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Published in IET Power Electronics
Received on 18th July 2012
Revised on 25th December 2012
Accepted on 16th January 2013
doi: 10.1049/iet-pel.2012.0416
ISSN 1755-4535
Maximum power point tracking of single-ended
primary-inductor converter employing a novel
optimisation technique for proportional-integralderivative controller
Ahmad El Khateb1, Nasrudin Abd Rahim1, Jeyraj Selvaraj1, Mohammad Nasir Uddin2
1
UM Power Energy Dedicated Advanced Centre (UMPEDAC), University of Malaya, Kuala Lumpur, Malaysia
Electrical Engineering Department, Lakehead University, Ontario, Canada
E-mail: akhateb84@hotmail.com
2
Abstract: This study presents an optimisation technique for proportional-integral-derivative (PID) controller to achieve
maximum-power-point tracking (MPPT) of single-ended primary-inductor converter (SEPIC). A new weight function is
developed to optimise the PID parameters based on gradient-descent (GD) method by adding low-pass filter term. The
proposed optimisation method does not stick in the local minima, which happens frequently with the traditional weight
function used in GD method, where the low-pass filter term suppresses the noise and smooths the iteration process. The
prototype of the proposed optimised PID-based SEPIC converter for photovoltaic inverter applications is built using DSPbased TMS320F28335. The performance of the proposed optimised PID-based MPPT scheme is tested in both simulation
and experiment at different operating conditions. A performance comparison of the proposed GD method with the
conventional GD PID is also made in real-time. It is found that the proposed optimised PID-based SEPIC converter is
superior to the conventional GD PID controller in terms of power transfer and efficiency. Furthermore, the proposed
optimised PID controller for two-level inverter can achieve a better total harmonic distortion (THD) level as compared to the
multi-level inverter frequently used by researchers for the same purpose.
1
Introduction
Owing to its treatment to both transient and steady-state
response, proportional-integral-derivative (PID) controller
offers the simplest and most efficient solution to many
genuine control problems. Over the years, PID controllers
have been widely used in industry for converter control,
motor drives and other process controls [1, 2]. The
optimisation of the PID controller parameters reduces the
error signal significantly and comprehensively controls the
converter with maximum-power-point tracking (MPPT)
operation while minimising overshoot, settling time, rising
time and steady-state error.
A huge number of optimisation methods have been
introduced for PID parameters tuning in the literature.
Particle swarm, Taguchi, Chaos, gradient-descent (GD) and
genetic algorithms all improve the steady state and the
transient characteristics through the optimisation of the PID
parameters [3–6]. However, methods like particle swarm,
Taguchi and Chaos have some disadvantages. The particle
swarm optimisation has problems of dependency on initial
conditions and difficulty in finding the optimal design
parameters of the final outputs because of the absence of
the derivative. Taguchi optimisation method has difficulty
in determining the interactions between parameters, where
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the results obtained are only relative and do not exactly
indicate what parameter has the highest effect on the
performance characteristic value [7]. Chaos is not a
derivative-dependent optimisation method. It overcomes the
difficulties of the derivative-based methods because it
heavily depends on the gradient information but it has an
advantage since it avoids falling in local minima [6].
GD optimisation is a reiterative technique that is given a
starting point, and follows the negative gradient in order to
move the point towards a specific solution, which is
hopefully the desired value. GD method is popular for very
large-scale problems because it is simple, easy to
implement and it is guaranteed to find the minimum
through numerous time of iterations as long as it exists [8,
9]. As the GD method is an effective optimisation method
for solving the PID parameters problem, this work develops
GD-PID controller to search for the optimal PID
parameters. The GD method often becomes stuck in local
minima, which is the most common problem in this
method. Conversely, the improvement on this method by
adding filter term to the weighting function suppresses the
noise, fasten the process and avoid sticking in the local
minima. Therefore the proposed method combines between
the simplicity of the original method and the advantages of
the additional filter term especially avoiding the local minima.
