1

Design, Simulation and Implementation of aFull Bridge Series-Parallel Resonant DC-DC

Converter using ANN controller

Mohammad Jafari, Mohsen ImaniehDepartment of Electrical Eng, Islamic Azad

University-Fasa branchFasa, Iran

Mohammad_jafari@iaufasa.ac.ir

Zahra MalekjamshidiDepartment of Electrical Eng, Islamic Azad

University-Marvdasht branchMarvdasht, Iran

zmalekjamshidi@miau.ac.ir

Abstract- A new method of control for high-voltage FullBridge Series-Parallel Resonant (FBSPR) DC-DCconverter with capacitive output filter, using ArtificialNeural Networks (ANN) is proposed in this paper. Theoutput voltage regulation obtained via high switchingfrequency and Soft switching operation (ZCS and ZVStechnologies) to decrease the losses and optimize theefficiency of converter. In the following sections, a Small-Signal Model of FBSPR converter on base of firstharmonic analysis and the generalized averaging methodis derived. Then the obtained model is used to simulate thedynamic behavior of real converter using Matlabsoftware. It was also used to obtain ideal control signalswhich are the desired ANN inputs and outputs and weresaved as a training data set. The data set is then used totrain the ANN to mimic the behavior of the idealcontroller. In fact the ANN controller is trained accordingto the small signal model of converter and the idealoperating points. To compare the performances ofsimulated and practical ANN controller, a prototype isdesigned and implemented. The prototype is tested forstep changes in both output load and reference voltage atsteady state and under transient conditions. Comparisonbetween experimental and simulations show a very goodagreement and the reliability of ANN based controllers.

Key Words: Full Bridge, Series-Parallel ResonantConverter, Artificial Neural Networks, ANN, ZVS, ZCS

A. INTRUDUCTION

The design and analysis of resonant converters isoften complex due to the large number of operatingstates occurring within a pulse period. In this paper aFull Bridge Series-Parallel Resonant (FBSPR)Converter using an ANN controller is introduced andthe different steps of design, simulation andexperimental tests are discussed. The converter outputpower is controlled by duty-cycle variation while theswitching frequency should be adjusted to ensure thatone bridge leg commutates at zero current (ZCS). Thesecond bridge leg operates under zero voltage switchingcondition (ZVS) and this guarantees the soft-switchingoperation in the entire operating range [2].

To design an appropriate controller, an accuratesmall signal model of converter is needed. Manycontrollers are designed by trial and error methods andthis takes much time to set the controller parameters[3]. In this paper a generalized averaging method isused to obtain the small signal model [4], [2]. Thismethod overcomes the limitations of the traditionalstate-space averaging method because it does notrequire that the waveforms have small ripplemagnitude. Thus, it is able to describe arbitrary types ofwaveforms [2]. As this model doesn't need complexmathematical analysis, it simplifies the controllerdesign for FBSPR converters and minimizes the designtime, especially in the trial and error methods. Differentadaptive controllers for the FBSPR Converter issuggested, such as Sequential State Machine [2] [5],Gain Scheduled controller [6][2], Passivity Basedcontroller [7][8][2], and Fuzzy Controller. SequentialState Machine is an abstract machine composed offinite number of states that determines transition fromone state to another. It provides the gate signals forpower switches according to the previous value of somepower circuit parameters [2], [5]. Gain scheduling is afeed forward adaptation and it can be regarded as amapping from process to controller parameters. Themain advantage of gain scheduling is the fast dynamicresponse of the controller. The Passivity based controlis a very robust method but its dynamic response is notas fast as the response of the gain scheduled controllerbecause it depends on the speed of the estimate of theload [2] [7]. In this paper an ANN based controlstrategy is employed to provide a safe and stableresponse for regulation of converter output voltage, dueto any changes in load, reference voltage and inputvoltage. Figure 1 shows the structure of the FBSPRConverter. The block known as Control Circuitsincluded a DSP high speed microcontroller to providethe driving gate signals according to the trained ANNcommands and changes in several input Signals frompower circuit.

