Digital Control of a Half-Bridge LLC Resonant Converter - IEEE Xplore

15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia

Digital Control of a Half-Bridge LLC Resonant Converter Concettina Buccella, Carlo Cecati, Hamed Latafat and Kaveh Razi Dept. of Industrial and Information Eng. and Economics, and DigiPower s.r.l., University of L’Aquila, 67100 L’Aquila, Italy emails: [concettina.buccella, carlo.cecati, hamed.latafat, kaveh.razi]@univaq.it

Abstract—Recently, LLC resonant converters are gaining more and more interest in DC/DC conversion due to their high efficiency and power density. Usually, they are used in low power applications, i.e. in the range of few hundred Watt and with constant output load, however they are very appealing in high power and renewable energy applications as well as in many other applications affected by wide variations of the load and/or the source voltage. This paper presents and discusses a novel half bridge DC/DC resonant converter with digital control and fuzzy logic. The proposed system is compared with a more traditional PID controller. A variable frequency control algorithms are implemented using a low cost, high performance Texas Instrument TMS320F28069 DSP for the regulation of the output voltage. Simulation results using MATLAB are presented to evaluate the quality of the obtained result. A laboratory prototype has been realized and experimental results obtained using both PID and Fuzzy controllers are shown and discussed. Index Terms—Digital control, LLC resonant converter, adaptive PID, Fuzzy logic controller

I. I NTRODUCTION OWADAYS high power density (W/in3 ) is becoming one of the main challenges in the field of power converters and in particular in DC/DC power supplies. In fact, their use is becoming extended to almost all fields, including those imposing significant size constraints. Generally speaking, increasing the operating switching frequency of the power converter, dramactically reduce the size of magnetic components and filter capacitors, however, the effectiveness of this resizing greatly depends on the overall design, including the choice of the topology and of the control algorithm as well as the thermal design [1]. Among the numerous current topologies, LLC resonant converters are becoming more and more popular in many applications including consumer as well as industrial electronics, automotive and front-end applications. In fact, compared with hard switching counterparts, they offer many advantages, such as higher efficiency, lower harmonics level and Electro Magnetic Inferences (EMI); moreover, if properly controlled, they can handle large variations of the input voltage and/or of the load [2]. The latter feature is very appealing particularly when dealing with renewable energy sources such as photovoltaic or wind turbine applications. Usually, the control of DC/DC converters, particularly those operating at low voltage and with low power is analog and implemented using one of the numerous System-on-Chip (SoC) made available by semiconductor manufacturers. These integrated circuits have low cost and high bandwidth and

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offer satisfactory performance in many cases on practical interest, in particular in those applications with fixed inputoutput caracteristics and with limited tuning demand. When the input and/or the output vary in a wide range, or the power exceeds the few tenth or hundred Watt managed by the SoC, sophisticate converters and complex control algorithms must be considered and/or implemented, thus requiring significant computational and power resources which can be obtained only by using microcontrollers (MCU) or digital signal processors (DSP) as well as custom and discrete designs of the power section. It is well known that digital controllers are flexible, with low sensibility to noise and high robustness against aging, parameter variations, and environmental factors [3], [4], moreover, DSPs have more computational power than microcontrollers, hence advanced control algorithms, such as adaptive and nonlinear controllers, can be more easily implemented choosing a DSP [5], [6]. In this paper, an adaptive PID control and a Fuzzy Logic controller of a half-bridge LLC DC/DC resonant converter for photovoltaic applications, have been considered, implemented and compared, using a TMS320F28069 DSP [7]. The first algorithm was originally proposed in [8], here, it is used for compensating the large variations of the input voltage and/or of the load: the controller modifies its parameters automatically thus improving the overall transient response of the system. The second one, was recently proposed in [9] and offers both better compensating capability and robustness to non-linearities and parameter variations. In fact, Fuzzy logic control (FLC) is very powerful in controlling nonlinear systems and especially those where the precise system model is unknown. Once a fuzzy logic controller has been designed, it can be easy extended, with minor modifications, to other systems [10]. In the following, Section II deals with topology and design requirements of Resonant Converters. Hence, an adaptive PID controller capable to change the switching frequency of IGBT is discussed in Section III. Later, Section IV describes the FLC applied to the aforementioned converter. Simulation results are presented in Section V-A using MATLAB/Simulink to test the response of the system to sudden changes of load and input voltage in a wide range. Experimental results are shown and discussed in Section V-B, where performance of the developed prototype are analyzed. Some conclusions are drawn in Section VI.

