Fuzzy Sliding Mode Control of DC-DC Boost Converter
Zeynep Bala Duranay EEE Department
Firat University, Technology Faculty Elazig, Turkey
Hanifi Guldemir EEE Department
Firat University, Technology Faculty Elazig, Turkey
Servet Tuncer EEE Department
Firat University, Technology Faculty Elazig, Turkey
Abstract—A sliding mode fuzzy control method which combines sliding mode and fuzzy logic control for DC-DC boost converter is designed to achieve robustness and better performance. A fuzzy sliding mode controller in which sliding surface whose reference is obtained from the output of the outer voltage loop is used to control the inductor current. A linear PI controller is used for the outer voltage loop. The control system is simulated using Matlab/Simulink. The simulation results are presented for input voltage and load variations. Simulated results are given to show the effectiveness of the control system.
Keywords-boost converter; DC-DC converter; FLC; fuzzy logic;
sliding mode
I. INTRODUCTION
Voltage-mode control and current-mode control are two methods used to control DC-DC converters [1]. The voltage- mode control is robust to disturbances, but slow. Current-mode control has a fast transient response but is more complex than voltage mode control. Classical PI and hysteretic controllers are the most used controllers for DC-DC converters. The linearized converter model around an operating point obtained from the state space average model [2] is used for conventional linear controllers. The classical controllers are simple to implement but the effect of variation of system parameters cannot be avoided, due to the dependence of linearized model parameters on the converter’s operating point [3]. The controller for DC-DC converters must account the nonlinearity and parameter variations. It should maintain stability and provide fast response in any operating condition. Classical control methods for DC-DC converters are not much efficient in achieving the desired performance [4-5]. A nonlinear control technique developed in [6] derived from variable structure control theory is called sliding mode control (SMC) has advantages of simple implementation, robustness and fast transient response [7]. SMC is used to maintain the output voltage of the converter to be independent of parameters, input and load variations [8]. It provides invariant system dynamics to uncertainties when controlled in the sliding mode [9]. SMC has a problem of chattering. Chattering is undesirable oscillations having finite amplitude and frequency due to the presence of unmodeled dynamics or discrete time implementation [10]. Some methods such as equivalent control
and boundary layer approach are used to reduce the chattering.
Equivalent control based methods cannot be used to reduce chattering because of their finite number of output values. The boundary layer approach has a problem of reaching sliding mode due to the replacement of the discontinuous control action with a continuous saturation function [10]. Fuzzy sliding mode control (FSMC) is another method used to avoid the chattering problem [11]. Fuzzy logic control is a non- conventional and robust control technique which is suitable for nonlinear systems characterized by parametric fluctuation or uncertainties [12-13]. FSMC has the advantage of not being directly related to the mathematical model of the controlled systems as the SMC. FSMC combines fuzzy logic and SMC to control the DC-DC converter to achieve better performance. In FSMC, the fuzzy system is used to estimate the upper bound of the uncertain disturbances to reduce the chattering. Fuzzy logic controller (FLC) has an increased level of efficiency regarding nonlinear converters. In this method, the control action is generated by linguistic rules which do not require an accurate mathematical model of the system, hence the complexity of the nonlinear model is decreased [14-15]. FLC overcomes the deficiency resulting from using linearized small signal models and improves the dynamic behavior.
II. DC-DC BOOST CONVERTER MATHEMATICAL MODEL
The output voltage of a boost type DC-DC converter is higher than the input source voltage. This is achieved by periodically opening and closing the switching element in the converter circuit. The DC-DC boost converter is shown in Figure 1. The switching period is T. The switch is kept open for time (1-D)T and is kept closed for time DT. The analysis is done by examining voltage across and current through the capacitor for both times, when the switch is open and when the switch is closed. Continuous conduction mode (CCM) will be assumed in which the inductor current will have a nonzero value due to load variations. When the switch is closed, the diode in the circuit is reverse biased and becomes open circuit as shown in Figure 2(a). Then the voltage across the inductor is:
= = (1)
and the current through the capacitor is:
2(bbec Th
the
equ cur (1) val clo
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= ,
ere x is the s nction vector.
face S(x)=0 th , , = The aim is t ctor x tracks a
= en with the quired control i
= 1 0 Since the aim ding surface an ould ensure the
filled [16]:
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ectories hit the IV.