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The main part of the MPPT operation is selecting the
proper DC–DC converter. Among all the converters
available, both the single-ended primary-inductor converter
(SEPIC) and the Ć uk converters provide the choice to have
either higher or lower output voltage compared to the input
voltage. Furthermore, they have contentious input current
and better efficiency compared to buck–boost and fly-back
converters [10]. Unlike buck–boost converter, the SEPIC
has a non-inverted output, and it uses a series capacitor to
isolate input from output [11]. The buck and buck–boost
converters have discontinuous input current, which causes
more power loss because of input switching. The boost
converter usually has higher efficiency than the SEPIC,
however, its output voltage is always larger than the input
which causes inflexibility in power extraction. Even though
there is no general agreement in the literature on which one
of the two converters is better; the SEPIC or the Ć uk
[12–17], this paper seeks to use the SEPIC converter
because of the Ć uk converter inverted output.
The MPPT method extracts additional power from
photovoltaic (PV) array under specific conditions. It
represents an optimal load for PV array, producing
opportune voltage for the load. The PV cell yields
exponential curves for current and voltage where the
maximum power occurs at the curve’s mutual knee [18].
The applied MPPT uses a type of control and logic to look
for the knee, which, in turn, allows the SEPIC converter to
extract maximum power from the PV array. The tracking
method, Perturb and Observe (P&O) [19], provides a new
reference signal for the controller and extracts maximum
power from the PV array.
In [20–25] have been working on integrators for the control
of their converters, especially the PI controllers. Integrators
eliminate steady-state error but degrade system stability. On
the other hand, differentiators with a tiny gain improves
system stability. Therefore the use of integrators and
differentiators is an integrated process, that is, PID. The
PID controller can eliminate the steady-state error as well as
improve system stability and settling time if the derivative
part has been accurately optimised and selected. Therefore
there is a need to formally optimise the PID controller
parameters. Furthermore, the optimised PID will decrease
the THD level of the output current signal and the cost of
the system will also decrease because of fewer switches as
compared to multi-level inverter which is mainly used to
decrease the total harmonic distortion. Wherefore, if we
managed to prove that optimised PID has better THD level
than that of multi-level inverters, certainly this will lead us
to such an optimised PID for multi-level inverters that will
show much better THD levels.
This paper introduces a novel optimisation technique of
GD method for PID controller applied for MPPT-based
SEPIC converter showing that the extracted power using the
proposed method is 3.4% more than that power extracted
using the conventional GD method. The controller shows a
high-precision in current transition and keeps the voltage
without any changes in variable-load case, represented in
small steady state error, short rising time and small
overshoot. As the inverter is used in a PV system, the
proposed controller is employed for more-accurate output
sine-wave, higher dynamic performance under rapidly
varying atmospheric milieu and improved total harmonic
distortion as compared to the conventional controlled
inverters [20–25]. It is worth noting that PI controller is
used in many inverter applications that are suitable for 240
V rms and power more than 1 kW as shown in [20, 26, 27].
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2
Overall system description
The SEPIC converter is supplied from the PV panels, and the
output is connected with the single-phase inverter. The output
signals of the inverter and the converter are fed back to the
respective PID controller. The converter is controlled by the
optimised PID controller. The converter’s main function is
to increase the level of voltage fed to the inverter. In this
work, however, voltage level increases or decreases
according to the MPPT scheme. Furthermore, the controller
changes the voltage level by changing the duty cycle of the
pulse-width modulation (PWM) signal, which tracks the
reference signal. The sinusoidal reference signal is
compared with the overall output signal, and the error is
processed through PID controller which generates PWM
signals for the single-phase inverter. The SEPIC’s output
signal is, thus, compared with the adaptive reference signal
to feed the inverter by the most suitable power.
The maximum power transfer operation from the PV array
is achieved through optimisation of the PID controller based
on a combination of PID parameters tuning and measuring the
negative gradient of the step response, which is used to
achieve the PID variables; iterations were made by means
of changing PID variables until the step response achieved
the desired response.
