사각형입니다.

https://doi.org/10.6113/JPE.2018.18.3.766

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718



Modeling, Dynamic Analysis and Control Design of Full-Bridge LLC Resonant Converters with Sliding-Mode and PI Control Scheme


Kai Zheng, Guodong Zhang*, Dongfang Zhou*, Jianbing Li*, and Shaofeng Yin*


†,*Zhengzhou Information Science and Technology Institute, Zhengzhou, China



Abstract

In this paper, a sliding mode and proportional plus integral (SM-PI) control combined with self-sustained phase shift modulation (SSPSM) for LLC resonant converters is presented. The proposed control scheme improves the transient response while preserving good steady-state performance. An averaged large signal model of an LLC converter with the ZVS modulation technique is developed for the SM control design. The sliding surface is obtained based on the input-output linearization concept. A system identification method is adopted to obtain the transform function of the LLC resonant converter, which is used to design the PI control. In order to reduce the inherent chattering problem in the steady state, the combined SM-PI control strategy is derived with fuzzy control, where the SM control is responsive during the transient state while the PI control prevails in the steady state. The combination of SSPSM and the SM-PI control provides ZVS operation, robustness and a fast transient response against step load variations. Simulation and experimental results validate the theoretical analysis and the attractive features of the proposed scheme.


Key words: LLC resonant converter, Phase shift modulation, Proportional plus integral control, Sliding mode control, Transient response, Zero voltage switching


Manuscript received Jun. 5, 2017; accepted Jan. 6, 2018

Recommended for publication by Associate Editor Hao Ma.

Corresponding Author: 401221515@qq.com Tel: +86-186-2552-0283, Zhengzhou Information Sci. and Tech. Inst.

*Zhengzhou Information Science and Technology Institute, China



Ⅰ. INTRODUCTION

LLC resonant converters have been attracting more and more attention due to their inherent merits, including high efficiency, high power density, soft switching, and low EMI [1]-[4]. This topology has been extensively employed in industrial applications, such as renewable energy, electric vehicles, and the microwave transmitters of communication and radar systems. In some applications, the power converter encounters large signal disturbances including step load changes, large input-voltage changes, and large changes of the circuit parameters. For example, in microwave transmitter applications, the power converter load can change suddenly and repeatedly with the pulse modulation of the microwave transmitter. Considering these large signal disturbances, power converters should have a good transient response [5]-[8]. Although large signal disturbances exists in several applications, this paper focuses on the power converters used in pulse microwave transmitters.

Nowadays, proportional plus integral (PI) control is being widely applied to power converters, since they can realize local stability and good steady-state accuracy around the steady working point. However, PI control is not very effective in the presence of large signal variations [8]. Therefore, the nonlinear control approaches have drawn a lot of attention. The benefits of these approaches include improvements of the transient response, robustness, and stable behavior against parameter uncertainties. In the case of resonant converters, different nonlinear control methods have been reported such as fuzzy control [9], model predictive control [10], optimal control [11] and sliding mode (SM) control [12]-[15].

Sliding mode control is a special nonlinear control method with several advantages including a wide stability range, good dynamic response and strong robustness. There are several references on the SM control used in DC-DC resonant power converters [16]-[20]. In [16], SM control with strong robustness is used in LCC resonant power converters. In [17], SM control is used in series resonant power converters, where the transient response is insensitive to load variations. In [18], SM control is used in CLL-T resonant power converters with discrete self-sustained oscillating modulation. In this case, input-output linearization control is adopted to design the sliding surface. Experimental results show that the proposed controller can provide robustness and a good transient response against load changes. In [19], [20], SM control is used in LLC resonant power converters with discrete pulse frequency modulation, which can significantly improve the system robustness and dynamic performance.

However, in these studies, the inherent chattering phenomenon of the SM control is not taken into consideration, which leads to a large output voltage ripple. In order to solve this chattering problem, some methods have been proposed, such as the boundary layer method, the equivalent control- based method, the observer-based method and the intelligent control method [8]. In addition, a combination of the sliding mode control and the proportional plus integral control (SM-PI) can also reduce the chattering phenomenon by using the SM control in the transient state and the PI control in the steady state [21], [22].

