A Neural Controller for quasi-resonant converters

A NEURAL CONTROLLER FOR QUASI-RESONANT CONVERTERS J.M. Quero, J.M. Carrasco and L.G. Franquelo E.T.S. Ingenieros Industriales. Avda. Reina Mercedes sin, Sevilla. Spain Abstract. A neural controller implementing an energy feedback control law is proposed to improve the stability and dynamic characteristics of the series resonant converter (SRC). The cnert)' feedback control is introduced and analysed in discrete time domain. A novel formulation of the control law is suggested. The adaptive control law is learnt by an analog neural network (ANN). An easy imple· mentation of this controller is proposed and applied to a SRC circuit. Simulation results show a good improvement in the SRC response and confirm the validity of the controller. Keywords. Resonant converters, optimal control, adaptive control, neural networks. I. INTRODUCTION Multi-Loop control schemes have been used to improve the stability and dynamic characteristics of many different SRC topologies (Ridley, 1991; Kim, 1991). These schemes imply two feed-back loops: a fast inner one around the power stage and an outer voltage feed-back loop via the error amplifier ($Ce figure I). As a result, some quite remarkable improvements in the dy· namic behaviour of the resonant converters have been achieved. All these approaches analyse the response of the SRC when its behavioural equations are linearized about its equilibrium state. That is the reason why they fail to provide a good response when changing its stable state. Stable adaptive laws for the adjustement of parameters assure the global stability of the relevant overall sys tems. Multilayer networks have proved extremely successful in iden tification and control of dynamical sy5tems (Narendra, 1990; Quero 1990). They adaptiveJy change their connections by means of a learning algorithm. In this paper we show how a multilayer perceptron (Rumelhart, 1986) is able to re<XllI:nize the state of the SRC and to provide the switching schedule that ensures optimal response. ., " This paper is organized as follows: section 11 deals with mod eling of SRC's and energy feed-back control. In section III, the multilayer perceptron and its dynamic learning algorithm are in troduced. Section IV is devoted to describinll: the proposed con trol scheme. Section V shows the simulation rc:sults using Hspice ( Hspice, 1987). Fina!ly, in section VI some ideas are given for futUre work. II. DISCRETE TIME DOMAIN MODELING OF ENERGY FEEDBACK CONTROLLED SRC Development of this neural oontro!ler is illustrated in tbis sec tion by its application to the SRC circuit shown in figure 1. Basic operation of a SRC Many authors (Kim, 1991; Elbuluk, 1988) have analysed tbe steady state operation of the SRC. In this subsection a brief de scription of the behaviour of this converter is included. Figure 1 shows a SRC with the control switch implemented by transis tors QI Q2 Q3 Q. and their antipara!!el diodes 01 O2 03 O. respectively. The transistors are trigger<.'<1 in a time sequence as il!ustrated in figure 2. !"Z"i + r[ .. "-, I -- ., - - <-_., .... I f-"" � , -" 7' - , .' ' ..II of " �; , 1. .. -� ., I '"''" I -""'. "� .. J - " I - - ._- Figure I: Schematil diagram of SHe witl, prophSt!d lIlulti· loop control. --�- ' .. , Figure 2: Waveforms of a site for different conduction intervals. All the transiston are driven with 50% of duty cycle gating signals. Transistors Q,. Q3 are triggered according to a clock signal whose frequency determinl'!ll the operating frequency of the converter. Transiston Q, Q. are triggered with a controllable time delay with respttt to the triggering of Q" Q). A typical circuit operation of a SRC is nJustrued in figure 2. At t""O transistors Q, and Q3 turn on, while all diodes Are off. At I = T1, II. decreases to uro, due to resonance. and diodes DI, D3 begin to conduct. The first hlJ( switching cycle finishes at f = T./2. At the bqinning of the second half of the switching cycle, the transistors Q2 and Q. are triggered and a similar process occurs with the roles of Q" Q3, D" Q3 &lid Q" Q., D2, Q. interchanged, respectively. Dynamic modelin!!j Very little work hIlS been done in the area of dynamic modeling of a fe!1Onant converter. A general sample data representation of power electronic circuit dynamics ha.s been used (Elburuk,J988) : to mudcl the discrete time domain behaviour of the SRC. The discrete time domain modeling is carried Out under the following a.!1umptions: • All components are ideal. • The input \"Oltage v" tbe output voltllge v. and the control input v""" are constant. • The turns ratio transfor,.,er is 1:1. The series converter gen through four switch configurations every cycle. Each configuration hAll a linear time in\'ariant (LTI) state space description of the form A.;r(t)+IJ,u(l), ,=1.2,3,4 ( 1 ) where (2) and where 'It) = [ "�It) 1 v.