Design and Experimental Operation of a Control

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    in a variable operating-point condition. Here lies thecomplexity of this inverter. Several techniques have beenproposed to control the buckboost [616]. Many of themare based on the well-known small-signal linear models suchas current-mode control [69], robust control, H

    Ncontrol

    and fuzzy logic control [1014]. However, small-signalmodels are calculated for a particular point of operationand are valid to control the DCDC converter only forsmall variations around this point. In the buckboostinverter, the output voltages of both buckboost convertersexperience large variations, and therefore these controltechniques are not appropriate to achieve an accurate andstable control of both the buckboost converters in such avariable operating condition. The sliding-mode control is atechnique that can deal with this condition [2, 15, 16].However, it has some disadvantages related to the requiredcomplex theory, the variable switching frequency, the lackof control of the average inductance current and the con-straints in the selection of the controller parameters [17, 18].

    To control both buckboost converters, this paperproposes a double-loop control strategy that is able tocontrol them in a variable operating point condition. Aninitial first theoretical approach of the proposed controlstrategy was introduced in [4]. Now, a prototype has been

    physically implemented and experimentally tested. Thecontrol strategy is based on the averaged continuous-timemodel of the buckboost converter [19] and consists of anew inner control loop for the inductor current and an alsonew outer control loop for the output voltage. Both loopsinclude compensations to decouple the converter modelseen by the controller from the point of operation. In thisway, the strategy is able to control both buckboostconverters in a variable operating condition such as that onerequired by the buckboost inverter. Additionally, thecontrol strategy makes use of some feed-forward compen-sations to improve the robustness against both input voltageand output AC disturbances. Simulation and experimentalresults validate the good qualities of the proposed controlstrategy. As shown, both buckboost output voltages, andthen the differential output alternating voltage, areaccurately controlled, with high robustness against externaldisturbances. In addition, the direct control of the currentmakes possible to achieve a high reliability against transientshort circuits and nonlinear loads, which can be in fact asource of small short circuits. The proposed controltechnique can be therefore considered as an advantageousalternative to the previously mentioned techniques.

    2 Control scheme for buckboost DCDC converter

    2.1 Buck-Boost averaged continuous-time

    modelThe proposed control strategy is now developed andcustomised for the buckboost 1 of Fig. 1. The controlscheme for the second buckboost is the same.

    The averaged continuous-time model of buckboost 1 isgiven by the following expressions, where iC1, iL1 and iO1 arethe capacitor, inductor and output currents, vL1, vINand vO1are the inductor, input and output voltages, and d1 is theaveraged continuous-time duty cycle

    vL1 vINd1 1 d1vO1 1iC1 1 d1iL1 iO1 2

    Concerning the inductance L1 and capacity C1, whoseinternal resistances are rL1 and rC1, their differential

    equations are

    vL1 rL1iL1 L1 diL1dt

    3

    iC1 rC1C1 diC1dt

    C1 dvO1dt

    4The model given by (1) to (4) describes the buckboostdynamic behaviour up to half the switching frequency [19].These equations show bilinear dynamics that make thecontrol of the buckboost quite difficult. To deal with it, adouble-loop control scheme is proposed with a new innercontrol loop for the inductor current and an also new outercontrol loop for the output voltage.

    2.2 Proposed inner control loop forinductor currentThe proposed inner control loop for the inductor current isshown in Fig. 2. Capital letters are used for the variables inthe block diagram. The system to be controlled is defined by(1) and (3). In this system the term vO1+vIN behaves as avariable gain, and vO1 as an external disturbance. The inputto the system is the duty cycle d1. If this variable is chosen tobe the control variable, the variable gain vO1+vIN makesvery difficult, almost impossible, the design of a controllerthat stabilises the system under a variable operatingcondition. The proposal is to choose the inductor voltagevL1 as the control variable instead of the duty cycle d1, asshown in Fig. 2. From the inductor voltage referencegenerated by the controller vL1ref, the duty cycle d1 can beobtained by means of the following expression, derivedfrom (1):

    d1 vLref vO1vO1 vIN 5

    The proposed control scheme can also be considered fromanother point of view. First, the variable gain vO1+vIN iscompensated by means of its inverse value. This compensa-tion can be made thanks to the much higher bandwidth ofthe current loop in comparison with the output voltagebandwidth. Secondly, the influence of vO1 is cancelled by

    adding to the loop its sensed and filtered value withopposite polarity, which acts in fact as a feedforwardcompensation. With these compensations, the plant to becontrolled is just the inductor transfer function, and then a

