Abstract: Introduced one kind based on the overtone compensation’s invertor profile control technology, has analyzed system’s principle of work, has discussed the control system parameter design method in detail, and has obtained the test result.
Key word: Overtone compensation; Invertor; Profile control
Introduction
The invertor is one kind of important DC/AC transducer. Weighs its performance an important target is the output voltage profile quality, a good invertor, its output voltage profile should as far as possible close sine, 
the total overtone distortion factor (THD) be supposed to be as far as possible small. The invertor needs to meet the rectification load frequently in the practical application, in this case uses the SPWM modulating technology merely the invertor, its output voltage profile will have the very big distortion.
In order to obtain the THD small output voltage, the profile control technology obtained the enormous development in recent years. Repeatedly controlled [1] is the recent years the quite studies many one kind of control plans. This article from overtone compensation’s angle embarking, uses the advanced version FFT algorithm to carry on the real-time spectral analysis to the output voltage error signal, the process pre-distortion’s overtone signal which produces by the software algorithm pours into the invertor, from this achieves suppresses the misalignment perturbation, thus adjustment output voltage profile goal.
1 control system structure and principle of work analysis
Figure 1 is control system structure diagram [2]. G1(s) expression controlled member, outputs the LC filter’s transfer function in here, its discretization form by G1(z) expressed. G2(z) expresses the internal model, it and G1(z) equal.
1.1 perturbation suppress the principle
Consideration disturbing signal d(z) in an output response. May very easy obtain the disturbing signal biography letter by Figure 1
Hd(z)=1-{[Gc(z)G1(z)]/1 [G1(z)-G2(z)]Gc(z)} (1)
As a result of G1(z)=G2(z), therefore Hd(z) may simplify as
Hd(z)=1-Gc(z)G1(z) (2)
Obviously, so long as Gc(z)=G1-1(z), then Hd(z)=0, namely the perturbation may be under complete suppression.
Unfortunately, the actual invertor’s z territory transfer function includes a pure time delay link, this means that overtone compensator Gc(z) must include a in advance link, this is unable in physics to realize. But we only need suppress the low order overtone in the practical application to be possible to obtain the good output voltage profile, therefore, only needed to cause the overtone compensator low frequency band frequency characteristic is controlled member G1(s) low frequency band frequency characteristic counter may. But this is very easy to achieve, this article this kind of low frequency band frequency characteristic significance in counter named “equivalent counter”.
1.2 internal models
The internal model G2(z) was equal to that G1(s) discretization form G1(z), its function is the analogue control object characteristic, takes the reference supply oscillator. In the actual system, the internal model takes an entire numerical control system’s part, realizes by the DSP software algorithm.
1.3 overtone compensators
The overtone compensator is composed of the FFT harmonious wave generating apparatus. The FFT algorithm carries on the real-time spectral analysis to the output voltage error, because, the invertor meets the rectification load, its output voltage distortion is mainly because has superimposed the number of times low odd harmonic in the out-port, therefore, only need analyze 1,3,5,7,9 subharmonics the peak-to-peak value and at the beginning of the phase may satisfy the request.
Supposes x(n) is N spot finite sequence, its FFT is
In the formula: k=0,1,…, N-1;
Obviously, conventional FFT algorithm, its output points and entrance point
The number is equal, but only need extract in this system X(1), X(3),
X(5), X(7), X(9) and so on 5 output spots, other output cannot calculate. According to may know based on FFT butterfly-shaped computation flow chart [3], in only need calculate in a certain output situation which assigns, may reduce the computation load greatly, saves the massive DSP clock, this causes in computing power not formidable F240 on fixed-point DSP, realized based on the FFT algorithm real-time spectral analysis into possibility. This article the algorithm which simplifies this kind of process is called the advanced version FFT algorithm.
Harmonic oscillator’s function is the overtone which analyzes FFT carries on the pre-distortion, then gives the pre-distortion’s overtone signal as the compensation instruction the controlled member. The reason that must carry on the pre-distortion to the overtone, is because the controlled member has the difference to the overtone track, this causes the overtone signal to arrive through the controlled plant when the perturbation pours into, with the disturbing signal shape is not same, but is the phase just right difference 180° signal, like this is unable to counter-balance the perturbation well. Harmonic oscillator’s pre-distortion algorithm expression is as follows:
In the formula: |X(n)| is the overtone peak-to-peak value;
pha(n) is the overtone at the beginning of phase, they obtain by the FFT algorithm computation;
modcoeff(n) is the peak-to-peak value compensation coefficient;
phacoeff(n) is the phase compensation coefficient.