3
Optimisation of the PID parameters
The overall control scheme of the proposed MPPT-based
optimised PID control of SEPIC converter is shown in
Fig. 1. The tuning of PID parameters can bring them to the
region of convergence but cannot guarantee that the optimal
solution is achieved. As mentioned in [28], PID tuning
cannot achieve exact values for PID parameters, but can
ensure their existence around the optimal solution. There
are two possibilities when the optimisation is done for out
of convergence values: the first is that the optimisation
process takes a heavy long time to achieve the optimal
solution. The second is that the process goes towards
infinity. These two problems can be avoided by the
proposed optimisation process. The searching process for
the optimal controller parameters kp, ki and kd starts by
specifying the lower and upper bounds of the PID
parameters and initialising the parameter values using
Ziegler–Nichols method [29]. For each iteration, the
closed-loop system stability is tested and the values of
overshoot, steady-state error, rising time and settling time
are calculated. Fig. 2a presents the flowchart of the
optimisation process. The weight matrix of the learning
process at time k is calculated as shown in (1)
Wk = Wk−1 − b
∂F
∂Wk−1
(1)
Where β is the optimising step-size or learning rate. Then, the
minimum of the objective function is found when ∂F/∂Wk−1
= 0. From (1), the GD equation updating depends on the
integration. Thus, (1) can be expressed as in (2)
Wk = −
b
∂F
−1
1 − z ∂Wk−1
(2)
The GD learning procedure is presented as a feedback system
when the reference signal is set to zero and the output weight
is W as shown in Fig. 2b. The system error is assumed to be
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Fig. 1 Overall control scheme for the proposed MPPT-based SEPIC converter for PV inverter applications using DSP TMS320F28335
−∂F/∂Wk−1, which is e(k) = 0 − ∂F/∂Wk−1. The controller
purpose is to design zero-error signal in a fast and stable
response. Therefore the fine response can be obtained by
selecting proper values for PID parameters. The z-transform
of the PID controller can be expressed as shown in (3)
C(z) = kp +
ki
+ (1 − z−1 )kd
1 − z−1
(3)
After simplifying the PID controller equation, it becomes as
follows
kp 1 − z−1 + ki + 1 − 2z−1 + z−2 kd
C(z) =
1 − z−1
(4)
The GD method with incremental tuning motivated by PID
control parameters is derived in (5)
∂F
∂F
∂F
− ki
−
∂Wk−1 ∂Wk−2
∂Wk−1
∂F
∂F
∂F
− kd
−2
+
∂Wk−1
∂Wk−2 ∂Wk−3
Wk = Wk−1 − kp
(5)
Small change in weighting can be expressed below
DWk = −b
∂F
∂Wk−1
(6)
and
Wk = −
Fig. 2 Flowchart of the optimisation
a Flowchart of GD optimisation method
b GD learning procedure as a feedback system
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b
∂F
−1
1 − z ∂Wk−1
(7)
In this algorithm, we will add a block to suppress
high-frequency noise and smooth the iteration process
which is low-pass filter. Equation (7) can be rewritten as
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Fig. 3 Step-response iterations for the SEPIC converter
presented in (8) with low-pass filter term
Wk = −
b
az−1
∂F
−1
1 − z 1 − 2dz−1 + z−2 ∂Wk−1
(8)
Based on the same idea, the PID GD algorithm, with an
addition of the filter term, can be obtained as shown in (8)
defining ∂F/∂Wk−2 = z−1∂F/∂Wk−1 and ∂F/∂Wk−3 = z−2∂F/
∂Wk−1. Then
Wk = −az−1 k1 − k2 z−1 + k3 z−2
∂F
−1
−1
−2
∂Wk−1
1−z
1 − 2dz + z
(9)
where k1 = kp + ki + kd, k2 = kp + 2kd and k3 = kd. The best
performance of the proposed algorithm depends on
selecting a proper combination of the poles and the zeros in
(9). The proposed method presents tuning the k1, k2 and k3
using Ziegler–Nichols first. Then, the zeros of the controller
are fixed and the parameter α and δ are tuned. Both α and δ
should be smaller than one to ensure an asymptotic
stability. The GD method often becomes stuck in local
minima. Local minimum will lead to ∂F/∂Wk−1 = 0. The
update of W will stop at this point. Therefore the process is
trapped in the local minimum. In such way, it is possible to
avoid local minimum if ΔWk−1 is not equal to zero.
