Implementation of a Full Bridge Series-Parallel Resonant DC-DC Converter using ANN and SSM controllers

Transcription

1 Implementation o a Full Bridge erie-parallel Reonant DC-DC Converter uing ANN and M controller Zahra Malekjamhidi**, Mohammad Jaari*, Mohen Imanieh* ** Department o Electrical Eng, Ilamic Azad Univerity-Marvdaht branch *Department o Electrical Eng, Ilamic Azad Univerity-Faa branch zmalekjamhidi@miau.ac.ir, mohammad_jaari@iauaa.ac.ir Abtract In thi paper, two method o control or high-voltage Full Bridge erie-parallel Reonant (FBPR DC-DC converter are propoed and the reult are compared. ot witching operation uing Zero Current witching (ZC and Zero Voltage witching (ZV technologie i employed to decreae the loe and optimize the eiciency o converter. The way o obtaining mall-ignal model o FBPR converter uing the generalized averaging method i dicued. Then two control method uing Artiicial Neural Network (ANN and equential tate Machine (M are eplained and the eperimental reult are compared. The ANN controller i trained according to the mall ignal model o the converter and operating point and the M controller operate on bae o a inite number o tate, action and unction and determine tranition rom one tate to another according to FBPR converter conduction tatu. To compare the perormance o two controller, a prototype i deigned and implemented. The prototype i teted or tep change in both output load and reerence voltage at teady tate and under tranient condition. Comparion between eperimental reult or both ANN and M controller how better peed perormance or M controller in mall change in load and more reliability or ANN controller in cae o large variation. Key Word: Full Bridge, erie-parallel Reonant Converter, Artiicial Neural Network, equential tate Machine, ZV, ZC A. INTRUDUCTI The deign and analyi o reonant converter i oten comple due to the large number o operating tate occurring within a pule period. In thi paper a Full Bridge erie-parallel Reonant (FBPR Converter uing two control method are introduced. They are baed on Neural Network and equential tate Machine. The dierent tep o deign, imulation and eperimental tet are dicued. The converter output power i controlled by duty-cycle variation while the witching requency hould be adjuted to enure that one bridge leg commutate at zero current (ZC. The econd bridge leg operate under zero voltage witching condition (ZV and thi guarantee the ot-witching operation in the entire operating range []. To deign an appropriate controller, an accurate mall ignal model o the converter i needed. Many controller are deigned by trial and error method and thi take ome time to et the controller parameter [3]. In thi paper a generalized averaging method i ued to obtain the mall ignal model [], []. Thi method overcome the limitation o the traditional tate-pace averaging method becaue it doe not require that the waveorm have mall ripple magnitude. Thu, it i able to decribe arbitrary type o waveorm []. A thi model doen't need comple mathematical analyi, it impliie the controller deign or FBPR converter and minimize the deign time, epecially in the trial and error method. Dierent adaptive controller or the FBPR Converter i uggeted, uch a Gain cheduled controller [6][], Paivity Baed controller[7][8], equential tate Machine [] [5] and Fuzzy Controller. The Gain cheduling i a eed orward adaptation and it can be regarded a a mapping rom proce to controller parameter. The main advantage o gain cheduling i the at dynamic repone o the controller. The Paivity baed control i a very robut method but it dynamic repone i not a at a the repone o the gain cheduled controller becaue it depend on the peed o the etimate o the load [] [7]. The equential tate Machine i an abtract machine compoed o inite number o tate that determine tranition rom one tate to another []. It provide the gate ignal or power witche according to the previou value o ome power circuit parameter [] [5]. In thi paper two ANN and M baed controller are employed to provide a ae and table repone during any variation in output voltage in cae o any change in load or reerence voltage. A prototype alo i implemented to obtain eperimental reult on bae o a high peed Digital ignal Proceor (DP. Figure how the tructure o the FBPR Converter. The block known a Control Circuit provide the gate driving ignal according to everal electrical ignal rom power circuit.

