Download On the design of sliding mode control schemes for quantum

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
On the Design of Sliding Mode Control Schemes for
Quantum Resonant Converters
Miguel Castilla, Member, IEEE, Luis García de Vicuña, Member, IEEE, Mariano López, Member, IEEE,
Oscar López, Student Member, IEEE, and José Matas, Student Member, IEEE
Abstract—The design of sliding mode control schemes for
quantum resonant converters is introduced by means of two
different approaches. First, an easy-to-use procedure for devising
nonlinear control structures is established, using Lyapunov’s
well-known stability criteria. Second, an alternative method that
provides linear sliding surfaces is also developed, considering
reaching, existence, and stability conditions. The application of
both control design techniques is illustrated in detail by means of
three selected examples. The advantages and drawbacks of the
resulting control circuits are examined. Simulation and experimental results corroborate the expected features of the close-loop
quantum converters.
Index Terms—Linear sliding surfaces, Lyapunov-based control,
quantum resonant converters.
I. INTRODUCTION
A
T PRESENT, most control schemes for power resonant
converters are based on frequency or phase domain techniques. In both cases, the behavior of the output voltage is highly
nonlinear and largely dependent on line and load conditions.
In addition, the switching losses become severe when both the
switching frequency deviates from the resonant frequency and
the phase difference becomes large [1].
To overcome these disadvantages, a time domain control
technique has been studied over the last few years, resulting in
a new family of converters named quantum resonant converters
(QRC) [1], [2]. The main advantage of these converters is
that zero-current or zero-voltage switching conditions can be
guaranteed in all the power devices because the switching
frequency is always the resonant frequency [3]. However, the
discrete time duration of the control cycles generates quantized
output levels and large ripple in the resonant waveforms.
Two main classes of close-loop control schemes can be
found in the literature to solve these drawbacks: one employing
predictive techniques, which are based on output voltage
error estimation methods, and the other using sliding mode
control strategies. In predictive approaches, very accurate
discrete-time models are used both to describe the converter
dynamic behavior and to design the estimation control routine
[4]–[6]. However, the implementation of these controllers is
Manuscript received April 12, 1999; revised July 14, 2000. This work was
supported by the Spanish Ministry of Education and Culture (CICYT TIC990743) and Universidad Politécnica de Cataluña (FIU PR99-02). Recommended
by Associate Editor A. Kawamura.
The authors are with the Departamento de Ingeniería Electrónica,
Universidad Politécnica de Cataluña, Barcelona 08800, Spain
(e-mail: [email protected]; [email protected]; [email protected];
[email protected]; [email protected]).
Publisher Item Identifier S 0885-8993(00)09807-0.
difficult, since many calculations are required in the real-time
control algorithm [7].
Sliding mode control schemes for QRC converters are
frequently designed using continuous reduced-order averaged
models. Such models provide enough state information to both
correctly regulate the output voltage in dc-to-dc applications
[8]–[11] and force the output voltage to follow an external
sinusoidal reference in ac waveform generation [12], [13]. In
addition, control schemes offer robustness against external disturbances and parameter variations. However, the application
of sliding mode control to QRC converters is still only explored
today in a short number of studies, which basically involve the
control design of the series-type topology.
In a clear-cut contrast, linear and nonlinear control design
techniques have been extensively tested in hard-switching
dc-to-dc conversion cells. On the one hand, the structure of the
sliding surface is proposed as a linear combination of all the
state variables, using linear control techniques [14]–[18]. In
such a case, the design procedure consists in determining the
appropriate gain parameters that satisfy a set of conditions for
the existence and reachability of a sliding regime. Although
this class of sliding surfaces leads to a good dynamic response,
the price to pay is the need for sensing and processing all the
state variables, thus increasing the complexity of the control
circuit implementation.
On the other hand, several systematic approaches for the
synthesis of nonlinear sliding surfaces with suitable stabilizing
properties have been investigated, using nonlinear control
techniques. Sliding mode control via feedback linearization
[19], extended linearization [20], and other nonlinear control
methods [21]–[23] is just a short list of examples. In those
cases, the sliding surfaces are composed of nonlinear functions,
which, in turn, depend on the input voltage, the load, and circuit
parameters. Consequently, control circuits generally require the
use of multiplier and divider circuits as well as the sensing of
the input voltage and the load, thereby increasing the difficulty
of their practical implementation and operation.