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Figure.1 Structure of purposed FBSPR converter

In the Following sections, the steady state analysisof FBSPR Converter is reviewed in section B, the smallsignal model is discussed in section C. section Dallocated to the ANN controller discussions andsimulation and experimental results are discussed insections E and F.

B. STEADY STATE ANALYSIS OF FBSPR CONVERTER

The FBSPR Converters can operate in threecommutation mode known as Natural, Forced andMixed modes [2]. In the natural mode transistorsoperate with Zero Current Switching (ZCS) in the turnoff time. To reduce the turn off losses, fast recoverydiodes should be used as the current spikes take placeduring the turn off process [2][9]. In the forced modeall switches operate with Zero Voltage Switching(ZVS) and turn on when their anti-parallel diodes are inconduction mode and turn off with current [2]. In themixed mode, switches of one bridge legs (Q1,Q2) workwith the ZVS during turning on and the switches ofother legs (Q3,Q4) operate in ZCS during turning offtime. In this mode the conduction losses are minimizedand the converter efficiency increases. In our projectthe converter works in boundary between forced andmixed commutation modes. In this mode the switchesQ3 and Q4 turn on and off with zero current and theswitches Q1 and Q2 turn on with ZVS according tooperation above resonant frequency [2]. The resonantcurrent LSI is almost sinusoidal form during theoperation and so its spectrum contains only the firstharmonic component. However waveforms of ABV ,

DI ′ and cpV do not have sinusoidal form. The voltage

transfer ratio of the resonant converter ( )sG can becalculated as a function of the output rectifierconduction angle (which is proportion to loadvariations) and the normalized switching frequencyaccording to equation (1) [2].

( )KKnv

vsGin

o

′== .4

π (1)

In this equation n is high frequency transformerratio, K and K ′ are defined as:

21

2

22

1)(.

]..

)(tan1.1)(1[

−

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=

o

s

s

p

ep

S

P

o

s

s

p

ff

CC

RCC

C

ff

CC

Kω

(2)

⎟⎠⎞⎜

⎝⎛+=′ 227.01 ϕSinK (3)

Where, ϕ is the conduction angle of output rectifier

which changes according to load variations, Sf denotes

the switching frequency and Of is the series resonantfrequency and is calculated according to equation (4).

( ) 2/10 2 −= SSCLf π (4)Figure 2 presents the three dimensional graph of

( )sG as a function of ⎟⎠⎞⎜

⎝⎛

o

sf

f and load

variations ( )ϕ .

11.5

22.5

3

0.81

1.21.4

1.61.8

2

4

6

8

10

12

Fs,nφ

Vo/Vin

Figure.2 three dimensional graph of G(s) as a functionof

O

Sf

f and load variation ( )ϕ

The resonant frequency of the circuit ( )of changes

with the conduction angle ( )ϕ and load variations.

This is because of the influence PC on the resonantfrequency. The converter behaves as a series resonantconverter at lower frequencies and as a parallel resonantconverter at higher frequencies [2]. When the resonantcurrent flows for only a small part of the switchingperiod through PC and the load is increased, theconverter behaves as a series resonant converter. In thiscase the resonant frequency is almost equal to the seriesresonant frequency ( 0f ). On the other hand, theconverter behaves as a parallel resonant converter in

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low loads and while current flows almost the wholeswitching period through Cp [2][10].In the following sections, the operation of the series-parallel resonant converter above resonance withvariable frequency and phase-shift control is explainedin details. In this paper, FBSPR converter switchescommutate in a boundary between mixed and forcedmodes to combine the advantage of both commutationmodes. This mode of operation was described in [2].Figure 3 illustrates the waveforms of converter during apulse period from t1 to t10 and it is obvious thatresonant current is almost in sinusoidal form.

Figure 3. Waveforms of converter during a period

The steady state trajectory for the FBSPR converteroperating at full load is shown in figure 4. It is obviousthat the shape of the trajectory is almost circular whichmeans that the state variables of the converter circuit(ILS, VCS) are almost in sinusoidal form. The timesshown in the diagram are referred to figure 3.