The major contribution of this paper is the design and development of a novel SM-PI control method, which depends on the application requirements of the LLC power converters used in microwave transmitters. A full-bridge LLC converter with the SM-PI control and self-sustained phase shift modulation (SSPSM) is demonstrated based on a DSP. Note that the zero voltage switching (ZVS) operation can be guaranteed by adopting SSPSM [23]-[25]. The dynamic model of the proposed LLC converter is built with the averaged large-signal modeling method. Then, the SM-PI control is proposed based on the dynamic model, and the fuzzy control is introduced to implement a smooth transition between the SM control and the PI control. The SM-PI control scheme can realize a good transient response and strong robustness from the SM control, and good stability can be obtained from the PI control.

The rest of this paper is organized as follows. The operating principle is discussed in Section II. After that, a large signal model of the LLC resonant converter is presented in Section III. Then, the SM-PI controller is designed in Section IV. Simulation and experimental results are given in Section V. Finally, some concluding remarks are provided in Section VI.



Ⅱ. DESCRIPTION OF THE PROPOSED FULL-BRIDGE LLC CONVERTER

Fig. 1 shows a schematic of the proposed full-bridge LLC converter with a voltage multiplier rectifier. The switch pairs Q1, Q2, and Q3, Q4 form the full-bridge inverter. The resonant inductor Lr, the transformer magnetic inductor Lm and the resonant capacitor Cr form the LLC resonant tank. The diodes D5, D6 and the capacitors C5, C6 form the symmetrical multiplier rectifier. The SSPSM and SM-PI controls are adopted to implement the feedback control based on a DSP.


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원본 그림의 이름: image1.emf
원본 그림의 크기: 가로 461pixel, 세로 230pixel

Fig. 1. Schematic of the proposed full-bridge LLC converter.


SSPSM is a special modulation method for resonant converters, which was inspired by the timing signal from the resonant current [23]-[25]. The modulation system is insensitive to parameter uncertainties, and the gate pulses of the switches can be changed adaptively according to the operating condition. When compared to the conventional frequency modulation (FM) control, the SSPSM has a much smaller frequency variation range, which makes it easy to optimize the magnetic components and to realize miniaturization. When compared to the conventional phase shift modulation (PSM) control, the SSPSM can realize a higher efficiency.

Fig. 2 shows the operating principle of the proposed full- bridge LLC converter with SSPSM. γa is the phase angle between the reverse resonant current –iLr and the drain-source voltage vao of Q2, and γb is the phase angle between the resonant current iLr and the drain-source voltage vbo of Q4. The sawtooth wave vst is the modulation wave, whose amplitude Vp should be almost constant. vca and vcb are the two modulation lines. vca is the upper modulation line, and vcb is the lower modulation line, vcavcb. If the gradient k of vst is assumed to be constant, vca and vcb can be described by the following functions, vca =a, vcb =b. Usually, vca is kept constant, and vcb is used as a control variable to regulate the converter. If vca<Vp, the resonant current iLr lags the inverter output voltage vab, and ZVS can be implemented, which results in increased efficiency and improved reliability.


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원본 그림의 이름: image4.emf
원본 그림의 크기: 가로 439pixel, 세로 565pixel

Fig. 2. Operating principle of the proposed full-bridge LLC converter with SSPSM.


In general, the control angle γa is a continuous variable. In order to apply the SM control, a discrete SSPSM is proposed. In the discrete SSPSM, the control angle γb is changed between two fixed values (γb-max and γb-min). Then, the proper control angle is determined by a new control variable uSM. Then, the control angle γb is defined as:

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Ⅲ. DYNAMIC MODELING OF THE LLC CONVERTER

The averaged large-signal modeling method is adopted to build a dynamic model. The detailed modeling method can be found in [26], [27]. Assuming ideal circuit components, the converter behavior can be represented by the following equations:

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원본 그림의 크기: 가로 323pixel, 세로 157pixel        (4)

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원본 그림의 크기: 가로 754pixel, 세로 171pixel           (5)

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원본 그림의 이름: CLP00001ce00005.bmp
원본 그림의 크기: 가로 851pixel, 세로 160pixel       (6)

where iLr, iLm and vCr are the resonant variables (resonant current, magnetizing current and resonant capacitor voltage), vo is the output voltage, n is the transformer turns ratio, and Co represents the same value as the filter capacitors C5 and C6.

The resonant variables iLr , iLm and vCr can be approximated by the fundamental harmonics as:

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원본 그림의 크기: 가로 389pixel, 세로 91pixel     (7)

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원본 그림의 크기: 가로 608pixel, 세로 94pixel      (8)

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원본 그림의 이름: CLP00001ce00008.bmp
원본 그림의 크기: 가로 629pixel, 세로 92pixel      (9)

The nonlinear terms vab, sgn(iLriLm) and abs(iLriLm) in (3)-(6), can be approximated with the fundamental components or the DC components [28], [29].

