A Controller for a Boost Converter With Harmonic Reduction

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 12, NO. 5, SEPTEMBER 2004 717

A Controller for a Boost ConverterWith Harmonic Reduction

G. Escobar, A. A. Valdz, J. Leyva-Ramos, Member, IEEE, and P. R. Martnez

AbstractAn adaptive controller for the compensation ofoutput voltage ripple due to harmonic distortion in the inputvoltage is proposed for a pulse width modulated (PWM) boostconverter. Following the Lyapunov approach, we designed anadaptive law to cope with uncertainties in the disturbance signalsand parameters. Complexity of the proposed controller is reducedby rotations which transform the adaptive terms into a sumof resonant filters tuned at the frequencies of the harmonicsunder compensation, and operating on the output voltage error.To facilitate the implementation, we have tried to preserve thestructure of the proposed controller as close as possible to theconventional one, which includes a voltage outer loop (basicallya proportional plus integral (PI) control on the output voltageerror) and an inner control loop (basically a proportional controlplus a feedforward term). In the proposed controller, the bank ofresonant filters appears as a refinement term added to the innercontrol loop. Indeed, they insert notches in the audio-susceptibilitycurve, which are tuned at the harmonics under compensation.Thus, in addition to the benefits of a conventional feedforwardPWM control, the bank of resonant filters are able to cancelselected harmonics. Experimental results on a boost converterboard, using a poorly regulated voltage source, are presented toassess the performance of our approach.

Index TermsAdaptive control, audio-susceptibility, dcdc con-verters, harmonic compensation, ripple filtering.

I. INTRODUCTION

THE main role of a dcdc boost converter is to keep theoutput voltage as close as possible to a desired constantreference. Although this task may be fulfilled by a simpleopen-loop controller, it is usual to aggregate control terms toalleviate certain drawbacks. For instance, it is well known thatopen-loop control is not able to cope for steady-state errors dueto changes in the input voltage and load variations. Usually,proportional plus integral (PI) controllers have provided a goodanswer to the regulation task in dcdc boost converters. Due tothe nonminimum phase nature of this converter [1], the designeris forced to control the output voltage indirectly by directlycontrolling the inductor current, this technique is referred ascurrent or indirect control in the power electronics literature.Moreover, to facilitate the design, the designer usually appealsto the decoupling assumption, out of which the control design issplit in two loops, namely, the inner current loop and the outer

Manuscript received March 27, 2003; revised November 19, 2003. Manu-script received in final form February 4, 2004. Recommended by Associate Ed-itor A. Bazanella.

The authors are with the Department of Applied Mathematics and ComputerSystems (DMASC), Potosinian Institute of Science and Technology (IPICYT),San Luis Potos, SLP 78216, Mxico (e-mail: [email protected];[email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TCST.2004.826971

voltage loop. The former is aimed to guarantee fast regulationof the inductor current toward its reference, usually composedof a proportional term operating on the inductor current errorplus either, a feedforward term of the input voltage, or a simpleoffset. The outer voltage loop, usually a PI controller operatingon the capacitor voltage error, is aimed to provide an inductorcurrent reference to the inner current loop.

In this paper, we are especially interested in the compensa-tion of ripple in the output voltage caused by periodic distur-bances in the input line voltage at frequencies in the audiblerange. This issue arises in applications where the input voltagemay vary on a wide range, such as in power factor correctors(PFC), where the input voltage is mainly polluted by a secondharmonic component of the line voltage (due to the rectifica-tion process in PFC) which is propagated in the form of rippleat the output voltage. This is an issue of vital importance whena high-quality dc voltage is demanded, and in addition, it opensthe possibility of reducing the output capacitance, as pointed outin [2] and [3]. In [4][6], the authors present an interesting solu-tion referred as feedforward PWM for the output ripple reduc-tion issue. The authors show that, by simply feedforwarding theinput voltage signal, the harmonic distortion seen in the outputvoltage may be alleviated. Active ripple filtering presented in [2]and [3] is another technique addressing the problem of ripple re-duction in the output voltage. In this case, the authors proposeto sense the output voltage ripple, shift it 180 and inject it tothe output via a transformer connected in series. Active ripplefiltering was originally intended to reduce the ripple due to theswitching process, however, we believe that it can also be usefulin the reduction of ripple due to input voltage harmonic distor-tion. This technique reaches good ripple rejection, however, re-quires additional hardware. In [7], the authors present an exten-sive and very illustrative analysis of an integral-lead controllerfor a boost converter in continuous conduction mode using asmall signal model. This voltage-mode controller consists of anoutput voltage feedback loop plus an input voltage feedforwardterm. It is shown that the integral-lead controller significantlyimproves the audio-susceptibility curve.

