general closed-loop PWM control effect is not ideal. This paper uses TMS320F240DSP produced by TI Company of the United States as the control chip, adopts repetitive control [1] to improve the steady-state performance of the system, and adopts pole configuration [2] with the introduction of integral control [2] to improve the dynamic characteristics of the system. The experimental results show that this scheme can achieve high-quality steady-state and dynamic characteristics at the same time.

2 Repetitive controller design

The basic idea of repetitive control comes from the internal model principle [3] in control theory, that is, if the control system is expected to achieve zero static error tracking of a reference instruction, then the model that generates the reference instruction must be included in the stable closed-loop control system. Figure 1 is the block diagram of the repetitive control used in this system, and its various parts are analyzed and explained below.

Fig.1 Block diagram of discrete domain repetitive controller
P(z) is the discrete transfer function between the input and output of the inverter and is the control object in the system. The switching frequency of the inverter is much higher than the natural frequency of the LC filter. Its dynamic characteristics are mainly determined by the LC filter. P(z) is obtained by establishing the system state equation. In this system, L=0.88mH, C=60µF, the equivalent series resistance of the inductor is 0.4Ω, the switching frequency and sampling frequency are both 10KHz, and its discrete transfer function is derived as:

[page] The Bode diagram is shown in Figure 2. It can be seen that the inverter has a resonance peak and the damping ratio is very small.

Figure 2 Bode diagram of inverter P(z)
The dotted box in Figure 1 is the internal model of the repetitive controller, and N is the number of samples in one cycle. This internal model is actually a periodic delayed positive feedback link. As long as the input signal repeats in the fundamental period, its output is the cycle-by-cycle accumulation of the input signal. When Q(z) takes the value of 1, it can be regarded as an integral link with a period as the step length, which can achieve zero static error, but it brings N poles located on the unit circle to the system, causing the open-loop system to present a critical oscillation state. In this system, Q(z) is taken as 0.95 to improve system stability.
The repetitive controller in Figure 1 contains a compensator

The filter S(z) consists of the following two parts:

The notch filter S1(z) is mainly used to cancel the resonance peak of the inverter, and the second-order filter S2(z) mainly provides high-frequency attenuation. The lead link zk compensates for the total phase lag of the filter S(z) and the control object P(z), and Kr is the repeated control gain. The purpose of the compensator C(z) is to make the low-frequency gain of the corrected object close to 1, and the high-frequency gain is reduced to below -26dB as soon as possible, while the total phase shift of the system in the entire low-frequency band forward channel is as small as possible. Take Kr = 0.9, zk = z5, and make the Bode diagram of C(z)P(z), as shown in Figure 3, it can be seen that the design meets the requirements.

Figure 3 Bode plot of C(z)P(z)
The periodic delay link zN connected in series on the forward channel delays the control action by one cycle, that is, the error information detected in this cycle begins to affect the control quantity in the next cycle. The main reason for introducing the periodic delay link is that the system contains an advance link zk. If this system is to be physically realized, there must be a delay link.

[page]3 Pole configuration

Repeated control effectively improves the steady-state performance of the inverter, but the dynamic response is poor. In fact, the main reason why the natural dynamic characteristics of the inverter are not good is that the damping of the inverter itself is too weak. For this, the most direct and effective solution is to introduce state feedback, perform pole configuration, and increase the damping of the control object.
Figure 4 is the equivalent circuit of a single-phase inverter, and the damping is the smallest when the inverter is unloaded. Therefore, when implementing the pole configuration, it is assumed that the inverter is unloaded (the worst case). When configuring the poles, it should be noted that the damping ratio will increase after the inverter is loaded.

Figure 4 Single-phase PWM inverter model
Taking capacitor voltage vC and capacitor current iC as state variables, the no-load model of PWM inverter is:

Introducing state feedback

, where r is the reference command of the closed-loop system and K is the feedback gain matrix, then the state equation of the closed-loop system becomes:

The closed-loop poles are configured at the 0.74±0.3i point in the z domain. At this time, the system self-oscillation frequency ωn is 4454rad/s (roughly the same as the cutoff frequency of the LC filter); the damping ratio ξ is 0.5. Figure 5(a) is the system's sudden load simulation waveform. It is observed that the output voltage cannot completely return to the original trajectory after the sudden drop, but has an inherent static error. Analysis of the feedback system shows that the capacitor voltage vC feedback is equivalent to a proportional link P, and the capacitor current iC feedback is equivalent to a differential link D, neither of which can eliminate the static error. Therefore, we introduce an integral link in the control system, and use the integral of the output y and the state variable as the feedback quantity. Assume that this new variable is xI, that is

, the original second-order system becomes a third-order system

A new pole is added at 0.1 in the z domain. The sudden load simulation waveform of the system is shown in Figure 5(b). We can see that the original static error has been eliminated.

Figure 5: Sudden load simulation comparison

[page]4 Composite control

The above two control schemes constitute the entire control system, among which the state feedback pole configuration control is located in the inner layer of the control system, and its purpose is to improve the dynamic response characteristics of the system by reconfiguring the poles. The repetitive control is located in the outer layer of the control system, and its main purpose is to reduce the harmonic distortion caused by factors such as nonlinear loads. As long as the system is stable when the pole configuration and repetitive control act alone, the composite system is stable.

5 Experimental results

Figure 6 is the waveform of the pole configuration system with a rectifier-type nonlinear load, and the THD value is 6.89%. Figure 7 is the working waveform of the nonlinear load after adding the outer layer of repetitive control. The load current peak is 15A, and the THD value is reduced to 1.42%. The voltage spectrum analysis shows that the amplitude of harmonics below the 13th order has obvious attenuation, which verifies that the harmonic suppression ability of the repetitive control is mainly reflected in the medium and low frequency bands. Figure 8 is the voltage waveform of the composite system with a resistive load of 5A suddenly added. The system quickly ends the transition process and basically eliminates the static error.

6 Conclusion

This paper analyzes the application of two control methods, repetitive control and pole configuration, in digital CVCF inverters, and proposes a composite control strategy based on repetitive control and pole configuration. Experimental results show that this strategy enables the system to obtain relatively ideal steady-state characteristics and dynamic characteristics, and is easy to implement and has certain practical value.

References

1 Ying yu Tzou, Rong shyang Ou, Meng yueh Chang. High performance programmable AC power source with low harmonic distortion using DSP based repetitive control technique. IEEE Trans. Power electronics, 1997, 12(4): 715-725.
2 Gene F. Franklin , J.David Powell, Abbas Emami-
Naeini, Feedback control of dynamic systems, Addison-Wesley Publishing Company, Inc., 1991.
3 BAFrancis, WMWonham, The internal model principle for linear multivariable regulators. Appl. Math. Opt, vol2, no.2: 170-194, 1975.

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