Robust Digital Control for Interleaved PFC Boost Converters Using … · · 2014-03-03Robust...

Robust Digital Control for Interleaved PFC Boost Converters Using an Approximate 2DOF Current Controller 37

Robust Digital Control for Interleaved PFCBoost Converters Using an Approximate 2DOF

Current Controller

Yuto Adachi∗ , Kohji Higuchi∗1 ,Tomoaki Sato∗∗ , Non-members, and Kosin Chamnongthai∗∗∗ , Member

ABSTRACT

In recent years, improving power factor and re-ducing harmonics distortion of power supply used inelectrical instruments are needed. In general, a cur-rent conduction mode boost converter is used for anactive PFC (Power Factor Correction). Especially,an interleaved PFC boost converter is used to makea size compact, make an eciency high and make anoise low. In this paper, the design method usingan Approximate 2-degree-of-freedom (A2DOF) con-troller for a current control system and using a digi-tal PI controller for a voltage control system is pro-posed. The digital PI controller is designed to en-large the control bandwidth of the voltage controlsystem. By this design method, the power factor canbe improved more, the input current distortion canbe made smaller and the output voltage regulationcan also be suppressed smaller. These controllers areactually implemented on a micro- processor and areconnected to the PFC converter. Experimental stud-ies demonstrate that the combination of the digitalA2DOF current controller and the digital PI voltagecontroller are eective. And it is shown that this com-bination is better than the one of usual phase lead-lag compensation controllers in the power factor, theinput current distortion and the output voltage reg-ulation.

Keywords: Interleaved PFC, Boost converter, Dig-ital robust control, A2DOF, Micro-processor.

1. INTRODUCTION

In recent years, improving power factor and reduc-ing harmonics of power supply used in electrical in-struments such as servers are needed. A passive lterand an active lter in AC lines are used for improv-ing the power factor and reducing the harmonics [1-2].Generally a current conduction mode boost converteris used for an active PFC (Power Factor Correction)

Manuscript received on January 13, 2013 ; revised on Febru-ary 24, 2013.

∗ The authors are with The University of Electro-Communications, Japan, E-mail: [email protected]

∗∗ The author is with C&C SYSTEMS CENTER HirosakiUniversity, Japan∗∗∗ The author is with King Mongkut's University of Tech-nology Thonburi, Thailand.

in electrical instruments. Especially, an interleavedPFC boost converter is used in order to make a sizecompact, make an eciency high and make a noiselow.

In the PFC boost converter, if a duty ratio, aload resistance and an input voltage are changed,the dynamic characteristics are varied greatly, thatis, the PFC converter has non-linear characteristics.In many applications of the interleaved PFC convert-ers, loads cannot be specied in advance, i.e., theiramplitudes are suddenly changed from the zero tothe maximum rating. This is the prime reason of dif-culty of controlling the PFC boost converter.

Usually, a conventional PI controller or an ana-log IC controller designed to an approximated linearcontrolled object at one operating point is used forthe PFC converter, but the control performances arenot so good because the input current distortion andthe output voltage regulation are comparatively large[3-8]. Authors proposed an Approximate 2-degree-of-freedom (A2DOF) control method of buck convert-ers previously [9-10]. Moreover, this method was ap-plied to PFC boost converters, and the digital con-trol method using a A2DOF current controller and aA2DOF voltage controller was proposed [11-12]. Inthis design method, rst, when the current A2DOFcontroller is designed, the zeros of the controlled ob-ject near 1 in the unit circle is canceled by one of thepoles in the model matching system in order to elimi-nate the dierentiation characteristics. Next, the polecancelled is used as the dominant pole for designingthe voltage A2DOF controller. The zeros of the in-terleaved PFC boost converter (controlled object) isvery close to 1. Then if the cancellation pole is usedas the dominant pole for the voltage A2DOF con-troller, the output voltage response is very slow, andthe voltage regulation gets very bad. So this typevoltage A2DOF controller cannot apply to the inter-leaved PFC boost converter.

