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Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin CRC Press, CRC Press LLC ISBN: 0849398045 Pub Date: 11/01/98 |
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Now, using the membership functions of both fuzzy variables (Figure 9a), their degree of membership for the different fuzzy sets can be determined. For eI, these are the following:
μN(ei) = 0.2
μS(ei) = 0.8
The output error eo is a full member of N and, thus, its degree of membership is unity.
μN(ei) = 1
Then, using the fuzzy rules given in Figure 9b) the following fuzzy rules can be written for this particular case:
R1: if ei is N and eo is N then c is Out. |
R2: if eiis S and eo is N then c is In. |
Now, a method to determine which rule applies is required to actually make the control action, that is to decide which converter port is to be controlled. In this chapter, the fuzzy interface method employed for this purpose is the minimum operation rule used as a fuzzy implementation function. As has already been shown, the membership distribution functions of the fuzzy sets associated to each fuzzy variable and control variable, i.e., Aj, Bj, and Cj, are respectively given by μAj, μBj, and μCj. Then, the firing strength of the jth rule is represented by
where the firing strength αj is a measure of the contribution of jth rule to the fuzzy control action. In the example considered, the firing strengths of both active rules are given by
With fuzzy reasoning of the first type [18][19], Mamdanis minimum operation rule as a fuzzy implication function, the jth rule leads to the following control decision:
Therefore, the outputs membership function μC of the output c is pointwise given by
Since the output c is crisp, the maximum criterion is used for defuzzification. This criterion uses, as control, output the point where the possibility distribution of the control action reaches a maximum value. With this criterion, the output for the example under study would be the maximum of the two active rules, which is rule R2, of firing strength α2. Therefore, the converter port to be controlled would be the Input port.
This controller is in charge of the converters output line currents. The sole objective of this controller is to keep the loads current space vector within the accepted error zone of the reference current vector. This is the same control objective of the predictive current control; the difference lies in the way the objective is accomplished. Figure 6 shows the reference current vector and loads current vector in the α-β plane.
The controller will act upon reception of the order from the fuzzy controller, once this controller has determined that the output port has higher priority. It will then pass the command of the converter to the loads line current controller. Granted this, the controller will select the next converter state, which will be the one that will bring the current vector back to the reference current vectors error zone, and do so for the longest amount of time. The actual converter state selection is realized using the XSVM.
The output port control requires obtaining the input phase voltages, output line voltages, and the output line currents. To fulfill these requirements, only the input phase voltages and output line currents need to be physically measured by proper equipment, that is transformers and current sensors. The output line voltages are obtained by a software waveform reconstruction. This operation can be done using the converters transfer function H, as shown in (29).
Sinusoidal three-phase systems produce sinusoidal two-phase systems when transformed by Parks matrix, thus producing a rotating space vector of constant magnitude. This is not the case for the output line voltages reconstructed with (29), as the line voltages are pulses varying their average value in order to follow a sinusoidal reference. So, in order to obtain the desired line voltages space vector, the fundamental component of the line voltages is required. These are simply obtained by filtering the respective waveforms. To implement the filters, a digital approach is chosen, as it lacks all the problems associated to analog filters, specifically the parameters variation and the tuning of it. The digital filter is realized by software, and can be precisely designed to produce the required filtering characteristics.
The digital filter used for this converter is an IIR digital low pass filter [23]. It is used to obtain the fundamental frequency component Vlf out of the line voltages obtained with (29). The filter design parameters are shown in Table IV.
Filters | Type | Order | Cutoff f [Hz] | Pass/stop ripple [dB] |
---|---|---|---|---|
Vo, Iin | elliptic, low pass | 4th | 150 | 0.01 - 20 |
Iin | elliptic, band pass | 14th | 200 - 1050 | 0.01 - 20 |
After filtering the line voltages, these are transformed with Parks matrix into voltage space vectors together with the three phase load line currents Il which are transformed with (17) into a space vector as in (30).
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