IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO.

8, AUGUST 2004 1539

Sliding-Mode Control Design of a Boost–Buck

Switching Converter for AC Signal Generation
Domingo Biel, Member, IEEE, Francesc Guinjoan, Member, IEEE, Enric Fossas, and Javier Chavarria

Abstract—This paper presents a sliding-mode control design of modulation (PWM) have been proposed in the past for buck-
a boost–buck switching converter for a voltage step-up dc–ac con- based dc–ac converters [1]–[5]. However, these control strate-
version without the use of any transformer. This approach com- gies are designed by means of a power-stage model, thus leading
bines the step-up/step-down conversion ratio capability of the con-
verter with the robustness properties of sliding-mode control. The to output waveforms being sensitive to power stage parameter
proposed control strategy is based on the design of two sliding- variations, such as the output load. On the other hand, sliding-
control laws, one ensuring the control of a full-bridge buck con- mode control techniques have been proposed as an alternative to
verter for proper dc–ac conversion, and the other one the control a PWM control strategies in dc–dc switching regulators since they
boost converter for guaranteeing a global dc-to-ac voltage step-up make these systems highly robust to perturbations, namely vari-
ratio. A set of design criteria and a complete design procedure of
the sliding-control laws are derived from small-signal analysis and ations of the input voltage and/or in the load [6]–[8]. Taking ad-
large-signal considerations. The experimental results presented in vantage of these properties, sliding-mode control has also been
the paper evidence both the achievement of step-up dc–ac conver- applied to the design of high-efficiency buck-based dc–ac con-
sion with good accuracy and robustness in front of input voltage verters, where a switching dc–dc converter is forced to track,
and load perturbations, thus validating the proposed approach. by means of an appropriate sliding-mode control action, an ex-
Index Terms—boost–buck switching converter, dc–ac step-up ternal sinusoidal [12]–[18]. Nevertheless, the full-bridge buck
conversion, sliding-mode control. converter topology limits the ac output voltage amplitude to
values lower than the dc input voltage, except in the vicinity
I. INTRODUCTION of the output filter resonant frequency [19].
When ac amplitudes higher than the dc input voltage are re-

U NINTERRUPTIBLE power supplies (UPS) or ac power

sources constitute the most classical applications of power
conditioning systems designed to supply an ac load from a dc
quired, the classical design combines a step-up turns ratio trans-
former and a buck converter in the dc–ac conversion circuit.
However, this approach entails some drawbacks related to the
source. The design of these systems involves the design of both transformer nonidealities (leakage inductances, limited band-
a high-efficiency switching power stage circuit and a control width,…) and increases the weight and size of the converter cir-
subsystem in order to achieve a suitable dc–ac conversion in cuit. Alternatively, transformerless step-up conversion topolo-
the desired output frequency range. Concerning the generated gies could be considered. Nonetheless, although sliding-mode
output voltage, low harmonic distortion, and robustness in front control has been successfully applied to switching dc–dc con-
of input voltage and load perturbations (evaluated in terms of verters exhibiting a step-up voltage conversion ratio such as the
fast transient behavior and steady-state accuracy) are commonly boost converter [8], [22], the coupled-inductor Čuk converter
requested features. [9] and the boost–buck converter [10], [11], preliminary studies
Usually, the power stage circuits in charge of performing the have shown the analytical difficulties in applying sliding-mode
dc–ac conversion are based on a full-bridge buck switching con- control techniques to these power stages for a dc–ac step-up con-
verter topology. Regarding the control subsystem, several con- version ratio [20], [21].
trol schemes oriented to ensure a proper tracking of an external In order to overcome the drawbacks exposed above, this
sinusoidal reference have been suggested. For instance, many work focuses on a sliding-mode control design for a cascade
tracking control techniques based on high-frequency pulsewidth connection between a boost dc–dc converter with a full-bridge
buck inverter, as a transformerless power stage for a dc–ac
step-up conversion, this being referred as a boost–buck dc–ac
Manuscript received July 29, 2003; revised December 13, 2003. This work
was supported in part by the Spanish Ministry of Science and Technology and converter. Starting from the sliding-control-law design pro-
in part by the European Union from FEDER funds under Grant DPI2000-1503- posed by Carpita et al. [12] for a full-bridge buck-based dc–ac
CO3-2,3 and Grant DPI2003-08887-CO3-01. This paper was recommended by conversion, the work here reported presents how a well-known
Associate Editor M. K. Kazimierczuk.
D. Biel is with the Departamento d’Enginyeria Electrònica, Escola Politèc- linear sliding-control law for a single boost dc–dc converter
nica Superior d’Enginyeria de Vilanova la Geltrú, Barcelona 08800, Spain has to be designed when the previous cascade connection
(e-mail: biel@eel.upc.es). conversion is considered. Therefore, by properly combining
J. Chavarria is with Sony Corporation, Barcelona 98232, Spain.
F. Guinjoan is with the Departamento d’Enginyeria Electrónica, Escola the step-up/step-down conversion ratio of the boost–buck
Tècnica Superior d’Enginyers de Telecomunicació, Barcelona 08034, Spain dc–ac converter with the robustness properties of sliding-mode
(e-mail: guinjoan@eel.upc.es) control, a step-up dc–ac voltage conversion robust in front of
E. Fossas is with the Institut d’Organització i Control de Sistemes Industrials,
08028 Barcelona, Spain (e-mail: fossas@ioc.upc.es) input voltage and/or load perturbations can be generated in a
Digital Object Identifier 10.1109/TCSI.2004.832803 large frequency range without the use of any transformer.
1057-7122/04$20.00 © 2004 IEEE