In this paper, we propose an adaptive controller aimed to re-duce the effects, on the output voltage, of harmonic disturbancespresent in the input voltage. Specifically, the proposed controlleris aimed to reduce selected harmonics of the output capacitorvoltage, hence, improving the audio-susceptibility curve, whilemaintaining an acceptable dynamical performance and withoutinclusion of additional hardware. We follow the Lyapunov ap-proach to generate adaptation laws to estimate certain harmoniccomponents of the disturbance to be compensated. The adaptiveexpressions are later reduced, by means of rotations, into a bank

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718 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 12, NO. 5, SEPTEMBER 2004

Fig. 1. Boost converter circuit.

of resonant filters tuned at the frequencies of the harmonics tobe compensated. We also appeal to the decoupling assumption,hence, the final expression of the proposed controller includesan inner and an outer loops. In our case, the former is composedby a proportional term operating on the inductor current error, afeedforward term in function of the input voltage and a bank ofresonant filters operating on the voltage error. The outer voltageloop is formed by a low-pass filter (LPF) plus an integral term,both operating on the capacitor voltage error. We remark that,in our proposal, the usual proportional term has been substitutedby a LPF to prevent the reinjection of further harmonics into thecontrol loop due to the remanent harmonic content in the ca-pacitor voltage. Our controller turns out to be very similar tothe conventional one, where the main difference is the introduc-tion of the bank of resonant filters acting as a refinement to thefinal control signal. It could be observed that the conventionalcontroller and the feedforward control presented in [4] are par-ticular cases of the proposed controller. A slight modification tothe previous proposed controller is then presented for the casewhen the input voltage is not available from measurements. Thisis specially important in case the sensed input voltage signalis lost due to a failure and we want the controller to continueworking properly, or simply, because we want to eliminate avoltage sensor.

Finally, experimental results have been carried out in a boostconverter board to asses the performance of the proposed con-troller. The converter is fed by a poorly regulated voltage sourcepolluted by the second harmonic, i.e., 120 Hz. For the sake ofspace, we present only the results of the modified version ofthe proposed controller, i.e., without feedforward term. For im-plementation purposes the resonant filters (which have infinitegain at the resonant frequency) are replaced by bandpass filters(BPF) to guarantee a safer operation.

II. PROBLEM FORMULATION

A circuit of the boost converter is shown in Fig. 1. We haveneglected, without loss of generality, the equivalent series resis-tances (ESR) of inductor, capacitor and Mosfet, as well as thevoltage drop in the diode.

The system dynamics of the boost converter shown in Fig. 1are described by the following expressions:

(1)(2)

where is the inductor current, is the capacitor voltage,represents the voltage source (this signal is addressed indis-

tinctly as input voltage or voltage source all along the paper),is the inductance, is the capacitance and is the load re-

sistance. We assume that parameters , , and are unknownpositive constants. In the discontinuous model, i.e., ,the value corresponds to the situation where the tran-sistor is conducting, while corresponds to the case wherethe transistor is disconnected and thus the diode is conducting.In the average model [8], used along this paper, it is assumed asufficiently large switching frequency, hence, represents theslew rate of a PWM signal feeding the gate of the boost con-verter, i.e., where is the duty ratio.

We assume that the input voltage , polluted by higher orderharmonics, can be represented as

(3)

where represents a unitary vector rotating at a frequencyin counterclockwise direction, and are the real andimaginary parts of the phasor . is the set of index of theharmonic components contained in .