The inverter output voltage vab is also the input voltage of the LLC resonant tank. The frequency of vab is equal to the frequency of the LLC resonant variables. If vab is expanded to a Fourier series, only the fundamental component is the valuable excitation, and the other harmonics will be weakened by the resonant circuit.

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The frequency of sgn(iLriLm)nvo/2 is equal to the resonant frequency, which can be approximately represented by the fundamental component. The fundamental component of sgn(iLriLm) can be described as:

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where 그림입니다.
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원본 그림의 이름: CLP00001ce0000c.bmp
원본 그림의 크기: 가로 307pixel, 세로 79pixel.

Only the DC component of abs(iLriLm) is the valuable excitation. The DC component of abs(iLriLm) can be described as:

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원본 그림의 크기: 가로 1362pixel, 세로 299pixel       (12)

By substituting (7)-(12) into equations (3)-(6), based on the harmonic balance principle, the averaged large-signal model can be derived as:

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원본 그림의 크기: 가로 490pixel, 세로 182pixel           (14)

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원본 그림의 크기: 가로 486pixel, 세로 174pixel           (16)

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원본 그림의 이름: CLP00001ce00012.bmp
원본 그림의 크기: 가로 648pixel, 세로 191pixel     (17)

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원본 그림의 이름: CLP00001ce00013.bmp
원본 그림의 크기: 가로 952pixel, 세로 210pixel   (18)

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원본 그림의 이름: CLP00001ce00015.bmp
원본 그림의 크기: 가로 1418pixel, 세로 194pixel     (19)

where the upper bar symbol denotes the averaged values.



Ⅳ. SM-PI CONTROL DESIGN


A. SM Control Design

Firstly, the relative degree of the controlled variable should be determined. The relative degree is defined as the smallest derivative order of the output state variable with regard to time until the control variable appears explicitly. According to the control-oriented large-signal model, it can be shown that the relative degree is two. This is due to the fact that:

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원본 그림의 크기: 가로 956pixel, 세로 218pixel   (20)

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원본 그림의 이름: CLP00001ce00018.bmp
원본 그림의 크기: 가로 970pixel, 세로 210pixel   (21)

In order to realize input-output linearization, the linear relationship between the input and output of the system should be obtained. In this sense, the desired closed-loop output voltage dynamic is imposed as a linear equation of the output voltage derivatives. The order of the output voltage dynamic should correspond with the relative degree. Then, the linear equation is expressed as:

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원본 그림의 크기: 가로 916pixel, 세로 180pixel     (22)

Equation (22) can be further expressed as:

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원본 그림의 크기: 가로 753pixel, 세로 167pixel

where 그림입니다.
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원본 그림의 크기: 가로 343pixel, 세로 94pixel.

The sliding surface is found by combining the invariance condition 그림입니다.
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원본 그림의 크기: 가로 150pixel, 세로 79pixel. Then, the following equation is obtained as:

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By integrating (24), the sliding surface is derived as:

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원본 그림의 크기: 가로 772pixel, 세로 169pixel          (25)

where a2=kd, a1=kp and a0=ki. Equation (25) can be considered as an integral sliding mode surface, which has been widely analyzed in the PWM power converter [8], [30].

The equivalent control method is often used to design SM control systems. By applying the invariance condition and an averaged large signal model, the equivalent control signal can be obtained as:

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원본 그림의 크기: 가로 1402pixel, 세로 220pixel         (26)

where:

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원본 그림의 크기: 가로 1159pixel, 세로 214pixel

The equivalent control law in (26) is complicated, and the phase variables 그림입니다.
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원본 그림의 크기: 가로 95pixel, 세로 86pixeland 그림입니다.
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원본 그림의 크기: 가로 79pixel, 세로 81pixel are difficult to obtain. Therefore, the equivalent control law is not practicable in resonant converters.

In this case, the switching function shown in (27) is obtained as the control law of the SM control. This is done by applying the reaching condition 그림입니다.
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원본 그림의 크기: 가로 194pixel, 세로 79pixel. This control law is a bang-bang type control function. Its output is determined by the trajectory of the sliding surface.

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원본 그림의 크기: 가로 741pixel, 세로 192pixel   (27)

Here, 그림입니다.
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원본 그림의 크기: 가로 190pixel, 세로 83pixel is the reaching condition, which can simultaneously meet the reaching condition and the existence condition of the sliding control.