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II. LLC R ESONANT C ONVERTER Resonant DC/DC converters consist of an inverter and a diode rectifier coupled by a high frequency transformer, through a resonant circuit. The rectifier output is connected to the load through an output filter. Under certain conditions, the described configuration allows the inverter to switch at zero voltage and/or current condition. There are different structures realizing a resonant DC/DC converter [11]-[14]: • Series Load Resonant (SLR), in which the capacitor Cr is placed in series to the load • Parallel Load Resonant (PLR), in which the capacitor Cr is placed in parallel to the load • Series-parallel resonant converters that employs two capacitors (LCC) or two inductances (LLC). The circuit configuration of the considered half-bridge LLC Resonant Converter in this paper is shown in Fig. 1.









  

Figure 1.

Half-Bridge LLC resonant converter configuration.

Because of the topology, this circuit presents two distinct resonance frequencies, i.e.: 1 √ 2π Lr Cr

(1)

1  2π (Lr + Lm ) Cr

(2)

fr1 = and fr2 =

where Lr , C r and Lm are series resonant inductance, series resonant capacitance, and magnetizing inductance, respectively. At frequencies higher than fr1 , the zero voltage condition (ZVS) is ensured. The higher harmonic currents are being filtered by a resonant tank in which only sinusoidal currents flow through the resonant circuit. As a result, the current lags the voltage applied to the resonant circuit which allows the power switches to be turned on when the voltage is near to zero; thus minimizing turn-on losses. With a lower value of the total resonance inductance, it is possible to reach higher peak current and attain ZVS condition more easily. However, the current of the magnetizing inductor is a circulating current helpful in providing ZVS, but carries no energy to the load hence causes additional losses. In order to increase the efficiency of the converter, this circulating current has to be minimized. Increasing the switching frequency or the total inductance value could help at reducing this current, thus minimizing losses [15], [16].

For predicting the LLC operation behavior and design, the Fundamental Harmonic Approximation (FHA) method has been used in this paper [17], [18]. FHA is a simple approach that allows a derivation of the steady-state voltage conversion ratio of the converter by representing the rectifier AC port as an equivalent resistance. Equation (3) could be easily obtained from energy considerations where Req is the rectifier AC port equivalent resistance and Ro is the actual DC side load resistance 8 Ro . (3) π2 Resonant converter has high efficiency near the resonant frequency and its transient response is not sensitive to the step change of load. Optimal design of LLC converter is more difficult than conventional PWM converters, because there are multiple modes of operations including the Continuous Conduction Mode (CCM), Discontinuous Conduction Mode (DCM) both below and above resonance frequency and cutoff mode. Each mode has different resonant characteristics. Near the resonant frequency, the conduction is of CCM type and the commutations of the inverter switches are similar to that produced by a square wave commutating inverter with an inductive load: the turn-on occurs at zero voltage while the turn-off is characterized by significant switching losses that can be widely reduced by inserting a suitable snubber capacitor in parallel to each switch. In this way, both the switching and the conduction losses are adequately reduced. Because the converter operates at high frequency with high currents, components such as MOSFETs and rectifier diodes should have minimum losses in active mode and short switching times. As mentioned before, because of the soft switching the voltage stress is very low, so almost no care about the maximum operating voltage is needed when choosing these components. The input and resonant capacitors should be able to handle very high load current at high frequency. It is assumed that the power switches of the bridge are driven with duty-cycle of 50% without overlapping. A dead time tdead in which the MOSFET switches are both off and only one inner MOSFET diode is in conduction mode is considered. Digital controller regulates the output at desired DC value by changing the switching frequency of the power MOSFETs. Req =

