An Intelligent Theory for Switch Mode Flyback Converter

An Intelligent Theory for Switch Mode Flyback Converter

Vibha Janardhan

Electrical and Electronics Department Rungta College of Engineering and Technology

Kohka-Kurud Road Bhilai (C.G.) India

S. P. Dubey

Electrical and Electronic Department Rungta College of Engineering and Technology

Kohka kurud Road Bhilai (C.G.) India

Abstract- In this paper presents the intelligent theory is control the non-linear behavior of the flyback converter with voltage mode control. The flyback DC-DC converter is operating ~170V 50Hz ac supply providing regulated output voltage 42V DC. Fuzzy logic controller covers a wider range of operating conditions, and they are design in natural language terms, which are based on general knowledge of the plant, it does neither require a precise mathematical modelling of the system nor complex computation. Fuzzy control rules are regulates the output of the flyback converter.The non-linear controller fuzzy logic controller (FLC) provides improved performances in terms of overshoot limitation and sensitivity to parameter variations in dynamic condition. To show the performance variations of the converters output with the fuzzy logic controller, flyback converter is simulated using MATLAB/SIMULINK.

Keywords Component: Fuzzy logic controller, flyback converter, voltage mode control,

1. INTRODUCTION

   Efficient conversion of electrical power is becoming a primary concern to companies and to society as a whole.

   Switching power supplies offer not only higher efficiencies70 to 90 present but also offer greater flexibility to the designer. A switch mode flyback converter due to minimum number of semiconductor and magnetic components, are widely adopted for off-line low-cost power supplies. The flyback converter provides the isolation and short circuit protection by a single switch [1][2][3].

   The causes of instabilities in flyback converter disclose the non-linearity include the variable structure due to the saturating inductance, voltage clamping, single switching period etc[4][5]. Fuzzy systems has a vagueness, incomplete, linguistically described, or even inconsistent which is applicable on the advance control, adaptive control, robust control as well as non-linear control system[6][7]. An un- predictive theory is offered by the fuzzy logic control (FLC), which does neither require a defined mathematical modelling of the system nor Complex computations.

   e u

   e = Controller Input u = controller output

   Fuzzy Logic Controller

   Fuzzification

   Defuzzification

   Fuzzy Rule Base

   Fig.1. General Structure of a fuzzy logic controller

   The majority of fuzzy logic control systems are knowledge- based systems in that either their fuzzy models or their fuzzy logic controllers are described by fuzzy IF-THEN rules, which have to be established based on experts knowledge about the systems, controllers, performance, etc. Fuzzy logic controller (FLC) consists of three basic portions-(a) the fuzzification unit at the input terminal,(b) the inference system built on the fuzzy logic control rule base in the core, and (c) the defuzzification unit at the output terminal, as shown in figure 1.Thus, control design is simple, since it is only based on linguistic rules of the type: "if the output voltage error is positive and its rate of change is negative, then reduce slightly the duty-cycle", and so on[8][9]. This approach lies on the basic physical properties of the systems and it is potentially able to extend control capability even to those operating conditions where linear control techniques fail, i.e. large-signal dynamics and large parameter variations [10].

2. BASICS OF FUZZY LOGIC CONTROLLERS

   The fuzzy logic control is a new addition to non-linear control theory. The use of fuzzy logic control method in power electronics [zadeh 1994] has been increased in the last decades based on its simplicity design. Fuzzy logic control (FLC) is a new addition to control theory, which is one of the most successful applications of, fuzzy set theory. Fuzzy logic is a very useful device to treat nonlinear control phenomena and quantities in a logical way or the linguistic variables. Its design philosophy deviates from all the previous methods by accommodating expert knowledge in controller design. Its

   major features are it does not need any mathematical model and it will greatly reduce the development cost, takes less time and needs less data storage in the form of membership functions and rules. Fuzzy logic controller is adaptive in nature and can also exhibit increased reliability, robustness in the face of changing circuit parameters, saturation effects and external disturbances and so on[11][12].