When the sliding mode control is designed, the stability condition should be considered. In the sliding motion (그림입니다.
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원본 그림의 크기: 가로 122pixel, 세로 63pixel, 그림입니다.
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The stability analysis is carried out using (28). Based on the Roth criterion, the output voltage asymptotically tends toward its reference signal if the following conditions are satisfied.

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When selecting sliding mode coefficients, the coefficients must satisfy the stability condition, which can be inherently accomplished through the design of the sliding coefficients to meet the desired dynamical property.

Equation (28) can be rearranged into the standard second- order system form, which relates the sliding coefficients to the dynamic response of the converter during sliding mode operation.

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The relations can be expressed as functions of the bandwidth ω0 and the damping ratio ξ.

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The design of the sliding mode coefficients can result in three possible types of responses: under-damped (그림입니다.
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원본 그림의 크기: 가로 121pixel, 세로 74pixel). In order to obtain a small voltage overshoot and a fast response time, an under-damped response is usually expected, where, ξ=0.707. ω0=2πf0, f0 is the expected frequency, where f0 is designed to be one-tenth of the resonant frequency. Consequently, the design method of the sliding mode coefficients can be achieved. After selecting ξ, ω0 and kd, kp and ki can be calculated, where ξ=0.707, f0=11.5K, kd=2.25×10-3, kp=230 and ki=1.17×107.


B. PI Control Design

While designing the PI control, it is necessary to get the transfer function of the full-bridge LLC resonant converter. Considering the complex circuit structure and operating modes of the LLC converter, it is difficult to obtain an accurate transfer function. In this paper, the system identification method is adopted to obtain the transfer function by analyzing PSpice simulation input and output data with the least square parameter estimation algorithm. In this system identification method, a complex converter is regarded as a black box, with only the input and output data for modeling, which can avoid the complicated analysis of the converter’s working mechanism [31]-[33].

The simulation structure of the full-bridge LLC resonant converter is built with the PSpice simulation in Fig. 3. The main simulation parameters of the converter are shown in Table I. The converter can be treated as a black-box model structure, which is analyzed using the system identification method to fit the step response curve. Step response data can be collected with the simulation structure. The input and output data of this LLC simulation converter are sampled at the same time. Then, the least square parameter estimation algorithm is adopted to analyze the discrete data, and the least square estimation parameters can be obtained [31]-[33]. Based on the results of the parameter estimation, the discrete transfer function of the system is built as:

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원본 그림의 크기: 가로 1408pixel, 세로 157pixel         (32)


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원본 그림의 크기: 가로 1142pixel, 세로 843pixel

Fig. 3. PSpice simulation structure of a full-bridge LLC converter.


TABLE I CONVERTER SIMULATION PARAMETERS

Input voltage (Vin )

270 V

Resonant inductor (Lr )

64.6 μH

Resonant capacitor (Cr )

30 nF

Transformer magnetic inductor (Lm)

200 μH

Transformer turns ratio (n)

1:1

Output capacitor (Co)

10 μF


The zero-order-hold method is used to convert the discrete transfer function H(z) into a continuous transfer function H(s).

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Fig. 4 shows a bode diagram of H(s). As can be seen, the gain margin Gm is given as Gm=1.16dB, and the phase margin Pm is given as Pm=-1.5°, which does not satisfy the stability condition.


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Fig. 4. Bode diagram of H(s).


A PI regulator is adopted to perform serial correction, which can increase the system’s phase margin and reduce the gain crossing frequency. The PI control law uPI is shown as:

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where kps is the proportion coefficient, kis is the integral coefficient, and S is the sliding surface. The system can become stable by adjusting kps and kis. Then, the transfer function of the system can be expressed as:

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원본 그림의 크기: 가로 1402pixel, 세로 171pixel         (35)

Fig. 5 shows a bode diagram of H'(s), where, kps is determined to be kps=0.02 and kis is determined to be kis=100. As can be seen, the crossing frequency is given as ωc≈25kHz, the gain margin Gm is given as Gm=32dB, and the phase margin Pm is given as Pm=86°, which satisfy the stability condition.


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Fig. 5. Bode diagram of H'(s).