III. PID C ONTROLLER In DC/DC converters applications for renewables, it is desired to have a constant output voltage in spite of disturbances such as sudden changes of input voltage or load current. Negative feedback control is applied to DC/DC converters to automatically adjust the frequency to sustain output voltage at the desired value [6]. The standard equation of a PID controller is shown in (4) as described in [19]. 

 u(t) = KP e(t) + KI

e(t)dt + KD

de(t) dt

 (4)

The PID controller designers usually attempt to satisfy the phase and gain margin requirements using Bode plots or root locus methods. The design performance depends on the values

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of the proportional constant (KP ), the integral constant (KI ) and the derivative constant (KD ). Because of the numerous advantages of digital PID controllers over conventional analog controllers, implementation of a digital PID controller is discussed in this work. By descretizing the equation 4, the difference equation for the digital PID controller is obtained and shown in equation 5 [20]. u[k] = KP e[k] + KI T

k 

4) When the set point is reached and the output is still changing, a little change in frequency is necessary to prevent the output from moving away. In the present application, 81 rules based on the above assumptions are used. The schematic diagram of the FLC used for LLC resonant converter is shown in Fig. 2.

e[i] + KD {e[k] − e[k − 1]} (5)

i=0

u[k] and e[k] are the output and error for the k − th sample consequently. The error e[k] is calculated as follow: e[k] = VRef − ADC[k]

(6)

Where ADC[k] is the converted digital value of the k − th sample of the output voltage and VRef is the reference digital value of the desired output voltage. The system response with accurate numerical calculations will be very similar to the system response using analog control. For tuning the digital PID controller, usually ZieglerNichols technique is used [21]. For applications requiring precise control performances, this method is not suitable. In order to improve the performance of conventional PID controller, some modifications are proposed in [8] and implemented for a single phase buck converter in [22] where the Proportional, Integral and Derivative gains of the controller are modified during the transient operation mode. In this way, power converter has lower bandwidth during steady state and higher bandwidth in transient mode which means better dynamic response during large distortions. Therefore, this method is used in this paper to control the swithching frequency of power MOSFETs.

Figure 2.

Schematic diagram of the digital fuzzy controller.

The inference result of each rule consists of the weighting factor ωi and the degree of change of switching frequency, Ci . Mamdani-based system architecture has been realized using max−min composition techniques and the Center of Gravity Method (COG) has been employed for defuzzification. The output is the change in switching frequency and is given in (7), where n is the maximum number of effective rules. n 

u=

IV. F UZZY CONTROLLER In order to improve the performance of the resonant converter during large variations of input or load, FLC could be used [24]. In comparison with PID controllers, they were found to have better performance in terms of transient time and maximum overshoot. The fuzzy controller is robust to input DC voltage variations as well as for a wide load operating conditions [23], [9]. The inputs to FLC for the considered LLC converter are the error, the difference of error, and the sum of error. They are divided into nine triangular membership functions (MF) and labeled as “NVB”= negative-very-big, “NB”= negativebig, “NM” = negative-medium, “NS” = negative-small, “ZE” = zero, and so forth. Simple linguistic rules determine the control action as follow: 1) If the error is far from zero, change of switching frequency must be large to quickly bring the output to the reference voltage 2) If the error is near zero, small change of switching frequency is needed 3) If the error is near zero and the change in error is large, the frequency should be kept constant to prevent overshoot

ωi C i

i=1 n 

i=1

(7) ωi

V. C ASE S TUDY In this section, both simulation and experimental results are presented and discussed for a 500 W Vin = 100 V , Vout = 80 V LLC DC/DC resonant converter. A. Simulation results Simulation results for large load and input voltage variations were carried out using Matlab/Simulink® . The resonant frequency fr1 was chosen to be about 42 kHz, the circuit parameters were as follow:Vin = 100 V Vout = 80 V , Lr = 26.2 μH, Lm = 41 μH, Cr = 550 nF , n = 4 and RL = 40 Ω. Load resistance was suddenly decreased from 40 Ω down to 20 Ω at t = 20 ms and returns back to 40 Ω after 30 milliseconds. Simulations results for PID and FLC controllers are shown in Fig. 3 and Fig. 4, respectively. Transient response of the output voltage and current show that settling time is about 10 milliseconds for PID and 5 milliseconds for FLC. It

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can also be seen in the figures that the voltage overshoot in the FLC case is much less than in the PID case.