The aim of this paper is to deduce sliding mode controllers for
a wide range of series and parallel QRC converters, including
single- and multi-input topologies. Two different control design
approaches are proposed in order to compare the advantages
and drawbacks of the resulting close-loop controllers. In Section III, an easy-to-use procedure for devising nonlinear control
structures is established, using the Lyapunov’s well-known stability criteria. An alternative method that provides linear sliding
surfaces is developed in Section IV, considering reaching, existence, and stability conditions. The application of both con-
0885–8993/00$10.00 © 2000 IEEE
CASTILLA et al.: SLIDING MODE CONTROL SCHEMES FOR QUANTUM RESONANT CONVERTERS
Fig. 1.
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Basic topologies of quantum resonant converters: (a) series-type and (b) parallel-type.
trol design techniques is illustrated in detail by means of three
selected examples. Moreover, sliding mode controllers for all
QRC converters are proposed. Finally, in Section V, simulation
and experimental results corroborate the expected features of
the close-loop quantum converters.
TABLE I
SINGLE-INPUT QSRC
II. PRINCIPLE OF OPERATION AND LARGE-SIGNAL MODELS
OF QRC
The basic topologies of series and parallel QRCs are shown
in Fig. 1. For both converters, the switching frequency is always
the resonant frequency, so that each control-input state presents
a discrete time duration that coincides with an integer number
of half resonant periods. Moreover, control-input changes are always synchronized in the QSRC with the zero-current crossing
points in the resonant inductor and in the QPRC with the zerovoltage crossing points in the resonant capacitor. Consequently,
nearly zero switching conditions are guaranteed in all the power
devices [1], [2].
The direction of the energy flow between the dc source and
the load can be determined by two independent control inputs
(TCI): and . On the one hand, the control input regulates
,
the state of the full-bridge switching network. When
the pair of switches S1–S4 and S2–S3 are switching on and
off alternatively, thus continuously transferring energy to the
, the full-bridge network is
resonant tank; whereas if
blocked, thus not delivering energy to the resonant circuit. On
commands the state of S5
the other hand, the control input
, the resonant tank energy is partially
switch; so when
TABLE II
SINGLE-INPUT QPRC
discharged into the load, and if
, the load does not receive
energy from the resonant circuit [1], [2].
Quantum converters can also operate just like some singleand
as shown in
input conventional converters, driving
Tables I and II. In such a case, the state of the full-bridge network
and S5 switch are governed by the control input u only, which
can take the values 1 or 0.
For control design purposes, the appropriate dynamic
description of quantum converters is by means of averaged
large-signal models, which are essential to study their global
dynamic properties. The equivalent circuits of such models
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
Fig. 2. Averaged circuit models for quantum resonant converters: (a) series-type, (b) parallel-type.
Fig. 3. Averaged circuit models for single-input QSRC: (a) Buck, (b) Boost, and (c) Buck-Boost.
for the TCI QSRC and QPRC are shown in Fig. 2(a) and (b),
respectively. Details of the model derivation and averaged
variable definition are given in [9] and [25]. The averaging
procedure for resonant converter modeling is also described
in [26]. For the case of single-input converters, the averaged
models are obtained by replacing the control variables
and
as shown in Tables I and II. The equivalent circuits of
single-input series- and parallel-type models are represented in
Figs. 3 and 4, respectively.
method of Lyapunov. In addition, a set of sliding mode controllers for such converters is proposed.
A. Synthesis Procedure of Lyapunov’s Sliding Surfaces
Quantum resonant converters are multi-input nonlinear systems whose averaged state models can be represented as follows:
(1)
III. LYAPUNOV-BASED CONTROL DESIGN
In this Section, a systematic approach for the control design of
all single- and multi-input QRCs is developed, using the second
, the vector fields
where the state vector
, and are the control inputs (
,
,
).
CASTILLA et al.: SLIDING MODE CONTROL SCHEMES FOR QUANTUM RESONANT CONVERTERS
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Fig. 4 Averaged circuit models for single-input QPRC. (a) Boost with output filter, (b) buck with input filter, and (c) Cuk.
The sliding mode control structure for this kind of systems
and their associated
consists of a set of sliding surfaces
control laws:
for
for
respect to their average values in steady-state
):
(i.e.