    PI+

    +

    +

    +

    IL1ref

    IL1ref

    VL1ref

    V01

    V01

    filter

    filter

    filter

    11+T

    fs

    11+T

    fs

    freezing of integral

    1

    V01f

    +VINf

    d1

    VIN

    converter

    V01+V

    IN

    VL1

    IL11

    rL1

    + L1s

    1+Tfs1

    Fig. 2 Proposed inner control loop for inductor current

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    simple proportionalintegral (PI) controller can be used.The required division in (5) is not a problem as thedenominator is always greater than zero, and can be doneby means of either simple analogue circuits or digitalprogramming. Finally, the duty cycle is limited in order toavoid extreme voltages and a non-constant switchingbehaviour, with the corresponding freezing action of theintegral term.

    2.3 Proposed outer control loop for output

    voltageThe scheme of the outer control loop proposed for theoutput voltage is shown in Fig. 3. Again, capital letters areused for the variables. This scheme is based on the samephilosophy as the current loop. The system to be controlledis defined now by the (2) and (4), and the current controlloop. If the reference for the current loop iL1refwere chosento be the control variable, the plant seen by the controllerwould exhibit a gain defined by 1d1. This gain is variablebecause the buckboost operates in a variable operatingcondition. The proposal is now to use the capacitor currentas the control variable. However, the reference for theinductor current cannot be directly obtained by means of

    (2) as that implies the use of the duty cycle. The dynamics ofthe duty cycle are defined by the inner current loop, and itsuse to calculate the reference for this loop would coupleboth loops and could make the system unstable. Theproposed solution is to compensate 1d1 with (vIN+vO1)/vIN, as shown in the control scheme of Fig. 3. With thissolution, duty cycle variations up to the voltage loopbandwidth will be successfully compensated and voltagereferences in this frequency range will be accurately trackedby the control loop. In addition, the current iO1, which is thesame as iO, acts as an external perturbation that affects thecontrol loop, especially during sudden load variations. Afeedforward compensation is again used to minimize thiseffect. With these compensations, the current reference iL1ref

    is then obtained from the following expression, in which thecontrol variable is the reference for the capacitor currentiC1ref:

    iL1ref vIN vO1vIN

    iC1ref iO1 6

    Again, the proposed compensations can be done by meansof simple analogue circuits or digital programming. As theinductor current can be considered instantaneously con-trolled from the point of view of the voltage control loop,the plant to be controlled appears as the capacitor transferfunction. Therefore a PI controller can be again used and

    easily designed by traditional techniques. The currentreference is limited and the corresponding freezing actionis taken over the integral part in this situation.

    3 Control of buckboost DCAC inverter

    To achieve an alternating voltage at the output of theinverter, both buckboost DCDC converters are drivenwith two DC-biased 1801 phase-shifted voltage references

    vOref ffiffiffi2

    pVrms sin 2pft 7

    vO1ref VDC 12vOref VDC 1ffiffiffi

    2p Vrms sin 2pft 8

    vO2ref VDC 12vOref VDC 1ffiffiffi

    2p Vrms sin 2pft 9

    where vOref is the reference for the buckboost inverter,vO1refand vO2refare the references for both individual buckboost converters, f and Vrms are the frequency and RMSvalue of the output voltage, and VDCis the DC-bias voltage.The main disadvantage of the independent referencesshown in (8) and (9) is that the output voltage is notdirectly controlled. It can therefore be affected by DCoffsets and show a poor rejection to external disturbances.An alternative is to drive one buckboost with anindependent reference (e.g. buckboost 1), and then usethe other buckboost to control directly the inverter outputvoltage [4, 18]

    vO2ref vO1 vOref vO1 ffiffiffi2

    pVrms sin 2pft 10

    This alternative is used in the implementation of the controlstrategy on the prototype inverter.

    4 Simulation analysis

    4.1 Prototype inverterTo validate the proposed control strategy a prototypebuckboost inverter has been designed and built and theproposed control strategy implemented. The parameters ofthe prototype inverter are

    L1 L2 128mH C1 C2 80mFfs 20 kHz PN 1:5 kWvIN 48 V Vrms 125 VVDC 108 V f 60Hz 11

    where the only parameters that have not been mentionedbefore are fs, which is the switching frequency, and PN,which denotes the rated power. The inductances exhibitinternal resistances of around 10mO. Those of thecapacitors are close to 350 mO.