C. SM-PI Control Design

The output voltage ripple is influenced by the inherent chattering phenomenon of the SM control. Consequently, the steady-state performance of the SM control is poor. In order to realize good control performance in the whole operating condition, the SM-PI control method is proposed by combining SM and PI controls, which can achieve a good transient response and strong robustness from the SM control, and good stability from the PI control. In the SM-PI control, the SM control is in charge of the transient response, and the PI control prevails in the steady state. Fuzzy logic control is introduced to implement a smooth transition between the sliding-mode control and the PI control [21], [22], [34].

Fig. 6 shows a fuzzy logic diagram of the SM-PI control, where, S is the sliding surface and the input of the fuzzy logic controller, SMALL and LARGE are defined to be member functions, and μ is the degree of the memberships. The whole control region is divided into different sub-regions with the parameters m1 and m2. When S∈[–m1, m1], the PI control itself is in charge of the control. When S∈[–∞, –m2]∪[m2, ∞], the SM control itself is in charge of the control. When S∈[–m2, –m1]∪[m1, m2], the PI control and SM control work in tandem through a fuzzy nonlinear switching function to produce a single controller output. The fuzzy parameters m1 and m2 are mainly related to the output voltage ripple and transient response time, which can be determined by fuzzy experiences including simulations and experiments. In order to implement a smooth transition between the SM and PI controls, a fuzzy member function should be designed. If a traditional linear function is adopted, the control law may vary very quickly around the switching point, and the transition between the SM and PI controls may not be smooth. Accordingly, a nonlinear function should be adopted. In this case, a radial basis function is applied, which can realize a smooth transition around the switching points of the PI and SM controls.

From the previous definition of the controller, it follows that the linguistic rules of the fuzzy logic supervisory controller should be defined as:

Rule 1: If S is SMALL, THEN u=uPI

Rule 2: If S is LARGE, THEN u=uSMC

where, u is the control output, uPI is the PI control law, and uSMC is the SM control law.


그림입니다.
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Fig. 6. Fuzzy logic diagram.


By applying the weighted sum defuzzification method, the overall output of the SM-PI control law μSM-PI is given by:

그림입니다.
원본 그림의 이름: CLP00001ce00037.bmp
원본 그림의 크기: 가로 893pixel, 세로 274pixel           (36)

where, ui is the control output of the rule i, and μi is the degree of membership for each rule i. In this case, the coefficient kq can be represented as:

그림입니다.
원본 그림의 이름: CLP00001ce00038.bmp
원본 그림의 크기: 가로 1000pixel, 세로 466pixel           (37)

where, the variable 그림입니다.
원본 그림의 이름: CLP000031440001.bmp
원본 그림의 크기: 가로 42pixel, 세로 41pixel is related to the boundary variables m1 and m2, 그림입니다.
원본 그림의 이름: CLP000031440001.bmp
원본 그림의 크기: 가로 42pixel, 세로 41pixel=(m2m1)/4.

Note that the relationship between the SM-PI control law uSM-PI and the SSPSM angle 그림입니다.
원본 그림의 이름: CLP000031440002.bmp
원본 그림의 크기: 가로 51pixel, 세로 53pixel can be expressed as:

그림입니다.
원본 그림의 이름: CLP00001ce00039.bmp
원본 그림의 크기: 가로 885pixel, 세로 112pixel   (38)



Ⅴ. SIMULATION AND EXPERIMENTAL RESULTS


A. Simulation Results

In order to evaluate the performance of the proposed SM-PI control strategy, different simulation results have been presented in this section. These simulations were performed in MATLAB/SIMULINK simulator software. The main parameters of the designed converter are shown in Table II. Note that Co represents the same value as the output filter capacitors C5 /C6.


TABLE Ⅱ CONVERTER PARAMETERS

Input voltage (Vin )

270 V

Output voltage (Vo)

450 V

Resonant inductor (Lr )

64.6 μH

Resonant capacitor (Cr )

30 nF

Transformer magnetic inductor (Lm)

200 μH

Transformer turns ratio (n)

1:1

Output capacitor (Co)

10 μF

Proportional gain (kp)

230

Derivative gain (kd)

2.25×10-3

Integral gain (ki)

1.17×107

Constant angle (γa)

170°

Maximum control angle (γb-max)

170°

Minimum control angle (γb-min)

90°

Lower boundary variable (m1)

0.30

Upper boundary variable (m2)

0.40


Fig. 7(a) shows a simulation waveform of the output voltage with a traditional PI control in the presence of step load variations. Fig. 7(b) shows a simulation waveform of the output voltage with SM control in the presence of step load variations. Fig. 7(c) shows a simulation waveform of the output voltage with the SM-PI control in the presence of step load variations. The load resistance is changed between 500 Ω and 1000 Ω every 5 ms in the simulation. Obviously, it can be found that the SM-PI control has the best performance. The response time of the SM-PI control is faster, and the output voltage overshoot and undershoot of the SM-PI control are less than those of the PI control. The voltage ripple of the SM-PI control is less than that of the PI control in the steady-state.