However, the proposed optimisation method is more
Fig. 4 Power–voltage (P–V) curves for the prescribed PV array
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efficient to avoid local minimum. The weight is stuck only
when ∂F/∂Wk−1, ∂F/∂Wk−2, ∂F/∂Wk−3 and ΔWk−1 are all
equal to zero referring to (5). Therefore the probability in
this case is very small in local minima.
The desired response is 340 V DC voltage, which
corresponds to 240 V rms sine wave as output of the inverter
(experimentally, the output voltage of the SEPIC converter
has to be higher than 340 V to generate 240 V rms because of
some reasons such as: dead-time, delays in control circuitry,
less than one modulation index, efficiency and voltage droop),
but this desired voltage does not always achieve the maximum
power, which in variable reference signal can be less or more
than 340 V DC where the controller of the inverter can
achieve the 240 V rms on the current expense. Fig. 3 shows
the iterations of the step response of the closed-loop system,
starting with the first response and stopping at the last
response. It represents direct implementation for the weighting
function described in (9). The first response was obtained
Fig. 5 SEPIC converter’s output
a Reference voltage
b Output voltage
c Output current
d Voltage error
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using Ziegler–Nichols method, whereas the last response was
the desired and the finest response which was obtained via
iterations using the proposed PID GD method. In Fig. 3, the
optimised PID parameters for the last iteration were: kp =
0.3542, ki = 0.0237 and kd = 0.0018. As mentioned in the
introduction, tiny gain in the derivative controller improves
the system stability, and consistently in this work the
optimised derivative gain was found to be very small, 0.0018.
This small value is unobtainable via Ziegler–Nichols method,
but neither can it be obtained via GD method alone;
subsequently, the proposed method with the filter and tuning
should be used. The MPPT algorithm gives a new reference
voltage once the variation on irradiation happens. A new set
of optimised PID parameters are calculated before the DC/DC
converter begins to track the new operating point to guarantee
the best performance at each operating point.
4
MPPT control of SEPIC converter
The MPPT control technique is applied to achieve a new
reference voltage for the optimised PID controller.
It changes the duty cycle of the PWM signal for the SEPIC
converter.
The P&O algorithm has a simple structure and requires
only a few parameters (i.e. power and voltage), so it is
extensively used in many MPPT systems [30–33].
Furthermore, it can easily be applied to any PV panel,
regardless of the PV module’s characteristics for the MPPT
process.
The P&O method periodically perturbs duty cycle and
compares instantaneous power with past power (before
perturbation). Based on this comparison, the PV voltage
determines the direction of the next perturbation. P&O
shows that if the power slope increases and the voltage
slope increases too, the reference voltage will increase;
otherwise, it will decrease.
The step-size of the P&O method affects two parameters:
accuracy and speed. Accuracy increases when the step-size
decreases. However, accuracy leads to slow response when
environmental conditions change rapidly. Larger step-sizes
mean higher speed for MPPT operation, but this will lead
to inaccuracy and larger intrinsic oscillations around the
Fig. 6 SEPIC converter’s output voltage and current of
a Non-optimised
b Optimised PID controller at variable load condition
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Fig. 7 Inverter’s output voltage, current and voltage error signals with the proposed control scheme at variable load condition
maximum power point in steady state. Step sizes should, thus,
be chosen well to achieve high speed and accuracy.