    The simulation results have been obtained by means ofMatlab/Simulinks and are shown in this Section. The

    physical implementation of the prototype inverter isdescribed in the following Section together with theexperimental results.

    +

    +

    +

    V01ref

    V01fil

    +

    PI

    filter

    I01 1

    1+Tfs

    IC1ref

    1

    1+Tfs

    1

    1+Tfs

    VINf+V

    01f

    VINf

    VIN

    IL1ref IL1

    I01

    V01IC1

    1 1d1C

    1s

    1+rC1

    C1s

    converter

    current loop

    filter

    filter

    freezing of integral

    Fig. 3 Proposed outer control loop for output voltage

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    The prototype inverter incorporates the proposed controlstrategy. The double-loop control scheme already describedtogether with the proposed current and voltage controlloops is implemented in each buckboost. The controllersare designed to track voltage references of 60 Hz. Thespecifications for the PI controller of the current loop are abandwidth of 4 kHz and a phase margin of 501. For the PIcontroller of the voltage loop, the bandwidth is set to500Hz and the phase margin to 501. With these specifica-tions, the proportional and integral constants (KP and Tn,respectively) are 3.51 and 1.64

    104 for the current loop,

    and 0.202 and 4.31 104 for the voltage loop. Thesaturation limits for the current reference can be selected asa trade-off between the maximum allowable overcurrent intransient situations and the rated characteristics of theinverter elements. According to these design guidelines, thelimits are set to 125 and 50 A for the prototype inverter.Finally, the references for both buckboost of the inverterare set in the way described by (8) and (10).

    4.2 Simulation resultsSimulation results for the inverter operating at rated powerare shown in Fig. 4. As shown, the proposed controlscheme achieves an accurate control of the voltages and

    currents, with a Total harmonic distortion (THD) of theinverter output voltage of 0.68%.

    The robustness of the control strategy against distur-bances in the input voltage is shown in Fig. 5. Now, a 10%120Hz square-wave disturbance has been added to theinput voltage. Due to the compensations included in theloops, both buckboost reject effectively this disturbance,and then the inverter output voltage remains stable andcontrolled.

    The reliability of a generation unit when supplying loadsin an autonomous electric network, particularly its ability toovercome transient situations with no activation of itsprotections, is a very important aspect. Transient shortcircuits are a typical example of these situations. They canappear as a consequence of the connection of non-linearloads consisting of a diode bridge and a flat capacitor. Theycan also appear due to faults in the loads connected to theinverter. In this case, the short circuit lasts until the loadprotection fuse blows. These situations are tested in Fig. 6and 7. In Fig. 6, a nonlinear load consisting of a diodebridge, a flat capacitor and a resistive load, is suddenlyconnected while the inverter is already supplying 70% ofnominal power to a linear load. Figure 7 shows the inverterresponse to a short circuit of 1ms at the output when it issupplying rated power. In both situations, the currents arecontrolled up to their saturation limits (125 A and 50 A)during the short circuits, and the system returns to normal

    behaviour when they finish with high stability and nooscillations.

    5 Experimental validation

    5.1 Physical implementation of 1.5 kWprototype inverterThe parameters of the prototype inverter were indicated in(11). Inductors L1 and L2 are two 128mH 60 A-rated RMS-current inductors. The choice of inductor RMS-current isbased on the theoretical current waveform, which has beenobtained by means of solving the corresponding differentialequation by numerical methods. Capacitors C1 and C2 aretwo 80mF 500 V electrolytic capacitors. For the switching

    stage of both buckboost circuit two SemikronSKM150GB123D modules are used [20]. Both are mountedon a Semikron P16/350 heatsink. Drivers for the IGBT are

    of type SKHI 23/12, also from Semikron, and the on- andoff-gate resistances are 6.8O.