The control objective consists in regulating the output capac-itor voltage toward a constant reference despite of theharmonic distortion in the input voltage. That is, the controllershould be able to reject harmonic voltage disturbances presentin the power supply. It is well known that, due to the nonmin-imum phase nature of this converter, it is preferable to indirectlycontrol the capacitor voltage by directly regulating the inductorcurrent toward a constant reference (this scheme is referred inliterature as current or indirect control [9]). As it will becomeclear later, a solution to our problem treated here is obtained byforcing the inductor current to track a harmonic distorted refer-ence instead of the usual constant signal. The idea behind thisapproach is that, by distorting the inductor current reference,we incorporate a degree of freedom that allows compensationof harmonics in the capacitor voltage side.

Thus, we propose the following reference for the inductorcurrent:

(4)

where is a constant reference, usually obtained (in a conven-tional controller) from a proportional plus integrative (PI) con-troller; and a phasor representing the har-monic components introduced to be reconstructed in an outerloop as well. is the set of index of the harmonic com-ponents to be compensated. The time derivative of the inductorcurrent reference is given by

(5)

where we used the fact that .For the sake of simplicity, we assume that the inductor cur-

rent dynamics are faster than the capacitor voltage dynamics.

ESCOBAR et al.: CONTROLLER FOR BOOST CONVERTER 719

This is a usual time scale separation principle advocated in manyconverter circuits to facilitate their control design. That is, theconverter can be treated as two decoupled subsystems, a fastinductor current subsystem and a slow capacitor voltage sub-system, therefore, dividing the control design in a inner currentcontrol loop and an outer voltage control loop.

III. PROPOSED CONTROLLER ASSUMING IS AVAILABLEA. Current Control Loop

Let us rewrite the inductor current subsystem dynamics (1) interms of its increments as follows:

(6)

Assuming signal is available from measurements, then acontrol law can be proposed as

(7)

where is a positive design constant, , whereis obtained later in the outer loop.

The closed-loop dynamics yields

(8)

We observe that, if is bounded and positive, the systemis stable. Moreover, the second term on the right hand side is aharmonic perturbation which vanishes as . we conclude(based on the decoupling assumption) that converges to aball whose radio can be made arbitrarily small by proposing arelatively large (as usual in practice), i.e., we can considerthat approximately.

Remark III.1: If division by is considered, instead of di-vision by , then strictly, but this will complicate theimplementation, as one more division would be necessary.

B. Voltage Control LoopAs stated before, we can assume that after a relatively short

period of time the following holds:

(9)

Under this assumption, the control law takes the form

(10)

out of which the capacitor voltage subsystem yields

(11)

Direct substitution of expressions for and yields

(12)Using (3), and after multiplication, we obtain

(13)

From this expression, we highlight the following observa-tions:

1) the third term represents the effects of the harmonic dis-tortion in the voltage source in the case that the inductorcurrent reference is simply a constant, as in the conven-tional approach;

2) thanks to the distortion introduced in the inductor currentreference, the second term appears, which gives a degreeof freedom that will be used to alleviate the effects ofharmonic distortion in . That is, each can be seennow as a control signal whose purpose is to inject a thharmonic component that should reduce the effect of thecorresponding harmonic;

3) the fourth term produces higher order harmonics plus adc component;

4) the sixth term produces only higher order harmonics.Remark III.2: The feedforward PWM, containing only the

term as reported in [4] and [5], is indeed an open-loopcontroller producing a distortion in . Thanks to the systemstructure, this distortion somehow opposes the output voltageripple (just as the second term opposes the third term in ouranalysis above) improving the ripple rejection as observed in theassociated audio-susceptibility curve. Following the same idea,we are proposing a method to compute, with a higher degree ofaccuracy, the required distortion on that should cancel a setof selected harmonic components of the voltage ripple, whilekeeping an acceptable dynamic performance.

We conclude that introduction of harmonic distortion in theinductor current reference allows compensation of harmonicdistortion in the capacitor voltage and, at the same time, intro-duction of higher order harmonics in the capacitor voltage re-sponse. Fortunately, as observed in practice, and thanks to thesystem parameters, the contribution of these higher harmonics isconsiderably smaller than the benefits obtained by the compen-sation algorithm. Moreover, the harmonic components just cre-ated can be treated in their turn by the introduction of more andmore compensating harmonic components into the inductor cur-rent reference . Thus, to consider all these effects and for easeof presentation, we lump together all unknown harmonic com-ponents and consider only the harmonics that will be treated.


