Design of PI controller for Positive Output Super- Lift LUO Converter

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Design of PI controller for Positive Output Super- Lift LUO Converter

1K.Muthuselvi, ²L. Jessi Sahaya Shanthi

1Department of Electrical &Electronics, SACS MAVMM Engineering College, Madurai, India

2Department of Electrical &Electronics, Thiagarajar College of Engineering, Madurai, India Email:rajendran.urban@gmail.com

Abstract: The positive output super- lift LUO converter is one of the boost converters. It was developed in the year of 2003. The notion of this paper is to design and analyze a Proportional - Integral (PI) control for Positive Output Super- Lift LUO converter (POSLLC).Particularly for Triple-Lift LUO converter is focused. The function of the proposed converter is to convert positive source voltage to positive load voltage. The simulation model of the positive output super- lift LUO converter and its control circuit is implemented in Matlab/Simulink. The PI control for the above converter is tested for line voltage variations, load variations, component variations, steady State region and Dynamic region.

Keywords: DC-DC converter, Matlab, positive output super- lift LUO converter, proportional – Integral control, simulink. Steady state region, dynamic region

I. INTRODUCTION

DC-DC conversion technology has been developing rapidly and DC-DC converters have been mainly used in industrial applications such as dc motor drives, computer peripheral systems, insulation testing and medical equipments. The output voltage of pulse width modulation (PWM) based DC-DC converters can be changed by controlling the duty cycle [1]-[2]. The voltage lift technique is an important method that is widely applied in design of electronic circuit. This technique rejects the influences of parasitic elements and increases the output voltage greatly. Therefore these converters perform DC-DC voltage increasing conversion with large power density, higher efficiency and very high output voltage with small ripples [3].

Compared with classical DC-DC converters, Super – Lift LUO converters can provide the output voltages by increasing stage by stage along a geometric progression and obtain higher voltage transfer gains. They are divided into many categories according to their power stage numbers, such as the elementary circuit (single power stage), re-lift circuit (two power stages), triple – lift circuit (three power stages) etc.[4]. Their static and dynamic behavior becomes highly non-linear, because of the time variations and switching nature of the power

converters [5]. A good control for DC-DC converters always ensures stability in any operating point.

Moreover, good response in terms of rejection of load variations, input voltage variations and even parameter changes is also required for a perfect control scheme.

The PI control technique offers several advantages compared to PID control methods: stability, even for large line and load variations, reduces the steady state error, robustness, good dynamic response and simple implementation [2].

In this paper PI control with zero steady state error and fast response is focused. The static and dynamic behavior of PI control for positive output super- lift LUO converter is studied in Matlab/Simulink. For the purpose of optimizing the stability of positive output super- lift LUO converter dynamics, while ensuring correct operation in any working condition, a PI control is a more reliable approach. The PI control technique is insisted as a good alternative to the control of switching power converters [5]-[6]. The main advantage of PI control schemes is its ability to eliminate the effects of converter^’s parameter variations that leads to invariant dynamics and static response in the ideal case [2].

II. CIRCUIT DESCRIPTION AND OPERATION

The proposed Triple lift circuit is shown in Fig.1 and it consists of only one switch S, three inductors L₁, L₂ and L₃, Six capacitors C₁, C2, C3, C4, C5, C6 and eight freewheeling diodes. This converter is designed by implementing super-lift technique. This technique is more powerful than voltage –lift technique. In voltage- lift technique the same converter is designed with two power switches. The three output voltage levels are obtained. They are in arithmetic progression. Switching losses is also high[4].In super-lift technique only one switching element is used and particular numbers of diodes, capacitors and inductors are added for obtaining very high output voltage levels. The three output voltage levels are in geometric progression.

Fig.1 Triple- lift circuit

The voltage across capacitor C₁ is charged to V_in .Voltage V₁ across capacitor C₂ is V₁ =((2-k)/(1-k))V_in, and Voltage V₂ across capacitor C₄ is V₂=((2-k)/(1- k))²V_in .