    The overall implementation of the control strategy isshown in Fig. 8. The voltage control loops of both buckboost converters as well as the generation of their referencesare digitally implemented on a DS1104 board fromdSPACE [21]. The current control loops are implementedtogether with the generation of the PWM switchingcommands in an analogue board. This board receives fromthe DS1102 board the current references. The duty cycles d1and d2 are calculated from the current control loops, andthen the PWM switching commands are generated for theSKHI 23/12 drivers. The duty cycles are limited to between

    vO

    1,vO1ref,vO2,vO2ref,vIN,

    V

    0

    250

    200

    150

    100

    50

    time, s

    0 0.01 0.02 0.03 0.04 0.05

    iL1,

    iL1ref,

    iL2,

    iL2ref,

    A

    0

    120

    100

    80

    60

    40

    20

    20

    40

    0 0.01 0.02 0.03 0.04 0.05

    time, s

    0

    50

    200

    150

    100

    50

    100

    150

    200

    vO,vOref,vIN,

    V

    0 0.01 0.02 0.03 0.04 0.05

    time, s

    Fig. 4 Simulated inverter operation at rated power

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    0.05 and 0.95. Analogue protections for the currents andvoltages are included in the analogue the board. When they

    are activated an inhibit signal stops the operation of theboards and drivers. Finally the parameters for the PIcontrollers are those indicated in the previous Section.

    The electronic circuitry that implements the currentcontrol loop and the generation of the PWM switchingcommands for the buckboost 1 is shown in Fig. 9. Thecircuitry for the buckboost 2 is the same, and both areintegrated in the analogue board. Current measuring ismade by means of a LEM LA 125-P current sensor, whilevoltages measuring are carried out by means of LEM LV25-P voltage sensors. The operational amplifiers are TL084and the comparators are LM311. The mathematicaldivision required to compensate vO1+vINis made by meansof an AD632 from Analog Devices. From the duty cycle, aUC3637 from Unitrode generates the PWM switchingcommands for the SKHI 23/12 drivers, which have beenincluded in Fig. 9 to clarify the operation of the circuit. TheB-outputs of the UC3637 are used by the control circuitryof buckboost 2. The 1.5 nF capacitors together with the4.7kO resistances at the output of the LM311 comparatorsare used to implement a dead time of 2 ms. The inhibit signal

    00

    50

    100

    150

    200

    250

    time, s

    0.01 0.02 0.03 0.04 0.05

    0

    time, s

    0.01 0.02 0.03 0.04 0.05

    vO1,vO1ref,vO2,vO2ref,vIN,

    V

    vO,vOref,vIN,

    V

    200

    150

    100

    50

    50

    100

    150

    200

    0

    Fig. 5 Simulated robustness against disturbance in the inputvoltage of 10% 120 Hz square wave

    400

    200

    0

    200

    400

    0 0.02 0.04 0.06 0.08 0.1100

    0

    100

    200

    VO,

    VOref,

    V

    time, s

    iL1

    ,iL2,

    A

    Fig. 6 Simulated system response to 400 W nonlinear loadconnection while supplying 70% linear load

    200

    100

    0

    100

    200

    200

    100

    0

    100

    200

    time, s

    vO,vOref,

    V

    iL1,

    iL2,A

    0 0.01 0.02 0.03 0.04 0.05

    Fig. 7 Simulated system response to transient short circuit fromt 6ms to t 7 ms

    voltage control digital board

    (DS1104 )

    current control and

    PWM switching analog boardSKHI 23/12 drivers

    vOref

    vO1ref

    vO2ref

    generation

    of voltage

    references

    vO1

    vO1

    controlloop

    vO2

    control

    loop

    vO2

    vO1

    Inh Inh Inh

    iO2

    iO1

    vIN

    vIN

    iL1

    controlloop

    iL2

    control

    loop

    iL2

    vO2

    vIN

    vIN

    iL1

    vO1

    iL 2ref

    iL1ref

    d1

    d2

    generation

    of PWM

    swiching

    commands

    driver forbuck-boost1

    driver for

    buck-boost2

    T1

    T2

    T3

    T4

    Fig. 8 Overall implementation of proposed control strategy

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    can cancel the switching commands by means ofHEF4081B AND-gates.