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 1540 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO. 8, AUGUST 2004

switch of the buck stage (control variable ) for tracking an ex-

ternal sinusoidal reference, thus providing a dc–ac conversion.
A second law will be designed to control the dc–dc boost stage
(control variable ) in order to set the intermediate voltage
at a large enough value to ensure a global ac output voltage am-
plitude to dc input voltage step-up ratio.
The design of the sliding-control laws will be carried out by
applying the equivalent control concept [6], [7]. This technique
can be summarized in the following three steps for the case of
one control variable .

• The first step is the choice of a switching surface

(where is the system state vector) that provides the desired
Fig. 1. (a) Cascade connection of a boost converter with a full-bridge buck asymptotic behavior.
inverter. (b) Circuit model.
• Obtaining the equivalent control by applying the invari-
ance condition constitutes the second step.
The existence of the equivalent control assures the feasi-
bility of a sliding motion over the switching surface .
On the other hand, besides describing the averaged dynamic be-
havior of the power stage over the switching surface, the equiv-
alent control enables obtaining the sliding domain, given by

Fig. 2. Block diagram of a boost–buck dc–ac converter. where and are the control values for and
respectively. The sliding domain is the state plane region where
The paper is organized as follows. The next section presents the sliding motion is ensured.
the boost–buck dc–ac converter sliding-control strategy. Col- • Finally, the control law is obtained by guaranteeing the Lya-
lecting the results of previous studies [12]–[19], Section III de- punov stability criteria, i.e., .
signs a sliding-control law of the buck stage, whereas Section IV
focuses on a complete design procedure for the boost one. Fi- According to the aforementioned three steps, the design pro-
nally, the last two sections present both simulation and exper- cedure of the two sliding-control laws is given in the following
imental results validating the approach, and the conclusions of sections.
this work.
III. DC–AC BUCK STAGE SLIDING-CONTROL DESIGN
II. BOOST–BUCK SLIDING-CONTROL STRATEGY
There are several works reported in the literature dealing
Fig. 1(a) shows the boost–buck dc–ac converter circuit con- with sliding control of buck-based dc–ac converters [12]–[19].
sisting in the cascade connection of a boost dc–dc converter with In order to track a user-defined sinusoidal voltage reference
a full-bridge buck inverter. For analysis purposes, the converter at the buck stage output, i.e. ,
can be represented by the circuit model shown in Fig. 1(b), the following switching surface and the corresponding control
where S1 is a conventional power switch and S2, corresponds to law proposed by Carpita et al. [15] is adopted in this paper:
the full bridge switch to ensure the bipolarity of the ac output.
If and stand for the control signals of S1 and S2, re-
(2)
spectively, the system can be represented by the following set
of differential equations:
where and are the design parameters. The sliding
motion over the switching surface is given by

(1) (3)

thus leading to the desired steady-state behavior. As (3) points

out, the sliding-mode dynamic behavior depends on the
where and . As shown in Fig. 2, this time constant, which has to be as low as possible; however, as
work considers the design of two sliding-mode control laws for it is reported by the authors, if the time constant is too low, the
the and variables. state vector can leave the switching surface due to the bounds
Recalling the results of previous studies [10]–[17], a first on control. A complete set of design considerations of these
sliding-control law will be designed to control the full bridge switching surface parameters can be found in [15].

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BIEL et al.: SLIDING-MODE CONTROL DESIGN OF BOOST–BUCK SWITCHING CONVERTER 1541

The corresponding equivalent control resulting from the ap-

plication of the invariance condition to is given by

(4)

whereas the sliding domain can be obtained by imposing

, or equivalently

(5)

Finally, the power converter will reach the sliding surface if

, this leading to the following switching control law:

if
(6)
if
Fig. 3. Gain Bode diagram of (!). Parameters: L = 750 H, C = 60 F
and R = 10 .