Moreover, to simplify the notation in the sums we use insteadof in what follows. Then, the expression (13) is reducedto

(14)

where represents the introduced dc component, and con-centrates the contribution of all unknown harmonics.

We can further reduce the expression above by neglectingthe fifth term in (13). If this term is considered, then a lineartransformation is necessary to extract (which is requiredto reconstruct ). Nevertheless, its effect is negligible sincethe term is much smaller than for the harmonics ofinterest.

The expression above can then be reduced to the followinglinear time invariant (LTI) system:

(15)We observe that this LTI system is perturbed by two unknownsignals of different nature, i.e., a dc and a harmonic disturbance.

Following the descriptive function technique (also referredas harmonic decomposition) we can split the system responsein two parts

(16)

(17)

where is the dc component of , i.e., , andis the ac component of , i.e., , whereis the th harmonic component of , i.e., .

1) dc component: Subsystem (16) represents the conven-tional capacitor voltage dynamics, where is considered thecontrol input. For this subsystem, we propose the followingcontroller composed by a LPF plus an integral term

(18)(19)(20)

where , , , , and are positive designparameters.

The error dynamics yield

(21)(22)(23)

whose equilibrium point given by

(24)

is stable provided that all design parameters are chosen positive.2) ac component: For the sake of clarity, let us define the

following transformation

(25)

(26)

Recall that represents the th control input for this sub-system, while represents the th harmonic component ofthe perturbation.

The subsystem is now rewritten as

(27)

where .Following the Lyapunov approach, we propose the following

storage function:

(28)

whose time derivative given by

(29)

is made negative semidefinite by proposing the following adap-tive laws:

(30)where are positive design constants representing the adap-tation gains, and we used the fact that sinceare constants, for all . This yields the time derivative

, out of which is bounded and goes to zeroasymptotically. Moreover, following the Lassalles invarianceprinciple, implies .

C. Implementation DiscussionUsing the descriptions of and (4), (5), and the transfor-

mations (26), then the controller given in (7) can be rewritten interms of the estimate as follows:

(31)


Notice that the controller above requires the generation ofvectors , which might complicate its physical implementa-tion. To overcome this problem, we propose the following trans-formations:

(32)

which yields the following expression for the controller

(33)

with adaptive expressions given by

(34)(35)

which expressed in the form of transfer functions are

(36)

(37)

for every .Thus, the controller is rewritten as

(38)

where and .It is clear that and are not available from measure-

ments. Fortunately, thanks to the selective nature of the resonantfilters we can assume

(39)

and leaning on the LPF capability of the proposed controller(20) we can assume

(40)

In conclusion, the final expressions for the controller are

(41)

(42)

where . A block diagram of controller (41), (42)is shown in Fig. 2.

Remark III.3: Notice that this controller is composed by afeedforward term plus a proportional term ,which are the same terms appearing in the conventional ap-proach, and thus a similar improvement on the audiosuscepti-bility can be expected. Moreover, our proposed controller in-cludes, as well, a bank of resonant filters appearing as a refine-ment term added to the inner control loop. Indeed, they intro-duce notches in the audio-susceptibility curve, which are tunedat the harmonics under compensation. Thus, in addition to the

Fig. 2. Block diagram of proposed controller measuring v .

benefits of a conventional feedforward PWM control, the bankof resonant filters are able to cancel selected harmonics, and pre-serve a good dynamic performance.

IV. PROPOSED CONTROLLER ASSUMING IS NOT AVAILABLEIn this section, we present a controller that does not require

measurements of for its implementation. This is speciallyuseful in case the sensed input voltage signal is lost due to afailure and we want the controller to continue working normally,or simply, because we want to eliminate the input voltage sensor.As will be shown next, this modification reduces to the introduc-tion of a simple integral term in the original controller, in theplace of the input voltage. The development of this controllerfollows a similar procedure to the previous section, and thus wepresent only the most relevant steps.

A. Inner Control LoopConsider the dynamics of the inductor current subsystem

written in terms of the increments

(43)

where we have developed according to (3), ,with as described in (4). Moreover, we concentrate only onthe harmonics .

For this system we propose the following controller:

(44)

where , are design parameters.