    5.2 Experimental resultsThe prototype inverter with the proposed control strategy

    has been experimentally tested in different situations, whichare summarised in Fig. 10. As shown in this figure, the testsinclude linear and nonlinear load operation, and transientshort circuits. The linear load is a 10O resistive load, which

    makes the inverter operate at full power. The nonlinear loadconsists of a Semikron SKB 30/08 diode bridge, a 680 mFcapacitor and a 68O resistive load. The short circuit test iscarried out by means of directly short-circuiting the inverteroutput through a fuse. The short-circuit finishes when thefuse blows. A Tektronix TDS 5054 digital phosphor

    oscilloscope is used to register the obtained waveforms.Figure 11 shows the results when the inverter operates at

    full power and supplies the 10O resistive linear load. Figure11a shows the buckboost output voltages vO1 and vO2, andthe inverter input and output voltages, vIN and vO. Figure11b shows the inverter output voltage vO and current iO.Finally Fig. 11c presents the inductor currents iL1 and iL2 ofboth buckboost together with the output voltages vO1 andvO2. The practical results shown in these graphs validate theproposed control strategy and the simulation results. Figure11a and 11c show how the proposed control strategyachieves an accurate control of the inductor currents andoutput voltages, and consequently of the inverter outputvoltage at full power. Other than validating the proposed

    control strategy, these results highlight the advantages ofthe buckboost inverter. The DCAC conversion is carriedout in a single stage from DC levels that are lower than the

    inductor current measurement

    LA125-P M

    iL1

    iL1

    1k

    600nf

    33

    2.7k

    TL084

    +

    TL084

    +

    TL084

    +

    TL084

    +

    TL084

    +

    TL084

    +

    TL084

    +

    TL084

    +

    LM311

    +

    LM311

    +

    current

    referenceiL1ref

    10k

    10k

    10k

    5.6k

    3.6k

    18k

    10k

    10k

    integral

    freezing

    9.1nfPI controller vIN compensation

    10k

    10k

    10k

    10k10k

    30k

    output voltage measurement

    +VO1

    55k

    820

    1k

    180

    110nf

    +HT +HT

    HTHTLV25-P LV25-PM M

    input voltage measurement

    +VIN

    55k

    1k

    820

    180

    110nf

    10k

    10k

    10k

    10k

    20k

    +15V

    15V

    10k

    Z2

    Z1Y1X1

    X2Y2

    out

    AD632

    Vos

    vO1

    +vIN

    compensation and d1

    calculation

    1k10V

    825

    53.6

    k

    AIN+AIN

    UC3637

    BIN+BIN

    BOUTAOUTVTH

    +VTHCT

    ISET

    15V

    +15V 15V

    +15V +15V

    15V

    +15V +15V

    10nf

    100nf

    1.9

    6k

    4.7

    k

    12k

    1.0

    2k

    100nf

    7.5

    V

    2.2

    k

    4.7

    k

    1nf

    Inh

    7.5

    V

    2.2

    k

    4.7

    k

    1.5nf

    4081B

    4081B

    SKHI23/12

    T1

    T2

    1.5nf

    PWM switching orders generation and drivers

    Fig. 9 Circuitry for current control loop and generation of PWM switching commands for buckboost 1 (buckboost 2 is identical)

    prototype

    buck-boost

    inverter fuse

    diode bridge

    linear load (full power)

    nonlinear load

    transient short circuit

    Fig. 10 Experimental tests on prototype inverter

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    AC peak voltage. Furthermore, the buckboost outputvoltages vO1 and vO2 are not required to be greater than theinput voltage vIN as it happens with the boost DCACinverter. On the contrary, a disadvantage of the buckboostinverter lies in the inductor current waveforms, which canachieve high peak values and increase the losses in both the

    IGBTs and the inductors. The robustness against outputcurrent disturbances is shown in Fig. 12, where the 10Oresistive linear load, which consumes full power, is suddenly

    connected to the inverter. As shown, the output voltagesreject this disturbance even when the load is connected atthe maximum voltage.

    The inverter starting response is tested in Fig. 13.Initially, both buckboost capacitors are precharged up to

    their DC component. In Fig. 13a the starting of the inverteris carried out softly from zero volts. In Fig. 13b the startingis carried out at the peak values of the output voltagewaveforms. The inverter starting response is in bothsituations stable and accurately controlled.