A. Steady-State Design Constraints

In the subsequent developments the sub-index “ss” stands for
steady-state variables. In accordance to the sliding-mode control
theory, if the sliding domain is preserved the previous control
law will lead the buck stage to the desired steady-state sliding
motion, where the following relation holds:

(7)

The design must evidently preserve the steady-state sliding Fig. 4. Definition of the current i .
domain of the buck power stage which can be deduced by re-
stricting expressions (4) and (5) to the steady-state behavior
given by (7). Accordingly, (4) can be written as • The steady-state sliding regime is ensured for the values
of lying below the plot of the frequency response
of the buck converter output filter. It can be noticed that
(8) below the resonant frequency the ratio must verify
, in agreement with the step-down character-
From (5), (7), and (8), it can be easily proved that the steady- istic of the buck switched converter.
state sliding domain of the buck power stage is given by [17] • If load variations are considered, the design has to take
into account the most restrictive sliding domain that cor-
responds, according to (11), to the minimum load value
(9)
[19].

or equivalently, according to (7) It can be pointed out that the steady-state average value of the
boost output voltage, , must be time-varying. This statement
can be proved by analyzing the boost output current (or, equiva-
(10)
lently, the buck input one), referred as and defined as shown
in Fig. 4.
where According to (1), this current is given by

(11)
(12)

is the frequency response of the buck converter output filter, Therefore, provided that the buck converter has reached its
being the desired output frequency. Fig. 3 shows the plot of corresponding steady-state sliding motion, the steady-state
the steady-state sliding domain boundary given by (10)–(11) for boost output current can be written as
fixed values of , and .
From this plot, the following conclusions can be drawn: (13)

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 1542 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO. 8, AUGUST 2004

On the other hand, from (1), the following relation can be Finally, the switching control law can be derived applying
easily deduced assuming that the converter has reached the , this resulting in
steady state:
if
(14) (18)
if
If is a constant value, then, will be unbounded and
the system will become unstable [21]. As a consequence, for The parameters must be designed at least to keep
the case of a design requiring , two main constraints the ratio into the buck stage steady-state sliding domain
affecting the boost output voltage can be highlighted from given by (10)–(11). Since the output voltage amplitude is
the previous steady-state analysis, namely, the following. fixed by the user, an analysis of the intermediate voltage dy-
namic behavior in front of input voltage and load perturbations
• Referring to Fig. 1, if an amplitude higher than the dc
is mandatory. Accordingly, the following sections are oriented
input voltage is desired, the boost stage would carry
to deduce several design criteria for the parameters
out a large enough step-up voltage ratio .
by considering the influence of small and large perturbations of
• Since the voltage is time varying so is the ratio .
either the input voltage or the load over voltage .
This ratio must be kept into the boundaries of the buck
stage sliding domain, thus overcoming the loss of the buck
stage sliding motion. B. Design Criteria According to Small-Signal Dynamics
Analysis
As a result, the boost stage sliding control will be designed in
compliance with these constraints, as it is developed in the fol- This case analyzes the dynamic behavior of the intermediate
lowing section. voltage in front of small perturbations of the input voltage
and the load, under the following assumptions.
IV. BOOST STAGE SLIDING-CONTROL DESIGN • The power system dynamics remains on the sliding sur-
faces given by (2) and (16), therefore the expressions (4)
A. Switching Surface, Sliding Domain and Control Law
and (17) corresponding to the equivalent controls prevail.
Referring to Fig. 4 and according to (1), the boost stage dy- • The amplitude of the perturbations is small enough to ap-
namics can be modeled by the following set of differential equa- proximate the dynamic behavior of the voltage by a
tions: linear model.
Under these assumptions, the equivalent dynamics of the closed-
(15) loop boost stage can be described by

where the current is given by (12).