Notice that, by decomposing , this controller can also bewritten as

(45)

(46)

Remark IV.1: Notice that we could have proposed a non-linear control that completely decouples this subsystem fromthe capacitor voltage subsystem by using instead of inthe controller above, but we have preferred to propose the linearcontroller in order to stay closer to the conventional one.

The closed-loop dynamics are given by

(47)

(48)

Based on the time scale separation assumption we can con-sider , out of which we obtain

(49)

which is a stable system perturbed by a harmonic disturbance,provided all design parameters are positive, and is boundedand positive. Moreover, let us suppose that in the steady-state

, then the error dynamics above are reduced to

(50)

We observe that this system converges to a ball centered in theorigin whose radio can be made very small for a good selectionof the parameters and . That is

(51)

where , are vectors of very small amplitude.Moreover, it can be shown that

(52)

where , are vectors of a very small amplitude.

B. Outer Control LoopLet us consider that parameters and are selected appro-

priately in such a way that after a relatively short period of timethe contribution of vectors and is negligible. That is,

, i.e., , , then the controller can bereduced to

(53)

As before, we substitute these conditions in the capacitorvoltage equation, which yields

(54)which, after simple manipulations, and neglecting the higherorder harmonics, is reduced to

(55)where represents a dc component created by the productsbetween harmonics, and vectors represent the contributionof harmonics due to plus the harmonics created. As before,all these parameters are considered unknown constants.

Again, we can decompose the response of this system in twoparts, namely, the dc component and the periodic (or ac) com-ponent

(56)

(57)

where is the dc component of , i.e., , andis the ac component of , i.e., , whereis the th harmonic component of , i.e., .

Notice that these expressions coincide with the previous (16),(17). Now, we propose the following controller for the dc com-ponent:

(58)(59)(60)

where , , , and are positive designparameters.

Notice that the implementation of controller (45), (46) re-quires the term . This term is reconstructed inthe ac component dynamics as follows:

(61)

We now define the following transformation:

(62)


(63)

out of which we obtain the system

(64)

where .Similar to the previous section, and following the Lyapunov

approach, we propose the adaptive laws

(65)

Using transformations (32), i.e., ,, we can express the adaptive laws in the

form of a transfer functions as follows:

(66)

(67)

The controller expression can be rewritten as

(68)

(69)

Thanks to the selective nature of the resonant filters and to theLPF capability of the controller (58)(60), the final expressionfor the proposed controller is reduced to

(70)

(71)

where , , and. A block diagram of controller (70), (71) is shown in

Fig. 3.Remark IV.2: Notice that the feedforward term from

controller (41), (42) has been replaced by an integral term. The latter provides the dc component of the

original feedforward term, and thus letting the resonant filtersto exclusively handle the harmonic compensation, with theadvantage that, the steady-state performance is preserved.

V. EXPERIMENTAL RESULTS

A boost converter and controller (70), (71) have been imple-mented. The converter parameters are given in Table I. The in-ductor current is sensed via a precision resistor of 0.05 con-nected in series with the inductor. A typical circuit SG3524 isused to generate the PWM signal. A conventional nonregulatedpower supply using a full bridge diode rectifier with a 4700-

Fig. 3. Block diagram of proposed controller without measuring of v .

TABLE IPARAMETERS OF THE BOOST CONVERTER

capacitor filter is used as a voltage source. The voltage providedby this source is polluted mainly by a second harmonic, i.e., at120 Hz, which, as expected, increases for a higher current de-mand. To guarantee a safer operation, we have preferred to useBPFs instead of resonant filters (ideally, resonant filters have in-finite gain at the resonant frequency, while BPFs have a limitedgain at the resonant frequency). In our implementation only asingle BPF tuned at 120 Hz was included. This BPF has beenimplemented following the guidelines in [10], whose transferfunction is given by

(72)

where the design parameter is the desired gain of theBPF at the resonant frequency . Notice that, in the case of anideal resonant filter .

The tests performed include:1) enabling and disabling the harmonic compensation. That

is, connecting and disconnecting the BPF contribution,respectively, while keeping a constant load resistance

;2) step changes in load resistance between 18 and 36

are presented to show the robustness of the proposed con-troller against load variations.


Fig. 4. Transient responses after enabling the harmonic compensation, withR = 18 . From top to bottom: capacitor voltage x , inductor current x , anddc component of the inductor current reference I .