(4)
(2)
and
take the values 1 or 0, and verify
.
where
For the design of the control structure (2), the Lyapunov function approach proceeds by first defining a positive-definite func, and then using
as a global reaching
tion
the deviation of the state vector with
condition [21], being
). As the
regards to its steady-state value (i.e.
Lyapunov function candidate, we chose the following quadratic
form:
(3)
is the transposed of
and is a diagonal matrix
where
of positive constant elements. In fact, such a function coincides
with the incremental energy of the converter if the elements of
matrix are conveniently expressed in terms of the values of
reactive components [22].
, defining
The state model (1) can be rewritten in terms of
as the deviation of
with
a new set of control inputs
. In that case, the control
where
law (2) can be expressed as:
for
for
(5)
can be positive (
Note that the two possible values of
) or negative (
), as
must be bounded between their
.
minimum and maximum limits
By replacing (3) and (4) in the reaching condition, we obtain:
(6)
corresponds to the time-derivative of the
The term
incremental energy of the converter in open-loop operation. In
[24], it is demonstrated that this term is always nonpositive, due
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
to it coincides with the incremental power dissipated in the converter with the negative sign. In such a case, the fulfilment of
expression (7) ensures that the reaching condition is satisfied:
and, consequently, the incremental state vector
written as
can be
(13)
(7)
The sliding mode control structure can be directly obtained
from (7). In fact, we could select each control input
according to the sign of each value
, so that each
can always be negative:
product
Second, the incremental energy of the Buck QSRC takes the
form
(14)
From (3) and (14), the matrix
for
is given
(8)
for
(15)
Finally, when comparing (5) and (8), the sliding surfaces and
their associated control laws can be identified as
for
for
In using (11), (13), and (15), Lyapunov’s sliding surface for
the Buck QSRC results in
(9)
(16)
B. Lyapunov-Based Controllers for QRCs
We begin by illustrating in detail the synthesis of a sliding
mode controller for the Buck QSRC shown in Fig. 3(a). From
the analysis of the circuit, the state-space model can be expressed as
(10a)
where can take the values 1 or 0, depending on the switch
position. The state-space model can be rewritten as
(10b)
being
For the rest of QRCs, Lyapunov’s sliding curves are shown
in Table III. These control structures have been deduced by
applying the synthesis procedure to the averaged models
represented in Figs. 2–4. However, the utilization of such
surfaces is strongly limited by some practical drawbacks. The
first problem is the complexity of the hardware required to
implement these nonlinear functions, which usually depend on
the input voltage, the load, and a considerable number of state
variables. The second problem is caused by the appearance
of output voltage steady-state errors, due to the imperfections
involved in different parts of the system, such as relays, losses,
etc. (see Section V).
In the next Section, an alternative approach for the synthesis
of sliding surfaces is proposed. The focus will be on the use
of linear stabilizing terms as a way of generating simple and
low-cost control circuits.
IV. DESIGN OF LINEAR SLIDING SURFACES
and
From (9), the Lyapunov-based control structure for this
single-input converter has the expression
(11)
then, in order to obtain a practical description of the switching
and matrix must be
surface, the incremental state vector
deduced.
the state variable that is desired to regFirst, considering
, the steady-state solution of (10)
ulate to a constant value
in close-loop operation is
(12)
In this Section, an alternative approach for the design of
sliding mode controllers for single- and multi-input QRCs is
presented. First, an interesting class of linear sliding surfaces,
showing low-cost implementation and absence of steady-state
errors, is proposed. Second, a set of design constraints for the
gain parameters of such surfaces is deduced by using reaching,
existence, and stability conditions.
We begin by describing the control design procedure for
single-input converters, including a detailed example of application for the Buck QSRC. Next, the case of multi-input
converters is introduced together with a detailed example for
the TCI QSRC.
A. Linear Sliding Surfaces for Single-Input QRCs
In single-input nonlinear systems, the relative degree of a
state variable is defined as the smallest number of differentiations of the state variable with regards to time, so that the control input appears explicitly [21].