Fig. 2 Turn on equivalent circuit

In the description of the converter operation, it is assumed that all the components are ideal and positive output triple lift converter operates in a continuous conduction mode. Fig. 2 and 3 shows the modes of operation of the converter.

Fig.3 Turn off equivalent circuit

The voltage across capacitor C₅ is charged to V₂.The current flowing through inductor L₃ increases with voltage V₂ during switching-on period kT and decreases with voltage (V₀-2V₂) during switching-off (1-k) T.

Therefore, the ripple of the inductor current iL₃ is Δ iL3=(V₂/L₃) kT=(V₀-2V₂/L₃)( 1 -k)T (1)

V₀=((2-k)/(1-k))V₂=((2-k)/(1-k))²V₁= ((2-k)/(1-k))³Vin (2) The voltage transfer gain is

G= V₀/V_in =(2-k/l-k)3 (3)

Average current

ΔiL1=(Vin/L1) kT (4) Δi_L2=(V₁/L₂) kT (5) Δi_L3=(V₂/L₃) kT (6) Therefore variation ratio of output voltage v₀ is

ε =(Δv0/2V0)=(1-k)/2RfC6 (7)

III. DESIGN OF PI CONTROLLER

The PI control is designed to ensure the desired nominal operating point for POSLLC, then regulating POSLLC, so that it is very closer to the nominal operating point in the case of sudden load disturbances and set point variations. In the PI control scheme, proportional gain (K_p) and integral time (T_i) are designed using Ziegler – Nichols tuning method [6] In this method by applying the step test, S- shaped curve of response of POSLLC is obtained. The S- shaped curve of step response of POSLLC may be characterized by two constants, delay time L and time constant T. The delay time and time constant are determined by drawing a tangent line at the inflection point of the S-shaped curve and determining the intersections of the tangent line with the time axis and line output response c (t). From these values the proportional gain (K_p) and integral time (T_i) are calculated. In the proposed control scheme the proportional gain K_p is taken as 0.1 and integral time T_i is taken as 1.

IV. SIMULATION OF TRIPLE -LIFT CONVERTER

The simulations have been performed on the positive output super- lift LUO converter circuit with parameters listed in Table I. The static and dynamic performance of PI control for the positive output super- lift LUO converter is evaluated in Mat lab/Simulink. Before that a simple elementary circuit with it^’s PI controller is studied [2].The scheme provides only one output stage.

Topology and control scheme is also simple. The proposed triple-lift topology is little bit complex and their parameters are listed below.

TABLE – I

Parameter Name Symbol Value

Input voltage V₁ 12 Volts

Output voltage V₀ 324 Volts Inductors L_1, L₂ &L₃ 10 mH Capacitors C_1, C_2,

C3,C4,& C5 2 F

Capacitor C6 20 F

Switching

frequency f _s 450Hz

Load resistance R 30K

Duty cycle k 0.5

Table I. Circuit parameters

The Matlab/Simulink simulation model is shown in Fig.4. The difference between feedback output voltage and set point voltage is given to PI controller and output of PI controller, changes the duty cycle of the power switch (n- channel MOSFET)

Fig.4 Simulation model

The POSLLC performance is analyzed in various aspects. They are performance in transient region, performance during line variations, load variations, component variations and performance in constant Kp

with variable T_i, constant T_i with variable K_p. 1.1 Transient region

Fig.5. shows the output voltage of POSLLC with PI control in the transient region. It can be seen that the converter output has settled at time of 0.55sec with designed PI control.

Fig.5. Output voltage in transient region 1.2 Line Variations

Fig.6. shows the output voltage of converter for input voltage step changes from 12 V to 9 V (-25% supply disturbance). The converter output voltage has maximum overshoot of 200V and 0.55sec settling time with designed PI control. Fig.7 shows the output voltage variations for the input voltage step change from 12 V to 15 V (+25% supply disturbance). The converter output

voltage has maximum overshoot of 400 V and 0.75 sec settling time with designed PI control.

