T. M. Swathy Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 5, ( Part -1) May 2015, pp.62-65
RESEARCH ARTICLE OPEN ACCESS
Digital Voltage Control of DC-DC Boost Converter
T. M. Swathy*, Arun Kumar Wadhwani** *Research Scholar, Department of Electrical Engineering, MITS, Gwalior ** Professor, Department of Electrical Engineering, MITS, Gwalior
ABSTRACT The need for digital control for faster communication between power stage module & system controllers is increased with requirement of load complexity. The requirements also include stability of power module with the parametric variation. This paper presents a digital control of a dc-dc boost converter under nominal parameter conditions. The system controller has been verified in both frequency response as well as MATLAB-Simulink under nominal & parametric varying condition. The modeling of converter has been illustrated using state-space averaging technique. Direct digital design method is equipped to design the controller in frequency response to yield constant load voltage. The characteristic of load voltage before & after parametric variation is shown. Keywords – DC-DC Converter, Small-Signal modeling, Digital Direct Design approach
I. INTRODUCTION analog controller, low sensitive to external influence, With the necessity of higher efficiencies, get better performance, less effective to smaller output ripple and smaller converter size for environmental variations, better noise immunity, modern power electronic systems conventional improves system reliability and has flexibility to voltage regulator could be replaced by Switch Mode make the modifications so as to reach the desired Power Supplies. Based on the requirement of the needs [5]-[6]. As in current years, the enhancement in design, SMPS have reduced component, smaller size, microprocessor or in digital signal processors the lower cost, higher efficiency, higher reliability lower application of digital controller for high frequency switching stress, wide conversion range, power factor converters are developing interest. correction, output voltage regulation and better As the area of application of SMPS requires performance. Due to these features the trend of constant regulation of load voltage even for the SMPS has proliferated in various areas. Some of variation of load and source voltage and this is now a these areas that employ SMPS are personal complicated task for power supply design engineers. computers, battery chargers, space stations, critical In past years, the power stage of the converter medical equipments etc. The SMPS employ high has been modeled using conventional and developed switching frequency dc-dc converter and the modeling methods. The controller has to be improvement in these circuit are nowadays in developed in order to attain desired performance progress for the following reasons: 1) to improve characteristics. But due to parametric variation the performance; 2) to attain better reliability and 3) to system become unstable for some operating increase the power density [1]-[3]. These conditions. Hence there appear the requirements of developments are made in such a manner that they the controller that will control the switching of the meet the requirements of fast dynamic response and converter due to which it regulate the constant load low EMI. voltage even for any change in load, source or other Conventionally power electronic converters have parametric variations. been controlled using analog controller technology. II. MATHEMATICAL MODEL Analog controlling techniques were prevalent due to FORMULATION OF BOOST CONVERTER their ease of implementation and lower cost. In spite The circuit diagram of a dc-dc boost converter of this, they are sensitive to external influences such is shown in Fig.1. Here it is assumed that the as noise, temperature and aging [4]. Besides, converter is operating in CCM and in one switching execution of advanced control in analog circuit is cycle it exhibits two modes of operation which problematic. Earlier the price and performance depends on the switch „ON‟ and „OFF‟ time. In mode aspects of analog controllers were popular, but this I the switch is ON the inductor current rises and the ratio for digital signal processors has descended and diode becomes reverse biased at o T. M. Swathy Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 5, ( Part -1) May 2015, pp.62-65 models can easily be formulated, whereas small- [ẋ] = Ax Bu (2) signal models can be determined using state-space y Ex methods [7]. (3) L rl Where [A]-state matrix,[B] -input matrix,[E] - output matrix and,[x] -state vector,[y] -output vector,[u] -excitation vector. C rL / L 0 Vo Vg R A1 0 1/C(rC R) rc (rL / L) Rrc / L(rc R) R / L(rc R) A2 R /C(rc R) 1/C(rc R) (a) T T 1 2 L B 1/ L 0 B 1/ L 0 rl E1 0 R/(R rC) E2 rc /(1 rcR) R/(rc R) u vg T C x iL vc R Vo Vg rc III. ATTRIBUTES FOR COMPENSATOR DESIGN (b) After the power stage transfer function are L developed, then the digital controller can easily be to rl attain a desired characteristics. Two approaches can be used in the design of digital compensator. One is digital redesign approach and second one is digital direct design approach. In direct redesign method the C R Vo Vg compensator is first designed in s-domain then the rc continuous domain compensator is converted into discrete-time compensator by proper conversion technique. In digital direct design approach the compensator is designed directly in discrete-time (c) domain by including time delay. This method has the Fig.1. Boost converter and its operating modes. (a) advantage that pole-zero of the compensator are Boost converter circuit diagram. (b) Mode-I placed directly which results in better phase margin operation. (c) Mode-II operation. and bandwidth of the converter. In this paper the digital direct design approach has been implemented 2.1 Steady- State Analysis to develop a compensator for the converter. In In this section, the following assumptions are digitally