2 Figure. tructure o purpoed FBPR converter In the Following ection, the teady tate analyi o FBPR Converter i reviewed in ection B, the mall ignal model i dicued in ection C. ection D allocated to the ANN and M controller and imulation and eperimental reult are dicued in ection E and F. B. TEADY TATE ANALYI OF FBPR CVERTER The FBPR Converter can operate in three commutation mode known a Natural, Forced and Mied mode []. In the natural mode tranitor operate with Zero Current witching (ZC in the turn o time. To reduce the turn o loe, at recovery diode hould be ued a the current pike take place during the turn o proce [][9]. In the orced mode all witche operate with Zero Voltage witching (ZV and turn on when their anti-parallel diode are in conduction mode and turn o with current []. In the mied mode, witche o one bridge leg (Q,Q work with the ZV during turning on and the witche o other leg (Q3,Q operate in ZC during turning o time. In thi mode the conduction loe are minimized and the converter eiciency increae. In our project the converter work in boundary between orced and mied commutation mode. In thi mode the witche Q3 and Q turn on and o with zero current and the witche Q and Q turn on with ZV according to operation above reonant requency []. The reonant current I L i almot inuoidal orm during the operation and o it pectrum contain only the irt harmonic component. However waveorm o V, I D and Vcp do not have inuoidal orm. The voltage G can be traner ratio o the reonant converter ( calculated a a unction o the output rectiier conduction angle (which i proportion to load variation and the normalized witching requency according to equation ( []. G ( v K = o = n. vin π K ( AB In thi equation n i high requency tranormer ratio, K and K are deined a: tan ( CP C p C [ (. C o ω. C p. Re K = C p. ( C o ( = 0.7 in ϕ K (3 ] Where, ϕ i the conduction angle o output rectiier which change according to load variation, the witching requency and O denote i the erie reonant requency and i calculated according to equation (. / ( L C π ( 0 = Figure preent the three dimenional graph o G ( a a unction o o variation ( ϕ. Vo / Vin φ F,n and.5 load Figure. three dimenional graph o G( a a unction o and load variation ( ϕ O The reonant requency o the circuit ( o with the conduction angle ( 3 change ϕ and load variation. Thi i becaue o the inluence CP on the reonant requency. The converter behave a a erie reonant converter at lower requencie and a a parallel reonant converter at higher requencie []. When the reonant current low or only a mall part o the witching period through C P and the load i increaed, the converter behave a a erie reonant converter. In thi cae the reonant requency i almot equal to the erie reonant requency (. 0 On the other hand, the

3 converter behave a a parallel reonant converter in low load and while current low almot the whole witching period through Cp [][0]. In the ollowing ection, the operation o the erieparallel reonant converter above reonance with variable requency and phae-hit control i eplained in detail. In thi paper, FBPR converter witche commutate in a boundary between mied and orced mode to combine the advantage o both commutation mode. Thi mode o operation wa decribed in []. Figure 3 illutrate the waveorm o converter during a pule period rom t to t0 and it i obviou that reonant current i almot in inuoidal orm. C. MALL IGNAL MODEL In order to ind the mall-ignal model or the FBPR converter with capacitive output ilter, the irt tep i to ind an equivalent circuit. In thi circuit the component in econdary ide o high requency tranormer reerred to the primary ide a hown in igure 5. Figure 5. The equivalent circuit o FBPR converter or mall ignal analyi The tate variable o the circuit conidering the undamental harmonic o IL and VC are deined a [], []: Figure 3. Waveorm o converter during a period The teady tate trajectory or the FBPR converter operating at ull load i hown in igure. It i obviou that the hape o the trajectory i almot circular which mean that the tate variable o the converter circuit (IL, VC are almot in inuoidal orm. The time hown in the diagram are reerred to igure 3. Figure. The teady tate trajectory or tate variable o converter In the net ection, the teady tate mall ignal model or FBPR converter i obtained and analyzed. I L j 3 j 5 j6 = (5 V C = (6 V CP V O = = (7 (8 0 7 Where, 3 and 5 are repreentative o coine component o waveorm and, and 6 or inuoidal part. The tate variable 5 and 6 are written a a unction o and a they are repreentative o parallel capacitor voltage which could not be conidered a a tate variable. 5 6 Where πωc πω C P [ δ γ] = (9 P [ δ γ] = (0 γ π ϕ in (ϕ δ in ( ϕ = ( = ( According to thee variable, the tate vector o circuit can be written a: [ ] T 3 5 = (3 3

