M. Marimuthu , Dr.S.Saju , Dr.Vijayalakshmi

Discrete Controller for Zeta Converter M. Marimuthu1, Dr.S.Saju2, Dr.Vijayalakshmi3

1Department of EEE, 2Department of EIE, 1 Saranathan College of Engineering, 2Erode Sengunthar Engineering College

[email protected],[email protected]@first-third.edu

Abstract— In this paper an effort is attempt for applying the closed loop periodic sequence based discrete

controller for zeta converter which is commonly known as inverse sepic converter. Discrete controller deals an

upright forceful reaction, acceptable voltage regulation and it can be modified without peripheral passive

modules. Inverse Sepic Converter is accomplished of creating non oscillating output current and has a worthy

flexibility. Continuous and Discrete controllers are considered and the results are analyzed and tabulated in this

paper. Results shows that the Z-transform based controller provides a worthy transient response. Experimental

Validation of the controller is performed using Virtual Instrumentation with a Data Acquisition card (NI-6009).

Keywords—Zeta converter, Discrete controller, analog to digital conversion, Digital Pulse Width

Modulation .

I. INTRODUCTION

This DC-DC converters are broadly used for producing a voltage regulation from a source voltage that may

or may not be fine controlled to a loading device. DC-DC converters are in elevation of pulsating power

transformation device that use high pulsating switching circuits and inductors, transformers, and capacitors to

level out switching disturbances into regulated DC voltages. Feedback system provides a stable output voltage

even though there is a transition of input voltages and output currents. Normally much more capable for the

condition of 90% efficiency than linear regulators.

Inverse Sepic converter is a DC-DC converter which consists of two inductive coil and two sequential

capacitor design. It is well adapted for the operation of either boost up or boost down mode which

accomplishes a non-inverting buck-boost operation likely to that of a SEPIC converter. The ZETA converter

have an additional advantage for regulating an unregulated input power supply, like a low-cost wall wart. For

reducing the device space, a coupled inductive coil can be used. The Zeta converter is running in Continuous

Conduction Mode (CCM) with a coupled coil [1].

The most important task in the domain of DC-DC converter is the controller aspect. The method of

controlling requires the proficient mathematical modeling and facilitating systematic study of the converters.

Generally the converters are time invariant and non-linear, and it support with the huge passive components.

Usually the design of controller’s experiences higher complication in controlling, reduced tractability to larger

operations and systeriations, and have reduced consistency. The projected Z-transform based controller offers

lot of benefits than their analog controller.

A smaller number of of them could be i) not greatly inclined by the conservational deviations and aging ii)

lack of noise suppression, iii) No necessities to vary the primary hardware to revise the control strategy iv)

increased sensitivity to nonconformity in parameter v) tractability of its varying controller features vi) easiness

in procedure. It also agrees in its forceful reaction as determination, quick reaction and reduced damping [2].

JASC: Journal of Applied Science and Computations

Volume 5, Issue 11, November/2018

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The major steps in the scheme of digital controller are 1) In order to quantize the fault signal Analog to

Digital Conversion (ADC) proceeds 2) To compensate the fault signal digital compensator is to be employed 3)

To create good resolution Digital Pulse Width Modulation (DPWM) is to be considered. In this research work,

elevated degree Digital Pulse Width Modulation (DPWM) signals are produced by maintaining high system

switching frequency. The aim of controlling strategy in the plan of discrete controller has to operate the boost

converter along with a duty cycle so that the set point voltage and the desired output voltage of the dc signal are

equal. The support of stability factor in spite of variation in the regulatory or servo parameters. In addition to

the constraints in the planned discrete controller operations due to the duty cycle is limited between one and

zero. This constraints can be resolved by modeling the boost converter by means of state space averaging

methods. After putting on this procedure, the converter is expressed by a single equation approximately over a

amount of switching cycles. The discrete equation model constructs the controller and creates simulation much

quicker than its peer operation [6].

