Fuzzy frequency‐selecting sliding mode controller for LLC resonant converter
2019; Institution of Engineering and Technology; Volume: 2019; Issue: 15 Linguagem: Espanhol
10.1049/joe.2018.9384
ISSN2051-3305
AutoresZhongli Tian, Yu Fang, Na Guo, Xingcheng Zhou, Songyin Cao,
Tópico(s)Magnetic Bearings and Levitation Dynamics
ResumoThe Journal of EngineeringVolume 2019, Issue 15 p. 571-575 Jiangsu Annual Conference on Automation (JACA 2018)Open Access Fuzzy frequency-selecting sliding mode controller for LLC resonant converter Zhongli Tian, Corresponding Author Zhongli Tian tian_zhong_li@163.com Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorYu Fang, Yu Fang Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorNa Guo, Na Guo Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorXingcheng Zhou, Xingcheng Zhou Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorSongyin Cao, Songyin Cao Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this author Zhongli Tian, Corresponding Author Zhongli Tian tian_zhong_li@163.com Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorYu Fang, Yu Fang Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorNa Guo, Na Guo Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorXingcheng Zhou, Xingcheng Zhou Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this authorSongyin Cao, Songyin Cao Department of Automation Engineering, College of Information Engineering Yangzhou University, YangZhou, People's Republic of ChinaSearch for more papers by this author First published: 25 February 2019 https://doi.org/10.1049/joe.2018.9384Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract A fuzzy frequency-selecting sliding mode controller for LLC resonant converter is presented here. Based on the fixed high and low switching frequency of sliding mode controller in the LLC resonant converter, the fuzzy controller is used to generate the corresponding high and low switching frequency according to different power levels. The high or low switching frequency is then selected by the frequency switching signal generated by the sliding mode controller, thus the fuzzy frequency-selecting sliding mode controller is realised. The fuzzy control rules here come from the simulation and artificial summary of the application circuit and load characteristics, and the high and low switching frequencies varied with the load are generated by the fuzzy frequency-selecting sliding mode controller, so as to realise the stable control of the output power of the LLC resonant converter. The fuzzy frequency-selecting sliding mode controller for LLC resonant converter is applied to a 240 W all-digital adaptive dimming power supply prototype, which can effectively reduce the steady-state error of the output power of the LLC resonant converter, and has a consistent low ripple characteristic when the load changes. 1 Introduction LLC resonant converters usually use traditional PID control, which has the advantages of simple control, good stability, and strong applicability [1]. However, the PID controller is sensitive to the system parameters, especially when the load varies in a large range, with the disadvantages of slow dynamic response speed, distortion of output waveform [2].Therefore, a sliding mode controller is proposed to replace the PID control of LLC resonant converter. The sliding mode control mainly includes sliding mode control surface generating circuit, hysteresis comparison circuit, frequency generator, frequency switching circuit, and power switch signal driving circuit [3]. The output voltage of the resonant converter can be used as the negative feedback input signal of the control loop and is compared with the given voltage signal, then the error signal generated is the input signal of the sliding mode controller. For the given sliding mode surface, a frequency switching signal can be generated by the hysteresis comparator, which is used to select or switch two fixed high and low switching frequency pulse control signals. Then, the driving signal generated by the driving circuit controls the opening and closing of the switch in the LLC resonant converter [4]. According to the working principle of the LLC resonant converter, the high-frequency driving signal is used to reduce the output power, and the low-frequency output driving signal is used to increase the output power, thus maintaining the constant output voltage or current [5]. The sliding mode controller solves the problem that PID control is sensitive to the change of system parameters and improves the dynamic response speed of the system. However, the sliding mode controller with fixed switching frequency has some shortcomings. That is, when the load varies within a certain range, the ripple of the output power of the LLC resonant converter will be highly different, which is disadvantageous to some special loads such as LED lighting and corresponding dimming, and may even lead to the shortening of the load life [6]. Therefore, with the wide range of application of the LLC resonant converters, higher request to the fast dynamic response performance and high steady-state accuracy of the LLC resonant converters are put forward [7]. For this purpose, a more practical controller is needed to ensure the system has a faster dynamic response speed and a higher steady-state precision of the output. Here, the proposed fuzzy frequency-selecting sliding mode controller for LLC resonant converter can solve the problem well [8]. 