Figure 4. The steady state trajectory for state variablesof converter

In the next section, the steady state small signal modelfor FBSPR converter is obtained and analyzed.

C. SMALL SIGNAL MODEL

In order to find the small-signal model for theFBSPR converter with capacitive output filter, the firststep is to find an equivalent circuit. In this circuit thecomponents in secondary side of high frequencytransformer referred to the primary side as shown infigure 5.

Figure 5. The equivalent circuit of FBSPR converter forsmall signal analysis

The state variables of the circuit considering thefundamental harmonics of ILS and VCS are defined as[1], [2]:

211jxxILS += (5)

431jxxVCS += (6)

651jxxVCP += (7)

70xVO =′ (8)

Where 1x , 3x and 5x are representative of cosine

components of waveforms and 2x , 4x and 6x for

sinusoidal parts. The state variables 5x and 6x are

written as a function of 1x and 2x as they arerepresentative of parallel capacitor voltage which couldnot be considered as a state variable.

[ ]γδπω 215

1 xxC

xPs

+= (9)

[ ]γδπω 126

1 xxC

xPs

−= (10)

Where

)2(21 ϕϕπγ Sin+−= (11)

)(2 ϕδ Sin= (12)

According to these variables, the state vector ofcircuit can be written as:

[ ]Txxxxxx 54321= (13)

Where:

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( )s

in

sss L

DSinVLx

Lxx

dtdx

ππω +−−= 53

21 (14)

( )( )1641

2 −+−−−= ππ

ω DConLV

Lx

Lxx

dtdx

s

in

sss (15)

ss C

xxdtdx 1

43 +=ω (16)

ss C

xxdtdx 2

34 +−= ω (17)

( )[ ]ooo CR

xCosCxx

dtdx

′′′

−−+

=.

21.2 7

22

217 ϕ

π (18)

In these equations sω (switching frequency) is

selected as 1u (first control input variable) and D (duty

cycle of switching pulses) as 2u (second control input).On the other side the output voltage, the amplitudes ofILS and VCS are selected as output variables 1y , 2yand 3y respectively. Therefore the relation betweenstate variables, control inputs and outputs can bewritten as follow:

su ω=1 (19)

Du =2 (20)

71 xy = (21)

22

212 2 xxy += (22)

24

233 2 xxy += (23)

To obtain a steady state solution of the system andfinding the small signal model, the derivatives ofEquations (14)-(18) should be equal to zero.Furthermore, the equations providing the steady statesolution can be achieved using ( ssϕ ), the steady statevalue of ϕ according to below equations.

opsss RC ′

−=ω

πϕ 2tan.2 1 (24)

)2(21

ssssss Sin ϕϕπγ +−= (25)

( )ssss Sin ϕδ 2= (26)

ss

inpS VCK ss

δω ..

= (27)

pssss

pss

ss

CLCCM

..)( 2πωπγ

δ

−+= (28)

)(.21 πDSinK

Mx

x ss

ss+−= (29)

⎥⎦⎤

⎢⎣⎡ −+

+= }1)({).(

)1(.

2

2

2 ππ DCosMDSin

MMKx

ss(30)

ss Cx

xss

ss

ss .2

3 ω= (31)

ss Cx

xss

ss

ss .1

4 ω−= (32)

[ ]ssssps

ssss

ss

ssxx

Cx γδ

ωπ..

..1

215 += (33)

[ ]ssssps

ssss

ss

ssxx

Cx γδ

ωπ..

..1

126 −= (34)

[ ])(122

21

7 sso Cos

xxRx ssss

ssϕ

π−

+=

′ (35)

The small signal transfer function was achieved afterlinearization of model around the steady state. Thelinearized model according to below equations can give

)(SG which is ratio of output voltage to duty cycle.