The above mentioned limitations in DC-DC converter can be explained by constructing a forceful

compensator method depending on discrete Proportional-Integral-Derivative controller, this controller

operation is depending on continuous domain in which the dc-dc converter need such as transient response

likely (%) maximum peak overshoot, steady state error, rise time and settling time are encountered. The

modelling of Zeta converter is achieved using discrete domain averaging technique and the simulation is

performed out by MATLAB-Simulink software. The prototype model has been designed using NI-LabVIEW

along with DAQ card NI – 9221 and the results are figured out in later section [8],[9].

The schematic diagram of digitally controlled Zeta converter with complete setup is shown in Fig.1. The

Zeta converter results out a optimistic output voltage from an source voltage that differs up and down the

output voltage. The results of the Zeta converter is compared against the preferred value of the reference

voltage using the comparator1 (Operational Amplifier IC 741). The Digital compensator is constructed for the

Zeta converter using discrete PID controller. The error output thus acquired is fed into the intrinsic block

diagram of the LabVIEW through the Data Acquisition Card DAQ NI 9221.

NI-LabVIEW section consists of Analog to Digital conversion(ADC), discrete transfer function and Digital

to Analog conversion blocks. Exclusive of the DAQ card, Analog to digital conversion is performed and thus

resultant signal is feedback into the discrete transfer function block in which the planned controller value is

entered. The result of the controller is acquired back by Data Acquisition Card which converts digital to analog

signal and feedback into the comparator block which is designed using operational amplifiers (IC 741). This

resultant is high frequency carrier signal (ramp signal) with the preferred switching frequencies obtained from

the signal generator. The resulting Pulse Width Modulation switching pulses are fed to the switch of the

converter over the gate drive circuits [3].

Figure 1Block diagram of Zeta converter



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II. ZETA CONVERTER

Zeta converter is the DC-DC converter and it consists of the power electronic supply voltage and the results

can be reduced and greater than the conventional input. This can be achieved by switching method with the

semiconductor components such as diodes and transistors. Generally the proposed Converter is designed with

inductive-coil L1 & L2 in order to supress the production cost and also the ripple current. Its important merit is

to preserve the output voltage polarity as same as the input.

Since the operation of converter is based on a switch mode circuit, the entire result is then depending on

inductive coil current and Capacitive voltage Assume that the operation of zeta converter is in continuous

conduction mode (CCM),there are two modes of working within one switch mode when it is turned off. It

consists of Metal Oxide Semiconductor Field Effect Transistor (MOSFET) for switching, dual capacitors C1 and

C2, protective diode D, dual inductive coil L1 & L2 and load R. ON State Condition of Zeta Converter (MODE 1)

Figure 2Circuit diagram of Zeta converter

A. When switch S is in mode-1 the diode is in off condition. This is depicted in Fig. 3 as an open circuit (for

diode) and short circuit (for S). During this condition, inductive coil L1 and L2 are in charging mode ie.,the

inductor current iL1 and iL2 increased linearly. The capacitor C1 will discharge to Vo and it is connected in series

with L2. So that the voltage across the inductor (L2) is Vs and diode is Vs+Vo.

By applying Kirchoff’s voltage law, voltage across L1 will be,

(1)

= (2)

And voltage across L2 will be,

=

(3)

Figure.3 Zeta converter when S is closed



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= (4)

By applying Kirchoff’s current law the rate of voltage through the capacitors will be,

=

(5)

= (6)

= (7)

= (8)

A. OFF State Condition of Zeta Converter (MODE 2)

When Switch S is in Mode-2 (OFF-state), the diode D is on. Opposite to previous mode of operation, the

equivalent circuit of Fig. 4 figure out that the diode is short circuit and switch S is in open circuit. At this

condition, inductive Coil L1 and L2 are in discharge phase. Since the voltage polarity of the conductor varies, the

diode will get forward biased and it will conduct

Figure.4 Zeta converter circuit when the S is open

Energy stored in inductive coil L1 and L2 are discharged to capacitor C1 and output part respectively. As a

result, inductor current iL1 and iL2 is decreased linearly. By applying Kirchoff’s voltage law, voltage across

inductor L1 is expressed as,

=

(9)

