Received January 18, 2019, accepted February 8, 2019, date of publication February 25, 2019, date of current version

March 12, 2019.

Digital Object Identifier 10.1109/ACCESS.2019.2901441

Interval Robust Controller to Minimize

Oscillations Effects Caused by Constant Power
Load in a DC Multi-Converter Buck-Buck System
KEVIN EDUARDO LUCAS MARCILLO 1,2 , (Member, IEEE),
DOUGLAS ANTONIO PLAZA GUINGLA 1 , (Member, IEEE), WALTER BARRA, Jr.2 ,
RENAN LANDAU PAIVA DE MEDEIROS3 , ERICK MELO ROCHA2 ,
DAVID ALEJANDRO VACA BENAVIDES 1 , (Member, IEEE),
AND FABRICIO GONZALEZ NOGUEIRA4
1 Facultad de Ingeniería Eléctrica y Computación, Escuela Superior Politécnica del Litoral, Campus Gustavo Galindo, Guayaquil 09-01-5863, Ecuador
2 Faculty of Electrical Engineering, Federal University of Pará, Campus do Guamá, Belém 66075-900, Brazil
3 Department of Electricity, Federal University of Amazonas, Manaus 69080-900, Brazil
4 Electrical Engineering Department, Federal University of Ceará, Fortaleza 60020-181, Brazil

Corresponding author: Kevin Eduardo Lucas Marcillo (keveluca@espol.edu.ec)

This work was supported in part by the Personnel Improvement Coordination of Superior Level-CAPES Grant, and in part by the Escuela
Superior Politécnica del Litoral.

ABSTRACT Multi-converter electronic systems are becoming widely used in many industrial applications;
therefore, the stability of the whole system is a big concern to the real-world power supplies applications.
A multi-converter system comprised of cascaded converters has a basic configuration that consists of
two or more converters in series connection, where the first is a source converter that maintains a regulated dc
voltage on the intermediate bus while remaining are load converters that convert the intermediate bus voltage
to the tightly regulated outputs for the next system stage or load. Instability in cascaded systems may occur
due to the constant power load (CPL), which is a behavior of the tightly regulated converters. CPLs exhibit
incremental negative resistance behavior causing a high risk of instability in interconnected converters.
In addition, there are other problems apart from the CPL, e.g., non-linearities due to the inductive element
and uncertainties due to the imprecision of a mathematical model of dc–dc converters. Aiming to effectively
mitigate oscillations effects in the output of source converter loaded with a CPL, in this paper, an interval
robust controller, by linear programming based on Kharitonov rectangle, is proposed to regulate the output
of source converter. Several tests were developed by using an experimental plant and simulation models
when the multi-converter buck–buck system is subjected to a variation of power reference. Both simulation
and experimental results show the effectiveness of the proposed controller. Furthermore, the performance
indices computed from the experimental data show that the proposed controller outperforms a classical
control technique.

INDEX TERMS Constant power load (CPL), multi-converter buck-buck system, parametric uncertainties,
robust control based on Kharitonov rectangle, mitigation oscillations in multi-converter buck-buck system.

I. INTRODUCTION demand high dynamic performance, have applied different

Nowadays, multi-converter electronic systems are increas- types of converters for applications such as in variable speed
ingly used in industrial applications due to their simplicity DC motor drivers [3], renewable energy systems [4]–[6],
in structure, high power efficiency, low cost and high reli- transportation systems [7], [8], hybrid energy storage sys-
ability [1], [2]. Some modern industries, whose processes tem [9], [10], communications systems [11]. In several
of these applications, converters are controlled by switch-
The associate editor coordinating the review of this manuscript and ing through Pulse Width-Modulation (PWM) to transfer
approving it for publication was Ho Ching Iu. power from a power source to loads having a constant

2169-3536 2019 IEEE. Translations and content mining are permitted for academic research only.
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K. E. Lucas Marcillo et al.: Interval Robust Controller to Minimize Oscillations Effects

power characteristic. Because of switching, the convert- In research on dynamic systems with parametric uncertain-
ers have some inherent nonlinear behaviors, e.g., high fre- ties, the techniques that deal with this problem have been
quency of switching, increasing harmonics in the system, studied extensively over the last 40 years [42], [43].
current and voltage distortion, and instabilities occur due this To the best of the authors’ knowledge, it seems that most
effects [12], [13]. Therefore, it is a challenging task to ensure papers published so far focus on mitigating the destabilizing
the stability, transient performance and higher efficiency of effect of CPL without considering the uncertainties present
such converters [13]. in the system parameters. Therefore, studies reporting robust
A multi-converter system comprised of cascaded convert- parametric methodologies for DC-DC converters feeding a
ers has a basic configuration that consists of two converters CPL to mitigate oscillations effects caused by CPL still
in series connection, where the first is a source converter scarce in literature. However, in [39], a novel multivariable
while the second one is a load converter. The source converter robust parametric technique was used for minimizing cou-
maintains a regulated DC voltage on the intermediate bus, and pling effect in single inductor multiple output DC-DC con-
the load converter transforms the intermediate bus voltage to verter operating in continuous conduction mode. Moreover,
tightly regulated outputs for the next system stage or load. In a in [40] and [41], the use of Robust Parametric Control (RPC)
cascaded buck converter system a large variety of dynamic techniques is proposed to stabilize oscillations at the output
and static interactions are possible and these can lead to of a buck converter caused by parametric uncertainties.
irregular behavior of a converter, a group of converters or the Recently, the study developed in [44] addressed the impor-
whole system. tant problem of parametric uncertainties in DC-DC convert-
When a converter tightly regulates its output, it behaves as ers by using µ analysis. However, their approach is focused
a Constant Power Load (CPL), thereby, in cascaded systems, only on a posterior analysis of system stability. The important
load converter acts as a CPL when it is tightly regulated, subject of robust controller synthesis has been not addressed.
its dynamic response is faster than the dynamic response of In contrast, this paper is focused in the problem of robust con-
the source converter and its switching operation frequency troller synthesis, being thoroughly addressed from the onset,
is faster than source converter [14]. If the source converter providing a practical and simple robust controller design
is faster than the load converter, then it will compensate for algorithm with sufficient level of the detail in order to be
disturbances and will regulate its output before the feedback easily implemented.
loop of the load converter reacts to disturbances. Therefore, In this context, this paper proposes a robust controller
the load converter will not act as a perfect CPL for the feeding based on RPC theory. The proposed controller is applied to
converter [15]–[21]. source converter in order to mitigate oscillations effects due to
Different from a resistive load, CPL is a nonlinear load CPL in multi-converter buck-buck (MCBB) system, aiming
with variable negative impedance characteristics, i.e., the to reduce the control effort when the system is submitted to
input current increases/decreases with a decrease/increase variation of power reference.
in its terminal voltage [15]–[21]. Because of the negative The main contributions of this work are briefly summa-
impedance characteristics of CPL, the system may become rized in that following:
unstable, which may lead the system into oscillation or fail- • By using the proposed robust technique, structured
ure, and stress or damage the system equipment when feed- uncertainties of the type hyperbox, considering interval
ing a CPL [17]–[21]. For this issue, CPLs are receiving parametric type, are taking into account from the outset
more attention of researchers to give solutions aiming to in the controller design process, incorporating available
cancel or compensate the negative effects of CPL. information about components (resistors, inductors, and
Traditionally, the stability analysis and controller design capacitors) tolerances or defined by designer.
of cascaded DC-DC converters is carried out by using the • The proposed robust technique leads to easy-to-
impedance criterion applied to averaged and linearized mod- implement controllers having fixed low-order structure,
els [19]–[22]. The load converter under a tight control is allowing the deployment of standard industry structures
conventionally modeled CPL for stability analysis or for such as PID and Lead-Lag.
controller design [19]–[22]. • Aiming to evaluate the performance of the proposed
In order to mitigate the destabilizing effect of CPL, several robust methodology under the instability problem
methods have been proposed [23], such as passive and active caused by a CPL, the proposed robust methodology
damping [24]–[26], Lyapunov redesign control [8], nonlin- is compared with classical methodology carrying out
ear feedback linearization [27]–[29], Sliding Mode Control several experimental and simulation tests. The perfor-
(SMC) [30]–[32], fuzzy control [33], Model Predictive Con- mance index (ISE) is computed to analyze the con-
trol (MPC) [34], [35] and robust control [36], [37]. However, trol methodologies compared in this work. The results
there are other problems apart from the CPL, e.g., uncer- show the proposed methodology outperforms the other
tainties present in the system parameters, which may lead approach.
to performance degradation [38]. In literature can be found The remainder of this paper is organized as follows.
control strategies applied to DC-DC power converters that Section II presents a brief review about the multi-converter
deal with parametric uncertainties [39]–[41]. buck-buck system; Section III presents a brief review about