Two types of simulations for the MPPT converter were
applied using MATLAB/Simulink. The first simulation used
the characteristic equations for the PV array given in [34],
whereas the second one used the solar-cell module given in
Simulink. The MPPT algorithm was built via (.m) file and
linked with Simulink. The SEPIC circuit was built via
SimPower toolbox. Fig. 4 shows the curves for power
against voltage, at 25 and 50oC, for radiation variations,
from 250 to 1000 W/m2. For simulation purpose, the
PV-cell values and the number of PV arrays were taken
according to the experimental setup as detailed in the next
paragraph. Fig. 5a shows the reference voltage signal
tracking the maximum power. The relation between Figs. 4
and 5b can now be easily determined. Hence, it is evident
that the maximum power occurs around 330 V.
5
5.1
Simulation and experimental results
Simulation results
A simulation was applied on MATLAB/Simulink to verify
the practical implementation of the proposed SEPIC
controller for single-phase inverter. Fig. 5a presents the
reference signal for the SEPIC’s output, where it tracks the
maximum power. The voltage and current output signals of
the MPPT-based optimised PID controller at a constant load
condition are shown in Figs. 5b and c. It is noticeable that
the signals were not smooth; instead they carried a
component of the maximum power between voltage and
current. The voltage range changed from 320 to 360 V. The
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voltage signal (Fig. 5b) is similar to the reference signal
(Fig. 5a), while the error signal approached zero as Fig. 5d
shows.
Figs. 6a and b are the results of the variable load condition.
Fig. 6a shows voltage and current of SEPIC output, using
non-optimised PID controller. It is clear that the output is
presenting disturbance at each load change for both voltage
and current signals. The SEPIC output signals of the
optimised PID controller are presented in Fig. 6b, which
gives smooth transition for the current signal and zero
transition for the voltage signal.
The optimised PWM signal can achieve two things for the
inverter; first, it produces a smooth error-free sine-wave.
Second, it achieves a smooth transition for the current
signal and constant transition for voltage signal in
variable-load case. The smooth transition saves the load
from destruction by high-voltage pulses or disturbances.
Fig. 7 shows the inverter output voltage, current and error
signal, for variable loads.
The many variations in Fig. 5 clearly disappeared in Fig. 7.
They were cured by the PID controller of the single-phase
inverter. Furthermore, the transition in Fig. 7 appeared only
in current signal, not in voltage signal.
5.2
Experimental results
The experimental setup for the real-time implementation of
the MPPT SEPIC converter is shown in Fig. 8. An array of
19 series ‘PV-AE125MF5N’ solar modules was built to
generate 330 VDC voltage. Then, the PV array was
connected to the SEPIC converter, which uses controlled
PWM generated by ‘TMS320F28335’ DSP with 10 kHz
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Fig. 8 Real-time implementation of the MPPT SEPIC converter
a Photovoltaic array setup
b Experiment implementation of the SEPIC single-phase inverter
Table 2 Inverter specifications
Parameter
Value
Table 1 PV-AE125MF5N solar module
Parameter
maximum power
warranted power
rated current
rated voltage
short circuit current
open circuit voltage
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Value
125 W
118.8 W
7.23 A
17.3 V
7.9 A
21.8 V
S 1 − S4
LA
CA, CB
RL
voltage transducer
current transducer
kp-inv
ki-inv
kd-inv
IGBT, 600 V, GT50J325
3 mH, 14 A SMP
240 μF, 330 VAC
50 Ω, 500 W
LEM LV 25-P
LEM LA 25-NP
578
990.72
0.0279013
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carrier wave. Two 0.5 mH inductors were chosen to keep the
operating of the converter in continuous conduction mode.
Input capacitor C1 and output capacitor C2 were 470 and
2200 μF, respectively. Table 1 shows the details of the
PV-AE125MF5N module, whereas Table 2 shows the PV
inverter specifications and its controller parameters.
In Table 2, S1 − S4 express the switches of the inverters.
LA, CA and CB are the inductor and the capacitors of the
filter circuit, while RL belongs to the load. kp-inv, ki-inv, and
kd-inv are the PID parameters for the controller used in the
inverter’s PWM.
The experiment results are divided into three stages.
