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1、Neural Comput & Applic (2009) 18:93103DOI 10.1007/s00521-007-0161-3O R I G I N A L A R T I C L EDesign of intelligent power controller for DCDC convertersusing CMAC neural networkChun-Fei HsuReceived: 26 October 2006 / Accepted: 19 October 2007 / Published online: 8 November 2007 Springer-Verlag Lon

2、don Limited 2007AbstractDCDC converters are the devices which canconvert a certain electrical voltage to another level ofelectrical voltage. They are very popularly used because ofthe high efciency and small size. This paper proposes anintelligent power controller for the DCDC converters viacerebell

3、a model articulation controller (CMAC) neuralnetwork approach. The proposed intelligent power con-troller is composed of a CMAC neural controller and arobust controller. The CMAC neural controller uses aCMAC neural network to online mimic an ideal controller,and the robust controller is designed to

4、achieve L2trackingperformance with desired attenuation level. Finally, acomparison among a PI control, adaptive neural controland the proposed intelligent power control is made. Theexperimental results are provided to demonstrate the pro-posed intelligent power controller can cope with the inputvolt

5、age and load resistance variations to ensure the stabilitywhile providing fast transient response and simplecomputation.KeywordsAdaptive controlRobust controlCMAC neural networkDCDC converter1 IntroductionThe DCDC converters can convert a certain electricalvoltage to another level by switching actio

6、n. The outputvoltage is controlled by adjusting the ON time of theswitching action, which in turn adjusts the width of aC.-F. Hsu (&)Department of Electrical Engineering, Chung Hua University,Hsinchu 300, Taiwan, ROCe-mail: .twvoltage pulse at the output. This is known as pulse-width-modul

7、ation (PWM) approach HYPERLINK #111. By varying the duty ratioof the PWM modulator, the DCDC converter can convertone level of electrical voltage to the desired level. Formany years, the controller design for DCDC convertershas been carried out through analog circuits, which limitedthem to PI contro

8、ller structures HYPERLINK #111, HYPERLINK #112HYPERLINK #11. The selection of thecontroller parameters in the PI controller is a trade-offbetween robustness and transient response. In general, itinduces large overshoot in output voltage when the risetime of response is reduced.During the past decade

9、, there have been many differentapproaches proposed for PWM switching control designbased on sliding-mode control HYPERLINK #11HYPERLINK #113HYPERLINK #11, HYPERLINK #114, fuzzy control HYPERLINK #115, HYPERLINK #116HYPERLINK #11,and adaptive neural control HYPERLINK #11HYPERLINK #117HYPERLINK #11HY

10、PERLINK #119HYPERLINK #11 techniques. In the slid-ing-mode control design for DCDC converters HYPERLINK #113HYPERLINK #11, HYPERLINK #114, thecontrollers are easy to design and simple to implement.However, their performances generally depend on theworking point, thus these control parameters which w

11、ant toensure proper behavior in all operating conditions are dif-cult to design. In the fuzzy control design for DCDCconverters HYPERLINK #11HYPERLINK #115HYPERLINK #11,HYPERLINK #116, the fuzzy rule should be pre-selectedthrough trial-and-error to achieve satisfy performances;however, this trial-an

12、d-error tuning procedure is time-consuming. In HYPERLINK #117HYPERLINK #119, though satisfactory regulator perfor-mance can be achieved by using the developed onlinetuning algorithm, the computation loading of these learningalgorithms is too heavy.The neural-network-based control technique has beenr

13、epresented an alternative design method for various con-trol systems HYPERLINK #11HYPERLINK #1110HYPERLINK #1114HYPERLINK #11. The successful key point is theapproximation ability of neural network, where the neuralnetwork can approximate an unknown system dynamics oran ideal controller after learni

14、ng. Based on this property,the neural-network-based controllers have been developed12394Neural Comput & Applic (2009) 18:93103to compensate for the effects of nonlinearities and systemuncertainties, so that the stability, convergence and robust-ness of the control system can be improved HYPERLINK #1

15、1HYPERLINK #119HYPERLINK #11. Recently,the cerebellar model articulation control (CMAC) neuralnetwork have been adopted widely for the control of com-plex dynamical systems owing to its fast learning property,good generalization capability, and simple computationcompared with the neural network HYPE

16、RLINK #1115HYPERLINK #11HYPERLINK #1119HYPERLINK #11. The CMACneural network is classied as a non-fully connectedperception-like associative memory network with overlap-ViQN1D1N2VxD2LCRVoping receptive-elds HYPERLINK #1115HYPERLINK #11. The conventional CMAC neuralnetwork uses local constant binary