    The operation with the nonlinear load is shown inFig. 14. This test shows both the nonlinear load connection

    0

    0 3

    4

    VO1

    VO2

    VO

    VIN

    a

    VO1

    VO2

    0 4

    0 2

    c

    iL1

    iL2

    1

    b

    Vo

    io

    Fig. 11 Experimental results at full power with linear load (10ms/div)a Input and output voltages vO1, vO2, vIN, vO 100V/div

    b Inverter output voltage and current vO 50V/div; iO 10A/div

    c Inductor currents and output voltages of both buckboost vO1, vO2100V/div; iL1, iL2 50A/div

    0

    0 3

    4

    VO1

    VO2

    VO

    iL1

    Fig. 12 Experimental response to connection of linear loaddemanding full power (vO1, vO2, vO 100V/div; iO 20A/div; 2ms/point)

    VO1

    VO

    VO2

    VO1

    VO

    VO2

    1

    4

    0

    0

    1

    4

    0

    0

    a

    b

    Fig. 13 Experimental inverter starting response (vO1, vO2, vO100V/div; 10 ms/div)

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    and the normal operation with this load. The connection isin fact a short circuit, as the capacitor is discharged, and thisshort circuit appears again shortly at the maximum andminimum peaks of the voltage waveforms. The response of

    the inverter is stable and controlled. The stability of thesystem in these situations in which small short circuitsappear can be achieved thanks to the inner current controlloops, which control the currents to its maximumprogrammed value during the short circuits.

    Finally the last test involves a direct short circuit at theoutput of the inverter by means of the sudden connection ofa fuse. The upper and lower limits of the current referenceare set to 20- and 20 A to make possible a long short circuit(almost nine cycles). Higher limits decrease the melting timeof the fuse and the short-circuit duration. The results areshown in Fig. 15, where the short circuit lasts around140 ms. During this time, the output voltage vO goes zero,the buckboost voltages vO1 and vO2 are the same, and thecurrent iL1 is always controlled to its upper and lower limits.Although it has not been included, current iL2 has the sameevolution except for the 1801 phase shift. This test validatesthe high reliability of the inverter in these situations. As thecurrents are controlled to their limit values, no protectionsare activated and the system returns back to its normaloperation when the short-circuit finishes. Obviously, long-short circuits have to be always avoided, and the protectionscan be programmed to be activated when the short circuitlasts more than a given maximum time.

    6 Conclusions

    The two buckboost DCDC converters of the buckboostDCAC inverter are required to work in a variableoperating-point situation. To deal with this condition, adouble-loop control strategy for these DCDC convertershave been proposed that consists of a new inner controlloop for the inductor current and an also new outer controlloop for the output voltage. These loops include differentcompensations that make possible the control of the buckboost DCDC converter with variable operating points. Inaddition, feedforward additional loops were included toimprove the robustness against disturbances in the inputvoltage and output current.

    The proposed control strategy was designed andimplemented on a 1.5kW buckboost DCAC inverter.Several simulation and experimental tests were carried outto validate the strategy. The results show that the proposedstrategy achieves a stable and accurate control of both DCDC converters, and then of the inverter output voltage.Additionally to the tests carried out at normal operationwith linear loads, the strategy is also tested in challengingsituations. Experimental results with nonlinear loadsconsisting of a diode bridge and a flat capacitor, as well

    as with transient short circuits, show that the proposedstrategy is capable to deal with these situations and controlthe system with high robustness and reliability.

    7 References

    1 C!aceres, R.O., Garc!a, W. M., and Oscar, E.: A buckboost DCACconverter: operation, analysis, and control. Proc. of IEEE Int.Congress on Power Electronics (CIEP), Morelia, Mexico, 1998,pp. 126131

    2 V!azquez, N., Almaz!an, L., Alvarez, J., Aguilar, C., and Arau, J.:Analysis and experimental study of the buck, boost and buckboostinverters. Proc. of IEEE Conf. of Power Electronics Specialists.(PESC), Charleston, SC, USA, 1999, pp. 801806

    3 Kazimierczuk, M.K.: Synthesis of phase-modulated resonant DC/AC

    inverters and DC/DC converters, IEE Proc., Part B, Electr. PowerAppl., 1992, 139, pp. 3873944 Sanchis, P., Ursua, A., Gubia, E., and Marroyo, L.: buckboost

    DCAC inverter: proposal for a new control strategy. Proc. of IEEEConf. of Power Electronics Specialists (PESC), Aachen, Germany,2004, pp. 39943998

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    0

    0 2

    4

    VO2

    VO

    VO1

    Fig. 14 Experimental response to nonlinear load connection (vO1,vO2, vO 100V/div; 20 ms/div)

    VO1

    VO2

    VO

    iL13

    2

    4

    0

    0

    0

    Fig. 15 Experimental response to transient short circuit (vO1, vO2,vO 100V/div; iL1 40A/div; 20 ms/div

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