The first stage shows the performance of the proposed
optimised PID controller using different irradiation
conditions as presented in Fig. 9. The second stage shown
in Fig. 10 presents the effectiveness of the proposed method
in exploiting power from the PV array over about 2 h with
2 kW power consumption load. The third stage shows the
experimental results for the inverter presenting the sine
wave signal and the total harmonic distortion illustrated in
Fig. 11.
The experimental system is tested under different step
response operating conditions. Fig. 9a shows the result of
the proposed optimised PID controller. In each operating
condition, the maximum power is attained in a relatively
short time and has a small oscillation in steady state.
Moreover, when the weather conditions change, the
proposed controller forces the power to move directly to the
new operating point. The responses in Fig. 9a confirm
the effectiveness of the proposed controller over the
conventional GD optimisation of PID controller shown in
Fig. 9b. It is observed that the maximum power in the
proposed controller is obtained faster and has smaller
oscillation than that obtained using conventional GD
optimisation.
Fig. 10 clarifies the relation between the exploited power
for the SEPIC converter using the proposed optimisation
method for the PID controller and the normal GD method.
Although the calculated average exploited power using the
conventional GD method was 1.734 kW, the average
exploited power using the proposed method was 1.795 kW.
This power excluded the converter efficiency. As shown in
Fig. 10, it is very close to 98% in higher irradiation
conditions, and it remains above 92% even for lower
conditions. From the aforementioned measurements, it is
clear that the exploited power using the proposed GD (with
filter term) is higher 3.4% than the power exploited using
the scheme of the conventional GD method.
The optimisation method has been applied to the inverter’s
PID controller. Fig. 11a shows the experimental waveforms
of the inverter voltage and current for unity power factor
load while Fig. 11b illustrates the robustness of the
proposed controller under 0.766 lagging power factor load.
The modulation index used is 0.8 referring to [26]. THD
measurements for the proposed inverter are measured using
FLUKE 43B Power Quality Analyzer. The THD is shown
in Fig. 11b, which is measured corresponding to Fig. 11a.
The results of the optimised PID SEPIC inverter are
compared with those of the conventional controller in terms
of THD. In [26], five-level with PI controller was applied
to obtain 6.8% THD. That will consume more switches
because of multi-level. Also, the use of the PI controller
does not achieve low-enough THD even with the use of
multi-level topology. Multi-string five-level achieved 5.7%
THD in [27], but this value is still far away from 4.5%
THD which is achieved here. Furthermore, eight IGBTs
were used to build the multi-string five-level inverter. In
[22, 23], buck converter was used to adjust the tracking for
the maximum power. That will lose around half of the input
power because of discrete input current in case of direct
connection with PV array. In case of capacitor connection
to avoid losing power, the capacitors face a life time issue.
Fig. 9 Step response of the
a Proposed
b Conventional GD PID-based SEPIC converter
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Fig. 10 Exploited power of the proposed GD PID against
conventional GD PID
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Fig. 11 Experimental results for inverter output
a Voltage and current for unity power factor load
b Voltage and current for 0.766 lagging power factor load
c THD measurement of Fig. 11a
In this paper, four IGBTs were used to implement the
inverter, 4.5% THD was achieved, continuous input current
and tracking for the maximum power using SEPIC was
attained, all via optimisation for the PID controller.
6
Conclusion
A novel optimised PID controller of SEPIC MPPT-based
converter has been presented in this paper. The control
scheme has been implemented in real-time using DSP board
TMS320F28335. The proposed GD method has been
compared with the conventional GD optimisation method in
terms of system response and input power exploitation. The
performance of the improved GD optimisation method was
found better than the conventional GD method without
filter term. Experimental results indicated that the proposed
control scheme provided power transfer 3.4% more than the
control scheme of the conventional GD optimisation.
Furthermore, the proposed GD does not stick in the local
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minima where the low-pass filter term suppresses the noise
and smooths the iteration process.
