Comparison between Zeta Converter and Boost Converter using Sliding Mode Controller

Comparison between Zeta Converter and Boost Converter using Sliding Mode Controller

Kambli Omkar Vijay P. Sriramalakshmi

School of Electrical Engineering Ap, Select

VIT University, Chennai VIT University, Chennai India India

Abstract This paper presents a dynamic modelling and control of a Zeta converter as well as boost converter evaluated in MATLAB/SIMULINK based simulation. A Zeta converter topology provides a positive output voltage from an input voltage and also provides option for regulating an unregulated power supply. The Zeta converter is configured from buck converter but unlike buck converter, it includes two inductors and two capacitors. A comparison between Zeta converter and Boost converter is done using sliding mode controller under the load voltage variation. The feedback loop provides voltage regulation against any disturbance in load voltage by keeping input side constant. The simulated output voltage, current and graph between voltage gain and duty ratio are shown in the paper.

Keywords Zeta converter, Boost converter, Voltage mode control, Sliding mode controller etc.

1. INTRODUCTION

   Switched DC-DC converters aid in increasing the voltage from a low battery voltage thereby facilitating in accomplishing a regulated DC output voltage which would rather require multiple battery sources.

   Though zeta converter is similar to that of a buck-boost converter, it has an advantage of non-inverted output. It has a wider range of duty ratio than any other converter. The converter exhibits improved power factor, low input current distortion, low output current ripple and wide output-power range [1]. A boost converter is a DC-DC converter in which output voltage is greater than input voltage, while stepping down a current. As the control input appears in both voltage and current equation, the controlling of boost converter is difficult [7].

   In an open loop system output cannot be compensated or controlled if there is an input voltage variation or disturbance. Therefore to regulate the DC-DC converters, different control techniques are applied and a robust output voltage is achieved.

   Due to non-linearity of DC-DC converters, linear control techniques are not efficient; therefore to design a linear control system, small signal model is obtained by state space averaged model. The state space model is a time domain model where the system is described by differential equation.

   The property of hysteresis control is extended in sliding mode control to multi variable environment, and is able to constrain the system status to follow trajectories which lie on a suitable surface in the state space. The motion of the system as it slides along the boundaries is called a sliding

   mode and the geometrical locus that contains these boundaries is called the sliding surface [6].

   Fig.1. Block diagram for the whole system

   The proposed system consists of a DC source, a DC-DC converter, resistive load and a controller for regulating output voltage as shown in Fig 1. This system presents a dynamic modelling and voltage mode control of a Zeta converter and boost converter using a sliding mode controller.

2. OPERATING PRINCIPLE OF ZETA CONVERTER AND DC-DC BOOST CONVERTER

   1. Boost converter

      The conventional boost converter topology is as shown in Fig.2.Also two modes of operation of boost converter are shown in Fig.3 and Fig.4 respectively.

      Fig.2 Conventional Boost converter topology

      1. Mode 1

         In this mode, the switch S is ON, resulting in increasing inductor current. In this mode the equation becomes,

         = … (1)

      2. Mode 2

      Fig.3 Mode 1 operation of boost converter

      Fig.6 Mode 1 operation of zeta converter

      In this mode, switch S is OFF, the inductor current flows

      By Kirchhoffs Voltage law,

      through load and the equation becomes,

      1 =

      (3)

      1

      = ()(1)

      … (2)

      2 = + 1 2

      (4)

      2

      2

      2

      Fig.4 Mode 2 operation of boost converter

   2. Zeta converter

   The equivalent circuit of Zeta converter is as shown in Fig.5. It comprises of a switch, a diode, two capacitors 1 and 2 , two inductors 1and 2 and a standing resistive load.

   Fig.5 Zeta converter topology

   The operation of zeta converter is designed in Continuous Conduction Mode (CCM) and the circuit operation can be defined by two modes of operation are shown in Fig.6 and

   By Kirchhoffs current law,

   2 1

   2 1

   2 = (5)

   b) Mode 2

   In this mode, the switch 1is OFF and the diode 1 is forward biased. During this interval, previously charged inductor 1 starts to discharge. So stored energy in 1 and

   2 are discharged through capacitors 1 and 2. Therefore, the inductor currents iL1 and iL2 decrease gradually.

   Fig.7 Mode 2 operation of zeta converter

   By Kirchhoffs voltage law, voltage across inductor (1) is given by,

   1 1

   1 1

   1 = (6)

   Voltage across inductor (2) is given by,

   2 2

   2 2

   2 = (7)

   By applying Kirchhoffs current law, current through the capacitor 1 is,

   Fig.7 respectively.

   = 1

   1 1

   1 1

   (8)

   a) Mode 1

   In this mode, the switch 1 is ON and the diode 1 is reverse biased. Inductors 1 and 2 is charged from the

   The relation between input voltage, output voltage and the duty cycle (D) of zeta converter in CCM is given by,

   D = 0

   0+

   source and the inductor current

   and

   increases

   Therefore,0 = =

   (9)

   linearly. Also, discharging of

   1 2

   an chargin of

   take

   1

   1 d g 2

   By volt second balance,

   place.

   + (

   ) = 0

   1

   Taking average over one cycle,

   =

   1

   . (10)

   By applying volt-second balance, the relation between output voltage and input voltage is given by

   Where rC1 and rC2 are equivalent series resistors and rL1 and rL2 are DC resistors.