CASTILLA et al.: SLIDING MODE CONTROL SCHEMES FOR QUANTUM RESONANT CONVERTERS
TABLE III
SLIDING SURFACES FOR QRC (e
V
=
When considering
(
) the state variable that
, the following
is desired to regulate to a reference value
linear sliding surface is proposed:
0v
,e
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=V
0v
)
deviation of the equivalent control with regards to its
steady-state value takes the expression:
(17)
are constant gains and is the relative degree of
where
(
). Note that surface (17) satisfies the transversality
condition (i.e. depends explicitly on the control input ) and
removes the undesirable steady-state errors of , due to the
presence of the integral term. Moreover, a linear dynamics of
is achieved in sliding motion (
,
), which can be
expressed as follows:
(18)
However, in using surface (17), the equilibrium point of the
converter can be unstable, even when choosing appropriate .
For the analysis of such situation, we can examine the stability
. In fact, in open-loop operation, a
of the equivalent control
converter has always stable steady-state behavior, since the converter is composed of passive components [22]. Therefore, the
ensures the stability of the close-loop converter.
stability of
transfer function as
In defining the control-toand using (18), the small-signal
(19)
From (19), a necessary condition for local stability of the closeloop converter is minimum-phase control-to- transfer function.
is a nonminimum-phase transfer function, a
If
,
) must
new minimum-phase state variable (
be included in surface (17) to guarantee system stability:
(20)
and ,
Now depends on the relative degree of variables
and
).
defined as and , respectively (
In order to fulfill the transversality condition, must be exactly
if
; whereas if
, can take any value from 1
to , allowing for some freedom in the choice of the terms of
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
surface (20). Note that the incorporation of
in surface (20)
causes a moderate increase of the control circuit complexity.
Again, the system stability is investigated by testing the expression of the equivalent control. In such a case, when using
the control-to- and control-to- transfer functions and the
, the equivalent control can be exinvariance condition
pressed as
The attraction domain is depicted in Fig. 5 as function of
and . Such existence region of sliding regime is derived by
considering the boundaries of the equivalent control (i.e.
). The expression of
is obtained by using (10) and
the invariance condition
(26)
(21)
In order to make the system show optimum attraction-domain
size, the sliding curve parameters must have the following constraints:
being
(27)
Taking into account that
has been chosen among the state
transfer
variables observing minimum-phase control-tofunction, the stability of expression (21) is conditioned only
. That condition could
by the position of the roots of
be examined using classical control design techniques such as
are in the
root locus diagrams. Because of the poles of
left half-plane, it can be easily shown that a set of values for
guaranteeing the stability of
will always exist.
For all single-input QRCs, the linear sliding surfaces shown
in Table III have been deduced using the previous synthesis procedure. A set of design conditions for the gain parameters of
these surfaces is represented in Table IV. These constraints have
been derived testing the existence and reachability of a sliding
regime and the local stability of the steady-state solution. In the
following Subsection, the application of the control design algorithm to a Buck QSRC is illustrated in detail.
B. Example 1: Control Design of a Buck QSRC
of
By using the state-space model (10), the open-loop dynamics
can be expressed as
(22)
is two and
is a
Because the relative degree of
minimum-phase transfer function, as can be easily found from
(22), a linear sliding surface is obtained using (17)
(23)
,
where
In sliding motion (
results in
of
, and
,
.
), the close-loop dynamics
(24)
The steady-state solution of (24) shows asymptotic stability if
the following conditions are fulfilled:
(25)
From (26), the existence region in steady-state takes the form
, which corroborates the step-down behavior of
the Buck QSRC.
Finally, the control law is determined by means of the often, resulting in
used reaching condition
S<0
(28)
C. Linear Sliding Surfaces for Multi-Input QRCs
In multi-input converters, the design of linear surfaces
showing low-cost implementation and absence of steady-state
errors proceeds as follows. First, a specific control objective
must be assigned to each sliding surface, which usually involves
(
) to a constant
the stabilization of a state variable
. Second, according to expressions (17)
reference value
and (20), the composition of the sliding surfaces must be
proposed. The concept of the relative degree appearing in such
surfaces is extended for that situation of multiple control inputs.
In that case, the relative degree of a state variable is defined
as the smallest number of differentiations of the state variable
with regards to time, so that at least one of the control inputs
appears explicitly.
The local stability criteria for selecting between surfaces
(17) and (20) in single-input converters cannot be used here.