17、receptive-eld basisfunctions HYPERLINK #1120HYPERLINK #11. The disadvantage is that its output is con-stant within each quantized state and the derivativeinformation is not preserved. On the other hand, foracquiring the derivative information of input and outputPWMmodulatorFig. 1The forward DCDC con

18、verterdN dN1 ddN:feedbackcontroller1variables, several researchers developed a CMAC neuralnetwork with non-constant differentiable Gaussian recep-tive-eld basis function, and provided the convergenceanalyses of this network HYPERLINK #11HYPERLINK #1115, HYPERLINK #1116, HYPERLINK #1121.In this paper

19、, an intelligent power controller for the DCDC converter is proposed to achieve L2tracking perfor-mance with desired attenuation level. The proposedintelligent power controller is composed of a CMAC neuralcontroller and a robust controller. The CMAC neuralcontroller uses a CMAC neural network with a

20、 Gaussianreceptive-eld basis function to mimic an ideal controller,and the robust controller is designed to achieve L2trackingperformance with attenuation of disturbances includingapproximation errors and external disturbances. Moreover,the adaptation laws of the intelligent power control systemare

21、derived in the sense of Lyapunov function, thus thesystem can be guaranteed to be stable. Finally, the intel-ligent power controller is implemented in a PC-basedcomputer control system. The experimental results dem-onstrate that the proposed intelligent power controllerscheme can achieve favorable c

22、ontrol performance eventhe DCDC converter is subject to the variations of inputvoltage and load resistance.2 Problem formulation of DCDC converterThis duty cycle signal is then sent to a PWM outputstage that generates the appropriate switching pattern forthe switching power supplies. A forward DCDC

23、converteris discussed as shown in Fig. HYPERLINK #21, where Viand Voare theinput and output voltages of the converter, respectively, D1and D2are the diodes, L is the inductor,C is the outputcapacitor, R is the resistor, and Q is the transistor whichcontrol the converter circuit operating in differen

24、t modes.When the transistor is ON, Viappears across the primaryand then generates HYPERLINK #11HYPERLINK #111HYPERLINK #11N2VxViVlost2N1where N1is the turns of primary power winding, N2is theturns of slave power winding and Vlostdenotes the voltagedrop occurring by transistor and diodes and represen

25、ts theunmodeled dynamics in practical applications. The diodeD1on the secondary ensures that only positive voltages areapplied to the output circuit while diodeD2provides acirculating path for inductor current. By the averagingmethod, the output voltage can be expressed as HYPERLINK #111N2VoViVlostd

26、:3N1SinceN1, N2and Vi- Vlostare considered as constants,differentiating both sides of Eq. HYPERLINK #2(HYPERLINK #23) with respect to time,yieldsDCDC converter is very popular because of its highefciency and small size. Among the various switchingV_oN2ViVlostdd guN14control method, PWM which is base

27、d on fast switching andwheregN2N1ViVlostis the control gain which is aduty ratio control is the most widely considered one. Theswitch frequency is constant and the duty cycle,d(N),varies with the load resistance variations at the N-th sam-pling time. The output of the designed controller, dd(N), ist

28、he change of duty cycle. Then, the duty cycle is deter-mined by adding the previous duty cycled(N-1) to thechange of duty cycle dd(N), i.e. HYPERLINK #11HYPERLINK #111HYPERLINK #11123positive constant and u : dd is the controller output.3 Intelligent power controller designThe control problem of DCD

29、C converter is to controlthe change of duty cycle dd so that the output voltage ofNeural Comput & Applic (2009) 18:93103DCDC converterVocan provide an output referencevoltage Vref. The output error voltage is dened as95mimic the ideal controller u*in Eq. HYPERLINK #3(HYPERLINK #36HYPERLINK #3) based

30、 on the uni-versal approximation property of CMAC neural network.e VrefVo:5Since the number of neurons in the CMAC neural networkis not innite for the real-time practical applications, theThe control law of the change of the duty cycle isdetermined by the error voltage signal to provide fasttransien

31、t response and small overshoot in the outputvoltage. If the system parameters of DCDC converterare well known, an ideal controller can be designed as HYPERLINK #1122HYPERLINK #11approximation errors introduced by the CMAC neuralnetwork can not be inevitable. In order to ensure the sta-bility and rob

32、ustness of the closed-loop control system, therobust controllerurcis designed to compensate for theapproximation error between the CMAC neural controlleru g1V_ref ke:6and the ideal controller based on theL2control theory.Thus, the worst case effect on the tracking errors due to theApplying the ideal

33、 controller (HYPERLINK #36) into system dynamics HYPERLINK #2(HYPERLINK #24HYPERLINK #2)results in the following error dynamics_ ke 0:7If k is chosen to correspond to the coefcients of a Hurwitzpolynomial, it is implied that limt!1e 0:Since thesystem parameters of DCDC converter may be unknownor per