(t) (3) A"B, coefficient matrices, and the sub$Cript i is the number of the switching configuration, I� end of the klh cycle and the beginning of the (k + l)th cycle, T�., time from the end of the klh cycle till the end of the ith switchin$ conllguration. I� .• is the switching period T,. The state vcctor :t" is continuous across each change in the switcb configuration: the final Slate in one configuration is the initial state in nell"t. Therefore, by comoining the solution of J for the switch configuration over a cycle, Il large signal model that describes the stale :t"(I�+I) ill the end of the (k + 1)lh cycle in terms of the stille :«1.) is gi\'<:n by the follo ..... ing: where V.(I) v.(I) L c 7:'" T� .• ( ') (5) (6) r. is a veetor composed of indireetdy controlled transition times (T •. 1 and Tu). These are times thaI depends on the state trajectories of the system, specifically, when the inductor current goes to zero and turns off the diode that is on, as given by the following threshold equations: id1t+Tt.l) = idt� + Tk.3) cdz(t�, P�, Tin 0 cl(z(t.,P.,Tk» = 0 (7) p� is a vcctor of controlling parameters. These include the circuit parameter and the directly controlled transition times (Tu and TiA). All the computations involved in deriving this model can be carried Ollt using symbolic mllllipuilltion programs like Macsyma, as Verghese (J9S6) suggests. Ener&>, Feedback Control Law The proposed energy feedback control ],ny il of the form: (8) where I •• is the I'I1t'rg,v r��lback gain ratio. Exprel5sions 4 and 8 can be lineari2ed and combined to provide the small signal sampled data modeling. Analysins the eiSenval ues of the characteristic equation of the rC$ulting dynamic transfer function, a critical f .. can be found. When f .. is Ie" than the critical value, the rC$ponse of the controlled system after a distur· bance is underdamped, and o\'erdumped when f .. is sreater than the critical f .. (Kim, 1991). The critical f .. is given by: ' c f •• I ... , = + + vc v, v. (9) The above critical f .. can also be derived from the Olltimal trajectory control law (OTCL) (Oruganti, 1987) From 4 and 9 an adaptive l'Crsion of the optimal trajectory control law is obtained: (10) Ill. MULTILAYER NETWORKS A typical multilayer network with a hidden layCT is shown in figure 3, where 1 is the sismoidal tran,fer function [i.e., 1(r) = I -e-� /1 + e-�J and lV' are weight malrices. Each unit that composes the network can be regarded as a !ilter thal sums up its input signals linearly, &(cordins to (J I) [t has been shown (Hornic,1988), using the Stone-WeieTlltrass theorem, that a two layer network with an I\rbitrarily large number ; of nodell in the hidden layer can approximate any continuous func tion f cC(1V', n ... ) over a compact subset of X". In order to obtain a dCliired set of connections that approximAtes a gil'en function, the ollckproplIglltlon lellrning IIlgorlthm (Rumelharl.1986) can be used. The weight on each line sholild be chllnged by an amount proportional to the product of an error signal 6 available to the unit r«eiving input along that line and the output of lhe unit sending activation aloug that liue. (12) • I I cO,"" .- • "'.N.N. x. x H'dd(>n Loy(>..- .-, Fisure 3: Schematic representation of a two layer network. The determination of the error signal is a recursive procelS which starts with the output units, (13) where I" is the jth component of the dCliired output when the input pattern p is applied to the neural net and 1'() is the derivative of the transfer function. The error signal for hidden units for which there ill no specified target is (\1) IV. CONTROL SCHEME The proposed control scheme is prCliented in fisure 4. The stale variables It. and Io'C and the parameters v_" v, and v. are fed into the ANN. which calculates an approximation or the error signal e gh'en by 10. , Q,.Q] , ,eo " I , " Q2.Q4 * I ••• ,.() I , • , , ..... .......... , .. Figure 1 J>roll(."'od c(Jutr(Jl .. d' n ne. The ANN is previously confisured in a learnillS phase. This procedure is carried out usinS r .. ndom input Ilsn .. 