Sliding mode uations govern [18-19]. The p o presented ag in objective in ch the switchin
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= ∗
= ∗= 0 The sliding f fined as,
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018, 3054-3059
Sliding Mode u x
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III. SLIDING
eory uses a h trajectory to n the state spa ding surface is ol system on n sliding mod rameter variati e equation in st
,
state vector, u If the function hen,
, , , , to find a cont
desired traject
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model uncer input is given
0 0
m is to force nd slide toward e stability and
positive consta e sliding surfa
SLIDING MOD
e controller des ning the contro performance of gainst input v n sliding mod ng surface and ns for boost co put voltage sh
function is for
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high speed sw move and sta ace. The system
s called reach the sliding su de, the system ions and distu tate space form
u is the contro n vector f is d
0 0 trol action u s tory x* that is,
rtainties and by (12):
the system s ds the origin, t the following
ant that guar ace in finite tim
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sign procedure oller were der f the sliding m voltage and lo de control is to d stay on that s onverter given hould be the d
rmed by the s
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witching strateg ay on a path c
m trajectory b hing mode an urface is know m response rem urbances. Assu
m,
(9) ol input and f discontinuous
(10) such that the ,
(11) disturbances.
(12) states to reach the control str inequality mu
(13) rantees the sy me [17].
R DESIGN
e and the nece rived and pres mode controller
oad variations.
o force the err surface [20]. U n in (3) and (4 desired voltage
(14) (15) state variable
(16)
verter gy to called before nd the
wn as mains uming
f is a on a
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The
) h the rategy ust be ) ystem
essary ented r was . The ror to Using 4), the e V*.
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and
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and val So the
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d state variabl lues at the stea olving the ineq e existing cond
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The most im nguistic variabl
linguistic vari big and less ntrol is closer nsists of a set e linguistic co tomatic contro ocesses are chniques [21].
nsists of fuz own in Figure
+ V* d/dt
ef e
- c
Fig. 3
Input data ar embership fun d the linguistic d then control ed to convert k) which is easured curren he output of th , which is
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force the syste al is
e the state tra t, the reaching
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les are constan ady state, ∗= quality given dition of slidin
tput voltage s ng mode to exi V. FUZZY
mportant featu les rather than iables are sent , and represen r to human th t of linguistic ontrol rules ba
ol strategy. F too complex
A fuzzy logic zzification, in
3.
Ru
D Fuzzifier M
D ek
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re converted in nctions in the
c variables de ller action is o
the fuzzy res the differenc nt values is use
he fuzzy contr used to obtai
obtained from
em states to th
ajectory to rea g law condition
nt and coincide
= 0
in (19) by rep ng mode,
should be high ist.
Y LOGIC CONTR
ure of fuzzy l n numerical va tences in a nat nted by fuzzy hinking and n control rules.
ased on expert LC is used w
for analysis c controller fo nference and
ule Base
Decision Making Defu ata Base
controlled boost
nto linguistic v fuzzifier. Us finition, fuzzy obtained. Defu sults to contro ce between ed as input to t roller is the ch in the PWM s
m the output o
(17 he sliding line
(18 ach the slidin n,
(19
(20 e with the refe placing (17) w (21 her than the s
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logic is that it ariables [14]. V tural language y sets. Fuzzy natural langua . The FLC con t knowledge in with systems w s by conven or a boost con defuzzificatio
uzzifier Boost Converte
converter.
values by the u sing the know y rules are eva
uzzification st ol action. The the reference the fuzzy cont hange in duty
ignal for the s of the
7) e S=0,
8) ng line 9)
0) erence we get
) source
t uses Values e, such logic age. It
nverts nto an whose ntional nverter on as
er V0
use of wledge luated tage is e error e and troller.
cycle switch
in arch met MinAN pro qua the obt star inpu num due deg fuz con beh Fig dete indudete betw S is con 1.
2.
