039
1
Improved Dynamic Performance of Multiloop
Operation of Paralleled DC/DC Converters
Using Fuzzy-Logic Control
Idris Gadoura, Student Member, IEEE, Teuvo Suntio, Member, IEEE, Kai Zenger
Abstract—In this paper we utilizes the design of robust PI/PID
control for paralleled DC/DC converters that has been reported
in our previous work in order to design PID-like FLC for
voltage-loop and PI-like FLC for current-loop. The variations of
power components have been taken into account as an
uncertainty when designing the robust PI/PID control. The PIDlike FLC and PI-like FLC are designed to guarantee robust
output voltage and to equalize the output currents, respectively.
In the simulation the fuzzy-logic control has an advantage of less
control effort over the conventional PI/PID control.
Index Terms—DC/DC converter, uncertain system, PID
control, fuzzy-logic.
T
and for parallel-connected DC/DC converters as in [5,7]. This
paper is aim to design PI- and PID-like fuzzy-logic controllers
using the parameters of robust PI and PID controllers that are
presented in [6]. The design of fuzzy-logic controller by
utilizing the well-tuned conventional controller has firstly
been proposed in [9] and successfully applied to DC/DC
converters in [3]. However, there are more methods of
designing fuzzy-logic controller for DC/DC converters
presented in [8,12,19,21,24] gives good results. The fuzzylogic control design procedure presented is verified by
simulation of two-buck converters connected in parallel.
he main control issues in parallel-connected converters
are to equalize the output currents among converters
and to ensure the robust output voltage at the load.
Paralleling power converters adds complexity to the
system and typically entails accepting some performance and
cost compromises [20]. In practice, the control is needed to
ensure proper current sharing and many effective control
schemes have been proposed in previous studies [2,10,13-17].
The main purpose of this paper is to design a fuzzy control
system of paralleled DC/DC converters, as shown in Fig. 1,
based on our previous work, which is reported in [6]. In [6]
we assumed that the overall system is composed of twoMIMO subsystems, for voltage-loop and current-loop. Also
the voltage-loop consists of n-SISO subsystems, where n is
the number of converters in parallel that can be designed
separately. The actual plant models consist of nominal plant
models and uncertainty models. Parametric uncertainty is
modeled where the structure of the model is known, but some
of the parameters are uncertain [18]. The robust PID and PI
controllers are designed to achieve robust stability and robust
performance for voltage-loop and current-loop, respectively.
Also the robust µ-based control design has successfully been
designed for single DC/DC converter as presented in [1,4,22]
L1
Switch
I. INTRODUCTION
iL1
+
PWM
rL2
v_in2
iC2
PWM
+
+
v2
r2
rp2
C2
rC2
v2
_
kv2
+
vref
iL2
+
iref
k1
L2
Switch
i
_out1
+
+
r1
rp1
rC1
v1
_
kv1
v1
iC1 C1
v_in1
i_out2
iref
k2
+
vref
rpn
2
rp
(1+ n 2 )
+
vout R
ig
_
Ln
Switch
rLn
iLn
+
v_inn
iCn
PWM
I. Gadoura is with Control Engineering Laboratory, Helsinki University of
Technology, P.O.Box 5400, 02015 HUT, Finland. (tel: +358 9 4515221, fax:
+358 9 4515208, email: igadoura@cc.hut.fi).
T. Suntio is with Electronics Laboratory/Power Electronics,University of
Oulu, P.O. Box 4500, FIN-90401 Oulu, Finland. (tel: +358 8 5532889, fax:
+358 8 5532700, email: teuvo.suntio@ees2.oulu.fi).
K. Zenger is with Control Engineering Laboratory, Helsinki University of
Technology, P.O.Box 5400, 02015 HUT, Finland. (tel: +358 9 4515204, fax:
+358 9 4515208, email: kai.zenger@hut.fi).
rL1
_
kvn
+
vref
kn
rpn
rn
Cn
rCn
vn
+
vn
i_outn
+
iref
Fig. 1. Paralleled DC/DC converters feeding a resistive load with cascaded
fuzzy controllers for voltage- and current-loops.