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 K. E. Lucas Marcillo et al.: Interval Robust Controller to Minimize Oscillations Effects

parametric robust control background; Section IV proposes

a mathematical model for multi-converter buck-buck system;
Section V presents the proposed design methodology for
interval robust controller; Section VI presents the experimen-
tal and simulation environment, describing the experiments
to be performed in this paper; Section VII presents an assess-
ment of the simulation results and experimental data. Finally,
Section VIII presents the main conclusions.

II. SYSTEM DESCRIPTION AND PROBLEM FORMULATION

Multi-converter systems comprised of cascaded converters
have a basic configuration that consists of two or more
converters in series connection, where the first is a source
converter that maintains a regulated DC voltage on the inter-
mediate bus while remaining are load converters that trans-
form the intermediate bus voltage to tightly regulated outputs
for the next system stage or load.
In a cascaded buck converter a large variety of dynamic and
static interactions are possible and these can lead to irregular
behavior of a converter, a group of converters or the whole
system.
A typical cascaded system with N DC-DC buck converters
is shown in Fig. 1, where N represents the quantitative of buck
converters.

FIGURE 2. Multi-converter buck-buck system. (a) Cascaded system with

two power stages. (b) Source converter loaded by a CPL. (c) Tightly
FIGURE 1. Buck Converters in series connection: Cascaded system with regulated load converter.
N-converters.

When a power converter tightly regulates its output,

it behaves as a CPL [14]. CPLs have a negative incremental
resistance, which tends to destabilize the system [19]–[21].
CPL approximation model describe the behavior at the input
terminals of the load converter allows to capture its perfor-
mance in a frequency range where its open-loop gain is high
and an input voltage span where its controller is within its
dynamic range.

A. BUCK CONVERTER WITH CONSTANT POWER LOAD

Cascaded buck converter system and its representation with
CPL are shown in Figs. 2(a) and 2(b), respectively. It is
assumed that the output of the load converter is tightly regu-
lated as shown in Fig. 2(c).
CPLs introduce interesting nonlinear behavior to con- FIGURE 3. Input ‘‘V−I’’ characteristics of the CPL.

ventional buck-converter dynamics, but this behavior only

exhibit above a certain voltage. On the other hand, when vc1 is higher than (vc2 /d2max ), load
Fig. 3 shows the input ‘‘V-I’’ characteristics of load converter behavior will be as a CPL, thus, load converter will
converter. be operate in a constant power zone (CPZ).
When the input voltage of the load converter, vc1 , is lower Where voc1 is the input DC voltage of load converter; voc2 is
than (vc2 /d2max ), the load converter behavior will be as the the tightly regulated output voltage of load converter; ioinL is
resistive load. Therefore, in this range of operation, load the input operation current of load converter; imax
inL is the max-
converter will be operates in a constant resistor zone (CRZ). imum input current of load converter; d2max is the maximum

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K. E. Lucas Marcillo et al.: Interval Robust Controller to Minimize Oscillations Effects


operating duty cycle of load converter; and Po is the operating diL rL 1

 1 = − 1 iL1 + −vc1


power of CPL. dt L1 L1  d1 Ts1 < t < Ts1
dvc1 1 1 vc1 Po
In order to maintain a constant power level, in a DC-DC 
 = iL1 − + ,
dt C1 C1 RL1 vc1

converter when it acts as a CPL, input current increases
when input voltage decreases, and vice versa, thus, the prod- (3)
uct of the input current and input voltage of the load con-
where d1 and Ts1 are the duty cycle and switching period of
verter, (i.e., Po = iinL vc1 ) is a constant. The instantaneous
the source converter, respectively. L1 , rL1 , C1 and RL1 are the
value of the load impedance is positive (i.e., vc1 /iinL > 0).
plant parameter of source converter. Vi is the input DC voltage
However, the incremental impedance is always negative
of source converter. Po is the output power of load converter
(i.e., 1vc1 /1iinL < 0) due to once appearing any distur-
that is constant. iouts = iL1 .
bance, thus operating point will leave from previous point
Using the state-space averaging method [14], [20],
and never return. This negative incremental impedance has a
the buck converter dynamics can be written as:
negative impact on the power quality and stability of system. 
Fig. 4 shows the negative incremental impedance behavior diL rL 1

 1 = − 1 iL1 + Vi d1 − vc1


of CPL. dt L1 L1
dvc1 1 1 vc1 Po
 (4)