The reason is that the relationship among the control inputs is
unknown beforehand, and, therefore, the small-signal transfer
(
and
) cannot be
functions
found. In such a case, the validity of the proposed solution is
shown guaranteeing the existence and reachability of a sliding
regime and the local stability of the equilibrium points.
and
is to
For the TCI QSRC, the control objective of
regulate the input current and the output voltage to get
and
, respectively. Taking into account that the relative degree of and is one for both variables, the following
surfaces are proposed among other possible candidates:
(29)
. The choice of these control structures
being
is due to the fact that the close-loop converter behaves in sliding
CASTILLA et al.: SLIDING MODE CONTROL SCHEMES FOR QUANTUM RESONANT CONVERTERS
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TABLE IV
DESIGN CONDITIONS FOR LINEAR SURFACES
regime as a linear first-order system, as we will show in the next
Subsection.
For the TCI QPRC, surfaces and are conceived to stabilize the intermediate capacitor voltage to its reference value
and to provide output voltage regulation, respectively.
is one for
Considering that the relative degree of , , and
the first variables and two for the last one, the following surfaces
are proposed:
Finally, a set of design conditions for the gain parameters of
surfaces (29) and (30) are shown in Table IV.
D. Example 2: Control Design of a TCI QSRC
In this Subsection, the design of the proposed controller for
the TCI QSRC is illustrated in detail. From the analysis of the
circuit, the state-space model can be written as
(30a)
(30b)
being
.
(31)
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
Fig. 5. Existence region of sliding regime (k
k
= (k
=L
C
) + (k
0
k =RC =RC
= (k
E =L
C V
) and
)).
1
1
Fig. 7. (a) Unstable behavior of Boost QPRC using S = k
e
+k
e
dt
v (k = 0:01, k = 100) and (b) high-ripple steady-state behavior
i
and S = k e + k
e
dt
i
of TCI QSRC using S = I
(I
= 1:4 A, k = 0, k = 2500).
0
0
1
1
0
In considering that a sliding mode exists on the intersection
,
of the surfaces and using the invariance conditions
, the equivalent control
and
can
be expressed as
(32)
In such situation, the converter behaves as a linear first-order
system. In fact, replacing (32) in (31) and considering
(
), the converter dynamics in sliding regime is given by
(33)
Fig. 6. Transient responses using Lyapunov sliding curves. (a) Boost QPRC.
(b) TCI QSRC (I
= 1:4 A).
where
and
can take the values 1 or 0, depending on the
switch position.
. The equilibrium point of (33) shows asympbeing
totic stability if the following condition is satisfied
(34)
CASTILLA et al.: SLIDING MODE CONTROL SCHEMES FOR QUANTUM RESONANT CONVERTERS
Fig. 8. Comparison of (a) simulation and (b) experimental waveforms of Boost
QPRC using S i
i , being i
k
e
+ k e dt, k = 0:04,
and k = 1600. Top: Output voltage (5 V/div). Middle: Current i
(0.2
A/div). Bottom: Load control signal (low: 47 , high: 66 ).
=
0
= 1
1
In this multi-input converter, the attraction domain can be derived by considering the natural limits of the equivalent controls
and
. However, the interaction
expressed in (32) between the equivalent controls restricts the
possible values of such variables as follows:
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Fig. 9. Comparison of (a) simulation and (b) experimental waveforms of TCI
QSRC using S = I
i
and S = k
e
+ k e dt v
(I
= 1:4 A, k = 0, k = 212). Top: Output voltage (5 V/div). Bottom:
Load control signal (low: 10 , high: 20 ).
0
1
1
0
Finally, the design of the control laws is done by the
, resulting
often-used reaching condition
in
(37)
(35)
V. SIMULATION AND EXPERIMENTAL RESULTS
Therefore, the actual attraction domain is obtained by replacing
(32) in (35). From the analysis of such existence region in the
system start-up and in steady state, the control parameters must
have the following constraints:
(36a)
The proposed control schemes for quantum resonant converters are evaluated in this Section. The common power-circuit
parameters used in all simulations and experiments are
QSRCs:
H
nF
F
QPRCs:
(36b)
V
V
nF
H
H
H
F
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Fig. 10.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
Block diagram of the proposed controllers for (a) Boost QPRC and (b) TCI QSRC (k
First, the control performance of a single-input Boost QPRC
and a TCI QSRC are investigated. Fig. 6 shows transient responses using Lyapunov’s sliding curves expressed in Table III.
presents a load-dependent steady-state error,
Note that
thereby causing a poor regulation of the output voltage.