4 Where: ( Dπ d 3 5 Vinin = ω dt L L πl ( d 6 V in = ω ( Con( Dπ (5 dt L L πl d 3 = ω dt C (6 d = ω 3 dt C (7 d dt πc o 7 7 =. ϕ In thee equation [ Co( ] R. C o o (8 ω (witching requency i u (irt control input variable and D (duty elected a cycle o witching pule a u (econd control input. On the other ide the output voltage, the amplitude o IL and VC are elected a output variable y, y and y 3 repectively. Thereore the relation between tate variable, control input and output can be written a ollow: u = ω (9 u = D (0 y = ( 7 y = ( y 3 3 = (3 To obtain a teady tate olution o the ytem and inding the mall ignal model, the derivative o Equation (-(8 hould be equal to zero. Furthermore, the equation providing the teady tate olution can be achieved uing ( ϕ, the teady tate value o ϕ according to below equation. ϕ =.tan π ω C pro ( γ = π ϕ in(ϕ (5 δ in ( ϕ ω. C p. V in K δ δ M C p γ π ( πω. L. C C p = (6 = (7 = (8 = K. in ( Dπ (9 M K. M in( D. π = { Co( Dπ } ( M M (30 3 ω. C = (3 ω. C = (3 [. δ. γ ] = (33 5 π. ω. C p [. δ. γ ] = (3 6 π. ω. C p R o 7 = π [ Co( ϕ ] (35 The mall ignal traner unction wa achieved ater linearization o model around the teady tate. The linearized model according to below equation can give G ( which i ratio o output voltage to duty cycle. = A B. u. (36 y = C. D. u (37 Where A, B, C and D are matrice o ytem parameter and, y and u are tate, output and input vector repectively. The ymbol mean mall change in repective parameter. G( V D y u O = = (38 To achieve a complete model o ytem, variation o witching requency can be modeled by a contant diturbance becaue o it intantaneou change. It automatically adjuted to enure ZC operation o one bridge leg. The inalized model i hown in igure 6. It can be ued a an ideal model to produce ample data or training ANN controller in the net tage. Figure 6. Block diagram o ytem model D. DEIGN OF ANN AND M CTROLLER In thi ection the deign procedure or both Artiicial Neural Network (ANN and equential tate

5 Machine (M bae controller will be decribed in brie. I. Deign o M controller everal conduction mode took place during a complete witching period. Each tate ditinguihe by the tranitor and diode which conduct during their repected time. In general there are normally our baic tate but everal unepected or unwanted tate may alo take place which hould be conidered and included into the tate table. The M controller i an abtract machine which determine tranition rom one operating tate o converter to another on bae o atiaction o everal condition. The operation tate are illutrated in a tate tranition table a i hown below. load. The normal operation tate are T, T, T3 and T. T5 i related to dicontinuou mode tate and T6 and T7 are pecial tate to prevent operation below reonance. There i a tranition rom each tate to the Error tate, i ome abnormal behavior occur []. In thi cae, all witche are turned o and the tate machine can be retart rom tate (t. In thi controller, the witche Q3 and Q turn on and o with zero croing o current (IL and the witche Q and Q turn on with ZV according to operation above reonant requency and ynchronize with zero croing o IL. The gate drive ignal o Q and Q are generated by comparing a contant amplitude awtoothhaped ignal (Rt and a computed variable voltage (Vphi. The awtooth ignal with contant amplitude i generated according to below circuit []. Table: tate tranition table or conduction WITCH ZV-HI ZV_LO ZC_HI ZC_LO CURRENT TATE T T T3 T T5 T6 T7 Error Figure 8. The contant amplitude awtooth ignal generator The controller would determine what tate the converter witche hould move to. Thi guarantee a proper operation or power circuit o converter. To implement thi control trategy, a equential tate Machine (M controller i deigned to operate according to below tate diagram. The tate diagram i adapted to tate tranition table. The requency o awtooth-haped ignal change according to output voltage and current variation to guarantee the operation above reonant requency. The amplitude o voltage (Vphi i computed according to change in tate variable o reonant circuit (IL, VCP. The reulted PWM voltage tranerred to M controller to provide the gate drive ignal o witche. II. Deign o ANN controller Figure 7. tate diagram o equential tate machine The diagram in practice i realized through everal imple otware loop. The M ha eight tate (T,T,T3,T,T5,T6,T7,Error which witche are turned on or o or each tate conduction []. The control proce tart at tate T which two diagonal witche are on. Thi applie the ull input voltage acro the reonant circuit, tranerring power to the The econd controller i an Artiicial Neural Network which i trained according to an ideal imulated model o FBPR converter. In thi reearch, a multi-layer eed-orward artiicial neural network i employed to achieve real-time control. ince the output voltage i a nonlinear unction o duty cycle ( D and witching requency ( F, n, they are choen to be the output o the neural network controller. The input variable o ANN are, input voltage (Vin,output current(i0,output DC voltage(vo, erie inductor current (IL and parallel capacitor voltage (Vcp a torage element. The converter output voltage hould be kept at a contant while the ZV and ZC operation hould be guaranteed; otherwie, the duty cycle o control ignal hould be changed or both line and load regulation and the witching requency hould be changed or ZV operation. Thereore, the output o the ANN controller are the change in duty cycle and requency 5