34、turbed, the ideal controller u*in Eq. (HYPERLINK #36) can not beprecisely implemented. In order to efciently control theoutput voltage of the DCDC converter, this paperproposed an intelligent power controller as shown inFig. HYPERLINK #32HYPERLINK #3, i.e.uir unc urc8where uncis the CMAC neural cont

35、roller which is imple-mented by a CMAC neural network, and urcis the robustcontroller. The CMAC neural controller is investigated toapproximation error can be reduce to be less or equal adesired level.3.1 CMAC neural networkThe architecture of CMAC neural network is depicted inFig. HYPERLINK #33, wh

36、ich is composed of the input space, associationmemory space, receptive-eld space, weight memory spaceand output space. The signal propagation and the basicfunction in each space are introduced as follows HYPERLINK #1115HYPERLINK #11, HYPERLINK #1116:3.1.1 Input space STheSis a continuousn-dimensiona

37、l input space. For agiven s= s1, s2, ., snT, each input state variable must bequantized into discrete regions (called an element)according to given control space. The number of elements,PWMmodulatorViDC-DCconverterVooutputvoltagesensornE, is termed as a resolution.3.1.2 Association memory space Ad(N

38、) d(N 1) d(N)Several elements can be accumulated as a block. Thenumber of blocks,nB, in the CMAC neural network isduncCMAC neuralcontroller (15)d/dteVrefusually greater than two. TheAdenotes an associationassociation memory spaceAuirurcupdate law(27)-(29)robust controller(30)d/dtinput space Ss1sn1kn

39、kbkweight memory spaceWwkoutput space Yyintelligent power controllervia CMAC neural networkFig. 2The block diagram of the intelligent power controller forDCDC convertersreceptive-field space TFig. 3The structure of CMAC neural network12396memory space with nA(nA= n 9 nB) components. In thisspace, ea

40、ch block performs a receptive-eld basis function,which can be formulated as rectangular or any continu-ously bounded function. In this paper, the Gaussianfunction is adopted as the receptive-eld basis functionwhich can be represented as2#/iksi expsimik;for k 1; 2; . . .; nB9Neural Comput & Applic (2

41、009) 18:93103receptive-eld and zero for the outside, the schemediscussed above becomes the conventional CMAC neuralnetwork. The multidimensional receptive-eld can beexpressed in a vector notation asUs; m; r b1; b2; :; bnRT11wherem mT1;mT2;. . .; mTnRTandr rT1;rT2;. . .; rTnRT:In the CMAC neural netw

42、ork scheme, no receptive-eld isr2ikwhere /ik(si) presents the k-th block of thei-th input siwith the mean mikand variance rik. Figure HYPERLINK #44 depicts theschematic diagram of two-dimensional CMAC neuralnetwork operations with nE= 9 and q= 4 (q is the numberof elements in a complete block), wher

43、e s1is divided intoblocks A, B and C, and s2is divided into blocks a, b and c.By shifting each variable an element, different blocks willbe obtained. For instance, blocks D, E and G for s1, andblocks d, e and g for s2are possible shifted elements HYPERLINK #11HYPERLINK #1116HYPERLINK #11.Each block

44、in this space has two adjustable parameters mikand rik.3.1.3 Receptive-eld space TEach location of A corresponds to a receptive-eld. Thenumber of receptive-eld, nR, is equal to nBin this paper.The multidimensional receptive-eld function is dened asYbks; mk; rk /iksi; for k 1; 2; . . .; nR10i1where b

45、kis associated with the k-th receptive-eld, mk=m1k,m2k, ., mnkTand rk r1k;r2k; :; rnkT:Note that ifbkis a constant for the inside area covered by thek-thvariables2formed by the combination of different layers such as A,B, C and d, e, f. Therefore, Dd, Ff and Gg are newreceptive-elds resulting from d

46、ifferent blocks. With thiskind of quantization and receptive-eld composition, eachstate is covered byq(less than or equal toq) differentreceptive-elds. If the input falls within the kth receptive-eld, this eld becomes active. Nearby inputs can activateone or more of the same qweights, which can prod

47、ucesimilar outputs. This correlation provides a very usefulproperty of the CMAC, namely, local generalization. Theoutput generalization capability of CMAC is controlledmainly by the width of the blocks. If two inputs are farapart in the input space, there will be no overlap in their qelements sets i

48、n A, i.e., no generalization.3.1.4 Weight memory space WEach location of T for a particular adjustable value in theweight memory space with nRcomponents can be expres-sed as w w1; w2; . . .; wnRT; where wkis the connectingweight value of the output associated with the k-th recep-tive-eld and it is i