   = 1

   1

   State-Space Model of Boost converter:

3. DESIGN OF PROPOSED SLIDING MODE

   0 (1 )

   CONTROLLER

   To ensure stability in any operating condition, a suitable control technique should be employed for DC-DC boost converter that matches with their non-linearity in input voltage and load variations.

   = [(1 )

   1

   = [

   0

   ]

   1

   0

   1]

   Sliding mode controller is a nonlinear control method

   th

   = [0 1]

   at alters the dynamics of the system by applying a discontinuous control signal thereby forcing the system to slide along the cross section of systems normal behavior. The sliding surface is selected in such a way so that the system trajectories near the surface are directed towards the surface itself by the proper controlling of the converter switch irrespective of the circuit parameters. The controller variable provides a fast transient response along with tracking a certain reference path to achieve desired dynamic response. If these conditions are satisfied, the system status moves from its initial value towards the sliding surface thereby maintaining the switching action [6].

4. CONTROLLER FOR DC-DC CONVERTE State space averaging is important for mathematical

   modeling of sliding mode controller. To develop state space model, the equations for the rate of change of inductor current and the equations for the rate of change of capacitor voltage are used [5].

   A. STATE-SPACE MODEL OF ZETA CONVERTER

   State variable description of system is as follows:

   = +

   = +

   1 0

   = 0

   Instead of state variables, consider new state variable that is the error vector of state space variable X to be considered. So, the sliding surface equation in state space is expressed by,

   = 11 + 22 + 33 + 44 = … (11) Where, = [1234]

   1234 are control parameters termed as sliding coefficients.

   A sliding surface can be obtained by, S=0.

   For this system, it is appropriate to have a general SM control law that adopts a switching function such as,

   u=1 when S>0

   =0 when S<0

   A sliding mode control system is designed for boost converter as shown in Fig.8 [8].

   ( ) +

   ( )

   ( + )( + ) +

   =

   =

   ( )

   ( + )

   ( + )

   [

   ( + )

   ( + )]

   =

   ( + )

   Fig.8 Control scheme of Zeta converter using sliding mode controller

   [ ( + )]

   = [

   +

   ]

   +

   = [ ]

   +

   The control scheme for boost converter is designed as shown in Fig.9 using sliding mode control technique [8].

   Fig.9 Control scheme of Boost converter using sliding mode controller

   IV .DESIGN SPECIFICATIONS

   The Zeta converter is designed as follows; The input inductor 1 is given as,

5. SIMULATION STUDIES AND RESULTS

   The performance of controller with reference load voltage variation is analyzed. Under the load voltage variation from 90 V to 120 V, the output voltage and output current can be regulated and controlled by controller.

   1. Simulink model of boost converter

      The closed loop simulink model of the proposed converter has been designed according to Table 1 parameters.

      1

      1

      =

      1

      … (12)

      Where, 1 is the permitted ripple current in inductor 1

      and considered to be 10 % of output current 0.

      The value of input capacitor 1 is given as,

      1

      1

      = 0

      … (13)

      Where, is the permitted voltage ripple in capacitor 1

      and considered to be 2% of supply voltage .

      The output inductor 2 is given as,

      Fig.10 Simulink model of closed loop control of Boost converter

      Output voltage of boost converter in closed loop

      2

      =

      2

      … (14)

      configuration is shown in Fig.11.

      The value of output capacitor 2 is given by,

      8222

      8222

      2 =

      … (15)

      Simulink model of proposed converter is implemented with following design parameters;-

      Fig.11 Output voltage of conventional Boost converter

      Output current of boost converter in closed loop configuration is shown in Fig.12.

      Fig.12 Output current of conventional Boost converter

      1. Simulink model of Zeta converter

   The closed loop simulink model of the proposed converter using sliding mode controller is shown in Fig.13.

   Fig.13 Simulink model of closed loop control of Zeta converter

   The output current under dynamic condition is as shown in Fig. 14.

   Fig.14. Output voltage waveform of Zeta converter

   The output current under dynamic condition is as shown in Fig. 15.

   Fig.15. Output current waveform of Zeta converter From simulation results, the voltage and current

   stress across the inductor, capacitor and diode are tabulated as below:

   Table II. Voltage and current stress across passive components

   Attributes	Boost Converter	Zeta Converter
   Inductor current ()	2.11 A	1 = 2.22 2 = 0.9132
   Capacitor voltage ( )	109.4 V	1 = 110.5 2 = 110.5
   Diode current ()	2.11 A	0.9134 A

   A graph between voltage gain and duty cycle for both boost and Zeta converter is plotted as shown in Fig.16

   Fig.16. Voltage Gain Vs Duty cycle

6. CONCLUSION

A performance comparison between Zeta converter and Boost converter is done and simulation results using sliding mode controller under the load voltage variation are discussed. Also dynamic modeling of Zeta as well as Boost converter is presented. It is understood that the Zeta converter is suitable for various applications because boost converter has reversed polarity of output voltage and high ripples in output voltage. The output voltage of Zeta converter is boosted more than the voltage obtained with the boost converter. The sliding mode controller is analyzed to regulate output voltage and output current under any disturbance either in supply side or in load side. The simulation results are shown with sliding mode control.

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