→→•→

Δ+Δ=Δ uBxAx .. (36)→→→

Δ+Δ=Δ uDxCy .. (37)Where A, B, C and D are matrices of system parameters

and→

x ,→

y and→

u are state, output and input vectorsrespectively. The symbol Δ means small changes inrespective parameter.

2

1)(uy

DVSG O

ΔΔ

=ΔΔ

= (38)

To achieve a complete model of system, variation ofswitching frequency can be modeled by a constantdisturbance because of its instantaneous changes. Itautomatically adjusted to ensure ZCS operation of onebridge leg. The finalized model is shown in figure 6. Itcan be used as an ideal model to produce sample datafor training ANN controller in the next stage.

Figure 6. Block diagram of system model

D. CONTROLLER DESIGN STAGES

In this section the design procedures for ArtificialNeural Network (ANN) based controller will bedescribed in brief. Several conduction modes took placeduring a complete switching period. Each statedistinguishes by the transistors and diodes which

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conduct during their respected time. In general there arenormally four basic states, but several unexpected orunwanted states may also take place which should beconsidered. In this research, a multi-layer feed-forwardartificial neural network is employed to achieve real-time control. Since the output voltage is a nonlinearfunction of duty cycle ( DΔ ) and switching frequency( nFs,Δ ), they are chosen to be the outputs of theneural network controller. The input variables of ANNare, input voltage (Vin) ,output current(I0),output DCvoltage(Vo), series inductor current (ILs) and parallelcapacitor voltage (Vcp) as storage elements. Theconverter output voltage should be kept at a constantwhile the ZVS and ZCS operation should beguaranteed; otherwise, the duty cycle of control signalshould be changed for both line and load regulationsand the switching frequency should be changed forZVS operation. Therefore, the outputs of the ANNcontroller are the changes in duty cycle and frequencyof driving signals ( DΔ , nFs,Δ ). The overall structureof designed controller illustrated in figure 7.

Figure7. The overall structure of designed controller

The ANN based controller is trained according to anideal simulated model of FBSPR converter. The idealmodel is simulated using small signal equations of thesystem as described in section (C). At the first step, asimulated model using MATLAB software isdeveloped to represent the converter system and it isused to evaluate the converters states and outputs at anytime. Then we apply changes to the input controllerparameters and search by an offline iteration procedure,at each sampling point. This process gives us the exactvalues of the control variables needed to ensureconvergence of output signals to the desired values atthe next sampling point. The obtained ideal controlsignals which are the desired ANN inputs and outputsare saved as a training data set. The data set is then usedto train the ANN to mimic the behavior of the idealcontroller. In order to satisfy this requirements, a multi-layer feed-forward ANN, was selected to be trained. Itis clear that a multi-layer feed-forward ANN can

approximate any nonlinear function. The nonlinearsigmoid function is chosen as the activation function[9].

axexf −+= 1

1)( (39)

After simulation of converter according to smallsignal model and training of ANN controller, sensitivitybased neural network pruning approach is employed todetermine an optimal neural network controllerconfiguration [9]. In this approach, the contribution ofeach individual weight to the overall neural networkperformance is indicated by a sensitivity factor )( ijwj .The sensitivity of a global error function, with respectto each weight, ijS can be defined as the following [9]:

)()()()0(

ijijij

fijijijij

wwithJwwithoutJSwwJwJS

−=

=−== (40)

In these equations, ijw is the weight of the neural

network and fijw is the final value of weight after

training. The equation (40) can be approximated by(41) for the back-propagation algorithm [9].