 = iL1 − +
dt C1 C1 RL1 vc1


Consider small perturbations in the state variables due to

small disturbances in the input voltage and duty cycle


 Vi = V̄i + Ṽi

d = d̄ + d̃
1 1 1
(5)


 v c1 = VC1 + ṽc1

iL1 = IL1 + ĩL1

where, V̄i , d̄1 , VC1 and IL1 are the average values of Vi , d1 , vc1
and iL1 , respectively.
Substituting (5) in (4) and neglecting the internal resistance
of the inductor to simplify the calculations, the buck converter
model becomes
FIGURE 4. The negative incremental impedance behavior of CPL.
  
d ĩ
 dtL1 = L1 V̄i d̃1 + d̄1 Vi − ṽc1

1 
d ṽc1 P ṽ
 (6)
1
 dt = C ĩL1 − Vo 2c1

1 c1
B. STABILITY ANALYSIS OF STUDIED SYSTEM
The system, showed in Fig. 2(b), is used to show the insta- Note that the following approximation was made in (6),
bility of a DC-DC converter feeding a CPL. To obtain the V̄i  Ṽi and Vc1  ṽc1 .
large-signal behavior of the load converter, the CPL is rep- Therefore, the transfer function of the buck converter
resented by a dependent current source [14], iCPL = Po /vc1 , loaded with a CPL can be obtained from (6) as follows:
so the instantaneous current drawn from source converter is d̄1
given by ṽc1 L1 C1
G(s) = =   (7)
Ṽi Po 1
iouts (t) = iRL1 (t) + iCPL (t) s2 − C1 Vc2
s+ L1 C1
1
vc (t) Po
iouts (t) = 1 + Due to CPL, the transfer function in (7) have poles in the
RL1 vc1 (t)
right half-plane, thus, the buck converter, when it is loaded
iouts = iL1 (1)
with a CPL, is unstable.
Depending on switching of the source converter, the large- In (4), the nonlinear coefficient introduced by a CPL and
signal model of the converter in continuous conduction mode the constraints on the state variables make the equation diffi-
can be obtained based on the following equations: cult to solve. Therefore, any unwanted dynamics introduced
 in (4) cannot be damped, so trajectories will tend to have
diL rL 1
cycling or unbounded behaviors [20], [21].
 1 = − 1 iL1 + Vi − vc1


dt L1 L1  0 < t < d1 Ts1 The simulation results in Fig. 5 confirm the intuitive
dvc1 1 1 vc1 Po behavior suggested by (4).

 = iL1 − + ,
dt C1 C1 RL1 vc1

The system is analyzed by a phase-plane analysis,
(2) solving (plotting) the system differential equations giving

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 K. E. Lucas Marcillo et al.: Interval Robust Controller to Minimize Oscillations Effects

FIGURE 6. Closed-Loop system subjected to a variation of power CPL

of 10 W. (a) Capacitor Voltage of Source Converter. (b) Inductor Current of
Source Converter. (c) Phase-Plane of vc1 vs iL during the variation of
1
power CPL.

the energy storage elements in the system. This oscillatory

behavior is also observed when attempting regulation if the
controller is not adequately designed [16].
Fig. 6 shows voltage and current oscillations when a buck
converter is subjected (t = 1 s) to a variation of power CPL
(1Po ) of 10 W with Vi = 15 V , L1 = 2mH , C1 = 2000 mF,
Po = 5 W , regulated for an output voltage of 8 V with a
PID controller with integral gain of 2.41, proportional gain
of 0.011 and derivative gain of 1.05e−5 . Load converter acts
as a CPL due to the incremental negative resistance behavior
FIGURE 5. Phase-portrait obtained by simulating. (a) Phase-portrait of during the variation of CPL power as shown in Fig. 6(c).
source converter loaded with a CPL. (b) Zoomed area near the operating
condition.
III. ROBUST PARAMETRIC CONTROL BACKGROUND
Mathematical models naturally present errors that are
neglected, depending on the type of study. An important
an insight about how the system dynamics evolve with
consideration in model-based control systems is to keep the
time [16], [20], [21].
system stable, subject to parametric variations. However,
The phase-portrait of source converter feeding a CPL
generally in the classic controller design, models that ignore
(cf. Fig. 5) is simulated with the following parameters:
uncertainties are used [45]. In this way, it is common to use a
Vi = 15 V , L1 = 2mH , C1 = 2000 mF, Po = 10 W , and
nominal transfer function for the controller design. Although
d1 = 0.744.
the controller is developed based on a nominal transfer func-
The phase-portrait (Fig. 5(a)) shows the state plane divided
tion, the real system must be stable for all kinds of transfer
into two regions with distinct characteristics [16], [20]: one
functions that represent the whole set of uncertainties.
to the left of a separatrix σ , in which the bus voltage vc1 col-
Thereby, uncertainty of a system can be classified as
lapses being an unstable region, and the other to the right of σ ,
unstructured (non-parametric uncertainty) and structured
in which vc1 presents significant and undesirable oscillations
(parametric uncertainty) [38], [43].
because of the existence of a limit-cycle χ [16], [20]. These
oscillations are caused by energy imbalances, which occur
during the transient period when LC input filter and output A. ROBUST STABILITY
powers are not equal as it occurs in steady state. Therefore, A system with interval parametric uncertainties is gen-
without resistive components in the system, which can dissi- erally described by uncertain polynomials B(s, b) and
pate the energy imbalance, this energy will resonate among A(s, a), restricted within pre-specified closed real intervals,

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K. E. Lucas Marcillo et al.: Interval Robust Controller to Minimize Oscillations Effects