=

(10)

Voltage across inductor L2 is expressed as,

=

(11)



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=

(12)

By applying Kirchoff’s current law, current flows through the capacitor C1 is expressed as,

=

(13)

= (14)

Current flows through the capacitor C2 is expressed as,

= (15)

= (16)

B. Calculation of Output Voltage

By comparing the equations (2) and (10)

VS Ton = VC1 Toff

VC1=VS (17)

By comparing the equations (4) and (12)

(18)

Substitute equation (17) in (18)

(19)

(20)

(21)

Duty cycle D = (22)

Substitute equation 22 in 21

The output voltage (23)

III. DESIGN ANALYSIS All The ripple current through the energy transformation (input) can be expressed as,

(24)

(25)

(26)

(27)

The output inductor current ripple can be expressed as,

The capacitor ripple voltages ΔVC1 and ΔVC2 can be derived from the Kirchoff’s current law for first and

second mode as

(28)

(29)



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(30)

(31)

Where, F= Switching frequency

Then, Kirchoff’s Voltage Law are written in the loops consisting of the switch in the off-state infers that the

voltage stress on S and D is

(32)

A. Calculation of Duty Cycle

The output voltage of Zeta converter can be calculated from the formula

(33)

The duty cycle D for Zeta converter in CCM is given by,

(34)

(35)

TABLE I

CALCULATED CIRCUIT PARAMETERS OF ZETA CONVERTER

Parameter Value

Input voltage 14 V

Output voltage 21 V

Output current 1.5 A

Output power 15 W

Switching frequency 25 kHz

Duty cycle 0.6

Inductor L1 and L2 1.6 mH and 1.8

mH

Capacitor C1 and C2 480 μF and 10

μF

B. State Space Model

State-space averaging (SSA) otherwise discrete domain averaging method is a well-known used procedure for

the mathematical modelling of switching converters. To design the state space averaged model, the expression

for the rate of change of inductor current along with the equations for the rate of change of capacitor voltage

are employed. A state variable explanation of a system is written as follow

Ẋ = Ax + BU (36)

= Cx + DU (37)

Where A is n x n matrix, B is n x m matrix, C is m x n matrix and D is used to pointed out the duty cycle ratio.

For a system that has a two switching topologies, the state equations can be described as

When switch S is closed

Ẋ = A1x + B1U (38)

= C1x + D1U (39)

When switch is opened

Ẋ = A2x + B2U (40)

= C2x + D2U (41)



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For switch closed at time DT and open for (1-D)T, the weighted average of equations are

Ẋ = [ A1d + A2(1 d)]x + [B1d + B2(1 d)]U (42)

Vo = [C1d + C2(1 d)]x + [D1d + D2(1 d)]U (43)

Let us assume the variables,

x1 = iL1 (44)

x2 = iL2 (45)

x3 = VC1 (46)

x4 = VC2 (47)

U = VS (48)

C. Mode 1

State space equation for ON state is expressed from equation (49) to (54) as

(49)

(50)

(51)

(52)

Ẋ = A1x + B1U

(53)

= (54)

D. Mode 2

State space equation for OFF state is expressed from equation (55) to (60)

(55)

(56)

(57)

(58)

Ẋ = A2x + B2U (59)

(60)

Using ON and OFF state equations, the system state space equivalent equation becomes to be represented as

Ẋ = [ A1d + A2(1 d)]x + [B1d + B2(1 d)]U (61)

(62)



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Ẋ = Ax + BU (63)

(64)

(65)

After finding the values of A, B, C and D matrices, analyse them in MATLAB command window using to get

transfer function [4].

Transfer function is

(66)

IV. DESIGN OF DISCRETE PID CONTROLLER

Fig. 5 Closed loop control system of Zeta converter with Discrete PID controller

Fig. 5 illustrates discrete PID controller based Zeta converter. The aim of the controller design is to

reduce the error between Vref (Reference voltage) and output voltage (Vo) which create the output to traject the

set point that is measured as a step input. The resultant signal is controlled by implementing the feedback path

[5].

