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About of PI Fuzzy Controller in DC to DC Power Converters

JENICA ILEANA CORCAU

Division Avionics

University of Craiova, Faculty of ElectrotechnicsBlv. Decebal, nr. 107, Craiova, Dolj

ROMANIA

[email protected],[email protected]

ELEONOR STOENESCU

University of Craiova, Faculty of Electrotechnics

Blv. Decebal, nr. 107, Craiova, Dolj

ROMANIA

[email protected]

TEODOR LUCIAN GRIGORIEDivision Avionics

University of Craiova, Faculty of Electrotechnics

Blv. Decebal, nr. 107, Craiova, Dolj

ROMANIA

[email protected]

Abstract: - In this paper is presented a fuzzy PI controller. Fuzzy PI controller and principles their performing isconsidered in large applications. Based on a qualitative descripion of the system to be controlled, fuzzy controller iscapable of good performances when a mathematical description is not available. The PI like controller presented isgeneral and can be applied to any dc to dc power converters topologies. Simulation results of Buck converter show

control potentialities.Key-Words: -fuzzy logic control (FLC), PI-like FLC, dc to dc converters.

1 IntroductionFuzzy control has emerged of the most active andpromising control areas, especially because it cancontrol highly nonliner, time variant and ill-definedsystems [1].The dc to dc power converters are power electronicsystems that convert one level of electrical voltage intoanother level switching action.

The output voltage is controlled by adjusting the ONtime of the power switch , which in turn ajusts the with

of a voltage pulse at the output. This is known as pulsewidth modulator PWM control [2].Most of the modeling in Power Electronics is intendedto convert the non-linear and time varying model to anideal or non-ideal switch model.

A power electronics system, in general, has a complexnon-linear model with a parameter variation problemand the control needs to be very fast which is crucial tothe performance of Power Converters is choice ofcontrol methods.

In contrast with traditional linear and nonlinear controltheory, a FLC is not based on a mathematical model and

is widely used to solve problems under uncertain andvague environments, with high nonlinearities [3].

With Fuzzy Logic Control, the design concept is totallydifferent.

This control technique relies on the human capacity tounderstand the systems behavior which determines howeffective linguistic rules of the Fuzzy Controllers are andis based on qualitative control rules.

The PI like FLC is, however, known to give poorperformance in starting response due to the internalintegrating operation. To improve the starting responseof an PI-like FLC is not easy, especially to reduce thehigh starting inductor current, and to retain the goodsteady state performance at the same time.

A fuzzy PI controller is presented, which can provideimproved performance such as a reduction of the highstarting current and an well damped output voltage fordc to dc converters.So, a series of papers have considered the control of dcto dc converters based on output feedback linearization

theory, sliding-mode control approach and fuzzy controltechnique.

Proceedings of the 8th WSEAS Int. Conf. on ARTIFICIAL INTELLIGENCE, KNOWLEDGE ENGINEERING & DATA BASES (AIKED '09)

ISSN: 1790-5109 208 ISBN: 978-960-474-051-2

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2 Basic of fuzzy logic controllersThe basic scheme of a fuzzy logic controller is shown infigure 1 and comprises four principal components: afuzzyfication interface, which converts input data into

suitable linguistic values; a knowledge base, whichconsists of a data base with the necessary linguisticdefinitions and the control rule set; a decision-makinglogic which, simulating a human decision process, infersthe fuzzy control action from the knowledge of thecontrol rules and linguistic variable definitions; adefuzzification interface which yields non-fuzzycontrol action from an inferred fuzzy control action [2].

Knowledge Base

FuzzyFuzzy

Fuzzyfication

Interface

Decision

MakingLogic

Defuzzyfication

Interface

Controlled System

Fig 1. Basic configuration of FLC

The fuzzy control systems are based on expertknowledge that converts the human linguistic conceptsinto an automatic control strategy without anycomplicated mathematical model.Fuzzy logic controller has been proven to be superior to

the conventional PI controller in that it naturallyprovides the ability to deal with highly nonlinear, time-variant and ill defined systems where the mathematical

models are difficult to be obtained or the controlvariable are too hard measure.The equation for a conventional PI-controller is [4], [8]

u =KP e + KI , (1)

where KP and KI are the proportional and the integral

gain coefficients.When we derive (1) we get

=KP +KI e (2)

The PI-like FLC consists of arule of the formRi : Ifeiis Ai and eiis Bi then uiis CiWhere Ai and Bi (antecedent), Ci (consequent), arefuzzy variables characterized by fuzzy membershipfunction.