as shown in (8) [38]. designed according to Keel and Bhattacharyya [45], associ-
m ated with a linear goal programming formulation, which will
bi , bi s
P  − + i
lead to a set of linear inequality constraints.
B(s, b) i=0 Consider G(s, p) a uncertain plant of order n and C(s, x) the
G(s, b, a) = = n (8)
A(s, a) controller of order r, defined in (13) and (14) respectively.
ai , ai s
P  − + i
i=0 n(s) b1 sn−1 + · · · + bn−1 s + bn
G(s, p) = = n (13)
Many robust stability tests under parametric uncertainty d(s) s + a1 sn−1 + · · · + an−1 s + an
are based on analysis of uncertain characteristic polynomial nc (s) x0 sr + x1 sr−1 + · · · + xr−1 s + xr
assumed as an interval polynomial family [38], such as C(s, x) = = r (14)
dc (s) s + y1 sr−1 + · · · + yr−1 s + yr
n
X Let p be the vector of parameters that represent the plant
pi , pi s
 − + i
P(s, p) = (9) and x the vector of real parameters representing the controller
i=0
defined in (15) and (16) respectively. In addition, po rep-
Polynomial P(s, p) is stable if and only if all its roots are resents the nominal value of plant parameters defined in a
contained on the Left Half-Plane (LHP) of the s-plane. Then, hyperbox region of uncertainties.
P(s, p) is robustly stable if and only if all its polynomials
p := [ b1 b2 · · · bn−1 bn a1 a2 · · · an−1 an ] (15)
are stable for a set of operating point different from the
nominal operating point within its minimum and maximum p := [ x0 x1 · · · xr−1 xr y1 y2 · · · yr−1 yr ] (16)
limits [46]. However, it is not necessary to check stability According to [45], the solution of the Diophantine equa-
of an infinite number of polynomials to guarantee the robust tion (17) summarizes the pole-placement problem
stability. Robust stability can be checked through the analysis
of four polynomials within P(s, a); these polynomials can be d(s) = d(s)dc (s) + n(s)nc (s) (17)
found by Kharitonov Theorem [38], [47]. where, d(s) is the closed-loop characteristic polynomial.
Therefore, the parameters of the closed-loop characteristic
B. KHARITONOV STABILITY THEOREM polynomial are represented as follows:
The Kharitonov Theorem is a test used in robust control
theory to evaluate the stability of a dynamic system whose di = di (x, p) (18)
parameters vary within a closed real interval as follows: Assuming that the desired dynamic of closed-loop system
δ(s) = δ0 + δ1 s + δ2 s + δ3 s + · · · + δn s
2 3 n
(10) is represented by
1d (s) = si + φ1 si−1 + · · · + φi−1 s + φi (19)
where, the coefficient vector δ̄ = [δ0 , δ1 , δ2 , δ3 , · · · , δn ]
ranges over a box: where, φi represent the parameters of the closed-loop desired
polynomial.
1 = δ0− , δ0+ × δ1− , δ1+ × · · · × δn− , δn+
     
(11) In order to tune the controller, the closed-loop polynomial
parameters are compared with the desired closed-loop poly-
where, δn− and δn+ represent the lower and upper limit respec-
nomial, which represent the desired dynamics of the system
tively. Therefore, the Kharitonov polynomials are defined as:
follow as
K1 (s) = δ0− +δ1− s+δ2+ s2 +δ3+ s3 +δ4− s4 +δ5− s5 +δ6+ s6 +· · · di (x, po ) = φi , i = 1, 2, . . . , l (20)
K2 (s) = δ0− +δ1+ s+δ2+ s2 +δ3− s3 +δ4− s4 +δ5+ s5 +δ6+ s6 +· · ·
This problem can be written in its matrix format, presenting
K3 (s) = δ0+ +δ1− s+δ2− s2 +δ3+ s3 +δ4+ s4 +δ5− s5 +δ6− s6 +· · · the following relationship [38], (21), as shown at the bottom
K4 (s) = δ0+ +δ1+ s+δ2− s2 +δ3− s3 +δ4+ s4 +δ5+ s5 +δ6− s6 +· · · of the next page.
(12) When the system is subject to parametric uncertain-
ties, the controller performance may deteriorate. Therefore,
Theorem 1 (Robust Stability): The interval polynomial the controller must guarantee robust performance within an
family delimited by 1 is robustly stable if and only if its acceptable region of closed-loop parameters variation, so that
four Kharitonov polynomials are stable [38], [47], i.e., all the closed-loop poles are located in a certain region. Thereby,
roots of the interval polynomial are in the SPL of the complex a desired region is defined as follows:
plane [48].
8 := φi− ≤ φi ≤ φi+

(22)
C. ROBUST CONTROLLER DESIGN BY Therefore, according to [46], replacing the parameters of
INTERVAL POLE-PLACEMENT (22) in (20), it is possible to formulate a linear inequalities
To design the controller, a region of uncertainty is previously set, which restricted the controller and desired polynomial
defined, considering that the uncertainty is contained in the coefficients in the predefined intervals, as shown in (23).
parameter variation of the plant-model. The controller is Thus, the closed-loop system has its poles within the roots

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 K. E. Lucas Marcillo et al.: Interval Robust Controller to Minimize Oscillations Effects

space of interval-desired polynomial, ensuring the robust

stability [49].

φi− ≤ di (x, p) ≤ φi+ , ∀i = 1, 2, . . . , l (23)

The robust design problem is summarized in the choice of X

(if possible) to satisfy the set of inequalities (23) for all p ∈ P.
The aforementioned robust performance control design prob-
lem for the pre-established conditions can be rewritten as the
following optimization problem:

X = arg (minf (X ))
B(φ + )
   
A(p)
s.t. X≤ (24)
−A(p) −B(φ − )
FIGURE 7. Multi-Converter Buck-Buck System.
where, f (X ) is a linear cost function that must be built
and minimized according to the control goals. In this study,
the cost function f (X ) has been chosen to be the sum
respective equivalent circuits.
of the elements of vector of the controller parameter X ,
such as suggested by Keel and Bhattacharyya [45] and 
diL
Bhattacharyya et al. [50].

 L1 1 = d1 Vi − VC1 − rL1 iL1
dt




dV VC1

C1


IV. MATHEMATICAL MODEL FOR MULTI-CONVERTER C1 dt = iL1 − R


L1
BUCK-BUCK SYSTEM (25)
diL
In order to represent the dynamical behavior of DC Multi- 

 L2 2 = d2 VC1 − VC2 − rL2 iL2
converter buck-buck System, a small signal approximation



 dt
model is employed as an effective mathematical model.

 dV C2 VC
C2 = iL2 − 2


Fig. 7 represents the DC MCBB system with two decou- dt RL2
pled outputs, VC1 and VC2 , such that VC2 < VC1 , and a topol-
ogy employed to control the system. The main characteristic The duty cycle d1 regulates the output voltage (VC1 )
of this system is that it has two DC-DC buck converters of source converter, i.e. the DC bus voltage, and the duty
connected in series where the output of the first one converter cycle d2 regulates the output power of load converter,
is the DC source of the second one. i.e., VC2 2 /RL2 . Thereby, the outputs of system are described
Each converter can be considered an independent sub- below.
system; therefore, the dynamics of the system can be sim-  
y1 = 0 VC1
plified to the analysis of two independent converters. The h i
2
dynamic behavior of buck converter, in Continuous Conduc- y2 = 0 VRC2 (26)
L2
tion Mode (CCM), can be found in [40] and [41].
The following equations involving the state variables of Assuming that the electronic switches and diodes are ideal,
buck converters are written based on the analysis of their the linearized model that describes the dynamic behavior of

[b1 ] 0
··· 0 0 | 1 0 ··· 0 0
  
x0
.. .. .. ..
. . . .
  x 
 [b2 ] [b1 ] 0 | [a1 ] 1 0  1  
 .. .. .. .. .. ..   .. 

  [φ1 ] − [a1 ]
 . [b2 ] . 0 . | . [a1 ] . 0 . 
  . 
  [φ2 ] − [a2 ] 
.. . .. .. xr−1 

.  ..
 