Fig. 6.Analog to Digital Converter

The feedback loop confirms that the result must be unaffected to regulatory response, stable and offers

better time domain specification thereby enhancing the dynamic results. The error voltage Ve (difference

between Vref and Vo) is fed to Analog to Digital converter which quantized at a sampling rate approximate to

1µS. The purpose of the digital compensator is to produce the control signal by compensating the error (Ve).

Fig. 7. Discrete time compensation

The deviated signal is managed by digital compensator block with Proportional Integral Derivative

controller algorithm to produce the control signal. For the switching operation of digitalized zeta converter,

discrete Proportional Integral Derivative control can be recognized by its compensation block.



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The controlled compensator signal will disturb the converter performance considerably, so it is

important to recognize an appropriate compensation method to deliver enhanced converter operation by

creating the optimistic implementation of discrete controller. The resultant sampled signal control the switch by

producing gating pulses when it is operated through Digital Pulse Width Modulation (DPWM) block. The

DPWM is defined as a demodulator circuit that contains sample and hold block. It also consists of delay time

(td), A/D conversion time, switch transition time, computational delay and modulator delay.

Fig. 6 depicts the block diagram representation of Analog to digital converter (ADC) block. It is a device

that uses a sampling procedure for converting a continuous time signal to a discrete time. The converter consists

of delay, zero order hold, quantizer and saturation. The delay block performs out the duration between sampling

the differential signal and apprising the duty cycle ratio at the start-up of the next translation period. The zero

order hold is mainly for modeling the sampling effect. Quantizer is mainly used for rounding off or truncating

the signal that will plot an enormous set of input values to a reduced set such as rounding off values to desired

unit of precision [7]. The discrete time Compensation block is shown in Fig. 7. The resultant analog to digital

converter signal acts as an input to the discrete zero pole block which in turn is transformed into Pulse Width

Modulated signnal using DPWM blocks as shown in Fig. 8. The discrete time integral compensator thus

designed reduces the differential signal and sends the command signal to the switch in the arrangement of pulses

in order that the resultant signal tracks the reference signal. The resultant compensator signal is compared

against high frequency ramp signal in order to produce the duty cycle pulse for the switch [10]. Discrete

controllers are better in operation, and low cost than Analog controller

Fig. 8 Digital Pulse Width Modulation

. Discrete controllers are informal to handle, mainly elasticity, and nonlinear control expression involve

difficult in manipulation or logical operations. Extensive class of control laws can be deployed in Discrete

controllers than in Analog controllers. Discrete controllers are adapted to perform difficult manipulation with

stable accuracy rapidly and have almost any anticipated grade of manipulated correctness instead of minor

increase in cost. Discrete controller plays a vital role in the construction of Zeta converter to enhance a better

voltage regulation, sturdiness, fast switching transient and upgraded dynamic characteristics. Discrete controller

provides an additional performance on compared to analog controller. Discrete controller has reduced

component failure, reduced component prices, zero drift characteristic, high consistency and controllability.

Discrete PID controller is intended for the recommended Zeta converter. The designing of the discrete

controller consists of two steps, initially design an Analog PID controller for Zeta converter using Ziegler-

Nichols tuning methodology and to conclude roughly the characteristics of an Analog PID controller with a

Discrete PID controller which translates continuous domain into discrete domain. In order to achieve an exact

response, the controller anticipates the differential signal and trajects the distinct output in the discrete domain.

The passive components such as inductive coil and capacitors and switching devices presents

nonlinearities in the Zeta converter. As a moment, the linear control method cannot be rightly implement for

DC-DC converter, hence the importance for closed loop compensation rises, which is proceeded by applying

linear control technique. The analog PID controller expression can be written as (67)



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Figure. 9 PID controlled system

(67)

This expression is laid-back to find the transfer function of feedback system.

