Design, Simulation and experimental analysis of closed loop time domain based Discrete PWM buckboost converter are described. To improve the transient response and dynamic stability of the proposed converter, Discrete PID controller is the most preferable one. Discrete controller does not require any precise analytical model of the system to be controlled. The control system of the converter is designed using digital PWM technique. The proposed controller improves the dynamic performance of the buckboost converter by achieving a robust output voltage against load disturbances, input voltage variations and changes in circuit components. The converter is designed through simulation using MATLAB/Simulink and performance parameters are also measured. The discrete controller is implemented, and design goal is achieved and the same is verified against theoretical calculation using LabVIEW.
1. Introduction
Electronic control Switched mode DCDC converters convert an unregulated dc input voltage into regulated dc output by varying the duty cycle of the converter. These converters are smaller in size, more power efficient provides an efficiency of 75% to 98% therefore, they are used extensively in computer peripherals, personal computers, communication, medical electronics, Hybrid electric vehicle
[13

14]
and adapters of consumer electronic devices to provide different levels of DC voltages.
The buckboost converter also known as stepdown and stepup converter
[1]
. It is highly efficient and also very simple to design as it excludes the usage of transformer. Also there is minimal stress on the switch, and requires a relatively small output filter for low output ripple. This converter is widely used for energy management applications. The switching devices and passive components such as inductors and capacitors introduce nonlinearities in the converters. As a result, the linear control techniques cannot be directly applied for analysis.
The analog PID control scheme has been used successfully in many industrial control systems. Digital controllers are superior in performance and lower in cost compared to analog counterparts. Digital controllers are extremely flexible; easy to handle nonlinear control equations involving complicated computations or logical operations. A very much wider class of control laws can be used in digital controllers than in analog controllers. Digital controllers are capable of performing complex computations with constant accuracy at high speed and can have almost any desired degree of computational accuracy alternatively with little increase in cost.
Digital controller is introduced in the design of Buckboost converter to obtain a tight voltage regulation, robustness, fast switching transient and improved dynamic performance for buckboost converter. Digital controller offers many extra features compared to analog controller. Digital controller has low component aging, low cost, zero drift characteristic, high reliability and controllability. Numerous research work involves development of a digital controller for DCDC converter as mentioned in
[2

12]
.
Discrete PID controller is designed for the proposed buckboost converter. The controller design involves two steps 1) Design an analog controller in a continuous time domain for the buckboost converter. 2) Approximate the behavior of an analog controller with a digital controller which converts continuous domain into discrete domain. In the discrete domain, the controller compensates the error signal and tracks the accurate output. The digital controller is simple to design for all types of converters. It does not produce any limit cycle oscillation for any resolution of DPWM; also the performance of proposed controller is very good. The controller parameters such as rise time, settling time and peak overshoot are very low. It does not have steady state error and ripple voltage. For any uncertainty in input voltage and load, the controller continuously tracks the reference and produces a constant output voltage and proves its enhanced robustness. The errors caused by component variations up to certain limits are proportionately rectified by digital compensator by varying the duty cycle of the converter to produce the constant output voltage. The variations in the input voltage will not take more time to attain constant output.
The overall block diagram of the buckboost converter with the entire set up is shown in
Fig. 1
. The output voltage of the buckboost converter is compared against the desired value of the reference voltage using the comparator1 (Operational Amplifier IC 741). The Digital compensator is designed for the buckboost converter using discrete PID controller. The error output thus obtained is fed into the inbuilt block diagram section of the LabVIEW through the Data Acquisition Card DAQ NI 9221. LabVIEW section consists of Analog to Digital conversion, discrete transfer function and Digital to Analog conversion blocks. Inside the DAQ card Analog to digital conversion takes place and thus processed signal is fed into the discrete transfer function block in which the designed controller value is entered. The output of the controller is acquired back by DAQ card converts digital to analog signal and fed into the comparator 2 designed using operational amplifiers (IC 741). This signal is compared against high frequency carrier signal (ramp signal) with desired switching frequencies obtained from signal generator. The resulting PWM switching pulses are fed to the switch of the converter through the gate drive circuits.
Digitally controlled buckboost converter
2. Design of BuckBoost Converter
The schematic diagram of buckboost converter is shown in
Fig. 2
. The converter provides an output voltage that may be less than or greater than the input voltage. As the polarity of the output voltage is always opposite to that of the input voltage, it is also called as inverting converter
[15]
. V
_{o}
is the output voltage and V
_{s}
is the input voltage
[8]
.