Some examples of linear sliding surfaces not observing the
are depicted
proposed design criteria for the state variable
, the Boost QPRC has an unstable
in Fig. 7. Using
equilibrium point. In fact, the only state variable having minimum-phase control-to- transfer function is ; therefore, the
Boost QPRC exhibits a stable behavior when is selected as .
The transient response of the TCI QSRC using
and
is represented in Fig. 7(b).
in
is not a good choice because the dyUsing
is independent of
when sliding mode exists
namics of
on , resulting in a steady-state behavior with an undesirable
high-ripple.
Figs. 8 and 9 compare simulation and experimental results
of the Boost QPRC and the TCI QSRC using the linear sliding
curves shown in Table III. Excellent agreement was obtained
for steady state and large-signal transient responses. Moreover,
good output performances (such as nonzero steady-state errors,
large-signal stability, low steady-state ripple, fast transient responses, and high robustness) are obtained in relation to results
depicted in Figs. 6 and 7.
= 0).
A block diagram of the control schemes shown in Table III for
the Boost QPRC and the TCI QSRC is represented in Fig. 10,
showing the simplicity of the proposed solution. The sliding
surfaces can be built by linear analog circuits, and the control
laws by a comparator and a flip-flop. The goals of the flip-flip
are to synchronize the control input changes with the resonant
frequency and to limit the maximum operating frequency, thus
guaranteeing nearly zero switching losses and frequency stability.
All the linear sliding surfaces expressed in Table III have
output performances as good as those described above for the
case of the Boost QPRC and the TCI QSRC. For the purpose
of comparison, simulation results for all QSRCs and QPRCs
are shown in Figs. 11 and 12. According to a step-down and a
step-up behavior, two results are depicted in such figures for
each multi-input converter. Note that multi-input converters
present, in all cases, lower voltage overshoot and faster recovery time for start-up and load step changes than single-input
converters. Especially interesting is the dynamic behavior of
the TCI QSRC, which acts as a linear first-order system with
very low sensitivity to external perturbations and parametric
variations (see Figs. 9 and 11). The reason for this is that the
converter dynamics in sliding regime is independent of the
input source, the load, and the power circuit parameters, as it
can be seen in expression (33).
CASTILLA et al.: SLIDING MODE CONTROL SCHEMES FOR QUANTUM RESONANT CONVERTERS
Transient responses of QSRC. (a) Buck (k = 0:4, k = 1000). (b) Step-down TCI (k = 0, k = 2500, I
= 1500). (d) Buck-Boost (k = 0:4, k = 1500). (e) Step-up TCI (k = 0, k = 2500, I
= 7 A).
Fig. 11.
k
VI. CONCLUSIONS
The design of sliding mode control schemes for a wide
range of quantum resonant topologies is examined by means
of two different approaches. First, an easy-to-use procedure for
devising nonlinear control structures is established, using Lyapunov’s well-known stability criteria. Second, an alternative
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= 1:4 A). (c) Boost (k = 0:4,
method that provides linear sliding surfaces is also developed,
considering reaching, existence, and stability conditions.
The operation of Lyapunov’s controllers is strongly limited
by some drawbacks, which makes it unsuitable for their
practical use. All regulators using the proposed linear surfaces,
however, posses good output performances, such as nonzero
steady-state errors, large-signal stability, low steady-state
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
=
Fig. 12. Transient response of QPRC. (a) Buck (k
1:6, k = 1500). (b) Step-down TCI (k = 0:03, k = 200, k = 0:15, k = 100, V
= 20 V).
(c) Boost (k = 0:04,k = 400). (d) Cuk (k = 0:04, k = 400). (e) Step-up TCI (k = 0:03, k = 200, k = 0:5, k = 500, V
= 30 V).
ripple, fast transient responses, and high robustness. In using
such controllers, multi-input converters improve the dynamic
behavior of single-input converters, showing lower voltage
overshoot and faster recovery time for start-up and load step
changes. Simulation and experimental results corroborate the
above features.
REFERENCES
[1] G. B. Joung, C. T. Rim, and G. H. Cho, “An integral cycle mode control
of series resonant converter,” in Proc. IEEE PESC Conf. Rec., 1988, pp.
575–582.
[2] G. B. Joung and G. H. Cho, “Modeling of quantum parallel resonant converters controlled by integral cycle mode,” in Proc. IEEE PESC Conf.