(68)

(69)

(70)

(71)

Where ωo is the natural frequency oscillation, is the damping ratio of the system. The Zeta converter

under deliberation is of higher order and the desired poles can be simply located by considering the below

converter conditions,

Settling time ≈

Max Peak Overshoot ≈ 100 (72)

By applying the above said transient response expression and settings, the derived Analog PID

controller values of Zeta converter is KP = 0.07, KI = 1440 and KD =1.525x10-6. Then the Continuous controller

for Zeta converter can be expressed as

(73)

Fig. 10 Step response of Zeta converter with analog PID controller



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To validate the robustness of the Continuous PID controller, step input of size 1V is applied to the

transfer function of the converter with the controller setup. The respective generated result has been shown in

Fig. 10. From the figure, it is illustrated that the converter settles down quicker with the duration of 0.035 s and

it does not falls damping. The simulated result shows that the Continuous PID controller is suitable to recognize

the robustness of the Zeta converter.

The Discrete controller is tranquil to construct for different types of converters, it does not create any

limitation in damping for any determination of DPWM, and also the characteristics of the proposed controller is

exceptional. The controller transient response such as percentage peak overshoot, settling time, and rise time are

very small. It has fewer ripple voltage and steady state error only. For any abnormality in input voltage and load,

the controller boundlessly tracts the reference and establish a steady output response voltage and confirmed its

improved robustness. The deviated Signal obtained by device deviations up to definite constraints are

correspondingly resolved by Digital compensator by changing the duty cycle of the converter to establish the

staedy output voltage.

The analog controller which is explained in the above expression (73) is translated into the digital

controller by using Trapezoidal method. Thus the constructed Discrete PID controller transfer function can be

attained as follows:

Let n(t) be the integral of e(t), then the value of the integral of t = (K+1)T is equal to the sum of KT to

(K+1)T.

N[(K+1)T] = u(KT)+ (74)

Using bilinear transformation rule, e(t) is the area of the curve from t = KT to t = (K+1)T is estimated

as

(75)

hence

N(K+1)T = n(KT)+ (76)

Taking the Z-transform of equation (76), then

ZN(Z) = N(Z) +

Thus = (77)

Equation (77) represents the transfer function of a Discrete Integrator. Bilinear Transformation

approximates to differentiation, derivative of e(t) at t = KT is n(KT), then

(78)

Taking Z - transform of Equation (78)

= (79)

Then the Discrete PID controller transfer function becomes



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= (80)

U(Z) = E(Z) (81)

(82)

Fig. 11 Root locus response of Discrete PID controller for Zeta converter in Z-domain

The stability of the Discrete PID controlled Zeta converter is validated by the root locus plot and is drawn

for expression (82). The resultant root locus of the Discrete PID controlled Zeta converter is shown in Fig. 11,

it is evidently illustrated that the poles are neither neither outside the unit circle nor at -1. Multiple poles do not

occur. All the poles are placed in the right half of the Z-plane, thereby gratifying the firmness condition of the

transfer function for the recommended controller.

V. SIMULATION RESULT

The suggested closed loop Zeta converter is simulated using Matlab/Simulink. Table 2 describes the

characteristics of the various controllers using the identified Zeta converter. The resultant voltage is derived by

applying Discrete PID controlled Zeta converter resolves down at 4 ms with a rise time of 3 ms. The controller

characteristics under proposed work with steady state error, settling time, peak time, rise time, ripple output

voltage and overshoot which is related against its Discrete PI, Analog PI and analog PID controllers are

constructed for the identified Zeta converter. Steady state error examined for load change is much smaller than

1 % and no undershoot or overshoot are clear. The performance requirements for the Zeta converter with

Discrete PID controller are better than Discrete PI, Analog PID and Analog PI controllers. The results thus

attained with Discrete PID controller for Zeta converter is similar and concurrence with the mathematical

calculations. It is proved that the Discrete system illustrates an improved results than the Analog controllers.