Fig. 7. Output-voltage simulation waveforms in the presence of step load variations. (a) PI controller. (b) SM controller. (c) SM-PI controller.

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(a)

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(b)

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(c)


Fig. 8 shows the SM-PI control law. As can be seen, the SM control is in charge of the transient response and the PI control prevails in the steady state. Accordingly, the SM-PI control avoids the inherent chattering problem of the SM control in the steady state and the poor dynamic performance of the PI control in the transient state.


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원본 그림의 크기: 가로 1449pixel, 세로 478pixel


Fig. 8. SM-PI control law.


B. Experimental Results

In order to investigate the performance of the proposed control strategy, a laboratory prototype has been built, as shown in Fig. 9. The parameters of the converter are listed in Table II.


그림입니다.
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원본 그림의 크기: 가로 603pixel, 세로 410pixel

Fig. 9. Laboratory prototype.


1) Realization of a LLC Converter with the Proposed Control Scheme

Fig. 10(a) shows a block diagram of the LLC converter with SSPSM and the SM-PI control. A DSP board TMS320F2812 is used to implement the control scheme.

Fig. 10(b) shows a hardware schematic of an LLC converter with SSPSM. The general timer of the DSP event manager is set to the continuous incremental mode, and it is used to generate the sawtooth wave vst. The comparison unit registers CMPR1 and CMPR2 separately to represent the modulation lines vca and vcb. The logic signals vr1 and vr2 are obtained separately by comparing vst with vca and vcb. The zero-crossing moment of the resonant current can be captured by the DSP. Then, the signal vr3 can be easily generated. The logic signals vr1, vr2 and vr3 can be converted into the drive signals LQ1–LQ4 through the logic operations of NOT gate, NAND gate and RS flip-flop. After that, the dead-time of LQ1-LQ4 is generated by the RCD circuit. Lastly, two drive chips Si8235 are used to drive the switches.

Fig. 10(c) shows the zero-crossing detection circuit. Zero- crossing capture is a vital part of the SSPSM design. If the zero-crossing moment cannot be correctly captured, SSPSM may not work. A hall-effect current sensor TBC06DS3.3 is adopted to sample the resonant current. In addition, the zero-crossing square-wave of the resonant current is obtained through an ultrafast comparator LT1720. However, the rising edge and falling edge of the square-wave may have some chattering. Therefore, the figuration function of this square- wave needs to be achieved through a RC filter and NOT gate 74LS14. In this way, the zero-crossing signal can be obtained in the correct manner, and sent to the capture port of the DSP.

Fig. 10(d) shows waveforms of the LLC converter with the proposed control scheme. The control law is converted to the input signal vcb of the SSPSM. The sawtooth wave vst is generated by the general timer of the DSP event manager. The logic signals vr1 and vr2 are obtained separately by comparing vst with vca and vcb. Then, the logic signal vr3 is generated by using the zero-crossing moment of the resonant current. After that, the three logic signals vr1, vr2 and vr3 can be converted to the drive signals LQ1-LQ4 through the logic operation of NOT gate, NAND gate and RS flip-flop. Lastly, the drive signals of the switches can be obtained through the dead-time generator circuit and the two drive chips Si8235.


Fig. 10. LLC converter with SSPSM and the SM-PI control based on DSP. (a) Block diagram. (b) Hardware schematic. (c) Zero-crossing detection circuit. (d) Main waveforms.

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원본 그림의 크기: 가로 1434pixel, 세로 826pixel

(a)

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원본 그림의 크기: 가로 1174pixel, 세로 712pixel

 

그림입니다.
원본 그림의 이름: CLP000023400007.bmp
원본 그림의 크기: 가로 1197pixel, 세로 633pixel

 

그림입니다.
원본 그림의 이름: CLP000023400008.bmp
원본 그림의 크기: 가로 1200pixel, 세로 638pixel

(b)

그림입니다.
원본 그림의 이름: CLP000023400009.bmp
원본 그림의 크기: 가로 1565pixel, 세로 654pixel

(c)

그림입니다.
원본 그림의 이름: CLP00002340000a.bmp
원본 그림의 크기: 가로 650pixel, 세로 824pixel

(d)


In this paper, the SM-PI control is realized through a DSP, and the discretization process of the proposed method is expected.