. . [b1 ] . .

 [bm−1 ] 0 | [an−1 ] 1 0  .
   
 x r
  
. ..

 [bm ] [bm−1 ] . . [b2 ]
   
. [a1 ] − = [φ ] − [a ] (21)
 
[b1 ] | [an ] [an−1 ] 1  n n
   
  
. . .. .. y [φ ]

0
.. .. n+1
   
.
 
 0 0 . ..
   
[bm ] [b2 ] | [an ] [a1 ] 

y1  
.
   
 . . .. .. .. .. 

 .. . .. 
 
. [bm−1 ] . . . [an−1 ] . 
 . 
 
0 | 0  [φm ]
. ..


.. . . . [b ] [b .. 
y
. . [an ] [an−1 ]
 0 r−1
 | {z }
m m−1 ] | 0 
B
0 0 ··· 0 [bm ] | 0 0 ··· 0 [an ] yr
| {z } | {z }
X
A

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the converter is represented as follows: step 1, by defining the nominal plant (20) with its operating
d1o conditions; in step 2, the box region of uncertainties is built
VC1 (s) L1 C1 based on a previously specified uncertainty range delimited
=  rL
  rL1
 (27)
Vi (s) s2 + RL 1C1 + L11 s + L11C1 + by the designer. Since box region of uncertainties influence
RL1 L1 C1
1
 o  q  on the delimitation of the convex region where the control
d2 Po
2 gains will be determined, the correct selection of this box
VC2 (s) L1 C1 RL2
=  rL
  rL2
 (28) region is an important point to have success of the proposed
VC1 (s) s2 + RL 1C2 + L22 s + L21C2 + methodology. The lower-and upper-bound of each parameter
2
RL2 L2 C2
are provided in Table 1.
where, d1o
and d2o
are operational point for duty cycle of The characteristic closed-loop polynomial is obtained
outputs 1 and 2, respectively. Po is the operating power of (Step 3) by using the controller parameter and the nominal
output 2. model (20) selected in step 1, then by replacing the nominal
The nominal values of the parameters, operational point and interval values, defined in step 2, the interval closed-loop
and the meaning of each symbol in (27) and (28) are presented polynomial is calculated.
in Table 1. The controller function depends on the chosen control
structure. In this work, a controller with a PID structure is
TABLE 1. Values for the physical parameters of the DC multi-converter
buck-buck board test system. selected. The transfer function is given below.
U (s) kd s2 + kp s + ki
CPID (s) = = (29)
E(s) s
For simplification, transfer function presented in (20) can
be represented as follows:
VC1 (s) b0
G1 (s) = = 2 (30)
Vi (s) s + a1 s + a0
where
 
1 rL
a1 = + 1 (31)
RL1 C1 L1
 
1 rL1
a0 = + (32)
L1 C 1 RL1 L1 C1
do
b0 = 1 (33)
L1 C1
Finally, closed-loop interval polynomial is obtained by
using the controller parameters (22) and plant
parameters (23).
Pcl (s) = s3 + ϕ2− , ϕ2+ s2 + ϕ1− , ϕ1+ s + ϕo− , ϕo+
     
(34)
The nominal parameters of Pcl depend on the parameters
of source converter (cf. Table 1), resulting in the following
V. ROBUST CONTROLLER DESIGN METHODOLOGY nominal parameters:
This section presents a method to design a fixed order robust
controller that provides robust stability and performance for ϕ0o = b0 ki (35)
a predetermined uncertain family of models with parame- ϕ1o = a0 + b0 kp (36)
ters bounded in a hyperbox region. This study only con- ϕ2o = a1 + b0 kd (37)
siders uncertainties in the parameters of source converter
The lower- and upper-limits for these parameters must be
(see Table 1) because oscillations, caused by a CPL, occur
computed by replacing the nominal and interval presented
in the LC filter of the converter. Therefore, only output 1 will
in Table 1 by using interval analysis for (23)-(26). The region
be regulated by a robust controller. A classic controller, based
defined by the closed-loop interval polynomial of (27) must
on Classical Pole-Placement (CPP), will regulate output 2.
be inside the region determined by the desired performance
The robust controller is designed according to presented
polynomial (chosen in Step 4). Particularly, it was chosen for
by Bhattacharyya et al. [50]. In this paper, this method is
a maximum settling time of less than 0.15 sec and a damping
denominated as ‘‘Control Based on Kharitonov’s Rectangle
factor greater than 0.9, defining the desired performance
(CKR’’. The proposed controller must ensure robust stability
region (38). Note that an auxiliary pole must be added that
and performance for the entire region of parametric variation.
does not affect the desired dynamics of system to satisfy (20).
Fig. 8 illustrates a simplified flowchart of the methodology
for designing the robust controller. The process starts in 8 = s3 + [φ2 ] s2 + [φ1 ] s + [φo ] (38)

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FIGURE 8. Flowchart of methodology for designing of robust controller.

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FIGURE 9. Block diagram of the developed hardware system and

actuation of the system control signal.

The optimization problem is selected in step 5 and solved

in step 6, where the cost function is defined as the sum of
controller gains and the parameter vector X . The feasible
solution X ∗ (obtained in step 6) is used to set the control
structure (step 7).
The performance condition is verified in step 8 in case of
achieving it, advance to step 9, if not, go back to step 2, where
you must redefine the system’s uncertainties.
In order to obtain a discrete equivalent controller the Tustin
Method [51] was used (Step 9). A sampling period of 1ms was
chosen in order to comply with a sampling frequency between
2 to 10 greater than the frequency band of the system.

h0 z2 + h1 z + h2
CPID (z) = (39)
z2 − 1

VI. DESCRIPTION OF TEST ENVIRONMENTS

A. DESCRIPTION OF THE MULTI-CONVERTER
BUCK-BUCK SYSTEM TEST BOARD
Fig. 9 presents a control-generalized block diagram applying
to multi-converter buck-buck system using filters in the out-
FIGURE 10. (a) Block diagram of the Multi-converter buck-buck test
puts of system to avoid that ripples of the outputs interfere system developed for our experiments. (b) DC Multi-Converter buck-buck
in the performance of the designed controller. These filters, experimental setup.
H1 (s) and H2 (s), must be designed so that they do not affect
the system dynamics. Two SISO controllers are used to reg- than 0.9. To regulate output 2, requirements are: settling time
ulate system outputs. less or equal than 0.05 s and damping factor greater or equal
Fig. 10(a) presents a diagram of the subsystems used in than 0.9. Note that the dynamics of output 2 is faster than out-
the experimental tests and Fig. 10(b) shows the developed put 1, being this a necessary condition for the load converter
laboratory setup. acts as a CPL.
A DC Multi-Converter buck-buck (Fig. 10(b)) is devel- The experiments compare performance of controllers
oped for the experimental evaluation of the proposed con- tuned by CKR and CPP methodologies using PID control
trol approach. The controller has been implemented by structure.
using a 32-bit ARM core microcontroller AT91SAM3X8E Table 2 shows the controllers gains for the controllers
(Fig. 10(b)). The desired set point values are provided by a designed to regulate outputs 1 and 2. Note that only for the
microcomputer system via USB communication. output 1 is considered the robust control methodology.
The first experiment is performed to check the closed-
B. DESCRIPTION OF EXPERIMENTS loop performance for positive variation of power reference.
The Integral Square Error (ISE) is used to evaluate the The source converter is set to its initial operating condition,
performance of the proposed control strategy. as mentioned in Table 1, until the steady state is achieved.
In order to design the controllers, the following (nominal) Then, source converter starts feeding load converter. There-
requirements are chosen to regulate output 1: settling time after the steady state is achieved, the multi-converter is sub-
less or equal than 0.1 s and damping factor greater or equal jected to 0.5 p.u. a positive variation of power reference.