039
d (s)
2
Gdv ( s )
Wd ( s )
r ( s)
G pv ( s )
u∆ v ( s )
∆ pv ( s )
yuv ( s )
Wr ( s )
r ( s)
nv ( s )
Wr ( s )
Wnv ( s)
+
A/D
Kv (s)
D/A
_
+
+
uv ( s )
+
u ( s)
G pv ( s)
+
_
+
W pv ( s )
zv ( s )
Wpi ( s)
zi ( s )
a
K i (s)
D/A
Gdi ( s )
ui ( s )
G pi ( s )
u ∆i ( s )
Q
Wni ( s)
+
+
yv ( s )
A/D
ni ( s )
+
+
u( s)
+
+
∆ pi ( s )
G pi ( s )
yui ( s )
+
+
+
+
yi ( s )
Fig. 2 - The control configuration of paralleled DC/DC converters including all uncertainties. The control of voltage-loop is considered when it is isolated from
the current-loop by breaking the connection at point a. Note that Q block determines the active control scheme either democratic or master-slave scheme.
II. CONTROL DESIGN
From Fig. 1, the control system of “j” converter is a voltage
controller, kvj, ensuring robust output voltage cascaded with
current controller, kj, ensuring current sharing. The control
law can be written as
u j = kv j k j ei j + kv j ev j
(1)
= ki j ei j + kv j ev j
where j = 1, 2, 3, ………., n.
From the practical viewpoint, the controllers’ structure of
either voltage-loop or current-loop can be presented as a
diagonal transfer matrix as
(
= diag ( k
K v = diag kv1 , kv2 ," , kvn
Ki
i1
, ki2 ," , kin
)
)
(2)
(3)
where Kv and Ki are used in control design procedure as
shown in Fig. 2. Then, the control vector can be written in the
general form as follows.
u = K i ei + K v ev
(4)
where ei is a vector of current error and ev is a vector of
voltage error.
In order to model the uncertainty, we consider the worstcase model represented in state-space form as follows.
x = A p x + B p u
yv = C pv x and
yi = C pi x
(5)
where A p = Ap + ∆ A , B p = B p + ∆ B , C pv = C pv + ∆ Cv , and
C pi = C pi + ∆Ci . Also Ap, Bp, Cpv, and Cpi model the nominal
system, however ∆A, ∆B, ∆Cv, and ∆Ci model the uncertainty.
The uncertain perturbations are chosen into a block-diagonal
matrix as follows.
(
)
= diag(∆ A , ∆ B , ∆ C )
∆ pv = diag ∆ A , ∆ B , ∆ Cv
(6)
∆ pi
(7)
i
In Fig. 2, y is the vector of output voltages and output
currents, Gp is the plant model transfer matrix, u is the control
commands vector, Gd is the disturbance model transfer matrix,
and d is the disturbances vector. The subscript “v” stands for
voltage-loop subsystem and “i” for current-loop subsystem.
The high-pass filter matrices, Wnv(s) and Wni(s), are designed
039
3
to attenuate the measurement noise. The low-pass filter
matrices, Wpv(s) and Wpi(s), are designed to specify the desired
closed-loop performance for the voltage-loop and the currentloop, respectively. Also Wd(s) and Wr(s) are scaling matrices.
III. FUZZY-LOGIC CONTROL
Robust PID and PI controllers for voltage-loop and currentloop, respectively, are designed, as presented in [6], to achieve
all robustness issues in the presence of uncertainty, i.e.,
nominal performance, robust stability, and robust performance
for either a voltage-loop or the whole system. Next shows
how to design FLC using the parameters of well-tuned
controllers.
A. PI-like FLC
The FLC describes with the aid of fuzzy rules the
relationship between the control co(k) on one hand, and the
current error ei(k) and its change cei(k) on the other hand. The
internal mechanism of the FLC translates this relationship into
a mapping:
co (k ) = f ( ei (k ), cei (k ) )
vo (k ) = f ( ev (k ), cev (k ) )
The integral part I(k)is added to the output because it is
hard to write fuzzy rules for it [23]. The control law can be
written as
u (k ) = f ( ev (k ), cev (k ) ) + I (k )
The similarity between the conventional PID controller and
PID-like FLC can obviously be seen:
u (k ) = K P ev (k ) + K D cev (k ) + K I
cui (k ) = K P ei (k ) + K I cei (k )
(9)
where KP and KI are the parameters of the PI-controller and
cui(k) is the change in the control. However the relationship
between ei(k) and cei(k) on one hand, and ui(k) on the other
hand is linear in conventional PI-controller and nonlinear in
PI-like FLC. The reasoning mechanisms of the PI-like FLC
and PD-like FLC work basically in the same manner. The only
difference is the integrator located on the output in the case of
PI-like FLC.