The following switching surface, previously reported in the (19)
literature for controlling the dc–dc boost stages [8], [22], is
adopted in this paper:
where is given by (17), and in this case ,
(16) since the power system remains on the sliding surfaces. The
small signal analysis is carried out in a conventional way, by
where , is the desired dc steady-state
splitting the variables into their dc–dc steady-state and their per-
value of the voltage for a global step-up conversion
turbed counterparts. In this sense, the small signal analysis cor-
and are the sliding surface design parameters. The
responding to load perturbations can be carried out in terms of
corresponding sliding motion is given by .
the buck input current , since a load perturbation results in an
The equivalent control is obtained by applying the in-
input current one. Therefore, the variables of (19) can be written
variance condition, and can be expressed as
as

(17)
whereas the sliding domain can be deduced by imposing
, or equivalently in
this case , this leading to the following restric-
tions:
A. (20)

where, for any variable , and stands for the dc steady-

state and the perturbed values of respectively. The steady-state
B. values can be deduced taking into account that both and
as well as the load and the desired sinusoidal output amplitude
are user-defined parameters. Accordingly, the dc steady-state

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BIEL et al.: SLIDING-MODE CONTROL DESIGN OF BOOST–BUCK SWITCHING CONVERTER 1543

value of corresponds to the equivalent steady-state duty- transfer functions (25a) and (25b) to be real, whatever the
cycle of a boost converter and can be expressed as values of and are. According to (25a)–(25b) these poles
are the roots of
(21)

whereas, according to (14), is given by (28)

(22) which can be rewritten as where

At last, can be deduced assuming no losses in the boost

(29)
stage, i.e,

(23) therefore the root locus of in terms of the load parameter

will correspond to the roots of (28). Since the poles of
Finally, by replacing (20) into (19) and neglecting higher given by and are real,
order terms of perturbed variables, the closed-loop system de- the root locus will lie on the real left-half plane axis (thus leading
fined by (19) can be represented by the following linear one: to an overdamped response) for any value of if the zeros of
are real as well. This condition can be accomplished if the
design verifies

(24)
(30)

3) Steady-State Design: The previous small-signal analysis

The dynamic behavior of with respect to input voltage and can also be applied to infer additional design criteria when the
load perturbations can be inferred from (21)–(24) and can be ex- power converter operates in steady-state. When the buck con-
pressed in the form of the following closed-loop transfer func- verter is in steady-state sliding motion, the output boost stage
tions: current is given by (13), which can be written from (1),
(7)–(8), assuming that , in terms of its dc and ac coun-
(25a) terparts as

(25b)
where

where

(26)

As can be seen, these transfer functions exhibit one

closed-loop zero at the origin, thus confirming the robust-
ness of the sliding-control law in front of input voltage and (31)
current (i.e output load) step perturbations. Furthermore, these
transfer functions can be used to derive the following design
therefore is sinusoidal time-dependent and exhibits a ripple
restrictions.
at twice the desired output frequency, thus leading to a ripple of
1) Small-Signal Stability: The poles must be located in the
the voltage at the same frequency given by (25a), namely
left-half plane, this leading to the following constraint:
(32)

(27) thus evidencing the time dependence of the intermediate steady-

2) Overdamped Small-Signal Dynamics: In order to pre- state voltage pointed out in Section III. This voltage ripple
serve the buck inverter steady-state sliding domain given by amplitude can lead the ratio beyond the steady-state
(10), it would be desirable to guarantee a slightly overdamped sliding domain boundary of the buck dc–ac converter given by
dynamics of in front of input voltage and load perturbations. (10), thus leading to a loss of sliding motion. Therefore, in order
This design criterion requires the poles of the closed-loop to counteract this possibility, a proper attenuation of

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 1544 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO. 8, AUGUST 2004

has to be designed, this involving according to (25a) the sur-

face parameters as well as the boost converter compo-
nents and . The following design procedure is suggested
assuming that the next parameters are known.
The desired output voltage amplitude and frequency noted as
and , respectively.
The input voltage , the buck inductor and capacitor values
and and the dc steady-state boost output voltage .
The minimum load value, noted as .
Taking into account these previous assumptions, the max-
imum current ripple is also known from (31), namely

(33) Fig. 5. Simulation of a load step change from open circuit to R = 5 .

Parameters: L = 1 mH, C = 1000 F, L = 750 H, C = 60 F,
E = 24 V, A = 40 V, ! = 250 rad/s, = 0:8, = 0:0228,  = 1:573,
from which the corresponding voltage amplitude can be de- K = 1, a = 2000, a = 1, and v = 60 V.
duced according to (32), i.e.,

(34)

The design procedure starts by fixing a desired value of

such that
• is in compliance with the small-signal
analysis validity range. Regarding the voltage ripple as a
steady-state perturbation, this constraint can be usually
satisfied by fixing a perturbation level at most of 10% of
the dc steady-state value, therefore

where (35)

• The sliding domain of the buck inverter is preserved, i.e.

, this leading to:

(36) Fig. 6. Simulation of a load step change from open circuit to R = 5 .