In this paper, the digital control method using theA2DOF current controller and the PI voltage con-troller is proposed. The digital PI controller is de-signed to enlarge the control bandwidth of the volt-age control system, keeping the characteristics of thecurrent control system. By this design method, thepower factor can be improved more, the input currentdistortion can be made smaller and the output volt-

38 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.12, NO.1 February 2014

Fig.1: Interleaved PFC boost converter.

age regulation can also be suppressed smaller thanthe usual lead-lag control method. These controllersare actually implemented on a micro-processor and isconnected to the PFC converter. Experimental stud-ies demonstrate that the combination of the digitalA2DOF current controller and digital PI voltage con-troller are eective. And it is shown that this com-bination is better than the one of the phase lead-lagcontrollers in the power factor, the input current dis-tortion and the output voltage regulation.

2. INTERLEAVEDD PFC BOOST CON-

VERTER

The interleaved PFC boost converter shown in Fig.1 is manufactured. Fig.1, vin is an input AC voltage,iin is an input AC current, Cin is a smoothing capac-itor, Vi is a rectifying and smoothing input voltage,Q1 and Q2 are MOSFETs or IGBTs, L1 and L2 areinterleaved boost inductances, D1 and D2 are inter-leaved boost diodes, C0 is an output capacitor, RL isan output load resistance, iL is a sum of the induc-tor currents, vac is an absolute value of the input ACvoltage and vo is an output voltage. The inductor cur-rent iL is controlled to follow the rectied input volt-age vac for improving the power factor, reducing theharmonics and stabilizing the output voltage. HereVin=100[VAC ], Vi=140[VDC ], vo = 395[VDC ], L1=L2=400[µH], C0=440[µF], the switching frequency isfsw=35[kHz]. the sampling frequency is fs=70[kHz].

Using the state-space averaging method, the stateequation of the interleaved boost converter becomesas follows [13]:

d

dt

[i0v0

]=

d

dt

[ −R0

L0

−1L0

1C0

−1RLC0

] [i0v0

]+

[Vi

L0

0

]+

v0

[1L0

0

]+ i0

[0−1C0

]u

(1)

Here µ is a duty ratio. When the sum of induc-tor currents is controlled as 1-phase, io is iL , R0 is

Fig.2: The static characteristics of µs to Vs.

R1R2/(R1 +R2) and L0 is L1L2/(L1 + L2) (R1 andR2 are equivalent series resistances of inductances L1

and L2, respectively). The PFC boost converter hasnon-linear characteristics because this equation hasthe product of the state variable vo, io and the dutyratio Î¼.

At some operating point of eq. (1), let vo, iL andµ, be Vs, Is and µs, respectively. Then the averageof the output voltage Vs and the inductor current Isat the operating point become as follows:

Vs =1

1 + 1(1+µs)2

R0

RL

1

1− µsVi

Is =1

RL

Vs

1− µs

(2)

The actual measurement results of the static charac-teristics of µs to Vs are shown in Fig.2. In Fig.2, itturns out that the PFC boost converter is a non-linearsystem. The static characteristics of the PFC boostconverter are changed greatly with load resistances,and it inuences the dynamic characteristics of thePFC converter. In addition, the static characteristicswill be changed with input voltage variation

The linear approximate state equation of the PFCboost converter using small perturbations ∆iL = iL−Is , ∆vo = vo−Vs and ∆µ = µ−µs is as follows [13]:

x(t) = Acx(t) +Bcu(t)

y(t) = Ccx(t)(3)

where

Ac =

−R0

L0

−(1−µs)L0

−(1−µs)C0

−1RLC0

, Bc =

[Vs

L0

−IsC0

]

x(t) =

[∆iL(t)∆v0(t)

], u(t) = ∆µ(t), y =

[yiyv

], Cc =

[10

]From this equation, matrix Ac and Bc of the PFCboost converter depend on the duty ratio µs. There-fore, the PFC boost converter response will bechanged depending on the operating point and theother parameter variation. The changes of the loadRL, the duty ratio µs, the output voltage Vs and theinductor current Is in the controlled object are con-


sidered as parameter changes in eq. (1). Such the pa-rameter changes can be replaced with the equivalentdisturbances inputted to the input and the output ofthe controlled object. Therefore, what is necessaryis just to constitute the control systems whose pulsetransfer functions from the equivalent disturbancesto the output y become as small as possible in theiramplitudes, in order to robustize or suppress the in-uence of these parameter changes.