The simulation is taken out by changing the input voltage, load resistance, reference voltage and the

corresponding output voltage, and output current are depicted in Fig. 12. The input voltage is fixed as 10 V

until 0.03 s and then varied to 14 V, 18 V, 14 V and 10 V throughout the time instance 0.03 s, 0.06 s, 0.09 s, and

0.12 s respectively. The load resistance is also changed concurrently with an input voltage. The load resistance is

fixed as 14 Ω till 0.03 s, and then varied to 18 Ω, 22 Ω, 18 Ω, and 14 Ω during the instance 0.03 s, 0.06 s, 0.09 s,

and 0.12 s respectively. The reference voltage is also all together changed up to 0.075 s, it is 7 V afterwards it is

20 V as depicted in Fig. 12. In the simulated answer, the performance of Buck action up to 0.075 s and then

carry out as a Boost process in Zeta converter with the changes in input voltage and load resistance.



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In dual operation overshoot or undershoots are not observed in the output voltage and there is no mark for

steady state error, and output ripple voltage is forever smaller than 3 %. To verify the dynamic reaction of the

controller, the L, C and R values are differed and the output response of the system is illustrated in Table 3. By

changing the capacitance and inductance values of the Zeta converter, the simulated outcomes are tabulated.

The Table 3 confirms that the system is very much active in tracking the reference voltages in spite of the

changes in the inductances L1 and L2, capacitances C1 and C2 and Load resistance R values. The system does

not prove any steady state error, undershoot or overshoots and it settles down at a speedy rate with a settling

time of about 4 ms for all the values. Simulation is also brought out by changing the load not limiting to R, it can

extend to RL and RLE load.

The output voltage has not varied due to the variation in nature of the load. Therefore the above results

confirmed that the designed Discrete controller gives tight output voltage regulation, better stability and

robustness. The efficiency against load resistance graph of the Zeta converter and the Discrete PID controlled

Zeta converter is depicted in Fig. 13. The input voltage is 12 V, reference voltage is 21 V, and the changes load

resistance is between 2 Ω to 12 Ω, then the efficiency of the Discrete PID controlled Zeta converter efficiency

has been varied from 97.8 % to 96.8 % Whereas the efficiency of the uncontrolled Zeta converter is varied from

84 % to 90 %.The efficiency graph evidently validates that the suggested Discrete PID controlled Zeta converter

is more efficient than the uncontrolled Zeta converter and also the efficiency of the Discrete PID controlled

Zeta converter has been almost constant with the variations in load. In the uncontrolled Zeta converter, if load

is varied, the efficiency is varied which is not desirable. Fig. 14 depicts the output voltage response of the Analog

PID controlled, Discrete PID controlled Zeta converter. Fix the Zeta converter input voltage is 14 V and the

reference output voltage is 21 V, the attained Analog PID controlled Zeta has more ripple voltage, overshoot,

and steady state error. It has more rise time and less accurate settling time.

The Discrete PID controlled Zeta has low settling time & rise time, and the peak overshoot is less than

1 % with an insignificant steady state error with no ripple voltage. With this response, it is very well identify that

the performance parameters are outstanding in Discrete PID controller than in Analog PID controller. The

output voltage response of the Discrete PID controlled Zeta converter for change in load is depicted in Table 4.

The nature of load is changed as R, RL, and RLE and changing nature has not influenced the output voltage of

the converter is clear. In Table 4, the load resistance is differed as 14 Ω, 18 Ω and 10 Ω, the converter will be

capable to produce the output voltages as 21 V, 20.998 V and 6.996 V for the reference voltages of 21 V, 21 V

and 7 V respectively. Then the simulation result is taken for the inductance of 5 mH and 10 mH, inserted to the

resistance of 14 Ω and 18 Ω, the output voltage is acquired in the order of 7.001 V and 21.002 V respectively for

the fixed reference of 7 V and 21 V. Again the output has been obtained using RLE load with a resistance of 20

Ω, inductance of 1 mH and an voltage source of 2 V, the controller is capable to find the output voltage as

20.997 V for the specific reference of 21 V. Similarly, an output voltage of 7.001 V is tracked for the fixed

reference of 7 V, whose RLE values are 9 Ω, 5 mH and 3 V. From the table, it is proved that the controller is

able to respond to the load change and can produce an output voltage equal to the reference voltage.