   The basic configuration of a fuzzy logic controller (FLC) is represented in fig.2 and comprises four principal components:

   error (Input 1)

   Change in error

   (Input 2)

   FUZZY

   MAMDANI

   Output

   Fig.2. Basic configuration of fuzzy logic controller( FLC)

   1. Fuzzification

      Fuzzification interface is converts input data into suitable linguistic values. The first step in the design of a fuzzy logic controller is to define membership functions for the inputs. Seven fuzzy levels or sets are chosen and defined by the following library of fuzzy-set values for the error e and change in error ce as shown in the fig.3. Each variables control has been divided into five partitions. They are as follows-

      NB negative big; NM negative medium; NS negative small; ZE zero equal; PS positive small; PM positive medium; PB positive big.

      The number of fuzzy levels is not fixed and depends on the input resolution needed in an application. The larger the number of fuzzy levels, the higher is the input resolution. The fuzzy controller utilizes triangular membership functions on the controller input.

      The triangular membership function is chosen due to its simplicity as shown in the fig.4.

      Fig.3. Membership functions for error (e) and change in error(ce).

      Fig.4. Membership functions of the input linguistic variables

   2. Rule Base or Decision-making

      A knowledge base or rule base is consists of a data base with the necessary linguistic definitions and control rule set. Fuzzy control rules are based on the Mamdani rule based system. Decision making logic which, simulating a human decision process, infers the fuzzy control action from the knowledge of the control rules and the linguistic variable definitions;

      The control rules that associate the fuzzy output to the fuzzy inputs for the dcdc converter are derived from general knowledge of the system behaviour is tabulated in Table I as shown by the fig.5.

      A typical rule can be written as follows.

      If e is NB and ce is PS then output is ZE

      Where are the labels of linguistic variables of error (e), change in error (ce) and output respectively. Error (e), change in error (ce) and output represent degree of membership. The derivation of the fuzzy control rules is heuristic in nature and based on the following criteria –

      1. When the output of the converter is far from the set point, the change of duty cycle must be large so as to bring the output to the set point quickly.

         NB	NB	NB	NB	NM	NS	ZE
         NB	NB	NB	NM	NS	ZE	PS
         NB	NB	NM	NS	ZE	PS	PM
         NB	NM	NS	ZE	PS	PM	PB
         NM	NS	ZE	PS	PM	PB	PB
         NS	ZE	PS	PM	PB	PB	PB
         ZE	PS	PM	PB	PB	PB	PB

         NB NM NS ZE PS PM PB

         NB

         NM

         NS ZE PS

         Vin Rf

         Cin

         Lin LP

         NP

         ip

         LS VD Vo

         RL

         NS C

         is

         PM

         PB

         Fig.5. Fuzzy control rules

         Driver

         +

         –

         ON

         OFF

         Ve Kf

         +

         –

         Vf

         Vref

         TS Ve

      2. When the output of the converter is approaching the set point, a small change of duty cycle is necessary.

      3. When the output of the converter is near the set point and is approaching it rapidly, the duty cycle must be kept constant so as to prevent overshoot.

      4. When the set point is reached and the output is still changing, the duty cycle must be changed a little bit to prevent the output from moving away.

      5. When the set point is reached and the output is steady, the duty cycle remains unchanged.

      6. When the output is above the set point, the sign of the change of duty cycle must be negative, and vice versa

   3. Inference Mechanism

      The results of the inference mechanism include the fuzzy relation. The max-min composition has become the best known and the most frequently used.

      Max-min composition [R1 (max-min) R2]

      R1 ° R2 = {[(x, z), maxy {min { R1 x, y , R2 (y, z) }}] x X, y Y, z Z} (1)

      To obtain the control decision, the max-min inference method is used. It is based on the minimum function to describe the AND operator present in each control rule and the maximum function to describe the OR operator.

   4. De-fuzziffication

      Conservation of the fuzzy to crisp or non-fuzzy output is defined as De-fuzzification. A de-fuzzification interface

      Fig.6.Flyback converter with voltage mode control

      General schematic diagram for controlled duty cycle in voltage mode controlled flyback converter as shown in fig 6. In this voltage mode control scheme the converter output voltage is sensed and subtracted from an external reference voltage (Vref) in an error amplifier. The amplifier produces a control voltage that is compare to constant amplitude saw- tooth waveform. The comparator generates a PWM signal that is fed to drivers or duty cycle of controllable switches in the DC-DC converters. The duty ratio of the PWM signal depends on the value of the control voltage. The frequency of the PWM signal is the same as the frequency of the saw-tooth waveform. The control of the switch duty ratio adjusts the voltage across the inductor and hence the inductor current brings the output voltage to its reference value [13][14][15][16].