controlled converter system the loop gain is considered to determine the steady-state analysis of expressed by L(z)=Gc(z)Gvd(z), where Gc(z) is a the converter: an ideal switch, a constant digital controller. The closed loop of the converter is instantaneous input voltage Vg, and a purely resistive shown in Fig. 2. The foremost steps that are effective load. By making the use of Kirchoff‟s voltage and at the design stage are as follows: 1) to achieve better current laws, steady-state relationships among speed response higher the bandwidths, however the different voltages and currents can be obtained. The loop gain lies in the range of fs/10 T. M. Swathy Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 5, ( Part -1) May 2015, pp.62-65 3 2 a3z a2 z a1z a0 (4) 60 Gvdz L 3 2 b3z b2 z b1z b0 Gc L 40 k(z a) (5) GC(z) (z 1) 20 (dB) Magnitude 0 Converter model Vg iload -20 Input Gvg(z) Zo(z) Load variation variation 0 Error -45 signal d -90 Gc(z) Gvd(z) + - -135 noise Vre f (deg) Phase -180 + + - - L(z) -225 1 2 3 4 5 10 10 10 10 10 Frequency (Hz) Fig.2. Block diagram of closed loop of the converter Fig.3. Frequency response bode plot of Gvd(z),controller and loop gain transfer function of IV. RESULTS AND DISCUSSION the system A dc-dc boost converter with 50 kHz switching frequency is considered. The converter has been The controller designed for the converter is: developed in MATLAB- Simulink platform to (z z1) endorse the digital control of the converter at 28V, GC K 30W load. The components values of the converter (z 1) (6) are listed in Table I. The modeling and steady state The pole-zero placement of the controller analysis are discussed in section II. Fig.3 shows the depends on the required stability margins, the noise frequency response bode plot of small-signal transfer attenuation amount. The phase margin and gain function of the converter, loop gain and compensator. margin attained for open loop transfer function are It has been observed from the plot that the 51.6º and 12dB respectively. For practical compensator which has been developed yield high consideration, source voltage and load variations gain at low frequency for open loop transfer function. have been considered. It is assumed that a constant Hence this will reduce the steady state error in the source voltage is regulated but due to some faults power supply output. The frequency response bode fluctuations may be possible up to 30% around the plot of small signal transfer function of converter and nominal value (disturbance in source voltage Vg loop gain under parametric variation is shown in :9→12 V); similarly, the relative load variation is Fig.4. around 50% of the nominal value (disturbance of TABLE I load resistance R : 26→52 Ω). The simulated result CONVERTER PARAMETERS of the system under detailed parameter range:±30% Parameters Value source voltage variation and 50% load variation is Vg 12V shown in Fig.5 and Fig.6 respectively. Vo 28V R 26Ω±50% 80 L, r 63.72µH,0.08Ω L 60 C, rC 250µF,0.03Ω 40 fs 50kHz 20 Magnitude (dB) Magnitude 0 -20 0 -45 -90 -135 Phase (deg) Phase -180 -225 1 2 3 4 5 10 10 10 10 10 Frequency (Hz) Fig.4.Frequency response bode plot of loop gain transfer function of the system under parametric variation www.ijera.com 64 | P a g e T. M. Swathy Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 5, ( Part -1) May 2015, pp.62-65 REFERENCES 32 28.2 28.2 [1] B.Alexrod, Y.Berkovich and A.Ioinovici, 30 28 28 0.7 0.7001 1.1 1.1001 ”Switched-Capacitor(SC) switched 28 inductor(SI) structures for getting Vo 26 hybrid step-down Cuk/ Zeta/Sepic 24 converters” in Proc. IEEE ISCAS, 2006, pp. 5063–5066 22 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 [2] B.Alexrod, Y.Berkovich and A.Ioinovici,“ Time -16 Hybid Switched-capacitor Cuk/Zeta/Sepic in x 10 5 step-up mode” in Proc. IEEE Int.Sym. Circuits and Systems, 2005, pp. 1310–1313. 4 [3] B.Alexrod, Y. Berkovich and A.Ioinovici,“ 3 Io Switched capacitor/switched inductor 2 structures for getting transformerless hybrid 1 dc–dc PWM converters” IEEE Trans. 0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Circuits Syst. I, Reg. Papers, vol. 55, no. 2, Time pp. 687-696, Mar. 2008. Fig.5. Simulated result of the converter load voltage [4] J.-J.Lee and B.-H.Kwon, “DC-DC converter and current under source voltage variation from 12V- using multiple-coupled inductor for low 9V output voltages,” IEEE Trans. Ind. Electron., vol.54,no.1, pp.467-478, Feb.2007. 30 [5] Shamim Choudury, “Digital Control Design 28.2 28 28 29 and Implementation of a DSP Based High 0.7 0.7001 1.1 1.1001 1.1002 Frequency DC-DC switching Power 28 Vo converter”, Texas Instrument. Inc. 27 Ro=26 ohm Ro=52 ohm [6] Yan-FeiLiu, P.C.Sen, “Digital Control of 26 Switching Power Converters,” 2005 IEEE 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 time Conference on Control Applications, -16 x 10 Toronto, 2005, pp. 635-640. 6 [7] Mohan, Undeland, Robbin, “Power 5 Electronics” (Wiley, 1976, 3rd edn.2009). 4 Rev., vol.134, pp.A635-A646, Dec.1965. Io 3 2 1 0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Time Fig.6.Simulated result of converter load voltage and current under load variation from 26Ω-52Ω V. CONCLUSION A dc-dc second order boost converter has been digitally controlled to supply regulated 28V, 30W dc load. The power stage of the power supply is designed to operate in 50 KHz switching frequency. To analyze the frequency response of the converter a small-signal model is being formulated using state space averaging technique. In this paper he controller is developed using digital direct design approach with the help of frequency response of the power stage. The digital direct design approach has the advantage of direct placement of pole zero which results in better bandwidth and phase margin of the converter. The SMPS design is being simulated in MATLAB to show that it generates regulated desired output voltage with the ±30% in source voltage variation and ±50% load variation. www.ijera.com 65 | P a g e