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TABLE 2. Values of parameters for the designed controllers.

The second experiment evaluates the closed-loop perfor-

mance for negative variation of power reference. The system
starts to operate in the same way as for the positive variation
test until the system achieves its steady state. After that,
the system operates at an operating point of 0.7 p.u. in order
to obtain a 0.5 p.u. negative variation.
The third experiment evaluates the closed-loop perfor- FIGURE 11. Source converter performance. (a) Simulated results for
positive variations on the value of power reference of the Multi-converter
mance for positive and negative variation of power refer- buck-buck system using PID control structures. (b) Transient response.
ence. After the multi-converter system reaches its stable state, (c) Oscillations caused by the connection of load converter.
(d) Oscillations caused by the variation of power reference of system.
a positive variation of 0.5 p.u. is performed at the operating
point of power reference. Then, a negative variation of 0.5 p.u.
is performed to return to the initial condition.
These experiments aim to show that the proposed robust
controller is able to compensate oscillations caused by a CPL
at output 1 when the system is submitted to positive and
negative variations in its power operating condition, main-
taining the desired performance for the uncertainty region and
consequently different operation points. All the experiments
are performed in experimental environment using the devel-
oped DC MCBB system and simulation environment using
MATLAB/Simulink.

VII. ASSESSMENT OF RESULTS

A. EVALUATION OF SYSTEM UNDER A POSITIVE
VARIATION OF POWER REFERENCE
Figs. 11 and 12 show the simulated responses performed
FIGURE 12. Load converter performance. (a) Simulated results for
in the multi-converter model, using a PID control with a positive variations on the value of power reference of the Multi-converter
positive variation of power reference. Figs. 13 and 14 shows buck-buck system using PID control structures. (b) Transient response.
(c) Variation of power reference of system.
the experimental evaluation performed in the multi-converter
buck-buck system.
The multi-converter buck-buck system stars with load con-
verter disconnected until source converter achieves its steady its power reference (see Figs. 12(c) and 14(c)) using a PID
state (see Table 1), then the load converter is connected control based on CPP and CKR approaches.
(t = 0.5 s) causing a load disturbance at the output of source Fig. 12 and 14 show the simulated and experimental
converter. When the multi-converter buck-buck system is results, respectively, of load converter performance, using
operating in its steady state (8V and 0.3 p.u.), the system is a PID control based on CPP approach, when the output of
subjected to a positive variation of power reference (t = 1.0 s) source converter is regulated by a PID control based on CPP
within amplitude range from 0.1 to 0.5 p.u.. and CKR approaches.
Figs. 11 and 13 show the simulated and experimental Note that all information about transient response, refer-
results, respectively, of source converter performance, when ence tracking and load perturbation are given in Figs. 11 to 14,
the system is subjected to a positive variation of 0.5 p.u. of obtaining a better performance of multi-converter buck-buck

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FIGURE 13. Source converter performance. (a) Experimental results for

positive variations on the value of power reference of the Multi-converter
buck-buck system using PID control structures. (b) Transient response.
(c) Oscillations caused by the connection of load converter. FIGURE 15. Simulated Results for positive variations on the value of
(d) Oscillations caused by the variation of power reference of system. power reference of the Multi-Converter buck-buck system using PID
control structures.

FIGURE 14. Load converter performance. (a) Experimental Results for

positive variations on the value of power reference of the Multi-Converter
buck-buck system using PID control structures. (b) Transient Response.
(c) Variation of power reference of system.

system when the source converter is regulated by CKR

approach.
FIGURE 16. Experimental Results for positive variations on the value of
Figs. 15 and 16 show, respectively, the simulated and power reference of the Multi-Converter buck-buck system using PID
experimental evaluation performed in the multi-converter control structures.
buck-buck system, using a PID control structures for different
values of positive variation of power reference.
The simulated and experimental results demonstrate that However, the interval robust (CKR Method) controller
both controllers of source converter can compensate oscilla- proposed in this paper provides a better performance in
tions at output 1 caused by positive variations in the power comparison with classical controller (CPP Method). There-
operating condition of system. fore, the impact of positive power variation is lower for the

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FIGURE 17. The cost function ISE of system outputs for positive variations
of power reference. (a) Simulation assessment. (b) Experimental
FIGURE 19. The control effort test of experimental system, when the
assessment.
system is subjected to positive variations on the value of power reference.

FIGURE 20. The cost function ISE of effort control system for positive
variations of power reference. (a) Simulation assessment.
FIGURE 18. The control effort test of simulated system, when the system (b) Experimental assessment.
is subjected to positive variations on the value of power reference.

controller by CKR method as shown by the ISE performance For the simulated case, the control effort obtained was
indices in Figs. 17(a) and 17(b), ratifying the robustness of almost similar for controllers of system as shown their ISE
the proposed methodology. performance indices in Fig. 20(a). However, the performance
Figs. 18 and 19 show the control effort of controllers for presented by controllers in experimental tests was different as
simulated and experimental tests, respectively, using a PID shown in Fig. 20(b).
control structures. The DC multi-converter buck-buck system obtained
Note that the saturation of the control signal does not occur less degradation in the control system performance when
at any time. the robust proposed controller controls the output 1 of

