Sliding Mode Control for Half-Wave Zero Current Switching Quasi-Resonant Buck Converter

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1 Sliding Mode Contol fo Half-Wave Zeo Cuent Switching Quasi-Resonant Buck Convete M. Ahmed, Student membe, IEEE, M. Kuisma, P. Silventoinen Abstact This pape focuses on the pactical implementation of sliding mode contol (SMC) in a half-wave zeo cuent switching quasi-esonant Buck convete. SMC can manipulate efficiently the nonlinea phenomena that appea in switch mode powe supplies, futhemoe SMC is less affected by distubances compaed to othe contol techniques, and it is not opeating at a constant switching fequency. Since half wave zeo cuent switching quasi-esonant Buck convete is not opeating at a constant switching fequency and it is sensitive to dynamic vaiation, SMC is selected in this pape as a contol technique. An explanation of the implementation of SMC, and selecting its paametes is given. A detailed mathematical analysis is pefomed in ode to select the appopiate values of the tank components elements. The tank inducto value is assumed to be small and constant, and a ange of tank capacito values is obtained. The pototype of an analog sliding mode contol fo the convete is constucted. In ode to study the effect of SMC on the convete behavio, the system is tested in the steady state and unde diffeent load value conditions. The obtained gaphs show that the pefomance of SMC is good, even unde the wost load conditions, i.e. no load and full load. Index Tems half-wave zeo cuent switching, quasiesonant Buck convete, sliding mode contol, tank inducto value, tank capacito value. S I. INTRODUCTION LIDING mode contol (SMC) fo switch mode powe supplies has been studied in liteatue. Many papes and eseaches have shown that SMC is an effective contol tool fo switch mode powe supply [1], [2], and [3]. Unfotunately, most of these eseaches depended on theoies o simulation esults that have no pactical implementation. Pevious eseaches have shown that SMC has good immunity against M. Ahmed, Student membe, IEEE., Depatment of Electical Engineeing, Lappeenanta Univesity of Technology, P.O. Box 20, Lappeenanta, Finland. Phone: Fax: mohammad.ahmed@lut.fi. M. Kuisma, Depatment of Electical Engineeing, Lappeenanta Univesity of Technology, P.O. Box 20, Lappeenanta, Finland, Phone: Fax: Mikko.Kuisma@lut.fi. P. Silventoinen, Depatment of Electical Engineeing, Lappeenanta Univesity of Technology, P.O. Box 20, Lappeenanta, Finland. Phone: Fax: Petti.Silventoinen@lut.fi. distubances and component vaiations [2], [4], [5]. In this pape, an analog SMC cicuit is constucted using opeational amplifies in such a way that the signals geneated at each stage ae shown in the contol cicuit. Following a detailed analysis of the selection of the tank component elements is given. A pototype model of the half-wave zeo cuent switching quasi-esonant Buck convete with its contol cicuit is constucted. The elements of the main cicuit of the convete ae shown in TABLE 1.To pove that the cicuit functions coectly the output voltage wavefom, main wavefom, tank inducto wavefom, and tank capacito wavefom ae studied in the steady state, unde no load and unde full load conditions. II. SLIDING MODE CONTROL AND THE CONVERTER CIRCUIT Many eseaches have studied, analyzed, and designed the SMC to DC/DC convetes [1], [2], [3], [4], and [5]. These eseaches concluded and showed geat potential fo the use of SMC in switch mode powe supplies because it is a non-linea contol and can manipulate the non-linea phenomena that appea in switch mode powe supplies, it has a good immunity against distubances, and is not opeating at a constant switching fequency. Since half-wave zeo cuent switching quasi-esonant Buck convete is not opeating at a constant switching fequency and it is sensitive to dynamic vaiation [6], [7], [8], and [9], SMC is selected as a contol technique. The contol cicuit is epesented by two contol loops: an inne main contol loop (epesented in this pape by a hysteesis contol) and an oute voltage contol loop that is epesented by popotional plus integal contol (PI); the combined loops compose the SMC that is esponsible fo the zeo cuent switching. Fig.1 shows a simple block diagam of the implementation of SMC in switch mode powe supplies. The hysteesis paametes can be selected fom the peak-to-peak main. It is difficult to find a standad pocedue to detemine the integal gain of the linea pat. The eason fo this difficulty is that the SMC is a nonlinea contol and can not be linaized. It is not possible to choose the linea pat paametes based on the non-linea pat. Choosing a low integal gain educes the oveshoot but the steady state eo inceases. It is left fo the designe to choose the paametes depending on the application.