Parameters: L = 1 mH, C = 1000F, L = 750H, C = 60 F,
or, equivalently according to (35) E = 24 V, A = 40 V, ! = 250 rad/s, = 0:8, = 0:35,  = 1:573,
K = 21, a = 2000, a = 1, and v = 60 V.
(37)
(41)
Consequently, is selected to verify the most restrictive of the
constraints (35) and (37). Subsequently, the value of the desired
attenuation can be known from (34) and (35), i.e., (42)

(38) Therefore, from (39), the attenuation satisfies

Accordingly, the unknown parameters of the transfer function (43)

given in (25a) must be designed to fulfill (38). In order
to simplify the design, this transfer function is rewritten in a
normalized form as follows: The design is simplified by assuming that the ripple frequency
lies on the high frequency attenuation range of . In
(39) this case, (43) can be approximated by

where (40) (44)

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BIEL et al.: SLIDING-MODE CONTROL DESIGN OF BOOST–BUCK SWITCHING CONVERTER 1545

(a)

(b)
Fig. 7. (a) Buck inverter power stage circuit. (b) Boost converter power stage circuit.

According to this assumption, the following value of has These design relationships can be applied only under small-
been arbitrarily selected: signal perturbation assumptions. When large-signal perturba-
tions are considered, other design criteria complementing the
(45)
previous ones arise, as it is highlighted in the next section.
this enabling the design of real poles (i.e, an overdamped re-
sponse) with a damping factor such that in order to ful- C. Design Criteria According to the Large-Signal
fill the approximation given in (44). Therefore, from (38) and Transient Response
(44), the value of can be deduced as In order to infer additional design criteria, the following
(46) example is presented to illustrate the large-signal behavior of
the power stage in the state plane under the sliding-control laws
whereas, according to (40), (41), and (45), the following design given in (6) and (18). This example considers a boost–buck
relations holds: dc–ac power stage with the following parameter values:
1 mH, 1000 F, 750 H, 60 F,
(47)
1000 (i.e, open circuit) and 24 V; the desired output

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 1546 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO. 8, AUGUST 2004

(c)

(d)

Fig. 7 (Coninued.) (c) Buck inverter control circuit. (d) Boost converter control circuit.

signal parameters are fixed to 40 V (this corresponding deliberately selected to hold a pair of conjugate poles according
to a global voltage step-up dc–ac conversion from a 24-V dc to (30), namely , , , .
to 80 Vpp) and 50 rad/s, being the dc component of Fig. 5 shows the Matlab® simulation of he boost converter
the boost output voltage set to 60 V. Additionally, the state variables when, starting from the open circuit
buck switching surface parameters are , steady-state defined by ( A; V), a load step
whereas those corresponding to the boost one have been change from open circuit to is applied at .

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BIEL et al.: SLIDING-MODE CONTROL DESIGN OF BOOST–BUCK SWITCHING CONVERTER 1547

Fig. 8. (a) Measured and (b) Matlab simulation of the steady-state output voltage v . Scaling factor K = 0:1.

Fig. 9. (a) Measured and (b) Matlab simulation of the steady-state intermediate voltage v . Scaling factor K = 0:1.

Although a full analytical description is extremely cumber- Since the relation (48) holds, the state plane trajectory can
some, the dynamic behavior shown in Fig. 5 can be interpreted be written, according to (49), as
by initially neglecting the state variables ripple as follows. (51)
• : prior to the load step change, the boost converter is
in the steady state corresponding to open circuit; therefore, this corresponding to the equation of a straight line in the
according to (16), the following relation holds: plane with a slope of and a constant term
given by .
• For the integrative term increases and the system
(48)
leaves the straight line given in (51) evolving with a second
order underdamped dynamics, according to the complex
and particularly, for the open-circuit steady state (namely,
poles location, to the new equilibrium point.
0 A; )
Fig. 5 also shows how, even remaining on the straight line de-
fined in (51), the boost output voltage falls below the level of
(49) the sinusoidal amplitude , thus leading to a buck sliding mo-
tion loss since in this case . This behavior suggests
• : after the load step and during a time-interval that the absolute value of the slope must be as low as possible
the state trajectory remains on the switching to overcome this possibility. In accordance with this qualitative
surface . The main reasons for this be- analysis, the values of and are designed so that
havior are as follows.
a) The boost converter quickly recovers the switching (52)
surface due to the sliding-control
thus corresponding to a straight line in the plane defined
action.
by the points according to the open circuit and the load
b) The integrative term does not change significantly
values, thus preserving the buck converter sliding domain in the
and can be approximated by its steady-state value,
worst case. On the other hand, the value of has been rbitrarily
namely
fixed to set the integrative term value to zero in open circuit
steady-state operation; therefore, from (49)
(50)
(53)

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 1548 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO. 8, AUGUST 2004

Fig. 11.(a) Measured and (b) Matlab simulation of the output signal v and the load current i for a load step change (open circuit – R = 10 – open circuit).
Voltage scaling factor K = 0:1, current scaling factor K = 100 mV/A.

