The 7th International Conference on Power ElectronicsOctober 22-26, 2007 / EXCO, Daegu, Korea

WEE3·1

Fuzzy Logic Controller for Boost Converterwith Active Power Factor Correction

Ing. Esp. Fredy H. Martinez S.Distrital University Francisco Jose de Caldas

Technological Faculty - Technology in ElectricityCarrera 7 No 40 - 53, Bogota D.C., Colombia

Email: fhmartinezs@udistrital.edu.co

Ing. Teg. Diego F. Gomez M.Distrital University Francisco Jose de Caldas

Technological Faculty - Technology in ElectricityCarrera 7 No 40 - 53, Bogota D.C., Colombia

Email: dgomezm@codensa.com.co

I. INTRODUCTION

Fuzz,­

{'ont..olI Li:

: :

: :

output voltage reference is usually considered as an externalsignal, the inductor current reference depends on theoperating point; for this reason, it is computed by means of alow-pass filter in the assumption that the DC value of thecurrent is automatically adjusted by the converter accordingto the power balance condition [3]. This DC reference is usedby the control unit to construct a sine waveform signalreference in phase with the input voltage (a detector ofcrossing by zero is used). A block diagram of the fuzzycontroller structure is shown in Fig. 1.

The proposed control scheme has been verified on a Boostrectifier of 200 W, output voltage DC of 400 V and nominalinput voltage of 120 V at 60 Hz. The power factor reachedwas 0.924 with a total harmonic distortion of 21.1 %.

The basic theory of the developed design, the collecteddata, conclusions as well as suggestions are presented in orderto solve the identified problems in the implementation of thescheme.

II. THEORY

A. Fuzzy Logic ControllerIn this work, a fuzzy control is applied in the feedback loop

in order to use all the possibilities that this structure of controlcan offer to the active power factor correction. As anadvantage, it is not necessary to use a mathematical model ofthe converter, which supposes a quite complex work.

The control action in a fuzzy logic controller is determinedby a set of linguistic rules. It means, a certain knowledge ofthe converter behavior is required (knowledge of the expert),

uC-FPGA

FuzzyControlv,,{l)

DC-DC Converter

+Vi/I)

Abstract-This paper presents the successful use of fuzzy logicto derive a practical control scheme for boost converter withactive power factor correction. Aspects of sudden changes in theload and the input voltage are discussed and presented. Thefundamentals governing the design, control and performanceare also illustrated. Properties of the proposed controller are:(1) converter with active power factor correction, (2) goodperformance of transient responses under varying loadingconditions and/or input voltage, and (3) robustness around theoperating point.

In the eagerness to reduce the complexity of the circuitswhen implementing traditional solutions for the control ofconverters with active power factor correction, differentcontrol techniques are presented [1], [2], [4]. In classicalapproach, fuzzy controllers are designed by using the outputvoltage error and the change of voltage error, or a mixture ofthese variables. However, to reconstruct the current (powerfactor correction) and to improve the dynamic answer of theconverter; it is necessary for the control to have informationabout the absorbed energy of the network; in order to get that,the error of the input current is included like a variable [5].

In this scheme, the proposed fuzzy controller uses only twoinput variables: (1) Output voltage error (Eu) that is used forthe regulation of the output voltage, and (2) Inductor currenterror (Ei) that is used to improve the dynamic answer of theconverter, to correct the power factor and to limit the currentas a protection. It is important to point out that while the

((I)

Q uC Fig. 2: Detail of the proposed controller

Fig. 1: Converter with proposed controller

sufficient to create the linguistic control rules, but it is notnecessary to create the small signal model. Nevertheless, thefuzzy control cannot provide a better dynamic answer than theobtained by a very well tuned traditional system. The greatadvantage of the scheme is the possibility of considering

978-1-4244-1872-5/08/$25.00 © 2008 IEEE 936

The 7th International Conference on Power ElectronicsOctober 22-26, 2007 I EXCO, Daegu, Korea

3 Current (A)

simultaneously in a simple control scheme, regulation,dynamic answer and power factor correction aspects.

Where a y p are constants used to normalize the voltageand current error. The output variable of the fuzzy control ischange ofduty cycle in (2) [i.e., &l]. The actual duty cycle isdetermined by adding d[n -1] to the calculated change,

(1)E [] VORcf -vo[n] d E·[] ILRef[n]-iL[n]un= an In=......;;;;;;.;;.;..;;...~--

a p

compare directly by the microcontroller with theinstantaneous current value sensed through the inductor. Thissine reference is the signal that allows the fuzzy control tomake the power factor correction (Fig 3).