6 D, F, n o driving ignal (. The overall tructure o deigned controller illutrated in igure 9. = J ( w = 0 J ( w = J ( without w J ( with w = w (0 In thee equation, w i the weight o the neural network and w i the inal value o weight ater training. The equation (0 can be approimated by ( or the back-propagation algorithm [9]. n= η ( w N [ w ( n ] w w i ( Figure 9. The overall tructure o ANN controller The ANN baed controller i trained according to an ideal imulated model o FBPR converter. The ideal model i imulated uing mall ignal equation o the ytem a decribed in ection (C. At the irt tep, a imulated model uing MATLAB otware i developed to repreent the converter ytem and it i ued to evaluate the converter tate and output at any time. Then we apply change to the input controller parameter and earch by an oline iteration procedure, at each ampling point. Thi proce give u the eact value o the control variable needed to enure convergence o output ignal to the deired value at the net ampling point. The obtained ideal control ignal which are the deired ANN input and output are aved a a training data et. The data et i then ued to train the ANN to mimic the behavior o the ideal controller. In order to atiy thi requirement, a multilayer eed-orward ANN, wa elected to be trained. It i clear that a multi-layer eed-orward ANN can approimate any nonlinear unction. The nonlinear igmoid unction i choen a the activation unction [9]. = e ( (39 a Where N i the number o training pattern or each ANN weight update, η i the learning rate which i choen to be 0.6 and W i the weight update. The enitivity calculation were done on baed o Equation (. The weight are inigniicant and can be deleted i their enitivity actor wa maller than a deined threhold and alo a neuron can be removed when the enitivitie o all the weight related with thi neuron are below than the threhold [9]. Thi proce reduced the number o active weight and neuron and wa eective in development o ANN controller peed. A Matlab imulink model i developed on bae o mall ignal model o converter to train the neural network o-line. a three layer eed-orward neural network which ha one hidden layer with 0 neuron wa elected and the network weight are elected randomly with uniorm ditribution over the interval [-, ]. The total number o weight wa 8 at irt tage and thi reduced to the 7 Ater activation o pruning proce while till the ANN controller provide imilar perormance. E. EXPERIMENTAL REULT In order to veriy the reult obtained theoretically, a 500W prototype wa built a i hown in igure 0. Ater imulation o converter according to mall ignal model and training o ANN controller, enitivity baed neural network pruning approach i employed to determine an optimal neural network controller coniguration [9]. In thi approach, the contribution o each individual weight to the overall neural network perormance i indicated by a enitivity actor j w. ( The enitivity o a global error unction, with repect to each weight, can be deined a the ollowing [9]: 6