Fig. 12. Zoom of the (a) measured and (b) Matlab simulation of the output voltage v and load current i for a load step change ( R = 10 –open circuit).
Voltage scaling factor K = 0:1, current scaling factor K = 0.1 V=A.

Fig. 13. (a) Measured and (b) Matlab simulation of the intermediate voltage v and the converter input current i for an input voltage step from 50 to 24 V.
Voltage scaling factor K = 0:1, current scaling factor K = 0.1 V=A. Transient dynamics of the power supply have been included in the Matlab® simulations.

In order to validate this design criteria, Fig. 6 shows the of the previous sections, the following design procedure is
Matlab simulation of for a new set of values of and proposed.
modified according to (52) and (53), in front of the same
load perturbation. As can be seen, the buck sliding domain is – Fix and
preserved, whereas the boost dynamics exhibits the expected – Determine and according to (35) and (37)
overdamped behavior and reaches the new equilibrium point – Determine and according to (52) and (53)
( , ). – Determine and according to (33) and (46)
– Determine and according to (47).

D. Suggested Design Procedure

V. SIMULATION AND EXPERIMENTAL RESULTS
Provided that the values of the following parameters are The proposed design has been tested by means of both
known: , , , , , , , and collecting the results Matlab® simulations and measurements carried out on a

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BIEL et al.: SLIDING-MODE CONTROL DESIGN OF BOOST–BUCK SWITCHING CONVERTER 1549

Fig. 14. (a) Measured and (b) Matlab simulation of the intermediate voltage v and the converter input current i for an input voltage step from 24 to 50 V.
Voltage scaling factor K = 0:1, current scaling factor K = 0; 1 V=A. Transient dynamics of the power supply have been included in the Matlab simulations.

Fig. 15. (a) Measured and (b) Matlab simulation of the output voltage v and the output current i when the converter is loaded with a full-wave rectifier. Voltage
scaling factor K = 0:1, current scaling factor K = 0.1 V=A.

laboratory prototype which experimental set-up is shown in shoot. Fig. 11 corresponds to the measured and the simulation
Fig. 7(a)–(d). The circuit parameters have been fixed in accor- of the output voltage and the load current in front of the same
dance with the design procedure exposed in the paper, and are load perturbation profile, whereas Fig. 12 shows a zoom of these
as follows. output variables evidencing the robustness of the output voltage
• Output signal and minimum load: 40 V and in front of load perturbations. On the other hand, Figs. 13 and
50 rad/s, . 14 show the intermediate voltage and the input current for
• Input voltage and intermediate voltage: 24 V, a input voltage step from 50 to 24 V and from 24 to 50 V, re-
60 V. spectively, where the dynamics of the power supply transients
• Steady-state intermediate voltage ripple has been included in the simulations.
4,8 V (i.e, ) As it can be seen, the input voltage step does not modify
• boost–buck power stage: 1 mH, 1000 F, significantly the intermediate voltage , thus preserving the
750 H, 60 F, sliding domain of the buck converter. Finally, Fig. 15 shows
• Sliding surfaces parameters: , , , the output voltage and the output current when the boost–buck
, , dc–ac converter is loaded with a full-wave rectifier, highlighting
Fig. 8 shows the measured and the simulation of the steady- the robustness of the output voltage in front of nonlinear loads
state dc–ac converter output voltage , which confirms the as well. In this sense, a total harmonic distortion (THD) of 0.5%
achievement of a step-up conversion from 24 V dc to (80 V , for the resistive load and of 1.8% for the full wave rectifier
50 Hz) ac with good accuracy. Similarly, Fig. 9 shows the mea- have been also measured. Finally, it can be pointed out that all
sured and the simulation of the intermediate steady-state voltage the simulation results are close to the measured ones, thus con-
which can be approximated by firming the usefulness of the presented analytical approach.
, thus exhibiting as expected the desired ripple amplitude
at twice the output frequency. As far as the transient dynamics in
VI. CONCLUSION
front of load perturbations is concerned, Figs. 10–12 show the
measured and the simulation of the converter response in front This paper has presented a sliding-mode control design of
of a load step change from open circuit to 10 and back to open a boost–buck dc–ac switching converter for a voltage step-up
circuit. Particularly, Fig. 10 shows both the input current and dc–ac conversion without the use of any transformer. The pro-
the intermediate voltage which does not exhibit any over- posed approach has been based on the design of two sliding-con-