3. DESIGN OF DIGITAL CONTROLLERS

3.1 Discretization of controlled object

The continuous system of eq. (1) is transformedinto the discrete system as follows:

xd(k + 1) = Adxd(k) +Bdu(k)

y(k) = Cdxd(k)(4)

whereAd =

[eAcT

], Bd =

[∫ T

0eAcTBcdτ

], Cd = Cc

Here, in order to compensate the delay time by A/Dconversion time and micro-processor operation timeetc., one delay (state ζ1) is introduced to the input ofthe controlled object. Then the state-space equationis described as follows:

xdt(k + 1) = Adtxdt(k) +Bdtv(k)

y(k) = Cdtxdt(k)(5)

where

Adt =

eAcTs eAc(Ts−Ld)Ld∫0

eAc τBcdτ

0 0

Bdt =

Ts−Ld∫0

eAcτBcdτ

1

xdt(k) =

[x(k)ζ1(k)

]Cdt =

[Cc 0

]=

[1 0 0

]3.2 A2DOF digital current controller

The transfer function from the reference input r′

i

to the output yi is specied as follows:

Wr′iyi

(z) =(1 +H1)

(z +H1)

(1 +H2)

(z +H2)

(1 +H3)

(z +H3)

× (z − n1i)

(1− n1i)

(z − n2i)

(1− n2i)

(6)

Here Hi, i=1,2,3 are the specied arbitrary param-eters, n1i and n2i are the zeros of the discrete-timecontrolled object. This target characteristic Wr

′iyi

isrealizable by constituting the model matching systemshown in Fig.3 using the following state feedback tothe controlled object (5).

v = −Fxdt +Gir′

i (7)

Here F = [f1f2f3] and Gi are selected suitably. InFig. 3, qv and qyi are the equivalent disturbances

Fig.3: Model matching system using state feedback.

Fig.4: System reconstituted with inverse system andlter.

with which the parameter changes of the controlledobject are replaced.

It shall be specied that the relation of H1 and H3

become |H1| ≫ |H3| and H2 = n1i. Then Wr′iyi

canbe approximated to the following rst-order discrete-time model:

Wr′iyi

(z) ≈ Wmi(z) =1 +H1

z +H1(8)

The transfer function WQyi(z) between the equiv-alent disturbance Qi = [qv qyi]

T to yi of the systemin Fig.3 is dened as

WQyi(z) =[Wqvyi(z) Wqyiyi(z)

](9)

The system added the inverse system and the lterto the system in Fig.3 is constituted as shown in Fig.4.In Fig.4, the transfer function Ki(z) is as follows:

Ki(z) =kzi

z − 1 + kzi(10)

The transfer functions between ri − yi, qv − yi andqyi − yi of the system in Fig.4 are given by

yi =1 +H1

z +H1

z − 1 + kziz − 1 + kziWsi(z)

Wsi(z)ri (11)

yi =z − 1 + kziz − 1 + kzi

z − 1 + kziz − 1 + kziWsi(z)

WQyi(z)Qi (12)

where

Wsi(z) =(1+H3)(z+H3)

(z−n1i)(1−n1i)


Fig.5: Equivalent transformation of the robust dig-ital controller.

Fig.6: Approximate 2DOF digital integral type cur-rent control system.