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multi-converter buck-buck system. Fig. 20 shows the ISE

index performance of control effort of signal.
Although the control strategy to regulate the load converter
does not change, different performances can be observed
(see Fig. 20(b)) due to the oscillation in the output voltage of
source converter caused by the variation of power reference.
Thereby, the controller of the voltage regulation stage that
better compensates for the oscillations will cause less dete-
rioration in the performance of the controller of the power
control stage.
In the MCBB system, the load converter is considering a
load for the source converter, thus, any change in the operat-
ing conditions of load converter affects as a load disturbance
at the output of the source converter. Therefore, the greater
the reference variation at output 2 (Power CPL), the greater
the voltage oscillation at output 1 as shown in simulated
(see Fig. 15) and experimental (see Fig. 16) assessment.
The simulated and experimental tests performed show
that the robust proposed (CKR) approach outperforms the
classical (CPP) approach for several values of power vari-
ations (Po ). Therefore, the controller proposed provides a FIGURE 21. Source converter performance. (a) Simulated Results for
better performance with reduced oscillation amplitude at out- negative variations on the value of power reference of the
Multi-Converter buck-buck system using PID control structures. (b)
put 1 in comparison with the classical controller. Transient Response. (c) Oscillations caused by the connection of load
Fig 17 shows the comparison of ISE performance index for converter. (d) Oscillations caused by a positive variation of power
reference of system. (e) Oscillations caused by a negative variation of
the multi-converter test system between robust and classical power reference of system.
approaches. For most of the operating value of Po , the ISE
indices for CPP method shows higher values in comparison
with CKR method.

B. EVALUATION OF SYSTEM UNDER A NEGATIVE

VARIATION OF POWER REFERENCE
Figs. 21 and 22 show the simulated evaluation performed
in the MCBB model, using a PID control with a negative
variation of power reference. Figs. 23 and 24 shows the exper-
imental evaluation performed in the multi-converter buck-
buck system.
According to Figs. 21 to 24, the experiment begins in the
same way that the experiment described in Section VII(A)
until the MCBB system achieves its steady state (8V and
0.3 p.u.). Then, a variation in operating condition at out-
put 2 (Po ) occurs at t = 1 s, as explain in Section VI(B),
so the system will operate with the following conditions:
VC1 o = 8 V and Po = 0.7 p.u., after that, the system is
subjected to a negative variation of power reference (t = 1.5 s)
within an amplitude range from 0.1 to 0.5 p.u..
Fig. 21 shows the simulated results of source con-
verter performance, when the system is subjected to a
negative variation of 0.5 p.u. of its power reference (see FIGURE 22. Load converter performance. (a) Simulated Results for
Figs. 22(d) and 24(d)) using a PID control based on CPP negative variations on the value of power reference of the
Multi-Converter buck-buck system using PID control structures.
and CKR approaches, while Fig. 23 shows the experimental (b) Transient Response. (c) Positive Variation of power reference of
results of the same test. system. (d) Negative Variation of power reference of system.
Fig. 22 shows the simulated results of load converter per-
formance, using a PID control based on CPP approach, when
the output of source converter is regulated by a PID control Note that all information about transient response, refer-
based on CPP and CKR approaches, while Fig. 24 shows the ence tracking and load perturbation are given in Figs. 21 to 24,
experimental results of the same test. obtaining a better performance of multi-converter buck-buck

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FIGURE 23. Source converter performance. (a) Experimental Results for

negative variations on the value of power reference of the
Multi-Converter buck-buck system using PID control structures. FIGURE 25. Simulated Results for negative variations on the value of
(b) Transient Response. (c) Oscillations caused by the connection of load power reference of the Multi-Converter buck-buck system using PID
converter. (d) Oscillations caused by a positive variation of power control structures.
reference of system. (e) Oscillations caused by a negative variation of
power reference of system.

FIGURE 24. Load converter performance. (a) Experimental Results for

negative variations on the value of power reference of the FIGURE 26. Experimental Results for negative variations on the value of
Multi-Converter buck-buck system using PID control structures. power reference of the Multi-Converter buck-buck system using PID
(b) Transient Response. (c) Positive Variation of power reference of control structures.
system. (d) Negative Variation of power reference of system.

buck-buck system, using a PID control structures for negative

system for negative variation of power reference when the variations in operating condition at output 2 (Po ).
source converter is regulated by CKR approach. The simulated and experimental results that both con-
Figs. 25 and 26 show, respectively, the simulated and trollers have succeeded in correcting the load disturbance at
experimental evaluation performed in the multi-converter output 1 (VC1 ) caused by negative variations in the power

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FIGURE 28. The control effort test of simulated system, when the system
FIGURE 27. The cost function ISE of system outputs for negative is subjected to negative variations on the value of power reference.
variations of power reference. (a) Simulation assessment.
(b) Experimental assessment.

operating condition (Po ) of multi-converter buck-buck sys-

tem. However, the proposed robust controller (CKR Method)
more effectively compensates the oscillations in compari-
son with the classical controller (CPP Method). Therefore,
the impact of negative variation of power reference (Po ) is
lower for the CKR Method as shown in Figs. 27.
Figs. 27(a) and 27(b) show the comparison of ISE per-
formance index of classical and robust controllesr for sim-
ulated and experimental assessment, respectively. The ISE
index evaluates the impact of negative variation of power
reference (Po ) on system performance. Therefore, the robust
controller (CKR) shows the best performance under negative
variation of power reference (Po ) for simulated and experi-
mental tests confirming the robustness of the proposed robust
control methodology.
According to results while the greater the reference vari-
ation at output 2 (Power CPL), the greater the voltage oscil-
lation at output 1 as shown in simulated (see Fig. 25) and
experimental (see Fig. 26) assessment.
Figs. 28 and 29 show the control effort of controllers for
FIGURE 29. The control effort test of experimental system, when the
simulated and experimental tests, respectively, under power system is subjected to negative variations on the value of power
reference (Po ). Note that the saturation of the control signal reference.
does not occur at any time.
Note that for the simulated case, the obtained control effort C. PERFORMANCE EVALUATION UNDER
was almost similar for controllers of system as shown their CPL POWER VARIATION
ISE performance indices in Fig. 30(a). However, the perfor- Fig. 31 shows the experimental evaluation performed in the
mance presented by controllers was different. MCBB system, using a PID control based on CPP approach.
The multi-converter buck-buck system obtained less degra- Fig. 32 shows the experimental evaluation performed in the
dation in the control system performance when the robust MCBB system, using a PID control based on CKR approach.
proposed controller controls output 1. According to Figs. 31 and 32, the experiment begins
Fig. 30(b) shows the ISE index performance of control in the same way that the experiment described in
effort signal. Section VII(A) and VII(B) until the MCBB system achieves