PD-like FLC
ei
FLC - 2
1 - z-1
b2
cei
∑ e (k )
(12)
v
where KP, KD and KI are the parameters of the PID-controller.
êv
a1
1 - z-1
z-1 / (1 - z-1)
a2
(11)
b1
ev
FLC - 1
cev
ConstantVoltage
Controller
vo +
u
d1
+
(8)
The similarity between the classic PI controller and PI-like
FLC can obviously be seen:
êi
(10)
Current
Controller
co
d2
cui
z-1 / (1 - z-1)
ui
Fig. 3 - The structure of fuzzy current controller. The PI-like FL controller,
which is k in equation (1), has been selected to equalize the output current of
each converter to the current reference.
B. PID-like FLC
The FLC is the same as the PD-like FLC describes with the
aid of fuzzy rules the relationship between the control vo(k) on
one hand, and the incremental voltage error ev(k) and its
change cei(k) on the other hand. The internal mechanism of
the FLC translates this relationship into a mapping:
c1
Fig. 4 - The structure of PID-like FLC. The PID-like FL controller has been
chosen to regulate the voltage-loop in order to achieve the robust output
voltage in spite of line and load disturbances.
C. Tuning
The fuzzy control design procedure of PID-like FLC, which
is proposed in [9] can be simplified as follows.
Use the parameters of robust PI and PID controllers that
are presented in [6].
Replace the summation in robust PI and PID controllers,
as shown in Fig. 3 and Fig. 4, respectively, by fuzzy
controller, which has the following structure:
o It has two inputs that are an error and change in
error, and one output.
o Five memberships are chosen for input and output
variables, PB, PS, Z, NS, and NB, in order to
smooth the control action.
o Create the fuzzy rules in order to improve the
converter output performance and based on the
following criteria:
When the output of the converter is far from
the reference, the change of control signal
must be large to bring the output to the
reference quickly.
When the output of the converter is moving
closer the reference, the change of control
signal is small.
When the output of the converter is near the
reference and is moving closer to it rapidly,
the control signal must be kept constant to
prevent overshoot.
When the reference is reached and the
039
4
b1d1 = D = K PTd , so that b1 = a1Td .
K
a
c1d1 = I = P , so that c1 = 1 .
Ti
Ti
The construction of the fuzzy rules is the most difficult
aspect of FLC design [11]. There are no systematic tools to
write the fuzzy rules, however, it is based on intuitive
knowledge and experience as shown in Table I.
design than conventional ones presented in [6]. Also the
dynamic performance and control efforts presented in this
paper have good advantages over the results presented in [21].
54.1
54.02
54
54.01
53.9
54
53.8
53.99
53.7
53.98
53.6
0.02
40
> The line disturbance in first channel by +20V and
in second channel by -20V both at 0.02s.
> The load disturbance +5A at 0.035s.
20
0
0.005
0.01
0.015
0.02 0.025 0.03
Time (sec)
5.5
9
5
8
LP
LP
LP
LP
Z
SN
SP
LP
SP
SP
Z
SN
Z
SP
Z
Z
Z
SN
SN
SP
Z
SN
SN
LN
LN
SP
Z
LN
LN
LN
0.035
6
4
> The line disturbance in first channel by +20V and
in second channel by -20V both at 0.02s.
> The load disturbance +5A at 0.035s.
2
0
0
0.005
0.01
0.015
0.02 0.025 0.03
Time (sec)
0.035
0.04
0.045
0.05
Fig. 6 - The steady state and transient behavior of the output currents in the
presence of line & load disturbances with uncertainty.
0.5
0.35
0.4
0.3
0.3
0.25
0.02
0.0205
0.021
0.2
0.03490.035 0.0350.03510.0351
20
Control commands
In order to verify the control design procedure, the
configuration of two-identical parallel-connected buck
converters, as shown in Fig. 1, is considered with the
following parameters. The input voltage Vin = 140V, output
voltage Vo = 54V, maximum output power Po = 500W,
switching frequency fs = 100kHz, inductor L = 100µH,
capacitor C = 1000µF, output resistance R = 11Ω, equivalent
series resistor of capacitor rC = 50mΩ, equivalent series
resistor of inductor rL = 15mΩ, cable resistance r = 20mΩ.