1s uniformly dis tributed within �he rans:es of int('rr:st. When this phase is finished, the connection. IV .. re networks of resinors and the sis:moidal transfer function can � realiud usinS CMOS inverters, leadint; to an easy implementation V. SIMULATIO� RESULTS In order to e\· .. lu .. t(' the p('rformancc of thc neural controller. it il applied to II full.brid!c series rC$Onant colwerter. The paramo eters of the c;onverter IIrC; L = 0.113mll II, _ 3011 C = O.I20IlF II. = 12u The ANN used to implement the controller belons:s to class "'U.I (three inputs, eiSht hidden units and.one output uniL). Our· ins: the learnins: process, the followinS intC'!"vals for the s:eneration of random inpuls are used: Ilc t 1-100, 100) The nlues of the C'!"ror function e are limited by the maxi· mum and minimum nlues of the lismoid .. l transfer (unction. N tice that .... e are only concerned with the zero-crossins of the er· ror function. Durins the learnins phase, the ANN is trained for 100.000 time Itepi before it it �ins applied to the SRC. IIspice il beinS used to simulate the whole circuitry. The SR� is simulated usinS a constant I •• controllC'!" and the proposed neu· ral one in order to compare it. respon5('l to a change in the refer· ence. The transient output current of the ellergy feedback control with I .. "" 0.2 for the step chanse o{ 11« .. " from 1.2 to 3.75 can be seen in fisure 5. $howins a undesirable underdamped behaviour. In fisure 6 an improved tran.ieul resl"lnse is obtained when usinS the neural controller. The evolution of I ... is presented in figure 7. When the trantittors are trisscred, I •• evohoes from 0.76 to 0.52, correspondins to the optimal nlues predicted by 9. VI. CONCLUSIONS A neurAl controller IItililins the resonant tank eners,y as an adapth'e control law il pro� to improve the stability J.nd dy· namic dlluJ.Cteristic of the M'ries Il'SOnant converter. The con· troller sUIJI.·rl'iso tht' state of the COIII'CTtt'r and generalCli the Iwitchins schedlllt' that provides optilnllJ tr ... jectory control. Simu· lJ.tion resulu confirm the \·alidity of the controt1er. The electronic irnillenu�ntillion of thl' nenl·1I1 conlrolkr is bl'l.SC<i on the intesra· lion of a set of il)\'\'l"tCI"I interconnected \\'ith constant rninon. Although the IITOr10&i'd cOl1troller is beiliS applied 10 an specific COI1\'('rll'r, the design elln be casily gl'lwTaliozed to any kind of res· onllnt colII'Crter. " ,." .589 a.l.. ....... , • .... ••.• 1.. ." " I •••.••••. I •• "." •• L tl .. Illftl IH.'" 1111 .... 2111.'" JIIII.1hI Figure 5: Transient oulput current response to J. chanse of "_, from 1.2 to 3.75 when usinS const"'"t I .. = 0.2. 5.t - J.U - 2.al '"� '" .. _saa.a.l..·",· . M. &� Uu I. .. ... , tin Illnl 121 lu lSI h Figure 6; Transient output current response to ... chanse of "_, from 1.2 to 3.75 when usinS the neural network controller. I.' - ... .. - r, , 'Ha. 1 ..... 2n.'. • .. I ... •• " lu .. I.. 01 •• " .. -I..... .L II .. Il1n) • 121 �u ISI.lu 248 IhI JaU Iw I • Figure 7: E\'Ollltioli o{ I •. when the state variables change. VII. NO�IENCLATURE T, Switching period. . , Current in resonant tank inductor . ·c VoltAge on resonant tank capAcitor. L Resonant tank inductance. C Resonant tank capacitance. , Subscript used to indicate the I(-th e\-ent •• Input voltage . •• Output voltage . Z.(!A) Discrete state \·ariables. Z Characteristic impedance Z:J LIC f •• Enerll:Y feedback gain ratio '. Output of neuron j. W;j Connection between neuron i and j p , , , r PAttern currently presented to the network. Learning step site. Difference between the tarll:et and the output of the network (t·o). Desired output. SigmoidAl transfer function. VIII. REFERENCES J. Ridley. R.8., Tabisch, \V.A., Lee, F.C. and Vorperian V. (1991). �Multi-loop control for quasi-resonant converters�. IEEE Transactions on Power Electronic.. Vol. 6, n 1, 28-38. 2. Kim, M. and Youn, M. (1991). "A discrete time domain modelinll: and analysis of controlled series resonant ton· verter". IEEE Transattions on Industrial Electronics. Vol ; 38, n 1.32-40. 3. Narendra, K. and PuthiUarathy, K. (1990). "Identifkation and control of dynamital syatems".IEEE Transattions on Neural Networks. Vol 1, n I, 4-27. 4. Quero, J.�1. and Camac:ho, E.F.{1990). "Neural generalized predictive self-tunin! contro1!ersw• IEEE International Con ference on Systems Engineering. 160-163. 5. Oru!anti. R., Yang, J. J. and Lee, F. C. (1987). Kimple mentation of optimal trajectory control of series resonant converter". IEEE TrAnsattions on Power Elettronies, Vo1.3, n 3. 318-327. 6. Rumelhart, D. and McCle1!and, J. (1986). Parallel dis tributed processin!. MIT press. 7. flspite users' mAnUAI.(1987). Meta-Software Int. 8. Elbuluk. M.E., Ver!hese, G.C. and Kuu.kian, J.G. (1988). �Sample data modeling and digital control of resonant con verters". IEEE Transattions on Power Eledronia. 9. Hornik, K. and Stinchcomhe, M. and White. II. (1998). �Multila)-er feedforward ne�works are universal approxima tors�. Dept. Etonomics, University of Cl\lifornia, SM Diego, discussion (ll\p. / View publication statsView publication stats