[ ]∑= −Δ≈

N

niij

fij

fij

ijij www

nwS1

2

)()(

η(41)

Where N is the number of training patterns for eachANN weight update, η is the learning rate which is

chosen to be 0.6 and ijWΔ is the weight update. Thesensitivity calculations were done on based of Equation(41). The weights are insignificant and can be deleted iftheir sensitivity factor was smaller than a definedthreshold and also a neuron can be removed when thesensitivities of all the weights related with this neuronare below than the threshold [9]. This process reducedthe number of active weights and neurons and waseffective in development of ANN controller speed. AMatlab Simulink model is developed on base of smallsignal model of converter to train the neural networkoff-line. a three layer feed-forward neural networkwhich has one hidden layer with 10 neurons wasselected and the network weights are selected randomlywith uniform distribution over the interval [-1, 1]. Thetotal number of weights was 128 at first stage and thisreduced to the 72 After activation of pruning processwhile still the ANN controller provide similarperformances. The simulated FBSPR converter and itsload regulation abilities are presented in figures 8 and 9.As illustrated in figures 9(a) and 9(b) the output currentstep up and down by 10mA. It takes about 5 to 6ms foroutput voltage to settle on its stable value after a %0.5of rated value (200v) over and undershoot.

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Figure 8. Simulated circuit of FBSPR converter

(A)

(B)

Figure 8. Changes in output voltage and current for astep change in load (A) from 60mA to 50mA and (B)from 50mA to 60mA.

E. EXPERIMENTAL RESULTS

In order to verify the results obtained theoretically, a500W prototype was built on base of high speed DigitalSignal Processor (DSP) TMS320F2812 as is shown infigure 10. The nominal output voltage was 200V andthe maximum output current was 3A. The ANNsoftware was developed in C language and the 32 bit,high speed CPU provides an acceptable efficientprocessing speed in both load and line regulations.

(A)

(B)

Figure 10. The implemented FBSRP converter (A),and Wave forms of VAB for full and light loads (B)

Inductors are made of ferrite core and the capacitorsare made of plain polyester. Power MOSFETs IRF840are used as active switches. The fast recovery Schottkydiodes FR107 are used as rectifiers. Experimentalresults show that the ANN controller in case of smallchanges in load or reference voltage provides goodsystem response of Settling time, Overshoot and Risetime. The results are shown in figure 11(A) to 11(D).

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(A)

(B)

(C)

(D)Figure. 11. The regulation of converter output voltage for stepup and down changes in load and reference voltage.

The output current and voltage signals were quite noisydue to high frequency switching elements. It is obvious

from figures 11(A) and (B) that a 10mA step up ordown change in load current causes a 1200mv underand overshoot in output voltage which is about %0.5 ofrated value (200v). It takes about 6ms for controller tosettle on its stable value (200V). The figures 11(C) and(D) show the changes in output current in case of anincrease or decrease about %0.5 of rated value (200V),in reference voltage. These cause a 10mA over andundershoot in output current and a 1000mv over andundershoot in output voltage which compensated afterabout 6ms. The negligible difference betweensimulation and experimental results is due to off-linetraining of ANN controller on base of ideal simulinkmodel. To fine-tune the weights of ANN and reduce thedifference an online fine-tuning train can be useful.Experimental results show good agreement withsimulations which approve the reliability of smallsignal model and ANN controller.

F. CONCLUSIONThe ANN controller proposed in this paper can be a

reliable alternative to classic controllers for FBSPRconverters. In general the ANN controller providesgood characteristics in terms of overshoot, rise-time andsettling time. Comparison between simulated andexperimental results showed good agreement whichapproved reliability of proposed controller.

G. ACKNOWLEDGMENT

The authors would like to thank the Research centerof Islamic Azad University-Fasa Branch for thefinancial support of this research project.

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Current Source with a Resonance Circuit, United States Patent6849828, February 2005.[6]. K. J. Astrom, B. Wittenmark, Adaptive Control. Second Edition,Addison-Wesley Publishing Company, Inc, 1995.[7]. C. Cecati, A. Dell'Aquila, M. Liserre, et al., A Passivity-BasedMultilevel Active Rectifier with Adaptive Compensation for TractionApplications, IEEE Transactions on Industry Applications, vol.39,no. 5,[8]. R. Ortega, A. Loría, P. J. Nicklasson, H. Sira-Ramirez, Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical andElectromechanical Applications. Springer-Verlag, London, UK, 1998.[9]. Xiao-Hua Yu, Weiming Li, Taufik'' Design and implementation

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