Figure 5. Output response of LLC converter controlled by PID (middle) and FLC (bottom) to sudden input voltage change (top). Figure 3. Output Current (top) and voltage (bottom) response to step changes of load for LLC converter controlled by PID.

It is clear from these figures that the FLC regulates the output much better than PID while changes accure in the input voltage or output current. The transient response shows shorter settling time and lower overshoot for the Fuzzy controller. B. Experimental Results A small prototype of a DC/DC half-bridge LLC resonant converter has been designed and implemented in the laboratory of DigiPower Ltd. Control pulse trains were isolated by optocouplers before applying to power MOSFET drives. Internatinal Rectifiers integrated chips IR2110 were used for driving SPW35N60 power MOSFET by Infineon. The implemented laboratory prototype is shown in Fig. 6.

Figure 4. Output Current (top) and voltage (bottom) response to step changes of load for LLC converter controlled by FLC.

As mentioned before, for renewable energy applications, robustness of converter against input DC voltage variation is very important. Step change of 40 V were applied to the input DC bus at t = 20 ms and returned back to normal at t = 40 ms. Response of the system using both PID and FLC are presented and compared in figure 5.

Figure 6. converter

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Implemented prototype of DC/DC half-bridge LLC resonant

and upper curve is output current (0.5 A/div). It can be noticed that the output responds to the step change of load in about 5 milliseconds and the overshoot is less than the same experiment using PID controller.

Figure 8. Voltage (bottom) and current (top) responses to sudden load change using Fuzzy controller.

Figure 7. Current (top) and voltage (bottom) responses to sudden load change using PID controller.

In the last case for measuring the system response to wide input DC bus voltage variations, it was increased from 100 V to 130 V as a step, and the results are shown in Fig. 9 and 10 for PID and FLC. Better performance of the Fuzzy controller for regulating the output of the resonant converter is obvious regarding these results. VI. C ONCLUSION

Figure 9. Voltage (middle) and current (bottom) responses to sudden input voltage change (top) using PID controller.

Digital PID controller alghoritm as well as FLC were implemented using a Texas Instruments TMS320F28069 Piccolo controlSTICK. This controller includes a cheap floating point DSP which was used in this work to generate variable frequency pulse trains with adjustable dead-bands and to implement data acquisition and control. For output voltage feedback, the integrated ADC converter of the TMS320F28069 DSP was used and a fixed dead-band of 250 ns was applyed to the output pulse trains. The prototype was tested considering large input voltage change and sudden load variations. At first, fixed input voltage of Vin = 100 V was applied to DC bus of converter with resistive load of 53 Ω. In order to test the load variation effect, load was decreased suddely from 53 Ω down to 28 Ω. Fig. 7 shows the result with the PID controller in which lower curve is output voltage (5.0 V /div) and upper curve is the output current (0.5 A/div). As shown in this figure, output current increases from 1.5 A up to 2.8 A, and the output voltage responds to this distortion in about 15 milliseconds. The experimental result with Fuzzy controller is shown in Fig. 8 where the lower curve is output voltage (5.0 V /div)

In this paper, a DC/DC half-bridge resonant converter with digital adaptive PID and Fuzzy logic controllers was designed. Its MATLAB/Simulink model with both PID and Fuzzy controllers have been developed, and also their performance have been verified. To confirm the simulation study a small prototype with the same parameters was also designed and the aforementioned control algorithms were successfully implemented using a floating point DSP. Simulation and experimental results indicated that the Fuzzy logic controller is able to achieve fast dynamic response in comparison with the PID controller where large input changes and/or load variations are expected. Authors are working to build a multilevel inverter to connect several renewable energy sourses to the grid via DC/DC resonant converters.

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Figure 10. controller.

Voltage response to sudden input voltage change using Fuzzy

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