Here, if Wsi(z) ≈ 1 within the bandwidth needed,then eq. (11) and eq. (12) are approximated as fol-lows, respectively:

yi ≈1 +H1

z +H1ri (13)

yi ≈z − 1

z − 1 + kziWQyi(z)Qi (14)

From eq. (13) and (14), it turns out that the char-acteristics from ri to yi can be specied with H1 andthe characteristics from Qi to yi can be specied withkzi independently. That is, the system in Fig.4 isan A2DOF system, and its sensitivity against distur-bances becomes lower with the increase of kzi. If thecontroller in Fig.4 is transformed equivalently, we ob-tain Fig.5. Then, substituting the system of Fig. 3to Fig. 5, the A2DOF digital integral type controlsystem will be obtained as shown in Fig.6. In Fig.6,the parameters of the controller are as follows:

k1 = −f1 −Gkzi1 +H1

, k2 = −f2

k3 = −f3, kii = Gikzi, kri = Gi

(15)

3.3 PI digital voltage controller

The multiplier is added to the reference input riof the current control system. Let the inputs of themultiplier be vac and uv as shown in Fig.7. The vacis the absolute value of the input voltage vin, and uv

Fig.7: Current control system added multiplier.

Fig.8: Digital robust control system including theA2DOF current controller and the PI voltage con-troller.

is a new input. This addition is added for making theinductor current iL follow the AC voltage vac.

Next, the digital PI voltage controller is addedto the input of Fig.7. Then the digital robust con-trol system including the A2DOF current controllerand the PI voltage controller is obtained as shown inFig.8.

4. EXPERIMENTAL STUDIES

Experimental setup system shown in Fig. 9 ismanufactured. A micro-controller (RX) from Rene-sas Electronics is used for the digital controller. Thedigital A2DOF current controller and the PI voltagecontroller were implemented on 1 micro-processor.

The A2DOF current control system is designed atthe operating point shown in Fig.2. The design pa-rameters of the A2DOF current control system havebeen determined as

H1 = −0.8 H2 = n1i = −0.9998 H3 = −0.2 kzi = 0.3 (16)

Here since n2i is very large, it can be disregarded.Then the current controller parameters become as

k1 = −0.0144013 k2 = 0.000699749

k3 = 0.192984 ki = 0.00283157

kri = 0.00943857

(17)

And the parameters of the PI voltage controller have


Fig.9: Experimental setup system.

Fig.10: The gain and phase characteristics of thecurrent control system.

been determined as

krv = 8 kiv = 0.01 (18)

From these parameters the gain and phase character-istics of the current control system is shown in Fig.10.The control bandwidth about 10kHz is attained. Thegain and phase characteristics of the voltage controlsystem is shown in Fig.11. The control bandwidthabout 25Hz is attained. The transfer function of thelead-lag controller is as follows:

Gz(z) =a10 + a11z−1

1− b11z−1· a20 + a21z

−1

1− b21z−1·Kc (19)

The parameters of the current controller are deter-mined as

a10 = 0.008447 a11 = −0.004863

b11 = 0.9964 a20 = 1.089

a21 = −0.5136 b21 = 0.4246

Kc = 60

(20)

Fig.11: The gain and phase characteristics of thevoltage control system.

The parameters of the voltage controller are deter-mined as

a10 = 0.002509 a11 = −0.002491

b11 = 0.9999 a20 = 1.320

a21 = −1.083 b21 = 0.7627

Kc = 100

(21)