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the following conditions: VC1 o = 8 V and Po = 0.8 p.u.,

after that, the system is subjected to a negative variation of
power reference (t = 1.25 s) returning to the initial condition
(8V and 0.3 p.u.).
Figs. 31 and 32 show the CPL power variation and the
voltage oscillations in the feeder converter by using the
classical control methodology and robust control methodol-
ogy, respectively. It is worth note that the CKR approach
outperforms the other approach due to the minimum voltage
oscillation occurrence, in addition, the oscillation is quickly
corrected in comparison with the CPP approach, further-
more the CKR methodology presents the smaller voltage
ripple than the CPP approach. In order to ratify these results,
the integral index of this oscillation for all approaches was
calculated. the CKR approach presents 1.42 of the ISE value
and the CPP approach presents 2.16 ISE value, therefore,
it was ratified that the CKR approach outperform the CPP
approach when there is variation of a CPL power variation in
the system.
FIGURE 30. The cost function ISE of effort control system for negative
variations of power reference. (a) Simulation assessment. VIII. CONCLUSION
(b) Experimental assessment.
This paper proposes to use a robust parametric control tech-
nique for designing fixed order robust controller, in order
to minimizing oscillations effects caused by constant power
load in a DC Multi-converter buck-buck system guaranteeing
robust stability and robust performance for an entire prede-
fined uncertainty region.
The proposed technique has been exhaustively evaluated
in both computational simulations as well as by means of
experiments performed in a 20 W DC Multi-converter. The
proposed robust controller (CKR Method) performance is
compared with a classical controller based on pole-placement
(CPP Method).
According to the results obtained via simulations and
experiments, it is concluded that when the multi-converter
FIGURE 31. MCBB system performance, using a PID control based on CPP buck-buck system is subjected to a certain variation of
approach. reference power (Po ), the CKR method more effectively
compensates the oscillations at output voltage of source
converter (VC1 ) improving the performance of the whole
system as shown by the performance indicators obtained in
this work.
Therefore, the results indicate that the proposed robust
controller is justified and presents relevant improvements in
the Multi-converter control, offering robust performance and
stability.

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 K. E. Lucas Marcillo et al.: Interval Robust Controller to Minimize Oscillations Effects

[46] L. H. Keel and S. P. Bhattacharyya, ‘‘A linear programming approach to RENAN LANDAU PAIVA DE MEDEIROS
controller design,’’ in Proc. 36th IEEE Conf. Decis. Control, San Diego, received the B.E., M.Sc., and Ph.D. degrees in
CA, USA, vol. 3, Dec. 1997, pp. 2139–2148. electrical engineering from the Federal Univer-
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of robust pole assignment controllers,’’ in Proc. 41st IEEE Conf. Decis. He is currently an Associate Professor with the
Control, Las Vegas, NV, USA, Dec. 2002, Dec. 2002, pp. 1461–1466. Department of Electrical Engineering, Federal University of Amazonas.
[50] S. P. Bhattacharyya, A. Datta, and L. H. Keel, Linear Control Theory: He has experience in electrical engineering, with emphasis on automation
Structure, Robustness, and Optimization, vol. 1. Boca Raton, FL, USA: and control of industrial and electrical power systems, and multivariable
CRC Press, 2009. robust control and application. His main areas of expertise and research inter-
[51] K. J. Aström and B. Wittenmark, Computer-controlled Systems: Theory ests include nonlinear control, multivariable robust control, and modeling
and Design. North Chelmsford, MA, USA: Courier Corporation, 2013. and designing a robust control for electrical power systems.

KEVIN EDUARDO LUCAS MARCILLO received

the bachelor’s degree in electronic and telecom-
munications engineering from the Escuela Supe- ERICK MELO ROCHA received the bachelor’s
rior Politécnica del Litoral, Ecuador, in 2015, and and M.Sc. degrees in electrical engineering from
the master’s degree in electrical engineering from the Federal University of Paré (UFPA), Brazil,
the Federal University of Pará (UFPA), Brazil, in 2010 and 2012, respectively, where he is cur-
in 2018. rently pursuing the Ph.D. degree in electrical
He is currently a Researcher with the Power engineering.
Systems Control Laboratory (LACSPOT), UFPA. He is currently a Lecturer with the Department
He has experience in electrical engineering, with of Electrical Engineering, UFPA. He has experi-
emphasis on electronics, data acquisition system, control and automation ence in electrical engineering, with emphasis on
of electrical and industrial processes, power electronics, hydraulic system, industrial automation and control systems. His
and control systems applied in power generation. His main research topic research topics include detection and fault diagnosis, and robust control
includes modeling and robust control of industrial and electronic power techniques.
systems.

DOUGLAS ANTONIO PLAZA GUINGLA

received the bachelor’s degree in electrical engi-
neering from the Escuela Superior Politécnica del DAVID ALEJANDRO VACA BENAVIDES
Litoral (ESPOL), Guayaquil, Ecuador, in 2003, received the bachelor’s degree in electronic
the master’s degree in industrial control from the and telecommunications engineering from the
Universidad de Ibagué, Ibagué, Colombia, in 2008, Escuela Superior Politécnica del Litoral (ESPOL),
and the Ph.D. Diploma degree in electromechan- Guayaquil, Ecuador, in 2014, and the M.Sc.
ical engineering from Ghent University, Ghent, degree in electrical engineering from the Univer-
Belgium, in 2013. sity of Applied Sciences of Southern Switzerland,
From 2007 to 2012, he was a Full-Time Manno, Switzerland, in 2016.
Researcher with the Laboratory of Hydrology and Water Management, He has been a Lecturer with the Faculty of
Ghent University. He has been an Associate Professor with the Electrical and Electrical and Computer Engineering, ESPOL,
Computer Engineering Faculty, ESPOL, since 2013. He is currently the Chair since 2016. He has experience in electrical engineering, with emphasis on
of the Master Program in Automation and Control with ESPOL. His areas biomedical instrumentation, signal processing, and data acquisition. His
of expertise and research interests include Kalman filtering and smoothing, research topics include medical data processing on embedded systems and
sequential Monte Carlo methods, hydrologic modeling, hydrologic data mixed-signal electronic design for medical applications.
assimilation, model predictive control, and nonlinear control. He is the Chair
of the IEEE Control Systems and Industrial Electronics Societies, Ecuador
Section.

FABRICIO GONZALEZ NOGUEIRA received

WALTER BARRA, Jr. received the B.E., M.Sc., the B.E., M.Sc., and Ph.D. degrees in electrical
and Ph.D. degrees in electrical engineering from engineering from the Federal University of Pará,
the Federal University of Pará (UFPA), Brazil, Brazil, in 2007, 2008, and 2012, respectively.
in 1991, 1997, and 2001, respectively. He is currently an Adjunct Professor with the
He is currently an Associate Professor with Faculty of Electrical Engineering, Federal Univer-
the Department of Electrical Engineering, UFPA. sity of Ceará, Brazil. He has experience in elec-
He has experience in electrical engineering, with trical engineering, with emphasis on control of
emphasis on automation and control of industrial electrical power systems. His main research topics
and electrical power systems. His main research include system identification and robust control
topic includes modeling and robust control of with application in electric power systems.
industrial and electric power systems.

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