7
References
1 Algreer, M., Armstrong, M., Giaouris, D.: ‘Adaptive PD + I control of a
switch-mode DC-DC power converter using a recursive FIR predictor’,
IEEE Trans. Ind. Appl., 2011, 47, (5), pp. 1–6
2 Kim, K., Rao, P., Burnworth, J.A.: ‘Self-tuning of the PID controller for
a digital excitation control system’, IEEE Trans. Ind. Appl., 2010, 46,
(4), pp. 1518–1524
3 Gaing, Z.: ‘A particle swarm optimization approach for optimum design
of PID controller in AVR system’, IEEE Trans. Energy Convers., 2004,
19, (2), pp. 384–391
4 Hsieh, C., Chou, J.: ‘Design of optimal PID controllers for PWM
feedback systems with bilinear plants’, IEEE Trans. Control Syst.
Technol., 2007, 15, (6), pp. 1075–1079
5 Wai, R., Lee, J., Chuang, K.: ‘Real-time PID control strategy for maglev
transportation system via particle swarm optimization’, IEEE Trans. Ind.
Electron., 2011, 58, (2), pp. 646–629
6 Chen, W., Meng, X., Li, J.: ‘PID controller design of maglev ball system
based on chaos parameters optimization’. 2010 Int. Conf. Machine
Vision and Human-Machine Interface (MVHI), 24–25 April 2010,
pp. 772–775
IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121
doi: 10.1049/iet-pel.2012.0416
www.ietdl.org
7 Esme, U.: ‘Application of Taguchi method for the optimization of
resistance spot welding process’, Arab. J. Sci. Eng., 2009, 34, (2B),
pp. 519–528
8 Boyd, S., Vandenberghe, L.: ‘Convex optimization’ (Cambridge
University Press, 2004)
9 Chiu, Ch.: ‘The design and implementation of a wheeled inverted pendulum
using an adaptive output recurrent cerebellar model articulation controller’,
IEEE Trans. Ind. Electron., 2010, 57, (5), pp. 1814–1822
10 Chiang, S.J., Shieh, H.-J., Chen, M.-C.: ‘Modeling and control of PV
charger system with SEPIC converter’, IEEE Trans. Ind. Electron.,
2009, 56, (11), pp. 4344–4353
11 Rashid, M.H.: ‘Power electronics, circuits devices and applications’
(Academic Press, 2006)
12 Umamaheswari, M.G., Uma, G., Vijayalakshmi, K.M.: ‘Design and
implementation of reduced-order sliding mode controller for
higher-order power factor correction converters’, IET Power Electron.,
2011, 4, pp. 984–992
13 Fardoun, A.A., Ismail, E.H., Sabzali, A.J., Al-Saffar, M.A.: ‘New
efficient bridgeless Cuk rectifiers for PFC applications’, IEEE Trans.
Power Electron., 2012, 27, pp. 3292–3301
14 Hongbo, M., Jih-Sheng, L., Quanyuan, F., Wensong, Y., Cong, Z.,
Zheng, Z.: ‘A novel valley-fill SEPIC-derived power supply without
electrolytic capacitor for LED lighting application’, IEEE Trans.