Schematic diagram of buckboost converter
The relationship between the input voltage and the output voltage is
Where d is the dutycycle. The value of inductor L and capacitor C can be found by
[10]
:
_{Δ}
I is the ripple current,
_{Δ}
Vcis the ripple voltage, f is the switching frequency, L is the filter inductor and C is the filter capacitor of the circuit. The designed buckboost converter circuit parameters are input voltage V
_{s}
=14V, Switching frequency f=400 KHz, L=11 μH, C=14 μF, Load resistance R=14 Ω, d=60%, Output power P
_{o}
= 31.5 Wand Output voltage V
_{o}
=21V.
3. Modeling of BuckBoost Converter
After designing buckboost converter, simulation is done using state space averaging technique. The unique feature of this method is that the design can be carried out for a class of inputs such as step, ramp or impulse function in which all the initial conditions are also included. This technique is convenient to use for low frequency approximation of the true dynamics where the discontinuous effect introduced by the switching is ignored
[7]
. The Simulink requires the system equations of the power converter circuit. The state space analysis is given below.
The switches S is driven by a pulse sequence with a constant switching frequency f. The state vector for the buckboost converter is defined as
whereI
_{L}
is the current through an inductor;
V_{c}
is the voltage across the capacitor. For the given duty cycle d(k) for k
^{th}
period, the systems are illustrated by the following set of state space equations in continuous time domain :
The system is described by the following set of continuous time state space equations
[10]
:
Where x is a state vector, V
_{s}
is a source vector, A, B, C, D is the state coefficient matrices. State model of the buckboost converter is derived as
High power densities are possible only for continuous conduction mode (CCM) of operation. Diode D and MOSFET S are always in a complementary state, when SON, DOFF and vice versa. Two modes of operations are possible, corresponding state equations are
where
The state space model is of the following form:
where
where
The state space equations (4) can be converted into transfer function of the buckboost converter. The continuous state equations are discretized for the design of discrete PID controller. It is considered that the discrete system is same as that of the continuous system except that the system is sampled with a sampling time, which is assumed as 1μS. The state space solution is evaluated and finds an analog PID controller equation using ZieglerNichols method
[2]
.
4. Closed Loop Control System of BuckBoost Converter
Fig. 3
shows the closed loop control system of the buckboost converter with Discrete PIDbased feedback. The goal is to minimize the error between V
_{ref}
(Reference voltage) and V
_{o}
which make the system to track the reference signal that is considered as a step input. The output is regulated by using the feedback. The feedback ensures that the output must be insensitive to load disturbances, stable and provides good transient response thereby improving the dynamic performances. The error voltage V
_{e}
(difference between V
_{ref}
and V
_{o}
) is fed to Analog to Digital converter which samples at a sampling rate equal to 1μS. The function of the digital compensator is to generate the control signal by compensating the error (V
_{e}
).
Closed loop control system of buckboost converter with Discrete PID controller
The error is processed by digital compensator block with PID algorithm to generate control signal. For the digital control of buckboost converter switching, discrete PID control can be realized by its compensation block. The control signal from the compensator will affect the converter characteristics significantly, so it is vital to identify a suitable compensation technique to provide improved converter performance by making the best use of discrete controller. The output samples control the switch by generating gating pulses when it is processed through Digital Pulse Width Modulation (DPWM) block. The DPWM is nothing but a demodulator that consists of sample and hold block. It includes the delay time (t
_{d}
), A/D conversion time, switch transition time, computational delay and modulator delay.
Fig. 4
shows the block diagram of Analog to digital converter block. It is a device that converts a continuous time signal to a discrete time signal by using sampling. The converter block consists of delay, zero order hold, quantizer and saturation. The delay block carried out the total time between sampling the error signal and updating the duty cycle at the beginning of the next switching period. The zero order hold is mainly for modeling the sampling effect. Quantizer is mainly used for rounding off or truncating the signal that will map a larger set of input values to a smaller set such as rounding values to desired unit of precision.
Analog to digital converter
The discrete time Compensation block is shown in
Fig. 5
. The output of the A/D converter is fed to the discrete zeropole block which in turn is converted into PWM Pulses using DPWM blocks
[8]
as shown in
Fig. 6
. The discrete time integral compensator thus designed minimizes the error and sends the command signal to the switch in the form of pulses in order that the output tracks the reference signal
[6
,
7]
. The output of the compensator is compared against high frequency ramp signal in order to obtain the duty cycle pulse for the switch as discussed in
[11]
.