V ef -V o Linea Voltage Contol I* -I Sliding mode Cuent Contol V in u DC/DC Convete Fig. 1 A simple block diagam shows the implementation of SMC in switch mode powe supply.

2 V ef -V o Linea Voltage Contol I* -I Sliding mode Cuent Contol V in u DC/DC Convete Fig. 1 A simple block diagam shows the implementation of SMC in switch mode powe supply. The inne loop is the main loop, while the oute loop is the PI contol. The combined loop is the SMC. V o geneates signal 1. Op-amp3 is used to detect the inducto cuent with a shunt esisto R 1, geneating signal 2. In the next stage, signals 1 and 2 ae compaed using a compaato (LM111), in which Hysteesis is used to contol the switching fequency. The output level of the LM111 signal should be tanslated into the voltage diffeence between the gate-souce of the switching device IRF530. A high-side MOSFET/IGBT dive IR2117 is used fo this pupose. The cicuit was constucted in the Laboatoy of Applied Electonic at Lappeenanta Univesity of Technology. Fig.3 shows the constucted pototype fo a half-wave zeo cuent switching quasi-esonant Buck convete with SMC used in the Laboatoy whee the tests wee pefomed. II. CIRCUIT DESIGN A simplified cicuit diagam of the pototype cicuit fo a half-wave zeo cuent switching quasi-esonant Buck convete contolled by SMC is shown in Fig.2. Resonant convetes contain esonant L, C netwoks whee its voltage and cuent wavefoms vay sinusoidally duing one o moe subintevals of each switching peiod. The main inteest in esonant opeation of the convetes is the minimization of switching losses. Half-wave zeo cuent switching quasiesonant Buck convete, shown in Fig. 2, is a esonant convete, whee the esonant tank capacito (C ) is placed in paallel with the main Buck convete diode D 2, while esonant tank inducto (L ) is placed in seies with the active switch. Diode D 1 is in seies with active switch. The magnitude of the tank and hence also the DC load cuent can be contolled by vaiation of the switching fequency F s [10]. Fig.3 The pototype cicuit of the half-wave zeo cuent switching quasiesonant Buck convete with SMC. The cicuit was constucted and tested in the Laboatoy of Applied Electonics at Lappeenanta Univesity of Technology (Finland). TABLE 1 shows the main Buck convete paametes used in the pototype model. TABLE 1 CONVERTER MAIN CIRCUIT PARAMETERS Paamete name Symbol Value Input voltage V in 24 volts Output voltage V o 12 volts Capacito C 220 µf Inducto L 69 µh Load esistance R L 13 Ω Nominal switching fequency F s 100 khz Fig.2. Half-wave zeo cuent switching quasi-esonant Buck convete with a sliding mode contol. Combination of PI and cuent hysteesis contol cicuits composes the SMC. The opeation of the pototype in Fig.2 can be descibed as follows: The output voltage is subtacted fom the efeence voltage using op-amp1. The voltage diffeence signal is integated using op-amp2. The output of this amplifie III. CALCULATING AND SELECTING THE TANK COMPONENT ELEMENTS VALUES The esonant tank elements ae selected by assuming a constant and small L value and obtaining C. Thee ae two easons fo selecting small L value. Fist, a high L value stoes a high amount of magnetic enegy and since it is connected in seies with switch, it may damage the switch MOSFET. Second, the tank esonant fequency should be geate than the nominal switching fequency.