In this case, to obtain the value of the control output

variable u(k), the change of control output u(k) is

added to u(k-1). It is to be stressed here that this additiontakes place outside the PI-like FLC, and is not reflectedin the rules themselves.If we translate the equation (2) to a discrete form we getthe equation for action value change of the discrete PI

controller

u(k) =K(e(k) + e(k)) (3)

Where u(k)=(u(k)-u(k-1))/T, e(k)=(e(k)-e(k-1))/T,Tis the sampling period, kis the step.From [5] it is obvious that the time constant has a

relation to the change in error. Therefore we can modify

the equation (3) for a fuzzy PI controller

u(k) = ( e(k) + e(k)) (4)

In the next step it is necessary to map the rule base todiscrete state space e(k), e(k). We define the scalefactorM for the universe range M>0. This scale factorsets the universe range for the error and the firstdifference. We extended the equation (4) and get [5]

u(k) = ( e(k) + e(k)). (5)

The input or output value is multiplied by a constantwhich indicates a real range of the universe, figure 2.If the universe range is multiplied by a coefficient of 5

before fuzzification, the real range of the universe is[-0,2, 0,2]. For an coefficient of 0,1 the real range ofthe universe is [-10, 10]. Its evident that theres noconflict with the commonest and this procedure leads tothe significant simplicity of the fuzzy controller design

as will be demonstrated [5].Fuzzy sets must be defined for each inputs (error andintegral error) and output variable. As shown in figure 2seven fuzzy subsets PB (Positive Big), PM (PositiveMedium), PS (Positive Small), ZE (Zero), NS (Negative

Small), NM (Negative Medium), NB (Negative Big)have been chosen for input variables. For the output

variable seven fuzzy subsets have been used (PB, PM,PS, ZE, NS, NM, NB), in order to smooth the controlaction. As shown in figure 2, triangular and trapezoidalshapes have been adopted for the membership functions.The value of each input and output variable isnormalized in [-1,1] by using suitable scale factors.Fuzzy control rules are obtained from the analysis of thesystem behavior. In their formulation it must beconsidered that using different control laws dependingon the operating conditions can greatly improve the

converter performances in terms of dynamic responseand robustness [6].

Fig. 2 The membership functions for inputs and

outputWe apply fuzzification to input variables and afterdefuzzification we get the equation


ISSN: 1790-5109 209 ISBN: 978-960-474-051-2

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u(k) = D {F{ e(k) + e(k)}} (6)

where F is an operation for fuzzification and D for

defuzzification. For u(k) results

u(k)= = D{F{ e(k) + e(k)}} ( 7)

The control signal generated by the fuzzy PI controllerin step kis:

u(k) = D{F{ e(k) + e(k)}}+u(k-1) (8)

A realization of the fuzzy PI controller is presented infigure 2.

Fig. 3 Structure of the fuzzy PIThe FLC contains a number of sets of parameters thatcan be altered to modify the controller performance suchas:

- the scaling factor for each variable;- the fuzzy representation the meaning of linguisticvalue;- the if-then rules.A non-adaptive FLC is one in which these parameters do

not change once the controller is being used on-line. Ifany of these parameters are altered on-line, the

controller will be called an adaptive FLC. If differenttypes of FLCs are used in the same controlled processaccording to process over time, a variable structure FLCcan be obtained.In table 1 is presented a rule base table for PI-like FLC.

Table 1 The base rule for a PI-like FLC to calculate ( u)

e\e NB NM NS Z PS PM PB

NB PB PB PB PB PM PS Z

NM PB PB PB PM PS Z NS

NS PB PB PM PS Z NS NMZ PB PM PS Z NS NM NB

PS PM PS Z NS NM NB NB

PM PS Z NS NM NB NB NB

PB Z NS NM NB NB NB NB

The fuzzyfication process is done through fuzzytriangular, while the Mamdani's min fuzzy implication isused together with the max-min compositional rule ofinference methods; the Center of Area method wasselected for the defuzzification process.