Also the controllers’ parameters are identical for both
converters and as follows. PID-controller, Kp = 22.665, Ti =
0.745ms, Td = 0.169ms, N = 4, and b = 0.573. PI-controller, Kp
= 2 and Ti = 0.2ms. The simulation results of the worst-case
show that the system is robustly performed and stable as
shown in Fig. 5 and Fig. 6. Fig. 7 shows control efforts of the
cascaded fuzzy controllers providing more optimized control
0.035
8
0.4
IV. DESIGN EXAMPLE
0.035
10
Output currents (A)
LN
0.05
5
0.02 0.0205 0.021 0.0215 0.022
SN
0.045
6
ce
Z
0.04
7
4.5
3.5
SP
0.035
Fig. 5 - The steady state and transient behavior of the output voltage in the
presence of line & load disturbances with uncertainty.
4
LP
0.0349 0.035 0.03510.0352
60
0
TABLE I
THE FUZZY RULES OF FLC
e
0.0205 0.021 0.0215
80
Output voltages (V)
output is still changing, the change of
control signal is very small preventing the
output from moving away.
When the reference is reached and the
output is steady, the control signal is
constant.
When the output is above the reference, the
sign of the change of control signal must be
negative and vice versa.
o Normalize all values of input and output variables
by using the gains, a1, b1, c1, and d1, i.e. the
universe of discourse is transferred into the
normalized closed interval [-1,+1].
K
a1d1 = P = K P , so that d1 = P .
a1
15
10
5
0
-5
0
0.005
0.01
0.015
0.02 0.025 0.03
Time (sec)
0.035
0.04
0.045
0.05
Fig. 7 - The steady state and transient behavior of the control commands in the
presence of line & load disturbances with uncertainty.
039
5
V. CONCLUSION
The paper has presented a procedure to design fuzzy
controllers for voltage-loop and current-loop of paralleled
DC/DC converters. The PID-like FL controllers are designed
to regulate the voltage-loop and the PI-like FL controllers are
designed to regulate the current-loop of the system where the
outputs are injected into their voltage-loops. The output
voltages and output currents of two paralleled buck converters
in the presence of uncertainty are presented in Fig. 5 and Fig.
6, respectively. Conclusively, the overall system has good
rejection ability of line and load disturbances. Also the fuzzylogic controllers give the minimal needed effort to control the
system as shown in Fig. 7.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
Buso, Simone, “Design of a Robust Voltage Controller for a Buck-Boost
Converter Using µ Synthesis”, IEEE Trans. on Control Systems
Technology, Vol. 7, No. 2, pp. 222-229, March 1999.
Choi, Byungcho, “Comparative Study on Paralleling Schemes of
Converter Modules for Distributed Power Applications”, IEEE Trans.
on Industrial Electronics, Vol. 45, No. 2, pp. 194-199, April 1998.
Gadoura, I. and T. Suntio, “Implementation of Optimal Output
Characteristic for a Telecom Power Supply: Fuzzy-logic Approach”,
Journal of Control and Intelligent Systems, 2002. (In press)
Gadoura, I., T. Suntio, and K. Zenger, “Improved Stability Properties of
Boost and Buck-boost Converters Using IMC-based Controller”, Proc.
of the Int. Con. on Power Electronics and Intelligent Motion, June 1921, 2001 in Nuremberg, Germany, pp. 527-532.
Gadoura, I., T. Suntio, and K. Zenger, “Dynamic System Modeling and
Analysis for Multiloop Operation of Paralleled DC/DC Converters”,
Proc. of the International Conference on Power Electronics and
Intelligent Motion, Nuremberg, Germany, pp. 443-448, 2001.
Gadoura, I., T. Suntio, and K. Zenger, “Robust Control Design for
Paralleled DC/DC Converters With Current Sharing”, Proc. of the 15th
IFAC World Congress on Automatic Control, July 21-26, 2002 in
Barcelona, Spain.
Garabandic, D. S., and T. B. Petrovic, “Modeling Parallel Operating
PWM DC/DC Power Supplies”, IEEE Trans. on Industrial Electronics,
Vol. 42, No. 5, pp. 545-551.