Adopting the principle of the positional digital PID algorithm, the sliding surface 그림입니다.
원본 그림의 이름: CLP00002340000b.bmp
원본 그림의 크기: 가로 572pixel, 세로 121pixel can be discretized as:

그림입니다.
원본 그림의 이름: CLP00002340000c.bmp
원본 그림의 크기: 가로 1319pixel, 세로 295pixel         (39)

In order to decrease the calculating time, function (39) can be simplified as:

그림입니다.
원본 그림의 이름: CLP00002340000d.bmp
원본 그림의 크기: 가로 1332pixel, 세로 91pixel   (40)

where 그림입니다.
원본 그림의 이름: CLP00002340000e.bmp
원본 그림의 크기: 가로 460pixel, 세로 160pixel, 그림입니다.
원본 그림의 이름: CLP00002340000f.bmp
원본 그림의 크기: 가로 413pixel, 세로 158pixel, 그림입니다.
원본 그림의 이름: CLP000023400010.bmp
원본 그림의 크기: 가로 178pixel, 세로 156pixel, T is the sampling time, 그림입니다.
원본 그림의 이름: CLP000023400011.bmp
원본 그림의 크기: 가로 155pixel, 세로 95pixel is the output voltage error at the n time, 그림입니다.
원본 그림의 이름: CLP000023400012.bmp
원본 그림의 크기: 가로 241pixel, 세로 85pixel is the output voltage error at the n-1 time, and 그림입니다.
원본 그림의 이름: CLP000023400013.bmp
원본 그림의 크기: 가로 253pixel, 세로 79pixel is the output voltage error at the n-2 time.

Similarly, 그림입니다.
원본 그림의 이름: CLP000023400014.bmp
원본 그림의 크기: 가로 532pixel, 세로 118pixel can be discretized as:

그림입니다.
원본 그림의 이름: CLP000023400015.bmp
원본 그림의 크기: 가로 1063pixel, 세로 103pixel    (41)

where 그림입니다.
원본 그림의 이름: CLP000023400016.bmp
원본 그림의 크기: 가로 365pixel, 세로 102pixel and 그림입니다.
원본 그림의 이름: CLP000023400017.bmp
원본 그림의 크기: 가로 217pixel, 세로 86pixel.

Analog-to-digital conversion occurs in each period of the sawtooth wave. The sampling period T can be approximately equal to half of a resonant period. Accordingly, the control gain parameters can be calculated as: 그림입니다.
원본 그림의 이름: CLP000023400018.bmp
원본 그림의 크기: 가로 676pixel, 세로 150pixel, a=798, b=–1265, c=518, d=0.02 and e=–0.02.


2) Steady State Performance

Fig. 11 illustrates experimental waveforms of the resonant current iLr , inverter output voltage vab, and output voltage vo with the SSPSM, where the load resistance is 1000 Ω. SSPSM can ensure that the resonant current iLr lags behind the inverter output voltage vab under any operating conditions to realize zero voltage switching (ZVS) of the switches by adjusting the shifting-phase angle, which results in an increased efficiency and improved reliability. As can be seen, since the zero-crossing points of the resonant current are used to generate the drive signals of the switches, iLr can always lag behind vab. In this situation, when one switch is turned on, the resonant current flows through the antiparallel body diode, the drain-source voltage is clamped to zero, and ZVS can be realized which reduces the switching losses. The experimental efficiency is 94%. Moreover, it can be found that the output voltage ripple with SM control is noticeably larger than that with the SM-PI control. In addition, note that the steady-state experimental waveforms of the PI controller are similar to those of the SM-PI controller.


Fig. 11. Steady-state experimental waveforms. (a) SM controller. (b) SM controller. (c) SM-PI controller. (d) SM-PI controller.