      Mode-1

      Basic operation of flyback converter is divided on main two modes. In mode 1 show by the fig.7, when the switch (MOSFET) is turned on, the primary current i1 flows, while the diode is reverse biased preventing a flow of secondary current i2. During this MOSFETs turn on period, energy is stored in the transformer with a load current being supplied by the output capacitor.

      yields a non fuzzy control action from an inferred fuzzy control action.

      In the de-fuzzification operation a logical sum of the inference result from each of the four rules is performed. This logical sum is the fuzzy representation of the change in duty cycle (output).

3. VOLTAGE MODE CONTROLLER

   As for the control technique, two approaches, voltage-mode control and current-mode control, are applicable in the DC- DC flyback converter.

   V1

   i1

   Lm

   iLm

   is

   n : 1

   + +

   V1 V2

   – –

   i2

   + VD –

   C

   +

   RL V0

   –

   Fig.7.Equivalent circuit diagram of flyback converter for Mode 1

   The diode current iD ,

   iD = i2 = 0 (2)

   The current through the magnetizing inductance is show in fig.10

   I = – n V0 (t-DT) + V1D + i

   (0) (9)

   The primary current I

   = i / -n (3)

   Lm Lm

   fsLm Lm

   1 2 The converters main energy storage inductor may operate in

   The voltage across the magnetizing inductance Lm show in fig.8

   d

   two modes: DCM and CCM.

   At CCM/ DCM boundary the minimum value of the magnetizing inductance

   VLM = V1 = Lm.

   dt

   iLM (4)

   Lm(min) =

   (1Dmin )2n2 RLmax

   2fs

   (10)

   At time t=0, I

   LM(0) is the initial current in the magnetizing

   Lm(min) = n2 Vo (1Dmin )2

   2fs .Iomin

   (11)

   inductance .The peak-to peak value of the ripple current through the magnetizing inductance Lm is

   VLm

   V1

   il

   m

   iLm(max)

   iOB

   V1max /Lm

   V1min /Lm

   -n V0 /Lm

   0

   DT T t

   -nV0

   0

   DminT DmaxT T t

   Fig.8.Voltage across the switch

   Fig.10. Waveform of the current through the magnetizing inductance

   The energy transferred from the input dc voltage source V1 to

   ILm

   = V1DT

   Lm

   = V1D

   fs .Lm

   (5)

   the magnetizing inductance during one cycle for the boundary

   the transfer function of the flyback converter is

   case is

   W = Lm max iLm (max )2

   (12)

   V0 I0 D

   OB 2

   MvDC = =

   V1

   =

   I1 n(1D)

   (6)

   The total power output at the boundary

   Mode 2

   In mode 2 show by the fig.9, the switch (MOSFET) is tuned

   POB

   = WOB T

   = fS

   WOB

   = fs.Lmmax i2Lm (min )

   2

   (13)

   off, the primary current stop to conduct. The polarity of secondary voltage is become too negative. The diode is now forward biased enabling a flow of secondary current. During this turn off period, energy stored in the transformer is released to the output capacitor and load.

   The secondary voltage

   v2 = VO (7)

   V1 = -n v2 = -nV0 (8)

   i1 i =i

4. DESIGN OF FUZZY LOGIC CONTROLLER FOR DC-DC CONVERTERS

   In DC-DC converters fuzzy logic controller has applied to the regulation of load voltage and performance the robustness due to its non linear dynamic characteristics of the DC-DC converter.

   Design of fuzzy logic controllers is based on expert knowledge of the plant instead of a precise mathematical model. There are two inputs inside the fuzzy logic controller for the flyback converters. The first input is the error in the

   V1

   Lm

   iLm

   +

   Vs

   –

   n : 1

   + +

   V1 V2

   – –

   2 D

   + VD – C

   +

   RL V0

   –

   output voltage given by equation (14), where ADC[k] is the converted digital value of the kth sample of the output voltage and Ref is the digital value corresponding to the desired output voltage. The second input is the difference between successive errors and is given by the equation-

   e [k] = Ref ADC[k] (14)

   ce[k] = e[k] e[k-1] (15)

   The two inputs are multiplied by the scaling factors g0 and g1, respectively, and then fed into the fuzzy logic controller. The output of the fuzzy controller is the change in duty cycle d[k], which is scaled by a linear gain h. The scaling factors g0, g1, and h can be tuned to obtain a satisfactory response.