Discrete time compensation
Digital pulse width modulation
5. Design of Robust Digital Controller
In a closed loop system, PID controller block provides the compensation in the feedback control of the buckboost converter. PID controller has the advantages of both PD & PI controller. PD controller is a special case of phaselead controller that improves system stability and increases system bandwidth. PI controller reduces steadystate error which is a special case of the phaselag controller. Hence PID controller is also called as phase laglead controller
[9

10]
.
The continuous time PID controller can be expressed as:
Where u(t) is the control output, K
_{p}
is the proportional gain constant, T
_{d}
is the derivative time or rate time constant, T
_{i}
is the integral time or reset time constant and e is the error (difference between reference voltage V
_{ref}
and output voltage V
_{o}
). The value of K
_{p}
, T
_{d}
and T
_{i}
are tuned depending on the present error, accumulation of past errors and prediction of future error respectively
[12]
.
The Laplace transfer function of the corresponding PID controller is given as:
By proper choice of these tuning parameters a controller can be adapted for a specific converter to obtain a good behavior of the controller system. By using routh  array technique one can find the range of K
_{P}
. The values of T
_{d}
and T
_{i}
are obtained using Ziegler  Nichols tuning rule method.
Table 1
shows Ziegler  Nichols tuning formulae. Where K
_{cr}
is the critical gain and P
_{cr}
is the critical period. By solving characteristic equation, find natural frequency of the system ω
_{o}
and using the relation
, T
_{i}
and T
_{d}
. The transfer function of the PID controller is
ZieglerNichols tuning formulae
ZieglerNichols tuning formulae
Where K
_{p}
is the proportional gain, K
_{I}
= K
_{p}
/T
_{I}
is the integral gain, and K
_{D}
= K
_{p}
T
_{D}
is the derivative gain of the controller. Polezero cancellation technique is the most suitable one to remove unstable poles in the transfer function. In order to use polezero cancelation technique, the discrete PID controller equation can be rewritten in the form as:
This form is easy to determine the closed loop transfer function.
Then
Where,
ξ
the damping ratio and ω
_{o}
is the natural frequency oscillation of the system. The buckboost converter under consideration is of second order and the desired poles can be easily placed by assuming the following converter specifications,
For the system to be stable, the closed  loop poles or roots of the characteristic equation must lie within the unit circle. The K
_{p}
, K
_{I}
and K
_{D}
values are satisfying the above condition then the poles and zeros of the function should be placed within the unit circle and the system is said to be in stable condition.
The transfer function of the controller for buckboost converter is
By following the above equation and conditions, the value of K
_{p}
= 0.009, K
_{I}
= 143.54and K
_{D}
=1.40625*10
^{7}
and
𝜔_{o}
= 37416 rad /sec. Then the analog PID controller equation is
The continuoustime domain controller as mentioned in the above equation (29) is transformed into the discretetime domain using Trapezoidal method which is referred as Tustin method or BilinearTransformation method. This Tustin method tracks the analog controller output more accurately by sampling at frequent intervals and approximate to the analog integration are better than other methods. The trapezoidal approximation is given below:
Let n(t) be the integral of e(t), then the value of the integral of t = (K+1) T is equal to the value at KT plus the area added from KT to (K+1)T.
Using Trapezoidal rule, e(t) is the area curve from t = KT to t = (K+1)T is approximated as
Therefore
Taking the ztransform of (32) then
Hence equation (34) is the transfer function of a discrete Integrator. Trapezoidal approximation to differentiation, Derivative of e(t) at t = KT is n(KT), then
Taking ztransform of (35)
Now discrete PID controller transfer function becomes
[2]
Now applying equation (38) in the designed buckboost converter then the discrete controller for the buckboost converter is
6. Simulation Results
The proposed closed loop response of the buckboost converter is simulated using MATLAB / SIMULINK is shown in
Fig. 7
. Simulation has been carried out using the values same as that of the experimental values. The aim of this work is to achieve robust controller in spite of variations in load and uncertainty.
Closed loop response of buckboost converter using MATLAB/SIMULINK
Table 2
shows the performance of the various controllers using the same buckboost converter.