Fo F s, (1) 1 whee Fo = denotes the tank esonant fequency. 2π LC If F o < F s, the tank elements espond moe stongly to the hamonics of the input voltage than to its fundamental value.

3 Fo F s, (1) 1 whee Fo = denotes the tank esonant fequency. 2π LC If F o < F s, the tank elements espond moe stongly to the hamonics of the input voltage than to its fundamental value. In ode to obtain the ange of C values, two conditions have to be fulfilled. A. Condition 1 The tank esonant fequency should be geate than the nominal switching fequency, as given in equation (1). Using equation (1) and fo F s = 100 khz, L = 3µH we get C 844nF. (2) B. Condition 2 the DC convesion atio (µ) is less than one fo Buck convete V µ = o 1. (3) V in To guaantee that the tank each zeo, the condition in equation (4) should be satisfied [1] V in I, (4) L Z o whee L Z o = denotes the tank chaacteistic impedance. C By substitute equation Z 0 into equation (4) and fo L = 3µH, and R L = 13 Ω, it can be obtained that TABLE 2 HALF -WAVE ZERO CURRENT SWITCHING QUASI-RESONANT BUCK CONVERTER RESPONSE WITH CONSTANT L R VALUE AND TWO DIFFERENT C R VALUES Constant and small L Small C value High C value 1 Opeate at high switching Opeate at low switching fequency fequency 2 Slow tansient esponse without oveshoot Fast tansient esponse with oveshoot 3 Low output voltage ipple Low output voltage ipple 4 Moe tank wavefom distotions Less tank wavefom distotions 5 Lowe peak-to-peak tank 6 Lowe peak-to peak main Highe peak-to-peak tank Highe peak-to peak main IV. EXPERIMENTAL RESULTS OF THE PROTOTYPE To pove that the constucted cicuit functions popely and that SMC can be implemented with the pototype, as well as to show that SMC is esistant to load vaiations, the cicuit was tested in steady state and unde load vaiations (no load and full load). The output voltage, main, tank capacito voltage and tank wavefoms wee tested, and the coesponding gaphs ae shown in Figs. 4 to 9. The main convete paametes wee given in TABLE 1, assuming that C = 400nF, and L = 3µH. A. Steady state egion Fig. 4 shows the output voltage wavefom (ch1, uppe wavefom) has a 0.1-volt ipple and the main wavefom (ch2, lowe wavefom) has 4.1A peak-to-peak value in steady state. The gaph shows that in steady state the convete has a good esponse when contolled by SMC. C 4.5nF. (5) Equation (4) is the second condition fo selecting C. Fom equation (2) and (5) the ange of C is 4.5nF C 844nF. (6) TABLE 2 shows the effect of diffeent C on the convete s esponse, povided that these values ae within the tank capacito ange obtained fom equation (6). Designes of switch mode powe supplies pefe to wok at high switching fequencies. TABLE 2 shows it is possible fo a half-wave zeo cuent switching quasi-esonant Buck convete to wok at high switching fequencies by selecting small C values, but the two disadvantages ecoded ae the slow tansient esponse and moe tank wavefom distotions. The value of C was selected in this pape to be 400nF and L is assumed to be 3µH in this pape. All the esults obtained fom the pototype model ae based on L = 3µH, C = 400nF, and TABLE 1. Fig. 4 The output voltage (Ch1, uppe wavefom) and main (Ch2, lowe wavefom) of the half-wave zeo cuent switching quasi-esonant Buck convete contolled by SMC in steady state. Fig. 5 shows in steady state the tank capacito voltage wavefom (ch1, uppe wavefom) with 57volt and the peak-topeak tank wavefom (ch2, lowe wavefom)

that is 5.16A with negative evese ecovey. It can be seen in Fig.5 that zeo cuent switching occus. The F s is 32.46 khz, (ch2 Feq).

