Design of PI controller for Positive Output Super- Lift LUO Converter 1 K.Muthuselvi, 2 L. Jessi Sahaya Shanthi 1 Department of Electrical &Electronics, SACS MAVMM Engineering College, Madurai, India 2 Department 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 L 1, L 2 and L 3, Six capacitors C 1, 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 voltagelift 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. 11
Average current Δi L1 =(V in /L 1 ) kt (4) Δi L2 =(V 1 /L 2 ) kt (5) Δi L3 =(V 2 /L 3 ) kt (6) Therefore variation ratio of output voltage v 0 is ε =(Δv 0 /2V0)=(1-k)/2RfC 6 (7) Fig.1 Triple- lift circuit The voltage across capacitor C 1 is charged to V in.voltage V 1 across capacitor C 2 is V 1 =((2-k)/(1-k))V in, and Voltage V 2 across capacitor C 4 is V 2 =((2-k)/(1- k)) 2 V 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 C 5 is charged to V 2.The current flowing through inductor L 3 increases with voltage V 2 during switching-on period kt and decreases with voltage (V 0-2V 2 ) during switching-off (1-k) T. Therefore, the ripple of the inductor current il 3 is Δ i L3 =(V 2 /L 3 ) kt=(v 0-2V 2 /L 3 )( 1 -k)t (1) V 0 =((2-k)/(1-k))V 2 =((2-k)/(1-k)) 2 V 1 = ((2-k)/(1-k)) 3 V in (2) The voltage transfer gain is G= V 0 /V in =(2-k/l-k) 3 (3) 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 V 1 12 Volts Output voltage V 0 324 Volts Inductors L 1, L 2 &L 3 10 mh Capacitors C 1, C 2, C 3, C 4,& C 5 2 F Capacitor C 6 20 F Switching frequency f s 450Hz 12
Load resistance R 30K Duty cycle k 0.5 voltage has maximum overshoot of 400 V and 0.75 sec settling time with designed PI control. 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.6. Input voltage step changes from 12V to 9 V 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 K p 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.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.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 Fig.8 Variation of load from 30K to 27K 13
Fig.9 Variation of load from 30K 1.4 Component variations to33 K Fig.12.Variation of L 3 from 10mH to 15mH Fig.10. shows the output voltage when capacitor C 6 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 C 6 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 C 6 from 20 F to 25 F Fig.11.Variation of C 6 from 20 F to 15 F Fig.12. shows the output voltage when inductor L 3 value changes from 10mH to 15mH. The maximum overshoot is 500V and settled at 0.6 sec.fig.13.shows the output response when L 3 value changes from 10mH to 5mH.The response reaches the maximum overshoot of 400V and settled at 0.56sec Fig.13.Variation of L 3 from 10mH to 5mH Parameter Name Proportion al gain-k p Integral time-t i TABLE II Maximu m overshoo t in volts Settling time in seconds 14 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 Integral time-t i 1 Proporti onal gain-k p Maximum overshoot in volts 0.2 480 0.55 0.3 480 0.55 0.5 480 0.55 Settling time in seconds
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 K p 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 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 triplelift 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. The authors would like to acknowledge the management [5] P. Comines and N. Munro, PID controllers: of SACS MAVMM Engineering College and recent tuning methods and design to Thiagarajar College of Engineering, Madurai. specification, in IEEE Proc. control Theory applications, vol.149, no.1, pp.46-53, Jan 2002. 15