These input variables to the fuzzy control block are definedas:

t(5)

17m3.3m 5.3m 7.3m 9.3m 11 m 13m-0.5

Om

0.5

Fig. 3: Current error d[n]= 17 x &l[n]+d[n -1] (2)

In the classical approach, fuzzy controllers are designed byusing the output voltage error and the change of voltage error,or a mixture of these variables. However, to reconstruct thecurrent (power factor correction) and to improve the dynamicanswer of the converter; it is necessary for the control to haveinformation about the absorbed energy of the network. Inorder to obtain that, the error of the input current is includedlike a variable. This way, the basic information of the currentloop of the traditional schemes of control is included, but itallows the inclusion ofmore information in the control, thanksto the fuzzy control scheme.

Fig. 2 shows the configuration of the fuzzy logic control.The output voltage of the boost converter is scaled andcompared with the reference value, which is inside amicrocontroller. The current reference value is created bysensing the inductor's current, after being filtered through ananalog low-pas filter, since this value must change based onthe converter's load (operating point). This is supposed, ifthe DC value of the current is automatically adjusted by theconverter according to the power balance condition.

This DC value of the current is used to construct the sinesignal reference, which finally will be the current reference to

10J '00, LXXX: ,ro: I-1 -{l.8 -{l.6 -{l.4 -{l.2 0 0.2 0.4 0.6 0.8 1

Eu

EI ,00: LXXX: :~: 1-1 -{l.8 -{l.6 -{l.4 -{l.2 0 0.2 0.4 0.6 0.8 1

Ei

1° -1 -{l.8 -{l.6 -{l.4 -{l.2 0 0.2 0.4 0.6 0.8 1dd

Fig. 4: Membership functions

Where 17 represents the effective gain of fuzzy control.

Other signals that are introduced to the control block from themicrocontroller are: the value of the current sensed in theinductor, in order to protect the system in case of overcurrents; and a crossing by zero pulse, used as a reference tocreate the sine signal reference (sine reference, I LRef).

B. FuzzificationFuzzificattion is to map Eu and Ei in (1) into suitable

linguistic values. Five fuzzy levels are defined for Eu and Ei,including negative big (NG), negative small (NP), zero (ZE),positive small (PP), and positive big (PG). Each inputvariable is assigned a membership value 11 to each fuzzy set,based on a corresponding membership function. Fig. 4 showsthe membership functions, which are Gaussian fuzzy-setvalues.

Besides, as a way of protecting, an exclusive fuzzy set isused for the input current; it is called LIMIT and is really arestricted point set from 0.7. Whenever, the current is below0.7, normal conditions are assumed and the developed theoryof control is applied. Otherwise, if the current is over 0.7 (forexample, starting point) a special operation in the control isrequired to avoid overshoots. This is described in detail whenthe fuzzy rules are defined.

In order to facilitate the analysis, the input fuzzy variableshave been described by normalized singleton values. Thisway the measured values for these variables are used in theinference process and it is not necessary to use thefuzzification stage.

C. Rules offuzzy control

Construction of fuzzy control rules is a heuristic process,and in this particular case it is based on the followingconditions:

- In normal conditions (iL(t) is not LIMIT):When the output voltage is far from the set point (Eu(t) is

NG or PG), the corrective action must be strong to minimizethe response time (a huge value in the duty cycle increase andreach the set point quickly).

937

The 7th International Conference on Power ElectronicsOctober 22-26, 2007 I EXCO, Daegu, Korea

Fig. 5: Basic control structure

Ei \ Eu NG NP ZE PP PGPG NG PP PM PG PGPP NG ZE PP PG PMZE NG NP ZE PP PMNP NG NG NP ZE PPNG NG NG NM NP ZE

E. DefuzzificationDefuzzification is to convert the inferred fuzzy control

action to a nonfuzzy control action.For the change of d [n] output, seven fuzzy sets are used

(PG, PM, PP, ZE, NP, NM and NG) in order to get a uniformcontrol action. (the larger the numbers of fuzzy sets, thehigher resolution in the fuzzy control is). Fig 4 shows theGaussians membership functions used in the fuzzy control.Each input-output variable is normalized between [-1, 1] byusing suitable scales factors.

During this operation, a crisp value for &l [n] is calculatedby using the center of gravity method.

D. Decision-MakingDecision-Making infers a fuzzy control action from

knowledge of the fuzzy rules and the linguistic variabledefinition. The control rules that determined the output of thefuzzy logic control are based on the general knowledge of thesystem behavior or intuition of the process being controlled.

Fuzzy control inference works depending on the conditionsdefined by the expert, in the rules of fuzzy control. Table 1shows the fuzzy model based on fuzzy rules for the boostrectifier. The entries of the table are the normalized singletonvalues of the change of d[n] , stored in a digital device. Theinferred output of each rule is obtained by Mandani' s minfuzzy implication.