Power Electron., 2012, 27, pp. 3057–3071
15 Hyun-Lark, D.: ‘Soft-switching SEPIC converter with ripple-free input
current’, IEEE Trans. Power Electron., 2012, 27, pp. 2879–2887
16 Zengshi, C.: ‘PI and sliding mode control of a Cuk converter’, IEEE
Trans. Power Electron., 2012, 27, pp. 3695–3703
17 Don, L., Smoot, J.: ‘A SEPIC fed buck converter’. 2012 27th Annual
IEEE Applied Power Electronics Conf. and Exposition (APEC), 2012,
pp. 2333–2339
18 Mutoh, N., Ohno, M., Inoue, T.: ‘A method for MPPT control while
searching for parameters corresponding to weather conditions for
PV generation systems’, IEEE Trans. Ind. Electron., 2006, 53, (4),
pp. 1055–1065
19 Cirrincione, M., Pucci, M., Vitale, G.: ‘Growing neural gas
(GNG)-based maximum power point tracking for high-performance
wind generator with an induction machine’, IEEE Trans. Ind. Appl.,
2011, 47, (2), pp. 861–872
20 Rahim, N.A., Selvaraj, J., Krismadenata, C.: ‘Five-level inverter with
dual reference modulation technique for grid-connected PV system’,
Elsevier, Renew. Energy, 2010, 35, (3), pp. 712–720
21 Sera, D., Teodorescu, R., Hantschel, J., Knoll, M.: ‘Optimized
maximum power point tracker for fast-changing environmental
conditions’, IEEE Trans. Ind. Electron., 2008, 55, (7), pp. 2629–2637
IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121
doi: 10.1049/iet-pel.2012.0416
22 Femia, N., Granozio, D., Petrone, G., Spagnuolo, G., Vitelli, M.:
‘Optimized one-cycle control in photovoltaic grid connected
applications’, IEEE Trans. Aerosp. Electron. Syst., 2006, 42, (3),
pp. 954–972
23 Fortunato, M., Giustiniani, A., Petrone, G., Spagnuolo, G., Vitelli, M.:
‘Maximum power point tracking in a one-cycle-controlled single-stage
photovoltaic inverter’, IEEE Trans. Ind. Electron., 2008, 55, (7),
pp. 2684–2693
24 Rivetta, C.H., Emadi, A., Williamson, G.A., Jayabalan, R., Fahimi, B.:
‘Analysis and control of a buck DC-DC converter operating with
constant power load in sea and undersea vehicles’, IEEE Trans. Ind.
Appl., 2006, 42, (2), pp. 559–572
25 Dannehl, J., Fuchs, F.W., Hansen, S., Thogersen, P.B.: ‘Investigation
of active damping approaches for PI-based current control of
grid-connected pulse width modulation converters with LCL filters’,
IEEE Trans. Ind. Appl., 2010, 46, (4), pp. 1509–1517
26 Selvaraj, J., Rahim, N.A.: ‘Multilevel inverter for grid-connected PV
systems employing digital PI controller’, IEEE Trans. Ind. Electron.,
2009, 56, (1), pp. 149–158
27 Rahim, N.A., Selvaraj, J.: ‘Multistring five-level inverter with novel
PWM control scheme for PV application’, IEEE Trans. Ind. Electron.,
2010, 57, (6), pp. 2111–2123
28 Fang, C.C., Astrom, K.J., Ho, W.K.: ‘Refinements of the
Ziegler-Nichols tuning formula’, IEE Proc. Control Theory Appl.,
1991, 138, (2), pp. 111–118
29 McCormack, A.S., Godfrey, K.R.: ‘Rule-based autotuning based on
frequency domain identification’, IEEE Trans. Control Syst. Technol.,
1998, 6, (1), pp. 43–61
30 Wu, T., Chang, Ch., Chen, Y.: ‘A fuzzy-logic-controlled single-stage
converter for PV-powered lighting system applications’, IEEE Trans.
Ind. Electron., 2000, 47, (2), pp. 287–296
31 Femia, N., Granozio, G., Petrone, G., Spagnuolo, G.: ‘Predictive &
adaptive MPPT perturb and observe method’, IEEE Trans. Aerosp.
Electron. Syst., 2007, 43, (3), pp. 934–950
32 Agarwal, V., Aggarwal, R., Patidar, P., Patki, Ch.: ‘A novel scheme
for rapid tracking of maximum power point in wind energy
generation systems’, IEEE Trans. Energy Convers., 2010, 25, (1),
pp. 228–236
33 Pucci, M., Cirrincione, M.: ‘Neural MPPT control of wind generators
with induction machines without speed sensors’, IEEE Trans. Ind.
Electron., 2011, 58, (1), pp. 37–47
34 Yazdani, A., Dash, P.: ‘A control methodology and characterization of
dynamics for a photovoltaic (PV) system interfaced with a distribution
network’, IEEE Trans. Power Deliv., 2009, 24, (3), pp. 1538–1551
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