Fig.6. Input voltage step changes from 12V to 9 V

Fig.7 Input voltage step changes from 12 V to 15 V 1.3 Load Variations

Fig.8. shows the output voltage when the load changes from 30K  to 27K 

(-10% load disturbance). The maximum overshoot is 480V and settled at 0.6sec Fig.9 shows the variation of load from 30K to 33K  (+10% disturbance), the maximum overshoot of the response is 300V and settled at 0.65sec.

Fig.8 Variation of load from 30K  to 27K 

Fig.9 Variation of load from 30K to33 K

1.4 Component variations

Fig.10. shows the output voltage when capacitor C₆ value changes from 20 F to 25F. The maximum overshoot is 430V and settled at 0.75 sec.Fig.11.shows the output response when C₆ value changes from 20F to 15F The response reaches the maximum overshoot of 500V and settled at 0.48sec.

Fig.10.Variation of C₆ from 20F to 25F

Fig.11.Variation of C6 from 20F to 15F Fig.12. shows the output voltage when inductor L₃ value changes from 10mH to 15mH. The maximum overshoot is 500V and settled at 0.6 sec.Fig.13.shows the output response when L₃ value changes from 10mH to 5mH.The response reaches the maximum overshoot of 400V and settled at 0.56sec

Fig.12.Variation of L₃ from 10mH to 15mH

Fig.13.Variation of L₃ from 10mH to 5mH TABLE – II

Parameter Name Maximu m overshoo t in volts

Settling time in seconds Proportion

al gain-Kp

Integral time-Ti

0.1

0.9 480 0.55

0.7 480 0.55

1.5 480 0.55

2.5 480 0.55

4 480 0.55

5.5 480 0.6

7 480 0.6

30 480

0.6 with more ripples Table II. Performance analysis with constant K_p and

variable T_i TABLE – III Parameter Name

Maximum overshoot in volts

Settling time in seconds Integral

time-T_i

Proporti onal gain-K_p 1

0.2 480 0.55

0.3 480 0.55

0.5 480 0.55

0.9 480 0.55

0.7 480 0.55

0.09 480 0.55

0.05 480 0.55

0.001 200 Signal

oscillates Table III. Performance analysis with constant T_i and

variable Kp

V. CONCLUSION

The positive output super- lift LUO converter (POSLLC) performs the voltage conversion from positive source voltage to positive load voltage. The PI control scheme has proved to be robust and it has been validated with transient region, line and load variations.

The converter performances for constant K_p and variable T_i , constant T_i and variable K_p are not analyzed yet. This work is focused on that aspect also.

The positive output super- lift LUO converter with PI control is used in applications such as switch mode power supply, medical equipments and high voltage projects etc.

VI. ACKNOWLEDGEMENT

The authors would like to acknowledge the management of SACS MAVMM Engineering College and Thiagarajar College of Engineering, Madurai.

REFERENCES

[1] F.L.Luo and H.Ye, “Positive output super- lift converters,” IEEE Trans. Power Electron., vol.18, no.1, pp. 105-113, Jan 2003.

[2] K.RameshKumar and S.Jeevanantham. “PI control for positive output elementary super- lift Luo converter,” International Journal of Energy and Power Engineering, pp.130-135, Mar 2010.

[3] Fang Lin Luo and Hong Ye, Advanced DC/DC Converters. London: CRC Press,2003

[4] N.Dhanasekar, and R.Kayalvizhi. “Design and simulation of PI control for positive output triple- lift Luo converter”, International Journal of

Modern Engineering Research,

IJMER.vol.2,issue.6, pp. 4186-4188,Nov-Dec 2012.

[4] T.S. Saravanan, R. Seyezhai and V. Venkatesh

“Modeling and control of split capacitor type elementary additional series positive output super- lift converter”, ARPN Journal of Engineering and Applied Sciences, vol.7,no.5, May 2012.

[5] P. Comines and N. Munro, “PID controllers:

recent tuning methods and design to specification”, in IEEE Proc. control Theory applications, vol.149, no.1, pp.46-53, Jan 2002.

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