   Fig.9.Equivalent circuit of flyback converter in mode2

   Fig.11 show the general block diagram for fuzzy logic controlled flyback converter in which control for DC-DC

   DC-DC

   CONVERTER

   flyback converter is made from 2 inputs and 1 output variables, which are error and change in error as input variables, and the dty cycle as output variable.

   INPUT

   fuzzy controller gains go,g1 and h are obtained by the heat and trial method.

   (a) Simulation response for input power factor correction. The advantage of switch mode power supply (SMPS) is higher efficiency with high power factor. In SMPS a diode

   d(K) = d (K-1) +d(K)

   d(K)

   PWM STAGE

   DUTY CYCLE

   FEEDBACK

   (LINEAR GAIN)

   V0

   e(K) – +

   OUTPUT

   rectifier effects the ac/dc conversion, while the controller operates the switch in such a way to properly shape the input current ig according to its reference. An ideal power factor corrector should imitate a resistor on the supply side while maintaining a fairly regulated output voltage.

   From equation (2, 3), obviously, the sinusoidal input current is is inherently generated, and its current amplitude Is =Vs/wL

   FUZZY LOGIC

   CONTROLLER

   PREVIOUS SAMPLE

   ce(K) e(K-1)

   Fig.11. Schematic diagram for fuzzy controlled DC-DC converter

   The fuzzy logic controller works as an error amplifier. The output voltage V0 is feedback and sum with the reference voltage Vref, which gives the error in voltage (input 1) for controller. The second input change in error is the sum of the error signal and each sampling periods. The integrator is used to eliminate the steady state error.

   The output of the fuzzy logic controller is compare with the saw-tooth signals for generate the controlled duty cycle for switch (MOSFET) in the flyback converter. For the simulation purpose the model parameters are given in table 1. The simulation circuit diagram are shown in the fig 12

   SIMULATED CIRCUIT PARAMETERTABLE 1

   is proportional to the controllable phase without sensing current and current loop. Moreover, the sinusoidal input current is is in phase with the input voltage Vs. The simulated results as shown by the fig taken on the input side, which shows the input current waveform is , is less distorted and as close as possible with the input voltage waveform Vs. The simulated waveform shows fig.13 the input side power factor nearly 1.

   Input voltage

   			Input voltage waveform

   200

   0

   -200

   0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

   			Input current waveform

   Time

   Input current

   20

   0

   -20

   0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

   Time

   Input power factor

   		In	put power factor waveform

   Sr.No.	Parameter	Ranges
   a)	Input Voltage	90-230V
   b)	Output Voltage	41V
   c)	Load Resistance	10 ohms
   d)	Line Frequency	50 hertz
   e)	Total Output Power	160W(<200W)
   f)	Switching Frequency	200KHz

   2

   1

   0

   0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

   Time

   Fig.13. simulation response for input power factor

   1. Simulation response for transient condition of fuzzy logic controlled flyback converter

      For the circuit parameters in Table 1 the simulated waveforms are obtained in fig.14, the output current and voltage waveform. The output voltage and output current of the system are 42V and 3.9A respectively given by the fuzzy controlled flyback converter. The transient responses of the fuzzy controlled flyback converter are listed in Table 2.

      Sr.No.	Parameters	values
      a)	Rise Time	0.45 Sec.
      b)	Peak Time	0.65 Sec.
      c)	Overshoot	0.0124%
      d)	Settling Time	0.9Sec.

      TABLE 2

      Fig.12 Simulation circuit diagram for fuzzy logic controlled flyback converter.

5. SIMULATION RESULTS

   The simulation is closed loop flyback converter controlled with fuzzy controller is done for 5 second. The non- linear

   1. Simulation response for dynamic condition of the fuzzy logic controlled flyback converter

      The proposed non-linear fuzzy logic controlled flyback converter is evaluating using MATLAB/ Simulink is shown in fig.15. Dynamic condition of fuzzy logic controlled flyback converter where the load resistance is suddenly

      			Output current waveform

      changed parallel with the another resistance from 10.5 (W) to10.5||200 at t= 0.8 second. The response of the output voltage has a little drop at t=0.08 second and after some time its attain a finale output voltage value.