49、nitialized from zero and is automaticallyadjusted during online operation.3.1.5 Output space YThe output computation of CMAC neural network is thealgebraic sum of the activated weights in the weightlkihfc98765JjBbEeState (3,3)memory, and is expressed asXRy wkbks; mk; rk:k112Layer 4Layer 3Layer 2Laye

50、r 1jgedba4321Gg1ADG23J4BE56H7KC89FILvariable s1Layer 1Layer 2Layer 3Layer 4Then the output of the CMAC neural network can berepresented in a vector formy wTUs; m; r:133.2 Intelligent power controllerBy the universal approximation theorem, an optimalCMAC neural controller using a CMAC neural networkc

51、an be designed to approximate the ideal controller, suchFig. 4Two-dimensional RCMAC with q = 4 and nE= 9123that HYPERLINK #1115HYPERLINK #11Neural Comput & Applic (2009) 18:9310397u unc DwTU D14e_ guuncurc ke:23where D is a minimum approximation error, and w*and Uare the optimal parameter vector of

52、w and U; respectively.Substituting Eq. HYPERLINK #5(HYPERLINK #521) into Eq. HYPERLINK #5(HYPERLINK #523), the error Eq. HYPERLINK #5(HYPERLINK #523) can bere-expressed asMoreover, the optimal CMAC neural controller u*nc can notbe obtained, so that an online estimation CMAC neural_ g TU TA TB eurc k

53、e:24controller is dened asunc wTU15In case of the existence ofe, consider a speciedL2tracking performance HYPERLINK #11HYPERLINK #1123HYPERLINK #1125HYPERLINK #11ZTwhere wand Uare the estimate of the optimal parameter0e2dte20gw 0wT0g1mT0m 0g2T00g3vector w*and U; respectively. Dene the estimation err

54、or as uunc wTUwTU D:16 d2ZT0e2dt25Denew ww and U UU ;then Eq. (HYPERLINK #516HYPERLINK #5)can be rewritten as w w TU U wTU D17 wTU wTU wTU D:whereg1,g2andg3are positive gain, anddis aprescribed attenuation constant. If the system startswith initial conditionse0 0; w 0 0; m 0 0 and0 0; theL2tracking

55、performance in Eq. HYPERLINK #5(HYPERLINK #525) can berewritten ask keIn the following, the linearization technique is employedto transform the nonlinear fuzzy function into a partiallysupe2L20;Ted26linear form so that the expansion of Uin a Taylor serieswhere k ke2Re2dt ande2Re2dt: If d = ?, this i

56、s thecan be obtained HYPERLINK #11HYPERLINK #1115002b132ob13om66772ob13or6677case of minimum error tracking control without distur-bance attenuation HYPERLINK #1123HYPERLINK #11. Therefore, the following theoremcan be stated and proved.66b277-40U.77ob266om77ob266or774bnR564.obnRom75-93jmm64.obnRor75

57、jr hTheorem 1Consider the forward DCDC convertersystem represented by Eq. HYPERLINK #2(HYPERLINK #24). The intelligent power con-troller is designed as Eq. HYPERLINK #3(HYPERLINK #37HYPERLINK #3) in which the adaptive laws ofATm BT h18the CMAC neural controller are designed aswherehisavectorofhigher

58、-orderterms;w_ w_ g1eU27hm mm ; r; A ob1ob2obnRijmmm_ m_ g2eAw28hiomomomand B ob1ob2obnRjr;in which theoobmkandoobrkorare dened asororr_ r_ g3eB 29obkT00obkobk0019whereg1,g2andg3are the learning rates, and robustcontroller is designed asomobkorTk1nom1kobk00k1nor1komnknRknobk00ornknRkn20urcd2 12d2e:3

59、0Substituting Eq. HYPERLINK #5(HYPERLINK #518) into Eq. HYPERLINK #5(HYPERLINK #517), it is obtained that TU TAT BT h TU DThen, the desired robust tracking performance inEq. HYPERLINK #5(HYPERLINK #525) can be achieved for a prescribed attenuationleveld. wTU mTAw TBw e21ProofConsider a Lyapunov func

60、tion in the followingformwhere wTATm mTAw ; wTBT TBw ; and ewThwTU Ddenotesthelumpedapproximationerror.Substituting Eq. HYPERLINK #3(HYPERLINK #38HYPERLINK #3) into Eq. (HYPERLINK #24), yieldsV_o g unc urc:22V e; w ; m ; ; t 12e2g2g1w Tw gm Tm gT:2g22g331Combining Eqs. (HYPERLINK #36) and (HYPERLINK