TABLE 1Control rule of the fuzzy logic control

ITL EXPERIMENTAL DESIGN

The fuzzy controller has been implemented by a Xilinx'sFPGA SPARTAN 3. Based circuit and fuzzy computationshave been pre-calculated in MatLab® and stored in theFPGA. The AID conversion and the supervision of alloperation are made by Motorola's M68HC908GP32microcontroller.

Fig 5 shows the implemented control design schematically.It has three basic sections: (1) A pre-processing section,which evaluates the control's inputs. (2) A fuzzy controlbased on a table with the stored duty cycle set points as afunction of the input variables. (3) A PWM that applies thefinal duty cycle to the boost converter. Basically, the controlwas designed as easily as possible, using commonly usedequipment and devices.

Input signals are digitalized in the fuzzy control block, andinjected to the configured ports in the FPGA, because theseoutputs represent the concatenated digital address of the setvalue of the duty cycle. The signals were codified in 8 bits, forthis reason, it was necessary to store the information in aFPGA.

Microcontroller

...............................................· . . . . . . . .· . . . . . . . .· . . . . . . . .· . . .. ..."1" '10i'u/~' ,... ,.. 'l'omsi..·········'·5 ·Ai..·· 2"

ATRA~) RECUPE R ~ III H

119.9u:

Fig. 6: Steady-state input voltage and current wavefonns (Ch I: inputvoltage IOOV/div and Ch2: input current 5A/div, time base lOms/div)

When the output voltage is close to the set point (Eu(t) isNP, ZE or PP), the corrective action must be small or zero tominimize the overshoot possibility.

When the output voltage is on the set point (Eu(t) is ZE)and the output is still changing, the duty cycle must changejust a little, in order to avoid the strong change in the output.

When the output voltage achieves the set point (Eu(t) isZE), and the output is stationary, the duty cycle must keptconstant.

When the output is over the set point, the change in the dutycycle must be negative and vice versa.

When the inductor's current is below the reference~ dutycycle must be increased in order to reconstruct the currentwaveform; and vice versa, if the inductor's current is over thereference, duty cycle must be reduced.

- In limit current conditions, (iL(t) is LIMIT):If Eu(t) is PG, duty cycle increase must be zero, so that the

value of the current is limited.If Eu(t) is ZE, duty cycle increase must be negative to avoid

non desired overshoots (for example, low load starting).In agreement with these conditions, control tables have

been constructed and simulated in MatLab® for each andevery possibility, in order to get all the possible fuzzy controloutputs. The simulation results were codified in binary andstored in a FPGA.

...............................................· . . . . . . . .· . . . . . . . .· . . . . . . . .· . . . . . . . ................................................

938

The 7th International Conference on Power ElectronicsOctober 22-26, 2007 I EXCO, Daegu, Korea

. . . . ...................................· . . . . .· . . . . .· . . . . .· . . . . ...................................· . . . . .· . . . . .

. .. . . . . . . .';~~<+~4;lff~::"":"" ~ ....................................· . . . . .· . . . . .· . . . . .

· . . . . . .· . . . . . .....•.................................· . . . . . .· . . . . . .· . . . . . .· . . . . . ........................................· . . . . . .· . . . . . .· . . . .· . . . . . .. '1" '10i'u/~""" .. 5o.si..· .

1 ~I"59.97 Hz

1.90R100 %f

Do

50 ..

0 ...··1..1··......--.......- ........--11-.....••....------·5 9 13 11 21 25 29 33

........

ATRAS RECUPER ~ EI H

ARMOHICOS HOLD L~

~ .."iii)"'" .%f

Fig. 7: Hannonic distortion in steady-state Fig. 9: Output voltage (50V/div). RL is changed from 7500 to 15000

This control is tested using a boost converter at 50 Khz witha 2mH inductor, 330uF capacitor and resistive load RL of8000. The microcontroller takes 18us to digitalize eachanalog signal.

IV. DATA ANALYSIS AND CONCLUSION

Fig. 6 shows the experimental verifications in steady-stateon a 200 W boost rectifier (desired DC output voltage: 400 V,nominal input voltage: 120 V at 60 Hz), which reaches a0.924 power factor and THD of 21.1 %. Fig 7 shows the signalharmonic content. It is possible to observe how the signal ofthe current is in phase with the voltage signal (a power factorclose to the unit is obtained).

In order to investigate the behavior with load changes,when the system is in steady state, a step change in the load isapplied with a constant input voltage (RL =15000 to 8000).The output voltage waveforms in the transient are showed inFig 8.

The output shows an overshoot near 12% and a settlingtime of48ms, within the 5% band. Then, the resistance comesback to the 15000 value. The new transient is showed in Fig9. It presents an overshoot of about 18% and a settling time of70ms.