Table 2
shows that the output voltage obtained using digital controller settle down at 3mS with a rise time of 2mS. The controller parameters under considerations are settling time, Peak overshoot, rise time, steady state error and output ripple voltage which is compared against its Discrete PI, and analog PI and PID controllers are designed for the same buckboost converter.
Performance parameters of the closed loop Buckboost converter
Performance parameters of the closed loop Buckboost converter
Steady state error observed for load variations is much lesser than 1% and no overshoot or undershoots are evident. The performance specifications for the buckboost converter with discrete PID controller are better than PI and analog controllers. The results are thus obtained with digital controller for buckboost is in concurrence with the mathematical calculations. It is proved that the digital system shows improved results than the analog controllers.
The simulation is carried out by varying the input voltage, load resistance and the corresponding output voltage, output current, reference voltage are shown in
Figs. 8
and
9
. In
Fig. 8
the reference voltage is 7V, the input voltage is first set as 8V until 0. 05S and then varied from 8V to 12V and again at 0. 1S, 12V is varied to 16V. Similarly the load resistance is first set as 12Ω until 0. 05S and then varied from 12Ω to 16Ω and finally 20Ω is set at 0. 1S.
Fig. 8
shows the performance of buck operation in buckboost converter with the variations in input voltage and load resistance. Similarly the performance of boost operation in buckboost converter with the variations in input voltage and load resistance is shown in
Fig. 9
.
Output response of the discrete PID controlled buckboost (buck performance) converter
Output response of discrete PID controlled buckboost (boost performance) converter.
Fig. 9
shows the boost operation the input voltage is varied from 8V to 16V, load resistance is varied from 12 Ω to 20Ω, the reference voltage is 18V and the corresponding output response of the buckboost converter shows fixed output voltage regulation. In both operation undershoots or overshoots are not seen and the steady state error is also not apparent. In order to check the dynamic performance of the controller, the L, C and R values are varied and the output response of the system is shown in
Table 3
.
Variations in different parameters and performance of the discrete PID controller.
Variations in different parameters and performance of the discrete PID controller.
Table 3
proves that the system is very much dynamic in tracking the reference voltages in spite of the variations in the inductance L, capacitance C and Load resistance R values. The system does not show any steady state error overshoots or undershoots and it settles down at a faster rate with a settling time of about 0. 03S for all the values. In order to confirm the better performance of Discrete PID controller over its Analog PID controller, the output response of the reference voltage of 21V, discrete controlled buckboost converter is compared against the response produced by an analog PID controller and its graph is shown in
Fig. 10
.
Comparison between Digital PID and analog PID controller responses
In order to analyse the stability of the discrete controlled buckboost converter, Bode plot response is drawn as shown in
Fig. 11
. The stability properties are

1. Any closed loop pole outside the unit circle makes the system unstable.

2. If a simple pole lies at z = 1, then the system becomes critically stable.

3. Any multiple closedloop pole on the unit circle makes the system unstable.

4. Closed loop zeros do not affect the stability and therefore may be located anywhere in the z plane.
Bode plot response of proposed discrete PID controller for BuckBoost converter
The discrete PID controller transfer function of the designed buckboost converter is
The root locus plot has drawn for the above transfer function equation. From the root locus plot, it is clearly obvious that the poles are placed neither outside the unit circle nor at 1. Multiple poles have not occurred. All poles are placed in the right half of the zplane, thereby satisfying the stability condition of the transfer function frame for our proposed controller.
7. Hardware Implementation
The Buckboost converter with Discrete Controller has been implemented using LabVIEW (Laboratory Virtual Instrumentation Engineering Work Bench) as a controller platform. LabVIEW is primarily used as a platform for implementing any closed loop system and it can also be used for the improvement of a control system. It is extensively used software for analyzing the projects experimentally with a shorter duration due to its programming flexibility along with integrated tools designed especially for testing, measurements and control. The key feature of LabVIEW is that it extensively supports accessing the instrumentation hardware. The drivers and abstraction layers are provided for almost all types of instruments. The buses are also accessible for addition. The abstraction layers and drivers act as graphical nodes and enable to communicate effectively with the hardware devices thereby offering standard software interfaces
[12]
.