      5

      Output current

      4

      3

      2

      1

      0

      0 0.5 1 1.5 2 2.5 3

      			Output voltage waveform

      Time

      50

      Output voltage

      40

      30

      20

      10

      0

      0 0.5 1 1.5 2 2.5 3

      Time

      Fig.14.Simulation response for transient condition in fuzzzy controlled flyback converter

      			Output current waveform

      In order to support sufficient power to regulate the output voltage, the input current magnitude is increased from 3.8A to near 4.2A by the controller.

      5

      4

      Output current

      3

      2

      1

      0

      0 0.5 1 1.5 2 2.5 3

      			Output voltage waveform

      Time

      50

      Output voltage

      40

      30

      20

      10

      0

      0 0.5 1 1. 2 2.5 3

      Time

      Fig.15. Simulation response for dynamic condition in fuzzzy controlled flyback converter

      From this case, we can find that the input current is is always in phase with the input voltage vs under transient response. Consequently, the controller can keep good performance under the condition of load change. During this test the reference voltage of the converter is 42V.

6. CONCLUSION

The non-linear controller fuzzy logic controller(FLC) in the flyback converter has presented with a very useful device to treat non-linear behaviour and quantities in a logical ways of the flyback converter. Its design methodology is very simple and doesnt need any type of mathematical model.

Fuzzy logic controller produces less voltage deviation. Less overshoot and sensitive to parameter variation and low cost makes fuzzy logic control results in better transient and dynamic performance. FLC can also be applied to many converter topologies. Fuzzy logic controller (FLC) has advantages of faster response with higher accuracy.

REFERENCES

1. Dr.T.Govindaraj,Rasila R Development of Fuzzy Logic Controller For DC/DC Buck Converters Int J Engg Tech Sci Vol 2(2) 2011, 192-198

2. Neetu Sharma, Dr. Pradyuman Cchaturvedi, Rahul Dubey. Comparative study of PI controlled and Fuzzy logic controlled Buck converter.International Journal of Engineering Trends and Technology-Volume4, issue 3-2013ISSN: 2231-5381.

3. P.Rajesh Kumar & S.L.V. Sravan Kumar. Comparative study of PID based VMC and Fuzzy logic controllers for flyback converter. International Journal of Instrumentation, Control and Automantion (IJICA)volume-1, issue-2, 2011. ISSN: 2231-1890, Pages: 29-36

4. T.anitha, S.arulselvi Design and implementation of Intelligent control of a flyback quasi resonant converter. International Journal of Engineering Trends and Technology-Volume2, issue 4- Marcp013ISSN: 2277-3878

5. M.H. Rashid: Power Electronics: Circuits, devices and Applications, Pearson education Inc., Pearson Prentice Hall, 2010, pp. 186 190

6. Harold R., Chamorro and Gustavo A. Ramos. Fuzzy Control in Power electronics converters For smart Power Systems Intech open

7. Fuzzy logic, Knowledge and Natural Language Gaetano Licata. Italy. Intech open

8. Satya Prakash, S.C.Gupta Fuzzy Logic Based Trained Fault Locating Mechanism in Power Distribution Network International Journal of Emerging Technology and Advanced Engineering.ISSN2250- 2259,Vol-2,Issue-7,July 2012

9. M, Sai Babu Ch., Satyanarayana Subbarao S, Sobhan.P.V.S. Fuzzy controlled parallel AC-DC converter for PFC. Advances in electrical and Electronic Engineering. Power Engineering and Electrical engineering .Volume-9, Number-2, 2011 JUNE

10. P.mattaveli, L.Rossetto, G.Spiazzi, P.Tenti, General Purpose Fuzzy Controller For DC/DC Converter University of Padova-Italy

11. Technical Committee No.65 Industrial Process Measurement And Control Part 7-Fuzzy Control Programming International electrotechnical Commission(IEC).

12. A new defuzzification Method For Fuzzy Control of Power Converters. Yigang Shi and P.C. sen Fellow IEEE 07803-6404-2000

13. keng chin wu Pulse Width Modulated DC/DC Converters

14. Keith H.Bellings Switch Mode Power supply Handbook. McGraw Hill Inc.

15. Keng c. wu Switch-Mode Power Converters Design and Analysis Elsevier Academic Press.2006

16. Ned Mohan, Tore M. Undeland, William P. Robbins. Power Electronics: Converter, Applications and Design. Chapter 7, Page 164.