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Digital Voltage Control of DC-DC Boost Converter

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Digital Voltage Control of DC-DC Boost Converter 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<DTs. In mode II digital controlling technique turned out more popular. the switch is turned OFF and the diode becomes Certain limitations of analog controller seized by forward biased at DTs<t<Ts, where „D‟ is the duty digital controller and it offers some advantages such ratio of the switch. For the performance analysis of as faster design process, offers facility to integrate the converter it requires steady-state and small-signal with other digital system, consume low power than models. By using time domain analysis steady-state www.ijera.com 62 | 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 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 1 C E 0 R/(R r ) 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<fc<fs/5; 2) to voltage gain of the converter obtained: achieve higher low-frequency gain pole needs to be Vo 1 (1) placed at origin; 3) the phase margin of open loop Vg 1 D transfer function must be in the range of 45º-75º. 4) Gain margin of open loop transfer function should be 2.2 State-space Modeling at least 6dB [7]. These guidelines have to use while State-space modeling is well created in the controller design to attain desired characteristics. switch-mode power conversion systems. The Depending on the nature of the transfer function of following analysis is done to obtain a small-signal converter fine tuning of compensator is needed. The transfer function. In a continuous-conduction mode, loop-gain of the closed loop system, including there are two states: one state relates to when the compensator is in the form is shown in equation (4) switch is on and the other when the switch is off. and (5) respectively. During each circuit state, the state equations are given by: www.ijera.com 63 | 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 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 -45 Error 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.
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