2 Composition and basic principles of the system As shown in Figs. 1 and 2, the fuzzy frequency-selecting sliding mode controller 4 proposed here is composed of sliding mode controller 1, frequency conversion selecting switch 2 and fuzzy frequency-selecting controller 3. The output of the sliding mode controller 1 and the fuzzy frequency-selecting controller 3 is sent to the frequency conversion selecting switch 2. The error e-generated from the comparison of output sampling signal I o with the given signal I ref of the LLC resonant converter and the given signal I ref are sent to the fuzzy frequency-selecting sliding mode controller 4. The output working frequency f s of the fuzzy frequency-selecting sliding mode controller 4 is sent to the pulse frequency modulation (PFM) generator, which generates pulse control signal, and then it is sent to the power switch of LLC resonant converter through the driving circuit [9]. Fig. 1Open in figure viewerPowerPoint Control block diagram of the fuzzy frequency-selecting sliding mode controller Fig. 2Open in figure viewerPowerPoint Schematic diagram of a half-bridge LLC resonant converter based on the fuzzy frequency-selecting sliding mode controller According to the given output signal I ref of LLC resonant converter, the fuzzy frequency-selecting sliding mode controller 4, through the fuzzy frequency-selecting controller 3, can generate high switching frequency signal f max and low switching frequency signal f min. Then, it is sent to the input of frequency conversion selecting switch 2, which choose the corresponding switching frequency by frequency switching signal u sent by the sliding mode controller 1, and send the switching frequency to the PFM generator. Later, PFM generator generates the corresponding pulse control signal, and control the opening and closing of the power switch in LLC resonant converter by the driving circuit [10]. The output sampled signal I o of the LLC resonant DC–DC converter and the given signal I ref are sent to the input of the sliding mode controller 1 in the fuzzy frequency-selecting sliding mode controller 4 by the subtracter for generating the error signal e. The given signal I ref is sent at the same time [11]. To the fuzzy frequency-selecting controller 3, two switching frequency signals are generated by the fuzzy frequency-selecting controller 3, one is a high switching frequency signal f max, and the other is a low switching frequency signal f min for the frequency conversion selection switch 2 to select. The switch 2 selects one of the frequency signals f max and f min as the output operating frequency f s, as the switching frequency [12]. In the fuzzy frequency-selecting sliding mode controller 4, the frequency switching signal u output by the sliding mode controller 1 and the high and low two-way switching frequency signals f max and f min generated by the fuzzy frequency selection controller 3 are sent to the frequency conversion selector switch 2. The high and low switching frequency signals f max and f min are selected by frequency switching signal u, and the logic signals of the frequency switching signal u generated by the sliding mode controller 1,which are high level 1 and low level 0, respectively, the high-level logic signals 1 are used to select the low switching frequency signal f min, the low-level logic signal 0 selects the high switching frequency signal f max, and the frequency conversion selection switch 2 outputs the switching frequency signal f s to the input of the PFM generator to control the PFM generator generating pulse control signals with varying frequency [13]. 