Rec., 1989, pp. 744–751.
CASTILLA et al.: SLIDING MODE CONTROL SCHEMES FOR QUANTUM RESONANT CONVERTERS
[3] W. H. Kwon and G. H. Cho, “Optimum quantum sequence control of
quantum series resonant converter for minimum output voltage ripple,”
IEEE Trans. Power Electron., vol. 9, pp. 74–84, Jan. 1994.
[4] J. H. Ko, D. S. Oh, and M. J. Youn, “Improved current mode control
technique for quantum series resonant convertors,” Electron. Lett., vol.
26, no. 13, pp. 936–937, 1990.
[5] H. B. Shin, J. H. Ko, and M. J. Youn, “Switched optimal predictive
current control technique for improved quantum boost SRC,” Electron.
Lett., vol. 27, no. 25, pp. 2322–2324, 1991.
[6] J. H. Ko, S. S. Hong, M. G. Kim, and M. J. Youn, “Modeling and improved current control of series resonant converter with nonperiodic integral cycle mode,” IEEE Trans. Power Electron., vol. 7, pp. 280–288,
Mar. 1992.
[7] B. R. Jo, H. W. Ahn, G. W. Moon, H. C. Choi, and M. J. Youn, “Decoupled output voltage control of quantum series resonant converter for
improved Buck-Boost operation,” IEEE Trans. Power Electron., vol. 11,
pp. 146–161, Jan. 1996.
[8] F. Boudjema and J. L. Abatut, “Sliding mode. A new way to control
series resonant converters,” in Proc. IEEE IECON Conf. Rec., 1990, pp.
938–943.
[9] M. Castilla, L. García de Vicuña, and J. Ordinas, “An averaged continuous model for the quantum-series resonant converter,” in Proc. IEEE
ISCAS Conf. Rec., 1996, pp. 601–604.
[10] J. Ordinas, L. García de Vicuña, and M. Castilla, “Modeling and control
of a quantum parallel resonant converter,” in Proc. PEMC’96, Power
Electron. Motion Contr. Conf., pp. 1/273–1/277.
[11] M. Castilla, L. García de Vicuña, O. López, M. López, J. Majó, and J.
A. Lobato, “Sliding mode controllers for the quantum parallel resonant
converter,” in Proc. PEMC’98, Power Electron. Motion Control. Conf.,
pp. 5/105–5/110.
[12] P. Bidan, M. Valentin, and L. Martinez, “Modeling and current-mode
control of a zero-current switching resonant converter used for AC-sine
voltage generation,” in Proc. IEEE PESC Conf. Rec., 1993, pp. 636–640.
[13] M. Castilla, L. García de Vicuña, and J. Ordinas, “Modeling and
multi-input sliding mode control of the series resonant inverter,” in
Proc. PEMC’96, Power Electron. Motion Contr. Conf., pp. 1/210–1/214.
[14] V. I. Utkin, Sliding Modes and Their Application in Variable Structure
Systems. Moscow, Russia: MIR, 1978.
[15] H. Bühler, Réglage par Mode de Glissement. Lausanne, France:
Presses Polytechniques Romandes, 1986.
[16] R. A. DeCarlo, S. H. Zak, and G. P. Matthews, “Variable structure control
of nonlinear multivariable systems: A tutorial,” Proc. IEEE, vol. 76, pp.
212–232, Mar. 1988.
[17] H. Sira-Ramirez, “Differencial geometric methods in variable structure
control,” Int. J. Contr., vol. 48, no. 4, pp. 1359–1390, 1988.
[18] L. Malenasi, L. Rossetto, G. Spiazzi, and P. Tenti, “Performance
optimization of Cuk converters by sliding-mode control,” IEEE Trans.
Power Electron., vol. 10, pp. 302–309, May 1995.
[19] J. Majó, L. Martínez, A. Poveda, L. García de Vicuña, F. Guinjoan, A.
F. Sánchez, M. Valentin, and J. C. Marpinard, “Large-signal feedback
control of a bidirectional coupled-inductor Cuk converter,” IEEE Trans.
Ind. Electron., vol. 39, pp. 429–436, Oct. 1992.