The experiment results of the steady state at loadRL=500Ω and RL=1kΩ using the proposed methodare shown in Fig.12 and Fig.13, respectively. InFig.12, the input current waveform and the phase arethe almost same as the input voltage. Then the powerfactor is 0.993. The input current waveform in Fig.13is not distorted so greatly compared with the one inFig.12. It turns out that the current control systemproposed is robust. The experiment result of loadsudden change from 1kΩ to 500Ω using the proposedmethod is shown in Fig.14. In Fig.14, the output volt-age variation in sudden load change is less than 5V(1.27%). The experiment results of the steady stateat load RL=500Ω and RL=1kΩ using the phase lead-lag control method are shown in Fig. 15 and Fig.16,respectively. The power factor is 0.985 in Fig. 15 andthe distortion at zero crossing is seen. Therefore thecurrent in Fig.15 has more harmonics than the one inFig.12. It turns out that the proposed method is bet-ter than the phase lead-lag method in the power fac-tor. This is because the distortion at zero crossing islost in the proposed method. The input current wave-form in Fig.16 is distorted greatly and has become atriangular wave. It turns out that the current controlsystem using the phase lead-lag method is not robustand there are many harmonics in the input currentcompared with the one in Fig.13. The experimentresult of load sudden change from 1kΩ to 500Ω usingthe phase lead-lag control method is shown in Fig.17.In Fig. 17, the output voltage variation in suddenload change is less than 10V (2.53%) and the oscil-lation is seen. It turns out that the output voltageregulation of the proposed method is better than the


Fig.12: Experimental result of steady state wave-forms, at load RL=500Ω using the proposed method,PF=0.993.

Fig.13: Experimental result of steady state wave-forms, at load RL=1kΩ using proposed method,PF=0.983.

Fig.14: Experimental result of sudden load changefrom 1kΩ to 500Ω using the proposed method.

phase lead-lag control method. That is, the proposedcontroller is eective practically.

5. CONCLUSION

In this paper, the design method of robust con-troller for the interleaved boost converter combiningthe digital A2DOF current controller and the digitalPI voltage controller was proposed. From experimen-tal results, it was shown that the better characteris-tics of the power factor, the distortion and the outputregulation were realizable by the proposed controller.A future subject is verifying the characteristic whenthe input voltage is changed.

Fig.15: Experimental result of steady state wave-forms, at load RL=500Ω using the phase lead-lagmethod, PF=0.985.

Fig.16: Experimental result of steady state wave-forms, at load RL=1kΩ using the phase lead-lagmethod, PF=0.978.

Fig.17: Experimental result of sudden load changefrom 1kΩ to 500Ω using the phase lead-lag method.

References

[1] L. Rossetto, G. Spiazzi, and P. Tenti, Con-trol techniques for power factor correction con-verters, Proc. Power Electron. Motion Control,1994, pp.1310-1318.

[2] M. Xie, Digital control for power factor cor-rection, Unpublished master's thesis, VirginiaPolytechnic Institute and State University, 2003.

[3] M. Fu and Q. Chen, A DSP based controller forpower factor correction (PFC) in a rectier cir-cuit, IEEE Applied Power Electron. Conf. Ex-position, 2001, pp. 144-149.

[4] K. De Gusseme, D. M. Van de Sype, and J. A. A.Melkebeek, Design issues for digital control of


boost power factor correction converters, IEEEInt. Symp. Ind. Electron., 2002, pp.731-736.

[5] W. Zhang, G. Feng, Y. Liu, and B. Wu, A digi-tal power factor correction (PFC) control strat-egy optimized for DSP, IEEE Trans. PowerElectron., vol. 19, no. 6, pp.1474-1485, Nov.2004.

[6] N. Genc, and I. Iskender, DSP-based currentsharing of average current controlled two-cellinterleaved boost power factor correction con-verter, IET Power Electron., vol. 4, no. 9, pp.1015-1022, Nov. 2011.

[7] Y.-S. Kim, B.-K. Lee, and J. W. Lee, Topologycharacteristics analysis and performance com-parison for optimal design of high eciencyPFC circuit for telecom, Proc. IEEE 33rd Int.Telecommun. Energy Conf., 2011, Oct. pp.1-7.

[8] M. Pahlevaninezhad, P. Das, J. Drobnik, G.Moschopoulos, P. K. Jain, and A. Bakhshai Anonlinear optimal control approach based on theControl-Lyapunov Function for an AC/DC con-verter used in electric vehicles, IEEE Trans.Ind. Informatics, vol. 8, no. 3, pp. 596-614, Aug.2012

[9] K. Higuchi, K. Nakano, T. Kajikawa, E.Takegami, S. Tomioka, and K. Watanabe, Anew design of robust digital controller for DC-DC converters, IFAC 16th Triennial WorldCongress, (CD-ROM), Jul. 2005.