Fig. 5. Frequency spectrum of capacitor voltage x , with R = 18 . Top:without harmonic compensation. Bottom: under harmonic compensation.

Fig. 4 shows the responses of capacitor voltage , inductorcurrent and the dc component of the inductor current refer-ence (from top to bottom). In this figure, the harmonic com-pensation is enabled after a given period of time. We observedthat after a relatively short transient, the distortion in the outputvoltage capacitor is considerably reduced.

Fig. 5 shows the frequency spectrum of without andduring compensation (from top to bottom). We observed thatthe second harmonic component (the one under compensation)decreases almost 30 dB, while the rest of harmonics aremaintained almost unchanged.

Fig. 6 shows the responses of capacitor voltage , inductorcurrent and dc component of the inductor current reference

Fig. 6. Transient responses after disabling the harmonic compensation, withR = 18 . From top to bottom: capacitor voltage x , inductor current x , anddc component of the inductor current reference I .

Fig. 7. Frequency spectrum of inductor current x , with R = 18 . Top:without harmonic compensation. Bottom: under harmonic compensation.

(from top to bottom), when the compensation is disable aftera certain period of time.

Fig. 7 shows the frequency spectrum of the inductor currentwithout and under compensation (from top to bottom). As

predicted by theory, the harmonic content of the inductor cur-rent increases, roughly speaking, it is necessary to distort theinductor current in such a way to allow compensation in the ca-pacitor voltage .

Once the system is operating under compensation, i.e., withthe BPF connected, we proceed to change the load from 36to 18 . Fig. 8 shows the transient response of voltage andinductor current (from top to bottom). We observed that aftera small transient the voltage recuperates its desired value 24 V,in average. In Fig. 9, the inverse process is performed, that is,we switch the load resistance from 18 to 36 .


Fig. 8. Transient response for a load step change from R = 36 to R =18 . From top to bottom: capacitor voltage x , inductor current x , and dccomponent of the inductor current reference I .

Fig. 9. Transient response for a load step change from R = 18 to R =36 . From top to bottom: capacitor voltage x , inductor current x , and dccomponent of the inductor current reference I .

VI. CONCLUSIONWe have presented a controller for the boost converter whose

structure is very close to the conventional one. The maindifference consists in the introduction of a bank of resonantfilters aimed to compensate for a selected group of harmoniccomponents (in the audible range) contained in the outputcapacitor voltage. This type of disturbance is mainly due to avoltage source polluted by harmonics in the audible range. Theidea behind the proposed approach is that, by distorting theinductor current reference, we incorporate a degree of freedomthat allows compensation of harmonics in the capacitor voltageside. Implementation of the controller requires the measurementof the inductor current, capacitor voltage and input voltage. Aslight modification to the proposed controller is also presented

for the case when the input voltage is not measured. A set oftests have been carried out in an experimental prototype toassess the performance of the proposed controller. To guaranteea safer operation in the real implementation we have preferredto use BPFs instead of pure resonant filters. In the experimentalresults we compare the responses obtained with and without theaforementioned harmonic compensation. Transient responsesto step changes in the load are also presented to exhibit therobustness of the proposed controller against load variations.

REFERENCES[1] G. Escobar, I. Zein, R. Ortega, H. Sira-Ramrez, and J. P Vilain, An ex-

perimental comparison of several nonlinear controllers for power con-verters, IEEE Trans. Contr. Syst. Mag., vol. 19, pp. 6682, Feb 1999.

[2] A. C. Chow and D. Perreault, Design and evaluation of a hybridpassive/active ripple filter with voltage injection, IEEE Trans. Aerosp.Electron. Syst., vol. 39, pp. 471480, Apr. 2003.

[3] S. Y. M. Feng, W. A. Sander III, and T. G. Wilson, Small-capacitancenondissipative ripple filters for dc supplies, IEEE Trans. Magn., vol.MAG-6, pp. 137142, Mar. 1970.

[4] M. K. Kazimierczuk and L. A. Starman, Dynamic performance ofPWM dcdc boost converter with input voltage feedforward control,IEEE Trans. Circuits Syst. I, vol. 46, Dec. 1999.