Type (4) for the single overtone’s compensation instruction formula, type (5) all overtones which needs to compensate for the system always compensates the instruction formula, it is each single overtone compensation instruction simple accumulation.
Peak-to-peak value compensation coefficient modcoeff(n) and phase compensation coefficient phacoeff(n) may through a controlled member frequency, the phase-frequency characteristic basis “equivalent counter” the principle determined simply. Specifically speaking, modcoeff(n) is the amplitude-frequency characteristic frequency corresponding points reading reciprocal, phacoeff(n) is the phase-frequency characteristic frequency corresponding points reading negative number. May see, the overtone compensator compensation coefficient’s determination is very simple, this is this article uses the control plan a big merit.
2 control system parameter design
2.1 FFT sampling frequency fs and analysis window length L determination [4]
Uses the FFT algorithm to carry on the real-time spectral analysis, sampling frequency fs and the analysis window length L determination is very important. The supposition needs analytical signal upper frequency is fmax. According to the Shannon sampling law, only need satisfy
fs≥2fmax(6)
May cause by the analytical signal not to produce in the frequency range the aliasing. In here, the fundamental wave is 50Hz, highest only needs to analyze to 9 subharmonics, therefore fmax=450Hz. In order to leave leeway certain allowance, fs takes 1.6kHz in the actual system.
Analysis window length L regarding periodic signal’s spectral analysis is also extremely important, generally takes L for by the analytical signal cycle integral multiple, otherwise, will create serious frequency spectrum divulging, will reduce the spectral analysis precision greatly. Obviously, in the actual system the error voltage signal period which analyzes is the fundamental wave cycle, is 0.02s. Therefore takes L is 0.02s (i.e. for a cyclical time).
According to FFT data-in points N formula: N=fs×L, as well as sampling frequency fs and analysis window length L value,
May obtain N=32. That is, this control system must do 32 some FFT.
2.2 peak-to-peak value compensation coefficient and phase compensation coefficient determination
In Figure 2, potential source U represents from the contravariant bridge’s output voltage, inductance L and the electric capacity C constitution outputs the LC filter, the current supply I the electric current which derives on behalf of the load, with filter inductance L series connected resistance r is the filter inductance equivalent series resistance. May know by Figure 2, in regards as the contravariant bridge in a proportional component’s situation, invertor’s mathematical model is by outputs the second order system which the LC filter constitute. In this system, L=0.552mH, r=0.3Ω, C=135μF, therefore the invertor mathematical model is
G1(s)=3663 2/(s2 2×0.074×3663s 3663 2) (7)
Its discretization expression is
G1(z)=(0.1007z 0.09845)/(z2 -1.735z 0.9343) (8)
According to Figure 3, may obtain peak-to-peak value compensation coefficient modcoeff(n) and phase compensation coefficient phacoeff(n) very conveniently. Table 1 has given the final value.
Table 1 compensation coefficient value
|
Wave number |
Peak-to-peak value compensation coefficient (enlargement factor) |
Phase compensation coefficient (angle) |
|
Fundamental wave |
0.993 |
0.7 |
|
3 subharmonics |
0.934 |
2.3 |
|
5 subharmonics |
0.818 |
4.5 |
|
7 subharmonics |
0.643 |
7.9 |
|
9 subharmonics |
0.417 |
15.7 |
3 experimental results
The control plan which uses to this article has carried on the experiment, the invertor parameter for L=0.552mH, r=0.3Ω, C=135μF, turn-on frequency f=8kHz, output frequency 50Hz, peak-to-peak value 110V alternating voltage. Uses piece of TI TMS320F240 fixed-point DSP to realize all control function. The resistive load parameter is R=11Ω. The rectification load parameter is L=0.8mH, C=2460μF, R=27Ω.
Experiment profile like chart 4, Figure 5 and shown in Figure 6.
Figure 4 gave the invertor to meet the resistive load the steady-state output voltage and the current waveform. Figure 5 and Figure 6 gave the invertor to meet in separately the rectification load situation the split-ring stable state, the closed loop stable state experiment profile. May see in the split-ring situation the output voltage waveform distortion to be serious, the closed loop later output voltage profile had the enormous improvement.
4 conclusions
This article has used one kind with the redundant control different profile control plan. The experimental result indicated that this article uses the advanced version FFT algorithm reduced the computation load greatly, had guaranteed realizes the real-time spectral analysis in F240 on fixed-point DSP, and the entire control system has the good stable state performance. This indicated this article uses the control plan is theoretically correct, in the practice is feasible. Moreover, this kind also has the overtone compensator compensation coefficient design simple merit based on the overtone compensation thought’s control technology. In brief, this control plan has the good performance, but also has some unique merits, has certain use value.