This software is used to build up virtual instrumentation (vi) which comprises of the front panel and a functional block diagram. The front panel shown in
Fig. 12
is mainly used for user interactions. It is through the front panel the desired transfer function of the discrete controller is entered and the corresponding parameters of the closed loop control and hence the restructured condition of the system is obtained. The block diagram, data acquisition, transfer function and signal generation are built using the functional block diagram as shown in
Fig. 13.
It provides wide varieties of small icons to perform the desired task. The LabVIEW package provides many libraries with large number of tasks for data acquirement, signal production, arithmetical and statistical analysis, signal conditioning and investigation along with many graphical interface elements. These features make it a superior one when compared with other development environment.
Front panel
Functional block diagram
Interfacing Circuit
: The NI 9221 multifunction data acquisition (DAQ) device is used. It can be easily connected via PCI 6221 for data acquisition, generation and data sorting in a wide range of convenient and portable applications. It comprises of 8 analog inputs with referenced single ended signal coupling or 4 inputs with differential coupling, 2 analog outputs, 12 bits A/D and D/A converters and 32 bits counters. There are 12 channels of digital Input/output lines which can be used either as input or output. It eventually offers a tremendous platform for the proposed discrete controller.
The prototype model of the buckboost converter with discrete PID controller is shown in
Fig. 14
. The functioning of DC is substantiated well in the experimental study and the LabVIEW also provides the most feasible solution for the controller platform. To evaluate the performance, the reference value of 16V is set for which the output is obtained as 16. 04V. The steady state error thus observed is very small of the order of 0. 04V and the system settles down fast. The acquisition of the error signal from the hardware takes place instantaneous, when the program is run and at the same time the controlled signal from the LabVIEW package is also generated within a shorter duration of time without any delay or time lag. The experimental results thus obtained are in concurrence with the simulation results and mathematical calculations. Prototype model is developed using the values shown in
Table 4
.
Experimental set up
Experimental values
The input voltage and load resistance have been varied in the range of 12V, 14Ω and 18V, 10Ω, the corresponding output voltage is measured as 21. 042V, and 21. 068V respectively for the reference of 21V and is illustrated in
Figs. 15
and
16
respectively. In these Figures channel 1 indicates the input voltage and Channel 2 indicates the corresponding output voltage. It can be observed from the result that there are no undershoots or overshoots but steady state error is of very minimum order.
Fig. 17
shows the input and output voltage of the buck response of the buckboost converter. The input voltage is 14V, 18Ω reference voltage is 8V and the obtained output voltage is 8. 002V.
Output (boost) voltage obtained for 12V input and load resistance of 14Ω (ch2 5V/1mS & ch3 10V/ 1mS)
Output voltage (boost) obtained for 18V input and load resistance of 10Ω (ch2 5V/1mS & ch3 10V/ 1mS)
Output (buck) voltage obtained for 14V input and load resistance of 18Ω (ch2 5V/1mS & ch3 5V/1mS)
The output voltages for the references of 21V & 8V along with their switching pulses are shown in
Fig. 18
and
19
respectively. From the output waveforms, it is clearly understood, that the output observed shows better performance, thereby ensuring that the controller is more appropriate and can be tuned to track the references in spite of the variation in input voltage. The discrete controller changes the duty cycle according to change in reference voltage and is not subjected to any change in the input voltage.
Duty cycle obtained for 21V reference
Duty cycle obtained 8V reference
Table 5
given below provides the efficiency of conventional buckboost converter and the proposed Discrete controlled buckboost converter. It clearly justifies that proposed Discrete controlled buckboost converter is 2.5% more efficient than the conventional buckboost converter.
Efficiency comparison between conventional and discrete controlled Buckboost converter
Efficiency comparison between conventional and discrete controlled Buckboost converter
8. Conclusion
A discrete controller for buckboost converter has been designed. Simulation results demonstrate that the converter not only exhibits the steady state and transient performance but also improves the efficiency of conventional buckboost converter. The design of time domain based discrete PID controller for buckboost converter has been implemented to adapt to the variation in error signal by changes the duty cycle. The design incorporates an Analog to Digital Converter and discrete pulse width modulator. The discrete controller is thus designed for the buckboost converter and also implemented using LabVIEW as a control platform and the corresponding results are illustrated. The mathematical analysis, simulation study and the corresponding experimental results show that the controller thus designed achieves tight output voltage regulation and good dynamic performances. This topology is independent and is compatible to make itself suitable to extend for any sort of applications like as speed control, photo voltaic cell and medical electronics.