Table 2 Comparison of the various controllers for Zeta converter

Controller Settling

Time (ms)

Peak

Over

shoot

(%)

Rise

Time

(ms)

Steady

State

Error

(V)

Output

Voltage (V)

Discrete PID 4 0 3 0 0

Discrete PI 11 10 2 0.022 Less

Analog PID 19 3 18 0.011 More

Analog PI 21 12 20 0.032 More



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Table 3 Output voltage response of the Discrete PID controlled Zeta converter with the varying

component parameters R(Ω) L1 = L2

(µH)

C1(µF) C2 (nF) Reference

Voltage (V)

Output

Voltage(V)

15 965 10 383 8 8

30 900 15 300 8 8.002

25 850 20 350 16 16.001

22 950 15 275 7 7.001

20 925 12 325 16 16.001

10 875 15 400 22 22.001



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Table 4 Output voltage response of Discrete PID controlled Zeta converter for alter in load

S.

No

Load Reference

Voltage

(V)

Output

Voltage

(V)

R

(Ω)

L (H) E

(V)

1 14 - - 21 21

2 18 - - 21 20.998

3 10 - - 7 6.996

4 14 5 x 10-3 - 7 7.001

5 18 10 x 10-3 - 21 21.002

6 20 1 x 10-3 2 21 20.997

7 9 5 x10-3 3 7 7.001

VI. HARDWARE RESULTS AND DISCUSSION

The Zeta converter with Discrete PID controller has been executed using LabVIEW (Laboratory Virtual values

of the discrete PID controlled Zeta converter. LabVIEW is mainly employed as a platform for executing any

closed loop system and it can also be used for the betterment of a control system. It is widely used software,

planned for analyzing the projects experimentally with a smaller duration due to its programming flexibility

along with the integrated tools particularly designed for measurements, testing, and control.

Table 5 Experimental values of Discrete PID controlled Zeta Converter

Description Design

Values

Switching frequency

fS

20 KHz

Input voltage VS 14 V

Inductor L 550 nH

Capacitor C 700 nF

Load resistor R 14 Ω

MOSFET S IRF840

Diode D 1N 4001

DAQ NI 9221

The function of DC is validated well in the experimental setup and the LabVIEW also provides the most

possible solution for the controller platform. To assess the performance, the reference voltage of 21 V is fixed in

the Discrete PID controlled Zeta converter, for which the output is attained as 21.04 V. The steady state error

thus obtained is very small, in the order of 0.04 V and the system settles down fast in the rate of 1.5 ms. The

gaining of the error signal from the hardware takes place immediately, when the program is running and at the

same time the controlled signal from the LabVIEW package is also produced shortly without any time delay.

In the hardware setup, the input voltage to the Discrete PID controlled Zeta converter is 12 V, reference

voltage is fix as 21 V and the resistance of load is considered as 14 Ω then the obtained output voltage is 21.1 V

as depicted in Fig. 15. It has smaller settling time and rise time for the time period of 1.5 ms and has oscillation

at the initial time period, but it has settled shortly. No undershoot or overshoot is evident. The input voltage is

obtained at channel 2 and the output voltage is obtained at channel 3. In the output voltage response Steady

state error is 0.1 V which is lesser than 1%.



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Fig. 15 Output voltage response for 12 V input, R0 = 14Ω, andVref = 21V

In the same way the input voltage is 18 V, for 21 V reference and the load resistance is 14 Ω, then the

resultant voltage is illustrated in Fig. 16. It can be examined that there are no undershoots or overshoots but

steady state error has been attained in very minimum order. Instrumentation Engineering Work Bench) as a

controller platform. The table depicts the designed The figures clearly show that the variation in input voltage

and load resistance has not varied the output voltage.

Fig. 16 Output voltage acquired for 18 V input,

R0 = 14 Ω, and Vref = 21V

Fig. 17 Duty cycle obtained for 21 V reference

Fig. 18 Duty cycle attained for 8 V reference



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In the same research, duty cycle attained for 21 V, 8V reference is depicted in Fig. 17 and Fig. 18 respectively.