3 Simulation results

Control operation was verified by simulation using theMatlab/Simulink software. The parameters of Buck

converters are: L=100 H, C=200 F, R0=4 , =20V,

V0= 15V, [2]. The simulations results are for start up ofthe Buck converter from the zero initial state. Themembership functions in figure 4 are used. The

parameters, the denormalization factors, and ,

can be found in [4].Simulation results are obtained with a supply voltagechange from 20V to 15V and for load resistance changefrom 4 la 2,5 .Figure 5 give a graphical representation in table 1, i.e.the surface control and in figure 6 is presented thestructure of the fuzzy PI controller realized inMatlab/Simulink. In figure 7 is presented graphicalconstruction of the control signal in a fuzzy PIcontroller; generated in the Matlab Fuzzy Logic

Toolbox. In figure 8 is presented the structure of thesystem realized in Matlab/Simulink and the simulationresults obtained using PI fuzzy controller are presentedin figure 9.

Fig. 4 The membership functions for inputs and output

-20

-100

10

20

-1

-0.5

0

0.5

1

-0.5

0

0.5

errorintegralerror

output

Fig. 5 The surface control of controller


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S y s t e m c o n t r o l 7 : 2 i n p u t s , 1 o u t p u t s , 4 9 r u le s

e r r o r ( 7 )

i n t e g r a le

r r o r ( 7 )

o u t p u t ( 7 )

c o n t r o l 7

( m a m d a n i )

4 9 r u l e s

Fig. 6 The structure of the controller

Fig. 7. The rule view of the controller

Fig. 8. The block scheme realized in Simulink using PIfuzzy controller

0 0 .0 1 0. 02 0 .0 3 0 . 04 0 .0 5 0 . 06 0 .0 7 0 .0 8 0 . 09 0 .1-4

-2

0

2

4

6

8

10

12

14

16

t[s]

V0[V]

0 0 .0 1 0. 02 0 .0 3 0 . 04 0 .0 5 0 . 06 0 .07 0 .0 8 0 . 09 0 .1

0

1

2

3

4

5

6

7

8

9

10

t[s]

I[A]

Fig. 9 Simulation results of fuzzy PI controller

It is should be noted that the integrator in the fuzzy PI

controller reduces the steady state error but, fuzzy PIcontrollers generally give inevitable overshoot in outputvoltage and high initial inductor current when one triesto reduce the rise time response. This is because ofintegral saturation.

4 ConclusionIn this paper is presented the basic structure of PI-likeFLC. The new structure of an PI fuzzy controller isinvestigated, which can provide improved performancesuch as reduction of the high starting current and welldamped output voltage in fuzzy control for dc to dcBuck converters.

References:[1]. George Kopasakis.Fuzzy current mode control andstability analysis. AIAA -2003, pg. 1-18, June 2000;

[2] Corcau J., Constantinache P. An adaptive currentmode fuzzy logic controller for dc to dc converters. 6thInternational Conference Electromechanical and powersystems, Octomber 4-6, 2007, Chiinu, Rep. Moldova,Analele Universitatii din Craiova, vol. I, pag. 275-280,ISSN 1842-4805;[3]. Corcau J., Dinca L.Performance improvement of dc

to dc converters using the different slopes of embershipfunctions on fuzzy logic control. ICNPAA-2008,

Mathematical Problems in Engineering Aerospace andScience, June 25-27 2008;[4]. Abdullah I. Al. Odienat, Ayman A. Al-Lawama. The

Advantages of PID fuzzy controllers over theconventional types. American Journal of appliedSciences 5(6), 2008, ISSN 1546-9239;[5]. Pivonka P. Analysis and design of fuzzy PIDcontroller based on classical PID controllers

approach, Physica-Verlag, 2000;[6]. Tomescu B. On the use of fuzzy logic to control

paralleled dc-dc converters. Dissertation VirginiaPolytechnic Institute and State University Blacksburg,Virginia, October, 2000;[7]. Mattavelli, P., Rossetto, L., Spiazzi, G., Tenti, P.General-purpose fuzzy controller for dc/dc

converters,APEC, 1995;[8]. Edik Arakeljan, Mark Panko, Vasili Usenko.

Comparative analysis of classical and fuzzy PIDalgorithms, Physica-Verlag, 2000.


ISSN: 1790-5109 211 ISBN: 978-960-474-051-2

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