3 Designs for controller 3.1 Design of LLC converter sliding mode surface In general, linear combination of system variables is chosen for the sliding mode surface, and the output voltage v O is used as the output control variable. Due to the LED load is sensitive to current, output current Io is selected as the control variable. According to the system large signal model formula [14], the relative order of the system can be obtained by formula (1): (1) It follows that the relative order is 3 of the system. Therefore, the response characteristics of the output voltage or current can be assumed as formula (2). (2) The following formula (3) of output current I o can also be derived from the formula of the large signal model of the system. (3) Under ideal conditions, the invariant condition of sliding mode controls the sliding mode region is S = 0 and . Then, the equation of sliding mode surface can be written into the following form (4): (4) According to formula (4), it can obtain the corresponding sliding mode controller block diagram, as shown in Fig. 3. The sampling output current Io and the output filter capacitor current i c are feedback variables. The output filter capacitor current i c reflects the feedback variables of the primary side current i p of the transformer. Fig. 3Open in figure viewerPowerPoint Sliding mode control block diagram of LLC resonant converter The sliding mode control law of the system is obtained by the existed condition of sliding mode control. . (5) However, in the actual system, it needs to use a hysteresis comparator to guarantee the feasibility of the sliding mode control. Therefore, this control method can be optimised for (6). is the hysteresis comparator width. (6) 3.2 Design steps of fuzzy frequency-selecting controller The design steps are as follows: (a) Taking the given output signal I ref in LLC resonant converter as the input variable of the fuzzy frequency-selecting controller 3, and make the high switching frequency f max and low switching frequency f min as the output variable of the fuzzy frequency-selecting controller 3. (b) Fuzzification of the given input signal I ref by the fuzzy frequency-selecting controller 3, and the fuzzy signal is sent to the input of the fuzzy rule. Then, the fuzzy reasoning is completed, and the output fuzzy value obtained according to the fuzzy control rule. (c) Solving ambiguity the output fuzzy value in the fuzzy frequency-selecting controller 3, and the precise values of two high and low switching frequencies f max and f min are obtained. 4 Analysis of simulation and experiment on the system 4.1 Analysis of simulation The half-bridge LLC resonant converter, as shown in Fig. 2, can be applied to the LED dimming, and the fuzzy frequency-selecting sliding mode controller can be used to realise dimming [15]. The DC input voltage V dc = 430 V, rated output DC power Po = 240 W, rated output DC voltage Vo = 30 V, turns of the primary and secondary sides of the high-frequency transformer are NP and NS, the resonant inductor Lr in the primary side of the transformer is 158 uH, excitation inductance Lm = 700 uH, resonant capacitance Cr = 47 nF, output capacitance Co = 2000 uF, C 1 and C 2 are bus capacitances of the half-bridge, D 1 and D 2 are the commutation diodes of the vice edge, Ro is the equivalent resistance of load, and Io is the output current signal. The error from the comparison with output current Io and the given dimming current I ref will be sent to the fuzzy frequency-selecting sliding mode controller, the output of which will be sent to the PFM generator, which generate pulse control signal PWM1 and PWM2. Then, two driving signals V dr1 and V dr2, which are complementary to each other and whose duty ratio are 50%, are generated through driving circuit, in order to control the opening and closing of the power switches in the LLC resonant converter, so as to realise the regulation of the output current. After fuzzification of the given dimming current I ref, the precise control variables f min and f max can be obtained through ambiguity-resolving after fuzzy reasoning. The basic domain of input I ref and output f min and f max are as follows [16]: I ref = { 1,2,3,4,5,6,7,8}; F min = {55,000, 70,000, 90,000, 110,000, 200,000}; F max = {135,000, 140,000, 180,000, 200,000, 260,000}. The corresponding fuzzy domain of input fuzzy variable I REF, output fuzzy control variables F min and F max are, respectively, as: I REF = { 1,2,3,4,5,6,7,8}; F min = {5.5, 7, 9, 11, 20}; F max = {13.5, 14, 18, 20, 26}. The quantitative factor of the input variable is 1, and the quantitative factor of the output control variable is 1/10,000. The language values of IREF, F min and F max are chosen as: I ref = {darker(DR),dark(D),bright(B),brighter(BR,brightest (BT)}; F min = {minimum (MIN), small(S), middle (MID), big (BIG),maximum (MAX)}; F max = {minimum (MIN), small(S), middle (MID),big (BIG),maximum (MAX)}; The fuzzy control rules table of I REF, F min, and F max are as follows Table 1 : Table 1. Fuzzy control rules table if (I REF) DR D B BR BT then (F min) MAX BIG MID S MIN then (F max) MAX BIG MID S MIN The membership functions of input and output are triangular membership function, and the membership function curves of input and output are shown in Figs. 4-6. Fig. 4Open in figure