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 1550 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO. 8, AUGUST 2004

trol laws, one ensuring the control of the full-bridge buck con- [15] M. Carpita and M. Marchesoni, “Experimental study of a power condi-
verter for a proper dc–ac conversion, and the other one to con- tioning using sliding-mode control,” IEEE Trans. Power Electron., vol.
11, pp. 731–742, Sept. 1996.
trol the boost converter for guaranteeing a global dc–ac voltage [16] F. Boudjema, M. Boscardin, P. Bidan, J. C. Marpinard, M. Valentin, and
step-up ratio. Taking advantage of previous results for the buck J. L. Abatut, “VSS approach to a full bridge buck converter used for ac
sliding-mode control design, the work has been mainly focused sine voltage generation,” in Proc. IECON’89, 1989, pp. 82–89.
[17] H. Pinheiro, A. S. Martins, and J. R. Pinheiro, “A sliding-mode con-
on the design of a sliding-control law for the boost converter, troller in single phase voltage source inverters,” in Proc. IECON’94,
which has been oriented to preserve the buck sliding motion. 1994, pp. 394–398.
This design has been performed through a small-signal dynamic [18] L. Malesani, L. Rossetto, G. Spiazzi, and A. Zuccato, “An ac power
supply with sliding-mode control,” IEEE Ind. Applicat. Mag., vol. 2, pp.
analysis and has taken into account the large-signal behavior of 32–38, Sept./Oct. 1996.
the boost stage in the state plane. As a result, a set of design [19] D. Biel, E. Fossas, F. Guinjoan, A. Poveda, and E. Alarcón, “Applicac-
criteria and a complete design procedure have been suggested. tion of sliding-mode control to the design of a buck-based sinusoidal
generator,” IEEE Trans. Ind. Electron., vol. 48, pp. 563–571, June 2001.
Furthermore, the simulation and experimental results presented [20] E. Fossas and D. Biel, “A sliding-mode approach to robust generation
in the paper are in close agreement and have shown the achieve- on dc-to-dc converters,” in Proc. IEEE Conf. Decision Control , 1996,
ment of a step-up conversion from 24 V dc to (80 V , 50 Hz) pp. 4010–4012.
[21] E. Fossas and J. M. Olm, “Asymptotic tracking in dc-to-dc nonlinear
ac with a good accuracy and low THD for both resistive and power converters,” Discrete Continuous Dyn. Syst., ser. B, vol. 2, no. 2,
nonlinear loads, as well as robustness in front of input voltage pp. 295–307, 2002.
and load perturbations, thus validating the proposed design. In [22] V. I. Utkin, J. Guldner, and J. Shi, Sliding Mode Control in Electro-
mechanical Systems. London, U.K.: Taylor & Francis, 1999.
this sense, the approach presented in the paper can be applied
for a robust and accurate dc–ac step-up transformerless con-
version involving other output voltage amplitudes and frequen-
cies by applying the design procedure exposed in the paper, and
Domingo Biel (S’97–M’99) received the B.S, M.S.,
changing accordingly the buck converter sinusoidal voltage ref- and Ph.D. degrees in telecomunications engineering
erence. from the Universidad Politècnica de Cataluña,
Barcelona, Spain, in 1990, 1994, and 1999, respec-
tively. His thesis dissertation research was on the
application of sliding-mode control to the signal
generation in dc-to-dc switching converters.
REFERENCES He is currently an Associate Professor in the
Departamento de Ingenieria Electrónica, Escuela
[1] A. Capel, J. C. Marpinard, J. Jalade, and M. Valentin, “Large-signal dy- Politécnica Superior d’Enginyeria, Universitad
namic stability analysis of synchronized current-controlled modulators. Politecnica de Catalunya, where he teaches power
Application to sine-wave power inverters,” ESA J., vol. 7, pp. 63–74, electronics and control theory. He is the author/coauthor of several communi-
1983. cations in international congresses and workshops. His research interests are
[2] A. Kawamura and R. G. Hoft, “Instantaneous feedback controlled related to nonlinear control, sliding-mode control and power electronics.
PWM inverter with adaptative hysteresis,” IEEE Trans. Ind. Applicat.,
vol. IA-20, pp. 706–712, Mar. 1984.
[3] K. P. Gokale, A. Kawamura, and R. G. Hoft, “Dead-beat microprocessor
control of PWM inverter for sinusoidal output waveform synthesis,”