7 shows the tank capacito voltage wavefom equal 44 volts (Ch1 PK-PK, uppe wavefom) and the tank inducto cuent wavefom with a peak-to-peak value equal 3.

5 The tank capacito voltage wavefom (Ch1, uppe wavefom) and tank wavefom (ch2, lowe wavefom) of the half-wave zeo cuent switching quasi-esonant Buck contolled by SMC in steady state.

4 that is 5.16A with negative evese ecovey. It can be seen in Fig.5 that zeo cuent switching occus. The F s is khz, (ch2 Feq). Reducing the tank capacito value can incease the fequency, but moe distotion occus in the signals. Fig. 7 shows the tank capacito voltage wavefom equal 44 volts (Ch1 PK-PK, uppe wavefom) and the tank inducto cuent wavefom with a peak-to-peak value equal 3.56A (Ch2 PK-PK, lowe wavefom) unde no load conditions. Fig.5 The tank capacito voltage wavefom (Ch1, uppe wavefom) and tank wavefom (ch2, lowe wavefom) of the half-wave zeo cuent switching quasi-esonant Buck contolled by SMC in steady state. (Ch2 Feq) shows the fequency of the convete B. Load vaiation To study the effect of SMC on the behavio of the convete unde load vaiations, two tests wee pefomed on the convete with diffeent load values, which ae consideed to be the wost cases. Fist case is when the convete is opeating unde no load (2kΩ). Fig. 6 shows the output voltage and main tank inducto cuent wavefoms unde no load condition. The mean output voltage is 12.1volts (Ch1 Mean, uppe wavefom). The peakto-peak main is 3.68A (Ch2 PK-PK, lowe wavefom) and the fequency at which the convete opeates unde no load is khz (Ch2 Feq). Fig. 7 The tank capacito voltage wavefom with 44volt (Ch1, uppe wavefom) and tank wavefom = 3.56A (Ch2 peak-to-peak, lowe wavefom). The half-wave zeo cuent switching quasi-esonant Buck convete is unde no-load conditions. The convete in this case is opeating in discontinues conduction mode (DCM), and the SMC is functioning in a way that it keeps the convete stable with no load condition that is consideed to be one of wost load vaiation cases. Second case is when the load changes fom its nominal value to full load (the full load value is 1Ω). Fig. 8 shows the output voltage wavefom (uppe wavefom) and main tank inducto wavefom (lowe wavefom). The mean output voltage is 12.3volts (Ch1 Mean) and a ipple voltage is equal to 3.6volts (Ch1 PK-PK). The peak-to-peak main inducto cuent is 3.12A (Ch2 PK-PK), while the switching fequency of the convete unde full load is khz (Ch2 Feq). Fig. 6 The output voltage (Ch1, uppe wavefom) and main (Ch2, lowe wavefom) of the half-wave zeo cuent switching quasi-esonant Buck convete contolled by SMC unde no-load conditions. The switching fequency is khz, and SMC keeps the convete stable. Fig. 8 The output voltage wavefom (uppe wavefom) and main inducto cuent wavefom (lowe wavefom) of the half-wave zeo cuent switching quasi-esonant Buck convete contolled by SMC unde full-load condition. The convete is stable but high output voltage ipple occus.

Fig.9 shows the tank capacito voltage wavefom and tank wavefom unde full load condition. The peak tank capacito voltage is 58volts (Ch1, uppe wavefom), while the peak-to peak tank wavefom is 8.