Gupta, T., R. Boudreaux, R. Nelms, and J. Hung, “Implementation of a
Fuzzy Controller for DC/DC Converters Using an Inexpensive 8-b
Microcontroller”, IEEE Trans. on Industrial Electronics, 44(5), pp. 661669, 1997.
Jantzen, Jan, Tuning of Fuzzy PID Controller, Technical report no. 98-H
871, Technical U. of Denmark, Denmark, 1998.
[10] Jovanovic, Milan M., David E. Crow, and Lieu Fang-Yi, “A Novel,
Low-Cost Implementation of Democratic Load-Current Sharing of
Paralleled Converter Modules”, IEEE Trans. on Power Electronics, Vol.
11, No. 4, pp. 604-611, 1996.
[11] Lee, C. C., “Fuzzy-Logic in Control System: Fuzzy-Logic Controller
Part I and Part II”, IEEE Trans. on System, Man, and Cybernetics, 20(2),
pp. 404-435, 1990.
[12] Mattavelli, P., L. Rossetto, G. Spiazzi, & P. Tenti, General-Purpose
Fuzzy Controller for DC-DC Converters, IEEE Trans. on Power
Electronics, 12(1), 1997, 79-86.
[13] Panov, Y., J. Rajagopalan, and F. C. Lee, “Analysis and Control Design
of N Paralleled DC-DC Converters with Master-Slave Current Sharing
Control”, Proc. of the 1997 Applied Power Electronics Conference, pp.
436-442, 1997.
[14] Perreault, David J., K. Sato, R. L. Selders, and J. G. Kassakian,
“Switching-Ripple-Based Current Sharing for Paralleled Power
Converters”, IEEE Trans. on Circuits and Systems-Part:1: Fundamental
Theory and Applications, Vol. 46, No. 10, pp. 1264-1274, 1999.
[15] Rajagopalan J., K. Xing, Y. Guo, F. C. Lee, and B. Manners, “Modeling
and Dynamic Analysis of Paralleled dc/dc Converters with Master-Slave
Current Sharing Control”, Proc. of Power Electronics Specialists
Conference, pp. 678-684, 1996.
[16] Siri, K., C.Q. Lee, and T. F. Wu, “Current Distribution For Parallel
Connected Converters: Part I”, IEEE Trans. on Aerospace and
Electronic Systems, Vol. 28, No. 3, pp. 829-840, 1992.
[17] Siri, K., C.Q. Lee, and T. F. Wu, “Current Distribution For Parallel
Connected Converters: Part II”, IEEE Trans. on Aerospace and
Electronic Systems, Vol. 28, No. 3, pp. 841-851, 1992.
[18] Skogestad, S. and I. Postlethwaite, Multivariable Feedback Control:
Analysis and Design, John Wiley & Sons Ltd., West Sussex PO19 1UD,
England, 1997.
[19] So, W-C, C.K. Tse, & Y-S Lee, “Development of a Fuzzy Logic
Controller for DC/DC Converters: Design, Computer Simulation, and
Experimental Evaluation”, IEEE Trans. on Power Electronics, 11(1),
24-32, 1996.
[20] Thottuvelil, V. J., and G. C. Verghese, “Analysis and Control Design of
Paralleled DC/DC Converters with Current Sharing”, IEEE Trans. on
Power Electronics, Vol. 13, No. 4, pp. 635-644, 1998.
[21] Tomescu, B., and H. F. VanLandingham, “Improved Large-Signal
Performance of Paralleled DC-DC Converters Current Sharing Using
Fuzzy Logic Control”, IEEE Trans. on Power Electronics, Vol. 14, No.
3, pp. 573-577, 1999.
[22] Tymerski, R., “Worst-Case Stability Analysis of Switching Regulators
Using the Structured Singular Value”, IEEE Trans. on Power
Electronics, Vol. 11, No. 5, pp. 723-730, 1996.
[23] Yen, John, and Reza Langari, Fuzzy Logic: Intelligence, Control, and
Information, Englewood Cliffs, NJ: Prentice-Hall, Inc., 1999.
[24] Wang, F.H., & C.Q. Lee, “Comparison of Fuzzy Logic and CurrentMode Control Techniques in Buck, Boost, and Buck/Boost Converters”,
Proc. the IEEE Power Electronics Specialists Conference, Atlanta, GA,
pp. 1079-1085, 1995.