그림입니다.
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원본 그림의 크기: 가로 622pixel, 세로 353pixel

(a)

그림입니다.
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원본 그림의 크기: 가로 618pixel, 세로 337pixel

(b)

그림입니다.
원본 그림의 이름: image72.emf
원본 그림의 크기: 가로 630pixel, 세로 353pixel

(c)

그림입니다.
원본 그림의 이름: image73.emf
원본 그림의 크기: 가로 622pixel, 세로 331pixel

(d)


3) Transient State Performance

Fig. 12 and Fig. 13 show the transient response in the presence of step load variations. A comparison is presented among the PI control, the SM control and the SM-PI control. On the one hand, the SM-PI controller is faster than the PI controller, and the SM-PI controller can provide less voltage overshoot and undershoot. On the other hand, the SM-PI controller can provide a noticeably lower steady-state output ripple than the SM controller. It can be found that the proposed SM-PI control scheme can realize good steady-state performance from the PI control and good transient-state performance from the SM control.


Fig. 12. Transient response with a SM controller and a PI controller in the presence of step load variations. (a) SM controller (from 500 Ω to 1000 Ω). (b) SM controller (from 1000 Ω to 500 Ω). (c) PI controller (from 500 Ω to 1000 Ω). (d) PI controller (from 1000 Ω to 500 Ω ).

그림입니다.
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원본 그림의 크기: 가로 1389pixel, 세로 769pixel

(a)

그림입니다.
원본 그림의 이름: CLP00002340001a.bmp
원본 그림의 크기: 가로 1421pixel, 세로 780pixel

(b)

그림입니다.
원본 그림의 이름: CLP00002340001b.bmp
원본 그림의 크기: 가로 1392pixel, 세로 788pixel

(c)

그림입니다.
원본 그림의 이름: CLP00002340001c.bmp
원본 그림의 크기: 가로 1377pixel, 세로 766pixel

(d)


Fig. 13. Transient response with the SM-PI controller in the presence of step load variations. (a) SM-PI controller (from 500 Ω to 1000 Ω). (b) SM-PI controller (from 1000 Ω to 500 Ω).

그림입니다.
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원본 그림의 크기: 가로 622pixel, 세로 336pixel

(a)

그림입니다.
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원본 그림의 크기: 가로 615pixel, 세로 334pixel

(b)



Ⅵ. CONCLUSIONS

A SM-PI controller for full-bridge LLC converters is proposed in this paper. The SM controller is designed based on the large signal model of an LLC converter. The oriented- control model is derived for the converter under the SSPSM method, which guarantees ZVS operation. The sliding surface is obtained by using the input-output linearization concept. The PI control is designed based on a transfer function of an LLC converter, which is obtained with the system identification method. In order to address the chattering effect of the SM control, the SM-PI control is proposed by combining the SM control and the PI control. Fuzzy control is adopted to implement a smooth transition between the SM control and the PI control. Simulation and experimental results show that the SM-PI control can realize good steady-state and transient-state performance.



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그림입니다.
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Kai Zheng was born in Henan Province, China. He received his B.S. and M.S. degrees in Electrical Engineering from the New Star Research Institute of Applied Technology, Hefei, China, in 2005 and 2009, respectively. He received his Ph.D. degrees in Electrical Engineering from the Zhengzhou Infor- mation Science and Technology Institute, Zhengzhou, China, in 2016. His current research interests include the modeling and control of resonant power converters.


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Guodong Zhang was born in Henan Province, China. He received his B.S. degree in Electrical Engineering from the Xi’an Communication Institute, Xi’an, China, in 2003; and his M.S. and Ph.D. degrees in Electrical Engineering from the Zhengzhou Information Science and Technology Institute, Zhengzhou, China, in 2008 and 2015, respectively. His current research interests include power electronics and control.


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Dongfang Zhou was born in Zhejiang Province, China. He received his B.S. degree in Electrical Engineering from the Zhengzhou Information Science and Technology Institute, Zhengzhou, China, in 1983; his M.S. degree in Electrical Engineering from Xidian University, Xi’an, China, in 1989; and his Ph.D. degree in Electrical Engineering from Zhejiang University, Hangzhou, China, in 2005. He is presently working as a Professor at the Zhengzhou Information Science and Technology Institute. His current research interests include power electronics and control for microwave systems.


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Jianbing Li was born in Hubei Province, China. He received his B.S., M.S. and Ph.D. degrees in Electrical Engineering from the Zhengzhou Information Science and Technology Institute, Zhengzhou, China, in 1999, 2002 and 2006, respectively. He is presently working as an Associate Professor at the Zhengzhou Information Science and Technology Institute. His current research interests include power electronics and control.


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Shaofeng Yin was born in Henan Province, China. He received his B.S. and M.S. degrees in Electrical Engineering from the New Star Research Institute of Applied Technology, Hefei, China, in 2003 and 2007, respectively. His current research interests include the topology and control of power converters.