The attained output voltage is 20.95 V along with their PWM switching pulses with the duty cycle of 60.03 %

and 7.98 V along with their PWM switching pulses with the duty cycle of 36.3 %. From the output waveforms, it

is clearly understood that the output gives better performance, thereby more certain that the controller is more

suitable and can be tuned to track the references in spite of the change in input voltage. The Discrete PID

controller varies the duty cycle according to the variation in reference voltage and is not issued to any change in

the input voltage.

Fig. 19Output voltage is taken for VS = 12 V, R0 = 20 Ω to 10 Ω and Vref = 5 V

The output voltage response for 12 V input, load resistance of 20 Ω to 10 Ω, and the reference of 5 V as

illustrated in Fig. 19. The attained output voltage is 5.1 V and there is no maximum overshoot. The ripple

voltage and steady state error are less than 1 % and tolerable also. From the experimental outcome, it is

examined that the output voltage does not change with the step variation in load resistance, and thus confirming

its outstanding dynamic performance characteristics.

VI. CONCLUSION

In this paper, the Discrete PID controller for Zeta converter has been designed and implemented using

LabVIEW. The Discrete PID controlled Zeta converter has improved efficiency than the conventional Zeta

converter. The results attained with the proposed Discrete PID controller for DC-DC converter are in

concurrence with the mathematical calculations and also better perform than the existing analog controllers.

Simulation results reveal that the converters not only show the evidence of the steady state and transient

performance but also enhance the efficiency of the Zeta converter. The mathematical analysis, simulation results

and the experimental response reveal that the controller attains high output voltage regulation, good stability,

superior dynamic performances and more efficiency. This topology is well-suited with all other DC-DC

converter and also can be extended for any of the applications such as PV, Wind, telecommunication

applications, and speed control of DC motor drives.

REFERENCES

[1] Subramanian Vijayalakshmi and Thangasamy Sree Renga Raja, “Development of Robust Discrete controller for Double

Frequency Buck converter,” Online ISSN 1848-3380, Print ISSN 0005-1144 ATKAFF 56(3), 303–317(2015).

[2] Subhash Chander, “Auto-tuned, Discrete PID Controllers for DC-DC Converter for fast transient response,” in Proc.

IEEE-ICEMSC, 2011, pp. 1-4.



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[3] M.M. Peretz and S. Ben-Yaakov, “Time domain design of digital compensators for PWM DC-DC converters,” IEEE

Transactions On Power Electronics, Vol. 27, No. 1, pp. 887- 893, Jan 2012.

[4] Xiong Du, Luoweizhou, and Heng-Ming Tai, “Double – Frequency Buck Converter,” IEEE Transactions on Industrial

Electronics, Vol. 56, No. 5, pp. 16901698, May 2009.

[5] Jitty Abraham and K.Vasanth, “Design and Simulation of Pulse-Width Modulated ZETA Converter with Power Factor

Correction,” International Journal of Advanced Trends in Computer Science and Engineering, Vol.2 , No.2, Pages : 232- 238

(2013)

[6] KambliOmkar Vijay and P. Sriramalakshmi, “Comparison between Zeta Converter and Boost Converter using Sliding

Mode Controller,” International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 , Vol. 5 Issue 07,

July-2016

[7] H. Fakhrulkkin. Ali, Mohammed Mahmood Hussein, Sinan M.B. Ismael,“LabVIEW FPGA Implementation of a

PID Controller for D.C. Motor Speed Control”, Iraq J. Electrical and Electronics Engineering, 2010.

[8] R. Shenbagalakshmi, T. SreeRenga Raja, “Discrete Prediction Controller for DC-DC converter, ActaScientiarum.

Technology, 2014, pp. 41-48.

[9] S. Vijayalakshmi, Dr.T. SreeRenga Raja, “Design and implementation of a Discrete controller for soft switching DC-DC

converter, Journal of Electrical Engineering, 2013, pp. 1-8.

[10] Mohammed Alkrunz, IrfanYazıcı, “Design of discrete time controllers for the DC-DC boost converter”, SAÜ Fen Bil Der,

2016, 75-82.



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