IEEE Trans. Ind. Applicat., vol. IA-23, pp. 901–910, May 1985.
[4] P. Maussion et al., “Instantaneous feedback control of a single-phase Francisco Guinjoan (M’92) received the Ingeniero
PWM inverter with nonlinear loads by sine wave tracking,” in Proc. de Telecomunicación and Doctor Ingeniero de
IECON’89, 1989, pp. 130–135. Telecomunicación degrees from the Universitad
[5] K. Jezernik, M. Milanovic, and D. Zadravec, “Microprocessor control Politècnica de Cataluña, Barcelona, Spain, in 1984
of PWM inverter for sinusoidal output,” in Proc. Eur. Power Electronics and 1990, respectively, and the Docteur es Sciences
Conf. (EPE), 1989, pp. 47–51. degree from the Université Paul Sabatier, Toulouse,
[6] H. Sira-Ramirez, “Sliding motions in bilinear switched networks,” IEEE France, in 1992.
Trans. Circuits Syst., vol. CAS-34, pp. 919–933, Aug. 1987. He is currently an Associate Professor in the
[7] V. I. Utkin, Sliding mode and their applications in variable structure Departamento de Ingenieria Electrónica, Escuela
systems. Moscow, U.S.S.R: Mir, 1978. Técnica Superior de Ingenieros de Telecomu-
[8] R. Venkataramanan, A. Sabanovic, and S. Cuk, “Sliding mode control nicación Barcelona, Universitad Politècnica de
of dc-to-dc converters,” in Proc. IECON’85, 1985, pp. 251–258. Cataluña, where he teaches power electronics. His research interests include
[9] L. Martínez-Salamero, J. Calvente, R. Giral, A. Poveda, and E. Fossas, power electronics modeling, nonlinear circuit analysis and control, and analog
“Analysis of a bidirectional coupled-inductor Cuk converter operating circuit design.
in sliding mode,” IEEE Trans. Circuits Syst., vol. 45, pp. 355–363, Apr.
1998.
[10] A. E. Van der Groef, P. P. J. Van der Bosch, and H. R. Visser, “Multi-input
variable structure controllers for electronic converters,” in Proc. EPE’91,
Firenze, Italy, 1991, pp. I-001–I-006. Enric Fossas was born in Aiguafreda, Spain, in 1959.
[11] R. Leyva, J. Calvente, and L. Martínez-Salamero, “Tracking en el con- He received the graduate and Ph.D. degrees in math-
vertidor boost–buck de dos conmutadores,” in Proc. Seminario Anual ematics from Universitad de Barcelona, Barcelona,
Automática, Electrónica Industrial e Instrumentación (SAAEI), 1997, Spain, in 1981 and 1986, respectively.
pp. 233–238. In 1986, he joined the Department of Applied
[12] M. Carpita, M. Marchesioni, M. Oberti, and L. Puguisi, “Power con- Mathematics, Universitad Politecnica de Cataluña,
ditioning system using sliding-mode control,” in Proc. PESC’88, 1988, Barcelona, Spain. In 1999, he moved to the Institute
pp. 623–633. of Industrial and Control Engineering and to the
[13] E. Fossas and J. M. Olm, “Generation of signals in a buck converter with Department of Automatic Control and Computer
sliding-mode control,” in Proc. Int. Symp. Circuits and Systems, 1994, Engineering at the same university, where he is
pp. 157–160. presently an Associate Professor.
[14] K. Jezernik and D. Zadravec, “Sliding mode controller for a single phase His research interests include nonlinear control theory and applications, par-
inverter,” in Proc. APEC’90, 1990, pp. 185–190. ticularly variable-structure systems, with applications to switching converters.

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BIEL et al.: SLIDING-MODE CONTROL DESIGN OF BOOST–BUCK SWITCHING CONVERTER 1551

Javier Chavarria was born in Tortosa, Spain, in

1978. He received the degree in technical telecom-
munications engineering in 2001 from the Escola
Politècnica Superior d’Enginyeria de Vilanova la
Geltrú, Barcelona, Spain, in 2001, where, since
2002, he is working toward the M.S. degree in
electronics.
He was a Researcher in the Department of Elec-
tronic Engineering, Escola Politècnica Superior
d’Enginyeria de Vilanova la Geltrú,. From 2001
to 2002, he was with the Technologic Innovation
Center in Static Converters and Operations (CITCEA), Universitad Politecnica
de Cataluña, Barcelona, Spain. Since 2002, he is with Sony Corporation,
Barcelona.
Dr. Chavarria won two prizes from the Official College of Telecommunica-
tions Engineers, Spain, while at CITCEA. He is a member of the Spanish Offi-
cial College of Technical Telecommunications Engineers (COITT).

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