7 Figure 0. a The implemented FBRP converter b Wave orm o VAB or ull and light load Eperimental reult howed that the dierence between percentage o overhoot and ettling time in output repone in cae o mall change in load current, or both M and ANN controller i not noticeable. Although ANN controller provide lightly better ytem repone perormance in term o ettling time, Overhoot and Rie time a depicted in igure and. A illutrated in thee igure, the converter output voltage, wa regulated ater about 5m and 500mv (%0.5 over and underhoot or ANN controller in cae o %0.5 tep up or down change in load current. While thi time wa about 0m with a 000mv (%0.5 overhoot or M controller or the ame change in load current. The dierence wa more coniderable when change in load current were increaed. Figure 3 how the regulation o output voltage or a change o %.5 o rated current, in cae o ANN controller. It i obviou that the percentage o overhoot increaed in cae o larger change in load current. A can be een in Figure, there wa an overhoot in load current in cae o tep change in reerence voltage in both cae o ANN and M controller. Eperimental reult or a range o tep change in load current howed that or larger change, the percentage o overhoot and ettling time increaed or both controller but thi increae wa more coniderable or M controller. The reult howed that the ANN controller provide better provide better repone characteritic than MM controller epecially in cae o large variation in load current. The graph in igure 5 contrat the change in overhoot and ettling time or a range o tep change in load current or both controller. It i obviou rom the igure that the dierence between repone or two controller increaed a the tep change go up. The dierence alo wa more pronounced in cae tep change in reerence voltage. (b Figure.. The regulated output voltage and load current or a %0.5 tep up change in load (a or M controller (b or ANN controller (a (b Figure.. The regulated output voltage and load current or a %0.5 tep down change in load (a or ANN controller (b or M controller (a Figure. 3. The regulated output voltage and load current or a %.5 tep down change in load current or ANN controller 7

8 G. ACKNOWLEDGMENT The author would like to thank the R&D center o Ilamic Azad Univerity-Faa Branch or the inancial upport o thi reearch project. Figure.. The regulated output voltage and load current or a %0.5 tep up change in reerence voltage or ANN controller (a H. REFERENCE []. G. Ivenky, A. Kat,. Ben-Yaakov, A Novel RC Model o Capacitive-Loaded Parallel and erie-parallel Reonant DC-DC Converter. Proceeding o the 8th IEEE Power Electronic pecialit Conerence, t. Loui, Miouri, UA, vol., pp , 997. []. F.. Cavalcante and J.W. Kolar, Deign o a 5kW High Output Voltage erie-parallel Reonant DC-DC Converter, in Proceeding o the 3th IEEE Power Electronic pecialit Conerence, Acapulco,Meico, 003, vol., pp [3]. G. Garcia oto, J. Gaye, G. W. Baptite, Variable ampling Time erial-reonant Current Converter Control or a High-Voltage X-ray Tube Application. Proceeding o the 0th European Power Quality Conerence, Nuremberg, Germany, 00, pp []. J. A. abate, F. C. Y. Lee, O-Line Application o the Fied- Frequency Clamped-Mode erie Reonant Converter. IEEE Tranaction on Power Electronic, vol.6, no., pp , Jan. 99. [5]. H. Aigner, Method or Regulating and/or Controlling a Welding Current ource with a Reonance Circuit, United tate Patent 68988, February 005. [6]. K. J. Atrom, B. Wittenmark, Adaptive Control. econd Edition, Addion-Weley Publihing Company, Inc, 995. [7]. C. Cecati, A. Dell'Aquila, M. Lierre, et al., A Paivity-Baed Multilevel Active Rectiier with Adaptive Compenation or Traction Application, IEEE Tranaction on Indutry Application, vol.39, no. 5, [8]. R. Ortega, A. Loría, P. J. Nicklaon, H. ira-ramirez, Paivitybaed Control o Euler-Lagrange ytem: Mechanical, Electrical and Electromechanical Application. pringer-verlag, London, UK, 998. [9]. Xiao-Hua Yu, Weiming Li, Tauik'' Deign and implementation o a neural network controller or real-time adaptive voltage regulation (b Figure 5. Comparion between Overhoot (a and ettling time (b in output repone o ANN and M controller F. CCLUI It can be concluded that in general ANN controller provide better characteritic than the M controller in term o overhoot, rie-time and ettling time. Thi uperiority wa more noticeable or greater tep change in load current and reerence voltage. 8