[10] K. Higuchi, E. Takegami, K. Nakano, T. Ka-jikawa, and S. Tomioka, Digital robust con-trol for DC-DC converter with second-ordercharacteristics, Elect. Eng./Electron., Comput.,Telecommun. Inform. Technology Conf., 2009,May. pp.161-169.

[11] Y. Ohta, K. Higuchi, and K. Chamnongthai,Robust digital control for a PFC boostconverter, Elect. Eng./Electron., Comput.,Telecommun. Inform. Technology Assoc. Trans.Elect. Eng., Elect., Commun., vol.10, no.2, pp.164-172, Aug. 2012.

[12] Y. Ohta, and K. Higuchi, Approximate 2-degree-of-freedom digital control for a PFCboost converter, IEICE Electron. Express, vol.10, no. 10, pp.1-8 (20130152), May 2013.

[13] S. Sasaki, and H. Watanabe, Analysis of mul-tiple operating points for dynamical control ofswitching power converters, Inst. Electron., In-form. Commun. Eng. Tech. Rep., 2005, pp.33-38.

Yuto Adachi He is a master's coursestudent in the rst year of The Univer-sity of Electro-Communications, Tokyo,Japan. He received his B. Eng. de-gree from The University of Electro-Communications, in 2012. His re-search interests include Power Electron-ics, Control Engineering, Digital SignalProcessing and Embedded Systems De-sign.

Kohji Higuchi received his Ph.D. de-gree from Hokkaido University, Sapporo,Japan in 1981. In 1980 he joined theUniversity of Electro-Communications,Tokyo, Japan, as an Research Associate,where he became an Assistant Professorin 1982 and currently an Associate Pro-fessor in the Dept. of Mechanical En-gineering and Intelligent Systems, Elec-tronic Control System Course. His inter-ests include Power Electronics, Control

Engineering and Digital Signal Processing. He is a member ofIEEE, IEICE, SICE and IEEJ.

Tomoaki Sato received the B.S. andM.S. degrees from Hirosaki University,Japan, in 1996 and 1998 respectively,and the Ph.D. degree from Tohoku Uni-versity, Japan, in 2001. From 2001to 2005, he was an Assistant Professorof Sapporo Gakuin University, Japan.Since 2005, he has been an AssociateProfessor of Hirosaki University. And,he has been a Visiting Associate Pro-fessor of the Open University of Japan

since 2012. His research interests include VLSI Design, Com-puter Hardware, Computer Architecture and Computer andNetwork Security.

Kosin Chamnongthai currently worksas associate professor at Electronic andTelecommunication Engineering Depart-ment, Faculty of Engineering, KingMongkut's University of Technology(KMUTT), and also serves as editor ofECTI e-magazine, and associate editorof ELEX (IEICE Trans) during 2008-2010 and ECTI-CIT Trans since 2011until now. He served as assoc editor ofECTI-EEC Trans during 2003-2010, and

chairman of IEEE COMSOC Thailand during 2004-2007. Inorganizing conference, he has served as general chair of interna-tional and national conferences such as SISA 2012, ITC-CSCC2010, NICOGRAPH 2008, ISPACS 2008, ICESIT 2008, ICE-SIT 2007, IWAIT 2007, and 30th EECON.

He has recieved B.Eng. in Applied Electronics from theUniversity of Electro-communications, Tokyo, Japan in 1985,M.Eng. in Electrical Engineering from Nippon Institute ofTechnology, Saitama, Japan in 1987 and D.Eng. in ElectricalEngineering from Keio University, Tokyo, Japan in 1991. Hisresearch interests include image processing, computer vision,robot vision, and signal processing. He is a senior member ofIEEE, and a member of IPS, TRS, IEICE, TESA and ECTI.

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