A fast hysteresis control strategy based on capacitor charging and discharging

Transcription

1 LETTER A fast hysteresis control strategy based on caacitor charging and discharging Jianfeng Dai, Jinbin Zhao a), Keqing Qu, and Ming Lin College of Electrical Engineering, Shanghai University of electric ower, 2588, Changyang Road, Yangu, Shanghai, , China a) zhaojinbin shie edu cn Abstract: Based on inductor current rile and outut voltage rile to charge and discharge for caacitor C, a fast hysteresis control strategy is roosed in this aer. It is not only simle and solves the comensation roblem of the error amlifier in conventional voltage PWM control, but also rovides better transient resonse and stability to meet the challenges of the buck converter. Finally, the steady-state oeration of the roosed control strategy is analyzed and verified by simulation and exerimental results. Keywords: buck converter, hysteresis control, rile, fast transient resonse Classification: Electron devices, circuits, and systems References [1] A. Soto, P. Alou and J. A. Cobos: APEC (2004) [2] X. Zhou, P. L. Wong, P. Xu, F. C. Lee and A. Q. Huang: IEEE Trans. Power Electron. 15 [6] (2000) [3] X. H. Wu and X. B. Wu: APPEEC (2012) 1. [4] M. Castilla, L. Garcia de Vicuna, J. M. Guerrero, J. Miret and N. Berbel: IEEE Trans. Power Electron. 22 [4] (2007) [5] K. Lee, F. C. Lee and M. Xu: APEC (2008) Introduction Nowadays, the switching ower sulies for electronic devices are designed to regulate the outut voltage against the changes of the load current [1, 2]. However, comlicated comensation network is needed to ensure their stable oeration since the existence of the comlex oles in the loo gain transfer function for the conventional voltage mode control circuit of the buck converter [3],as shown in figure.1 (a). The outut voltage rile based control strategy, such as hysteresis control can rovide instantaneous load transient without comensation network. Due to the above advantage, there has been growing interest in rile-based control strategy [4, 5], and some commercial hysteresis controllers were introduced recently. A fast hysteresis control strategy based on the caacitor charging and discharging is roosed. The roosed control strategy imort the inductor 1

2 current information in the feedback loo of single outut voltage, and add inductor current and outut voltage as feedback variables, which imrove the caacitor charging and discharging rate effectively. Besides, there is no error amlifier and comlex comensating network, the faster resonse seed can be achieved when load sudden change. The oerating rinciles of the roosed strategy are introduced in Section 2. The steady-state of the roosed converter was analyzed in Section 3. The rototye board is tested and the simulation and exerimental results are verified in Section 4. Finally, the conclusion is given in Section 5. 2 Oerating rinciles The configuration of a buck converter with a synchronous rectifier emloying the roosed control strategy is shown in Fig. 1 (b), the key waveforms of comarator U during one switching cycle are shown in Fig. 2. The control circuit consists of a comarator U with hysteresis and a feedback resistor R f and R L. The outut voltage and inductor current are returned to caacitor C for the triangular wave generator through resistor R f and R L, resectively. In addition, the outut of hysteresis comarator was connected with it s noninverting inut terminal through resistor R 2, and then was connected with V ref through resistor R 1 in turn. So the uer and lower threshold of hysteresis controlled buck converter was obtained when the outut of comarator U changed. Fig. 1. (a) Conventional converter (b) Proosed converter Fig. 2. Key waveforms of the comarator 2

3 The oerate rincile of control circuit is as follow. When the outut voltage become large (small), the charging current of caacitor C in the on mode eriod increases (decreases) and the discharging current of caacitor C in the off mode eriod decreases (increases). Thus, the on time duration of the ulse decreases (increases), and the off time duration increases (decreases).therefore, the switching duty was changed, and the outut voltage can be regulated. 3 Steady-state analysis In Fig. 1, V f is the voltage across caacitor C, V L and V H are threshold levels of the comarator U, V U is the outut voltage of the comarator U. The switching cycle starts at the instant t=0, I state 1 0 t T ON When the outut signal V U is high level, the caacitor was charged through the feedback branch, the following equations are obtained: i ¼ C dv f dt ¼ V OH V f R þ V o V f R f þ V il V f R L (1) Solving the above equation under the initial condition of V f (0)= V L, the next equation is obtained. Where, T ON ¼ C ln 1 ¼ 1 R þ 1 þ 1. R V OH þ V o þ V il V L R V OH þ V o þ R (2) V il V H II state 2 T ON t T S When outut signal V U is low level, the caacitor was discharged through the feedback branch, the following equations are obtained: i ¼ C dv f dt ¼ V f R þ V o V f R f þ V il V f R L (3) Solving above equation under initial condition of V f (T ON )= V H, we have V H V o þ R V il R T OF F ¼ C ln f R L V L V o þ R (4) V il By combining (2), (4) and D=T ON /(T ON +T OFF ) the outut voltage is nearly obtained as follows R o V o ¼ V L D R R L R o þ R f K L R þ V L V H (5) Where, V H ¼ R 2 R 1 þr 2 V ref þ R 1 R 1 þr 2 V OH ;V L ¼ R 2 R 1 þr 2 V ref ;V il ¼K L i L 3

4 4 Simulation and exerimental results To verify the roosed control strategy, simulation model and rototye have been built. The circuit arameters are shown in Table I. The conventional PWM IC is TL5001 which is shown in figure.1 (a). Table I. Design arameters of the roosed converter Fig. 3 (a) shows the relation between the outut current and the outut voltage. It can be seen that the variations of the outut voltage are very small. The exerimental values of the outut voltage are in good agreement with the theoretic values. Fig. 3. (a) Relation of the outut current and outut voltage (b) Relation of the outut current and switching frequency Fig. 3 (b) shows the relation between the outut current and the switching frequency. It shows that the switching frequency remained at 120 khz when the load currend changed, it overcomes the drawback of variable frequency comared with some control technology. The exeri- Fig. 4. The waveforms of inductor current during load transients 4

5 mental values are also in good agreement with the theoretic values. Fig. 4 shows the outut voltage, the inductor current waveforms during load transients. First, the load current decreased from 5 A to 2 A, the excess inductor current was decreased slowly with a sloe roortional to V o. When the load current increased from 2 A to 5 A, oerations were in the Fig. 5. (a) Simulated and exerimental resonse to a 5 A to 2 A load current ste change. (b) Simulated and exerimental resonse to a 2 A to 5 A load current ste change 5

6 oosite direction, the outut voltage dros with magnitude roortional, the inductor current increased quickly with a slo roortional to V i V o. Therefore, it quickly took V o to recover, the regulator was always stable during the load transients. Fig. 5 show the simulated and exerimental resonses of the roosed controller and conventional controller undergoing 5 A to 2 A and 2 A to 5 A load current ste changes. It can be seen that the roosed controller not only has shorter resonse time, also has a smaller overshoot. Thus, it has better transient resonse characteristics than conventional controller. 5 Conclusion A fast hysteresis control strategy based on the caacitor charging and discharging is roosed and analyzed in this aer. Faster transient resonse and quasi constant switching frequency are achieved. Finally, the steady-state oeration of the roosed control strategy is analyzed and verified by simulation and exerimental results. Acknowledgments The authors would like to acknowledge the financial suort of the Program for Professor of Secial Aointment (Eastern Scholar) at Shanghai Institutions of Higher Learning and Innovation Program of Shanghai Municial Education Commission (Grant No. 13ZZ132). 6