[20] H. Sira-Ramirez and M. Rios-Bolívar, “Sliding mode control of dc-to-dc
power converters via extended linearization,” IEEE Trans. Circuits Syst.,
vol. 41, pp. 652–661, Oct. 1994.
[21] J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: A
survey,” IEEE Trans. Ind. Electron., vol. 40, pp. 2–22, Feb. 1993.
[22] S. R. Sanders and G. C. Verghese, “Lyapunov-based control for switched
power converters,” IEEE Trans. Power Electron., vol. 7, pp. 17–24, Jan.
1992.
[23] B. Nicolas, M. Fadel, and Y. Cheron, “Sliding mode control of
DC-to-DC converters with input filter based on the Lyapunov-function
approach,” in Proc. EPEA’95, Europ. Conf. Power Electron. Applicat.,
pp. 1338–1343.
[24] M. Castilla, L. García de Vicuña, M. López, and J. Matas, “Designing
multi-input sliding mode controllers for quantum resonant converters
using the Lyapunov-function approach,” in Proc. EPEA’97, Europ.
Conf. Power Electron. Applicat., pp. 3325–3330.
[25] M. Castilla, “Modelos no Lineales y control en modo deslizamiento de
convertidores de estructura resonante,” Ph.D. dissertation, Univ. Politécnica de Cataluña, Barcelona, Spain, 1998.
[26] M. Castilla, L. García de Vicuña, M. López, and V. Barcons, “An averaged large-signal modeling method for resonant converters,” in Proc.
IEEE IECON Conf. Rec., 1997, pp. 447–452.
973
[27] O. López, L. García de Vicuña, M. Castilla, M. López, and J. Majó,
“A systematic method to design sliding mode surfaces by imposing a
desired dynamic response,” in Proc. IEEE IECON Conf. Rec., 1998, pp.
381–384.
Miguel Castilla (M’99) received the B.S., M.S., and
Ph.D. degrees in telecommunications engineering
from the Universidad Politécnica de Cataluña,
Barcelona, Spain, in 1988, 1995, and 1998, respectively.
Since 1992, he has been an Assistant Professor
in the Departamento de Ingeniería Electrónica,
Universidad Politécnica de Cataluña, where he
teaches analog circuits and power electronics. His
research interests are in the areas of modeling,
simulation, and control of dc-to-dc power converters
and high-power-factor rectifiers.
Luis García de Vicuña (M’90) received the Ingeniero de Telecomunicación and Dr.Ing. de Telecomunicación degrees from the Universidad Politécnica de
Cataluña, Barcelona, Spain, in 1980 and 1990, respectively, and the Dr.Sci. degree from the Université
Paul Sabatier, Toulouse, France, in 1992.
From 1980 to 1982, he was an Engineer with
Control Aplicaciones Company. He is currently
an Associate Professor in the Departamento de
Ingeniería Electrónica, Universidad Politécnica de
Cataluña, where he teaches power electronics. His
research interests include power electronics modeling, simulation and control,
active power filtering, and high-power-factor ac/dc conversion.
Mariano López (M’98) received the M.S. and Ph.D.
degrees in telecommunications engineering from
the Universidad Politécnica de Cataluña, Barcelona,
Spain, in 1996 and 1999, respectively.
Since 1996, he has been an Assistant Professor in
the Departamento de Ingeniería Electrónica, Universidad Politécnica de Cataluña, where he teaches microelectronics and power electronics. His main research interests are distributed power system, control
theory, and modeling of power converters.
Oscar López (S’99) received the M.S. degrees in physics and electronic engineering from the Universidad de Barcelona, Barcelona, Spain, in 1994 and 1996,
respectively, and the Ph.D. degree in electronics engineering from the Universidad Politécnica de Cataluña, Barcelona, Spain, in 2000.
Since 1996, he has been an Assistant Professor at the Universidad Politécnica
de Cataluña. His research interests are in the area of nonlinear control systems,
in particular, in applications to power electronics.
José Matas (S’97) received the B.S. and M.S.
degrees in telecommunications engineering from
the Universidad Politécnica de Cataluña, Barcelona,
Spain, in 1988 and 1996, respectively, where
he is currently pursuing the Ph.D. degree in the
Departamento de Ingeniería Electrónica.
Since 1997, he has been an Assistant Professor
at the Universidad Politécnica de Cataluña. His
research interests include power electronics,
power-factor-correction circuits, distributed power
systems, and nonlinear control.