viewerPowerPoint Membership function curve of IREF Fig. 5Open in figure viewerPowerPoint Membership function curve of Fmin Fig. 6Open in figure viewerPowerPoint Membership function curve of Fmax The corresponding input fuzzy signal IREF can be obtained by membership function curve according to the given dimming current signal I ref. The input fuzzy signal IREF is taken as the input of the fuzzy rule and the output fuzzy control quantities F min and F max can be obtained according to the fuzzy rule when the fuzzy reasoning is completed. Here, the weighted average method is used to deblur the output fuzzy control, thus the precise values of the output control variables f min and f max can be obtained. For example, if the given dimming current signal of the LLC resonant converter is 4.5 A, it can be seen from Fig. 4 that the blurred signal is darker (DR) and dark (D) and the weight is, respectively, 0.5. Then, the fuzzy control signal can be obtained by fuzzy rules. The precise value of maximum operating frequency f max is 230 kHz and minimum operating frequency f min is 155 kHz by the weighted average method, which can be used as the two outputs of the fuzzy frequency-selecting sliding mode controller. Using a sliding mode control strategy with fixed high and low working frequencies of f max = 260 kHz and f min = 55 kHz, the LED modulation simulation, Figs. 7-9, respectively, give the waveform of output current Io corresponding to the different dimming current. Fig. 7Open in figure viewerPowerPoint Output current Io with the fixed high and low working frequency (@Iref = 4 A) Fig. 8Open in figure viewerPowerPoint Output current Io with the fixed high and low working frequency (@Iref = 4.5 A) Fig. 9Open in figure viewerPowerPoint Output current Io with the fixed high and low working frequency (@Iref = 5 A) It can be seen from Fig. 7 that the output current ripple Δi is 0.55 A when the given current signal is 4 A. In Fig. 8, the output current ripple Δi is 0.48 A for a given current signal of 4.5 A. In Fig. 9, the output current ripple Δi is 0.4 A for the given current signal of 0.4 A. Figs. 10-12 are the waveforms of output current Io when using the proposed fuzzy frequency-selecting sliding mode controller here. Fig. 10Open in figure viewerPowerPoint Waveform of the output current Io based on the fuzzy frequency-selecting sliding mode controller (@Iref = 4 A) Fig. 11Open in figure viewerPowerPoint Waveform of the output current Io based on the fuzzy frequency-selecting sliding mode controller (@Iref = 4.5 A) Fig. 12Open in figure viewerPowerPoint Waveform of the output current Io based on the fuzzy frequency-selecting sliding mode controller (@Iref = 5 A) In Fig. 10, the output current ripple ΔI is 0.018 A when the given current signal is 4 A and the high and low working frequencies are f max = 260 kHz and f min = 200 kHz at this time. In Fig. 11, the output current ripple ΔI is 0.006 A when the given current signal is 4.5 A and the high and low working frequencies are f max = 230 kHz and f min = 155 kHz at this time. In Fig. 12, the output current ripple ΔI is 0.009 A when the given current signal is 5 A and the high and low working frequencies are f max = 200 kHz and f min = 110 kHz at this time. It can be seen that the output current by the sliding mode control strategy with fixed switching frequency has a large tracking error, and the output current ripple is very large given the same dimming current. The output current of low ripple and with high tracking accuracy can be obtained by using the fuzzy frequency-selecting sliding mode control strategy proposed here. 4.2 Experimental results on the system A fuzzy frequency-selecting sliding mode controller for LLC resonant converter is studied here and is applied to a 240 W all-digital adaptive dimming power supply prototype. The prototype can be divided into three parts: the active power factor correction part of the former PFC, the resonant DC converter part of the latter LLC and the DSP controller. The DSP control board employs the TMS320F28035 to serve as the main control chip, to realise the digital control of the former PFC and the latter LLC parts. This experiment mainly studies the prototype efficiency. A total of nine test power points were selected for analysis and test in this experiment, and the test data shown in Table 2. V in is the input voltage, Io is the output current, P in is the input power, Po is the output power, and η is the overall efficiency of the prototype. At the same time, in order to verify the feasibility of hardware circuit design of LLC resonant DC converter. Fig. 13 shows the current waveform i Lr of the LLC resonant cavity. Table 2. Experimental data table V in, V Io, A P in, W P o, W η, % 110 4.01 95.19 82.8 86.98 110 5.525 178.48 157.6 88.30 110 7.949 