5 Fig.9 shows the tank capacito voltage wavefom and tank wavefom unde full load condition. The peak tank capacito voltage is 58volts (Ch1, uppe wavefom), while the peak-to peak tank wavefom is 8.9 A (Ch2 PK-PK, lowe wavefom). It can be said fom Fig. 8 and Fig. 9 that although the convete is woking unde full load, the convete is still stable and SMC has an efficient influence against distubances the signals ae geneated by the opeational amplifies at each stage. The contolle was designed using analog opeational amplifies. The values of the main convete paametes wee given and a mathematical analysis pefomed to select the tank inducto and tank capacito values, whee zeo cuent switching occus. To pove that the pototype model is effective and that SMC can be implemented in eal applications of a half-wave zeo cuent switching quasi-esonant Buck convete, the cicuit was tested in steady state and unde load vaiations (no load and full load). Ou analysis demonstated that SMC gives acceptable esults, not only fom theoetical point of view but also in pactical applications, and that SMC is an effective contol tool fo keeping the convete stable even in the wost cases (no load and full load). Fig. 9 The tank capacito voltage wavefom (Ch1, uppe wavefom) and tank wavefom (Ch2, lowe wavefom) of the half-wave zeo cuent switching quasi-esonant Buck convete contolled by SMC unde full-load condition. III. CONCLUSIONS Sliding mode contol (SMC) was implemented in a halfwave zeo cuent switching quasi-esonant Buck convete. The eason behind the selection of SMC to this kind of convete was that: fist, many eseaches studied theoetically the implementation of SMC to powe supply and poved that it is an efficient contol technique to switch mode powe supply. Second, SMC is not opeating at a constant switching fequency and esonant convetes have a highly nonlinea and time-vaying natue. Any change in opeating conditions leads to significant changes in system dynamical model so that desied pefomance and even stability can be lost. Due to the easons mentioned the pape linked the theoetical eseaches to a eal pototype model. SMC was implemented by dual contol loops; an inne main loop epesented by hysteesis contol (non linea pat) and an oute voltage loop epesented by PI contol (linea pat). A pototype of the contolle with the convete was constucted and a detailed analysis pefomed to ascetain how REFERENCES [1] N. Vazquez, C. Henandez, J. Alvaez, J Aau, Sliding mode contol fo DC/DC convetes: a new sliding suface Industial Electonics, ISIE ' IEEE Intenational Symposium on, Volume: 1, June9-11, 2003 Pages: [2] V. Utkin, J. Guldne, and J. Shi, Sliding Mode Contol in Electomechanical Systems, ISBN (cased), Taylo & Fancis [3] K. Young, V. Utkin, U. Ozgune, Contol Systems Technology, IEEE Tansactions on,volume: 7, Issue: 3, May 1999 Pages: [4] M. Ahmed, M. Kuisma, K. Tolsa, P. Silventoinen, Implementing Sliding Mode Contol fo Buck Convete, Powe Electonic specialist confeence (PESC) Poc. Mexico June, 2003, pp , Vol. 2. [5] M. Ahmed, M. Kuisma, P. Silventoinen, Implementing Simple Pocedue fo Contolling Switch Mode Powe Supply Using Sliding Mode Contol as a Contol Technique, XIII-th Intenational Symposium on Electical Appaatus and technologies (Siela). May 2003, pp 9-14, Vol. 1 [6] C. Chakaboty, S. Mukhopadhyay, A novel compound type esonant ectifie topology, The Fist IEEE Intenational Wokshop on Electonic Design, Test and Applications, Jan Pages: [7] A. Fosyth, G. Wa., V. Mollov, Extended fundamental fequency analysis of the LCC esonant convete, Powe Electonics, IEEE Tansactions on, Volume: 18, Issue: 6, Nov Pages: [8] J. Laza, R. Matinelli, Steady-state analysis of the LLC seies esonant convete, Applied Powe Electonics Confeence and Exposition, APEC Sixteenth Annual IEEE, Volume: 2, 4-8 Mach 2001 Pages: vol.2 [9] E. Lyshevski, Resonant convetes: nonlinea analysis and contol Industial Electonics, IEEE Tansactions on, Volume: 47, Issue: 4, Aug Pages: [10] R. Eickson Fundamentals of Powe Electonics, ISBN , Chapman & Hall [11] H. Bevani, Y. Mitani; K. Tsuji; Robust contol design fo a ZCS convete ECON 02, Industial Electonics Society, IEEE th Annual Confeence, Volume: 1, 5-8 Nov Pages: vol.1.

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