[5] M. K. Kazimierczuk and A. Massarini, Feedforward control of dc-dcPWM boost converter, IEEE Trans. Circuits Syst. I, vol. 44, pp.143148, Feb. 1997.

[6] B. Arbetter and D. Maksimovic, Feedforward control of dc-dc PWMboost converter, IEEE Trans. Power Electron., vol. 12, pp. 361368,Feb. 1997.

[7] M. K. Kazimierczuk and R. Cravens II, Closed-loop characteristicsof voltage-mode controlled PWM boost converter with an integral-leadcontroller, J. Circuits, Syst. Comput., vol. 4, no. 4, pp. 429458, Dec.1994.

[8] J. G. Kassakian, M. Schlecht, and G. C. Verghese, Principles of PowerElectronics. Reading, MA: Addison-Wesley, 1991.

[9] P. T. Krein, Elements of Power Electronics. New York: Oxford Univ.Press, 1998.

[10] G. Clayton and S. Winder, Operational Amplifiers, 4th ed. London,U.K.: Butterworth, June 2000.

G. Escobar received the Ph.D. degree from the Sig-nals and Systems Laboratory, LSS-SUPELEC, Paris,France, in May 1999.

He has worked as a Technical Assistant in theAutomatic Control Laboratory, Graduate Schoolof Engineering, National University of Mexico,Mexico City, from 1990 to 1991. From 1991 to1995, he was an Assistant Professor in the ControlDepartment of the Engineering School NationalUniversity of Mexico. He was a Visiting Researcherat Northeastern University, Boston, MA, from

1999 to 2002. In 2002, he joined the Research Institute of Science andTechnology, San Luis Potos, San Luis Potos, Mxico (IPICyT), where heholds a Professor-Researcher position. His main research interests includemodeling and control of power electronic systems, specially the control ofactive filters, inverters, and electrical drives using linear and nonlinear controldesign techniques.

A. A. Valdz was born in San Luis Potos, Mxico, in1978. He received the degree (with honors) in elec-tronic engineering from the Technological Institute ofSan Luis Potos, San Luis Potos, Mxico, in 2003.He is currently working toward the M.S. degree incontrol and dynamical systems in the Applied Math-ematics Department of the Research Institute of Sci-ence and Technology, San Luis Potos IPICYT.

He worked as a Technician of Maintenance from2000 to 2002. His main interest is the control ofpower electronic systems.


J. Leyva-Ramos (M78) received the B.S. degreein electrical and mechanical engineering from theUniversidad Autnoma de San Luis Potos, SanLuis Potos, Mxico, in 1975, the M.S. degree inelectrical engineering from the California Instituteof Technology, Pasadena, in 1978, and the Ph.D.degree in electrical engineering from the Universityof Houston, Houston, TX, in 1982.

He was an Associate Professor at the Iberoameri-cana University, a Radio Frequency and MicrowaveEngineer at the Jet Propulsion Laboratory, a Teaching

Fellow at the University of Houston, Dean of Professional Studies and Engi-neering at the Instituto Tecnolgico y de Estudios Superiores de Monterrey,San Luis Potos Campus, and a Professor of Engineering at the UniversidadAutnoma de San Luis Potos. He has held visiting appointments at Brown Uni-versity, Texas A&M University, and Rice University. Currently, he is the Head ofthe Applied Mathematics and Computer Science Department, Instituto Potosinode Investigacin Cientfica y Tecnolgica IPICYT, San Luis Potos, Mxico. Hisresearch interests are in the areas of modeling of switch-mode dcdc converters,robust control, and linear systems.

Dr. Leyva-Ramos is a member of Eta Kappa Nu, Tau Beta Pi, Sigma Xi, TheMexican Academy of Sciences, and Mexican Academy of Engineering.

P. R. Martnez was born in San Luis Potos, Mxico,in 1977. He received the B.Sc. degree in electricaland mechanical engineering and the M.Sc. degree inelectrical engineering from the Engineering Schoolof the Autonomous University of San Luis Potos(UASLP), in 2001 and 2003, respectively. He isworking toward the Ph.D. degree at the Institute ofScience and Technology, San Luis Potos (IPICyT).

His main research interest include linear and non-linear control design, study of switching power con-verts, PFCs and dcdc converters.

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A Controller for a Boost Converter With Harmonic Reduction