238.84 216.6 90.69 185 3.995 87.89 77.45 88.12 185 5.548 174.12 156.99 90.16 185 7.947 256.68 236.4 92.10 220 3.884 88.11 78.41 88.99 220 5.53 170.68 156.99 91.98 220 7.954 260.4 240.97 92.54 Fig. 13Open in figure viewerPowerPoint LLC Resonant cavity current waveform According to the test data from Table 2, it can be seen that the efficiency of the prototype is lower at light load, and then it reaches the maximum at full load with the power slowly increases. From Fig. 12, we can see the current waveform i Lr of the LLC resonant converter cavity is smoothly at full load output, which shows the circuit parameter design is correct. The experiment shows that, under the full load conditions, the output power of the prototype is maximum, and the stability of hardware circuit achieved. 5 Conclusion A fuzzy frequency-selecting sliding mode controller for LLC resonant converter is studied here, which can not only solve the problem that the traditional PID controller is sensitive to system parameters but also realise stable and accurate tracking. Compared with the sliding mode control based on fixed high- and low-frequency switching, the proposed fuzzy frequency-selecting sliding mode controller can effectively reduce the steady-state error of the output power of the LLC resonant converter and has a consistent low ripple characteristic when the load changes, which can ensure the life of LED lights when used in LED dimming. 6 Acknowledgments This paper was supported by the National Natural Science Foundation of China (No. 61873346), supported by the Industrial Foresight and Universal Key Technology Research and Development Project (Universal Key Technology Project) of Yangzhou Science and Technology project under Grant (No.YZ2017013), and Supported by the Science and Technology Cooperation Fund of Yangzhou City Hall project under Grant (No. YZ2018136), and Supported by the college students' innovation and entrepreneurship training plan of Jiangsu Province. 7 References 1Lee I., Moon G.: 'Analysis and design of a three-level LLC series resonant converter for high and wide-input-voltage applications', IEEE Trans. Power Electron., 2012, 27, (6), pp. 32 – 34 2Hu H., Wang W., Sun W.: 'Optimal efficiency design of LLC resonant converters', Proc. CSEE, 2013, 33, (18), pp. 64 – 68 3Edington M.C., Berle W.E., Dunford W.G.: 'Practical design considerations for a LLC multi-resonant DC-DC converter battery charging applications'. Proc. 27th Annu. IEEE Appl. Power Electron. Conf. Expo, Orlando, USA, 2012, pp. 24 – 28 4Xiaofeng S., Yanfeng S., Yun-e Z.: 'A boost integrated LLC resonant converter for a wide input voltage range', Proc. CSEE, 2015, 35, (15), pp. 1 – 6 5Yeon C.O., Kim D.K., Lee J.B. et al.: 'Digital implementation of optimal SR ON-time control and asymmetric duty control in LLC resonant converter'. Power Electronics and ECCE Asia, Seoul, South Korea, 6–8 March 2015, pp. 23 – 25 6Kowstubha P., Krishnaveni K., Reddy K.R.: 'Review on different control strategies of LLC series resonant converters'. Int. Conf. Advances in Electrical Engineering, Vellore, India, 2014, pp. 1 – 4 7Haibo D., Xinghuo Y., Michael C.: 'Chattering-free discrete-time sliding mode control', Automatica, 2016, 68, (6), pp. 68 – 71 8Shyam K., Jaime A., Moreno A.C. et al.: 'Continuous terminal sliding-mode controller', Automatica, 2016, 2, (1), pp. 69 – 71 9Xiaowei M., Jinhui Z., Jing W.: 'Design of disturbance observer based sliding mode control for fuzzy systems', IFAC Papers Online, 2017, 50, (1), pp. 124 – 132 10Liping G., John Y., Hung R.M.: ' comparative evaluation of sliding mode fuzzy controller and PID controller for a boost converter', Electr. Power Syst. Res., 2010, 81, (1), pp. 99 – 106 11Mithun S., Leangsan S., Gangbing S. et al.: 'A new optimal sliding mode controller design using scalar sign function', ISA Trans., 2014, 53, (2), pp. 267 – 279 12Nabanita A., Chitralekha M.: ' integral back stepping sliding mode control for under actuated systems: swing-up and stabilization of the cart–Pendulum system', ISA Trans., 2013, 52, (6), pp. 870 – 880 13Jianfeng L., Qing P., Zhiwu H. et al.: 'Enhanced sliding mode control and online estimation of optimal slip ratio for railway vehicle braking systems', Int. J. Prec. Eng. Manuf., 2018, 19, (5), pp. 655 – 664 14Qinwei L.: 'Study on sliding mode control strategy of LLC resonant converter' ZhejiangUnversity, 2014 15Yonghui L., Tinggang J., Yugang N. et al.: 'Design of sliding mode control for a class of uncertain switched systems', Int. J. Syst. Sci., 2015, 46, (6), pp. 993 – 1002 16Shabnam P., Mohammadali B.: 'A new fractional order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances', ISA Trans., 2016, 63, pp. 39 – 48 Citing Literature Volume2019, Issue15March 2019Pages 571-575 FiguresReferencesRelatedInformation
Referência(s)