Concerning a large-signal supply voltage change in Vim atest was made to change the input voltage from 120V to 80V,keeping the RL value constant. The transitory in the outputvoltage is showed in Fig 10. The input current is shown in Fig11.

The output voltage, in this case, presents a drop of voltageof 16%, and it returns to its nominal value after 80ms. It isimportant to point out that the input current is a sine signal inthis period of time.

In conclusion, this design presents a fuzzy control scheme,in order to develop a pre-regulator of voltage with activepower factor correction, and satisfy some internationalstandards like IEC 61000-3-2 with the purpose ofimplementing it in low and median power electronic devices.The results obtained experimentally show the viability of thescheme.

The fuzzy control scheme allows to work on three differentproblems at the same time: voltage regulation, dynamicresponse and active power factor correction; this is possiblebecause the fuzzy rules could be assigned for differentoperation areas.

Future developments must be dedicated to optimize thefuzzy rules to improve the converter performance. Also, it is

.. .. .· . . . . . . . .· . . . . . . . ..·AV.·.~A..·.·.·;,...•••• : ....~~J..Ij.·...yl.4,~.·I.·.·~·.·N.·/~.III ~ : ~;.~~~~~~ ~ ~ ~ ~ ~. .· . . . . . . . .· . . . . . . . .· . . . . . . . .· . . . . . . . .. .· . . . . . . . ... . . .... . . ..· .

· . . . ............................· . . . .· . . . .· . . . .· . . . ............................· . . . .· ..· ..· ..

..............

..............

· . . . . . . . ................................................· . . . . . . . .· . . . . . . . .· .· - .III .t.1t..~:..~~~..~..",,;:':..f ..l:..-F:r;..t..~~..t..·.

.... ~ ... :....

..............

. '1' . '10i'u/~' . s·omsi..······ .

............

. .

............

. ... ~ ... :....

. '1' . '10i'U/~ .. . s·o.si..· .

402.1 u= 402.1 u=ATRAS RECUPER ~ In H ATRAS RECUPER ~ In H

Fig. 8: Output voltage (50V/div). RL is changed from 15000 to 7500 Fig. 10: Output voltage (50V/div). Vin is changed from 120V to 80V

939

The 7th International Conference on Power ElectronicsOctober 22-26, 2007 / EXCO, Daegu, Korea

suggested to shift the control structure located inside themicrocontroller to the FPGA in order to use just one controldevice and increase the speed in the processing time, which isthe main reason for the high distortion in the currentpresented.

· . . . . . . . ................................................· . . . . . .· . . . . . .· . . . . .• •• "0 .' • • • ~.

2.5 AI.. 210ms/..

O.Omu=5mU/..

· . . . . . . . ................................................

.. ...................................................: ".. : : : : : : :

·~···~,j;?\~~./\~~Y~\L)~··\lf~\...............................................· . . . . . . . .· . . . . . . . .· . . . . . . . .

ATRAS RFr:IJPFR ~ .-. H

Fig. II: Input current (2.5A1div). Vin is changed from 120V to 80V

Power electronics future is not restricted to the powerdensity, to reduce EMI and to obtain high efficiency, it alsoinvolve the development of new strategies of intelligentcontrol that could be adapted to the conditions of the newapplications and market demands.

ACKNOWLEDGMENT

This work was supported by the group of investigationARMOS of the Distrital University of Colombia, and itsScientific Search and Development Center (CrnC),

REFERENCES

[I] H. S. H. Chung, E. P. W. Tam, and S. Y. R. Hui, "Development of afuzzy Logic Controller for Boost Rectifier with Active Power FactorCorrection," in 30th Annual IEEE Power Electronics SpecialistsConference, 1999, PESC 99, pp. 149-154.

[2] A. Khoshooei, and 1. S. Moghani, "Implementation of a Single InputFuzzy Controller for a High Power Factor Boost Converter," in IEEEAFRICON, 7th Africon conference in Africa, Technology innovation,2004, Gaborone, Botswana, pp. 69-72.

[3] A. Rubaai, M. F. Chouikha, "Design and Analysis of Fuzzy Controllersfor DC-DC Converters," in First International Symposium on Control,Communications and Signal Processing, 2004, pp. 479- 482.

[4] E. Vidal-Idiarte, L. Martinez-Salamero, F. Guinjoan, J. Calvente, andS. Gomariz, "Sliding and Fuzzy Control of a Boost Converter using an8-bit microcontroller," in lEE Proceedings Electric PowerApplications, 2004, pp. 5-11.

[5] F. Martinez, "Evaluaci6n de estructuras digitales para el diseno desistemas de control difuso (Unpublished work style)," unpublished,Distrital University of Colombia.

940