BIO
S. Vijayalakshmi She received AMIE degree in Electronics & Communi cation Engineering from Institution of Engineers (India), Kolkatta in 1992, Master of Science degree in Informa tion Technology from Bharathidasan University, Tiruchirapalli, and Master of degree in Power Electronics and Drives from Anna University, Chennai in 2007. Her research interests are Discrete controller for DCDC converter.
T. Sree Renga Raja He is working as an Assistant Professor in the Department of Electrical and Electronics Engineering, Anna University, BIT Campus, Tiruchirapalli, Tamil Nadu, India. He obtained B.E (Electrical and Electronics Engineering) degree from Manonmaniam Sundaranar University, Tirunelveli in 1998, M. E (Power Systems) from Annamalai University, Chidambaram in 1999 and Ph.D from Anna University, Chennai in 2007. He has published many papers in the field of Power System Engineering. His area of interest includes Power system optimization, Renewable Energy Applications, Energy Conservation Management and Insulation Engineering.
Sajeesh K. K.
2012
“Digital controller implementation for noninverting buckboost converter using runtime partial reconfiguration of FPGA,”
Proc. IEEEIICPE
1 
6
Mattuveli P.
2004
“Digital controls of DCDC boost converters with inductor current estimation,”
Proc. IEEEAPEC
74 
80
Chander Subhash
2011
“Autotuned, Discrete PID Controllers for DCDC Converter for fast transient response,”
Proc. IEEEICEMSC
1 
4
Peterchev Angel V
,
Sanders R
2003
“Quantization resolution and limit cycling in digitally controlled PWM converters,”
IEEE Trans. Power Electronics
18
301 
308
Peng Hao
,
Prodic A
,
Alarcon E
,
Maksimov D
2007
“Modeling of Quantization Effects in Digitally Controlled DCDC converters,”
IEEE Trans. Power Electronics
22
208 
215
Peretz M M
,
BenYaakov S
2012
“Time domain design of digital compensators for PWM DCDC converters,”
IEEE Trans. Power Electronics
27
887 
893
Shuibao GUO
,
Yanxia GAO
,
Yanping Xu
,
Xuefang LINSHI
,
Bruno ALLARD
2009
“Digital PWM Controller for HighFrequency LowPower DCDC switching Mode Power Supply,”
Proc. IEEEIPEMC
1340 
1346
Mariethoz Sebastein
2010
“Comparison of Hybrid Control Techniques for Buck and Boost DCDC Converters,”
IEEE Trans. Control systems Technology
18
1126 
1114
DOI : 10.1109/TCST.2009.2035306
Patella Benjamin J
,
Prodic Aleksandar
2003
“HighFrequency Digital PWM Controller IC for DCDC Converters,”
IEEE Trans. Power Electronics
18
438 
446
DOI : 10.1109/TPEL.2002.807121
Matsuo H
,
Kurokawa F
,
Etou H
,
Ishizuka Y
,
Chen C
2000
“Design oriented analysis of the digitally controlled DCDC converter,”
Proc. IEEEPSEC
401 
407
Peng L.
,
Kang X.
,
Chen J.
2001
“A novel PWM technique in digital control and its application to an improved DC/DC converter,”
Proc. IEEEPSEC
254 
259
Lee ChienMing
2006
“LabVIEW Implementaton of an AutoTuning PID Regulator via Greypredictor,”
Proc. IEEECISC
1 
5
You BongGi
2011
“Optimization of Powder Core Inductors of BuckBoost Converters for Hybrid Electric Vehicles,”
Journal of Electrical Engineering and Technology
6
(4)
527 
534
DOI : 10.5370/JEET.2011.6.4.527
Kavitha Anbukumar
2010
“Resonant Parametric Perturbation Method to Control Chaos in Current Mode Controlled DCDC BuckBoost Converter,”
Journal of Electrical Engineering and Technology
5
(1)
171 
178
DOI : 10.5370/JEET.2010.5.1.171
Chen Jingquan
2006
“Analysis and Design of a Low Stress BuckBoost Converter in UniversalInput PFC Applications,”
IEEE Trans. Power Electronics
21
(6)
320 
329
DOI : 10.1109/TPEL.2005.869744
2003
“A General Approach to Control a Positive Buck Boost Converter to Achieve Robustness against Input Voltage Fluctuations and Load Changes,”
IEEE Trans. Power Electronics
18
438 
446
DOI : 10.1109/TPEL.2002.807121