3.
pre
the converte hitecture is the thods are used nimum and m ND and OR op
oduct composi alitative action centroids of tain the crisp o rts with the
uts. The inpu mber of fuzzy e to its simpl gree of memb zifier interfac ntroller are de havior. Input a gures 4 and 5.
ermined from ductor. The va ermined by c ween 0 and 1.
s the error (e) ntrol rules are o
If the error b big meaning t reference poin the reference If the output a small chang If the desire steady, there
Fi
Fig
Surface view sented in Fi
er. A Mamd e one in which d in the infere maximum fun perators respec ition method n to a quantitat
all output m output. The de
definition of ut resolution y levels. The licity is chose ership for a g ce. The contro etermined from and output me
Values of the m the maximu
alues of the o considering th
The fuzzy rul ) and is the
obtained based between the re
that the outpu nt, then ∆ sh value quickly of the conver ge in duty cycl ed reference should be no c
ig. 4. Input m
g. 5. Output m
w of the rules igure 6. The
dani type fuz h max–min an ence engine a ctions are use ctively in the c has been us tive action. W membership fu esign of a fuz membership increases w triangular me en for the con given input is ol rules for th m the DC–D embership fun e input membe um current flo
utput member he duty ratio
les are given i change of err d on the follow eference and m ut of the conve hould be big to
.
rter is near the le is needed.
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membership funct
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zzy logic co nd center of gr and defuzzifica ed to describ control rules. S sed to change Weighted avera
unctions is use zzy logic contr functions fo with the incre embership fun ntroller input.
determined i he designed f DC boost conv nctions are giv
ership function owing through rship function
interval whi in Table I, in w ror (ce). The f wing criteria:
measured curre erter is far from o take the outp e desired refer
and the outp duty cycle.
ions.
tions.
zy logic contr derived from
ontrol ravity ation.
e the Sum–
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put is
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VI.
Fuzzy logic ccessfully app sign for uncer ee technique b
proach for co nlinearities or ntrol of uncert nventional tec pert knowled odel. Sliding m
ntrol the D rformance an iteria ensure uzzy system is estimating t hances the sys the differenc rrent which i nnected to the ltages is used ntrol input is d form of the con the controller e scaled outp riod’s duty cyc
= This represe ntroller outpu duces steady-s
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TABLE I.
ce e N N N Z NM P Z
g. 6. Surface
FUZZY SLIDIN
is a robust plied to stabil
rtain nonlinea based on heu ollecting hum
r uncertaintie tain systems th chniques. Fuz dge of the sy mode and fuzz DC-DC boost nd to improve the stability s used to reduc
the bound of stem robustne ce of measure is obtained by e error betwee
as the input t determined by nditional state r output. The put ∆ by
cle d[k − 1]. S
1 ∆
ents a discrete ut. Integrating state error. The
y & Applied Sci which are the e ut. Fuzzy log ed for DC-DC nverters [24]. T o presented ag nd that fuzzy c change in circ
SMF RULE TABL N Z P NB NM Z M Z PM Z PM PB
e: e ce: change of
view of the fuzzy
NG MODE CON
technique th lity analysis a ar systems [25 uristics metho an knowledge es. It is used hat cannot be
zy controller ystem besides
zy logic contr converter e robustness.
of the FSM ce the chatteri f the uncerta ess [21]. Slidin d current and y the output en reference an to the fuzzy co y a set of fuzzy ments. The du duty cycle is h and the So, the fuzzy co
e time integr g the fuzzy e block diagra
ience Research error and chan gic based cont C [22], buck The performan gainst input v controlled syst cuit parameter
LE P Z M B
error, error
y rules.
NTROLLER
hat has been and control s 5-28]. It is a m ods. It provid
e and dealing for modeling easily controll design is bas s the mathem rol are combin to achieve
Lyapunov sta controlled sy ing of the con ain disturbanc ng surface, obt d reference ind of a PI cont nd measured o ontroller. The y rules expres uty cycle is obt
obtained by a previous sam ontroller outpu (22 ration of the controller’s o am of the duty
h V
Durana nge in
troller [16], nce of oltage tem is rs and
n very system
model des an g with g and led by sed on matical ned to better ability ystem.
nverter ces. It
tained ductor troller output fuzzy sed as tained adding mpling ut is:
2) fuzzy output y cycle
calc con tria des
dyn load per con bot outp Sin outp inn is con outp concon refe var Tab
firs
Vol. 8, No. 3, 20
ay et al.: Fuzzy culation is giv ntrol signal u angular carrier signed overall
The aim is to namic perform d changes. Th rformance und ntrol and FSM th the disturba tput voltage lo nce the dynami
tput voltage, a er current loop controlled by nverter circuit.
tput voltage. F ntrolled boost ntrolled DC-D erence voltage riations. A bo
ble II is used fo
Fig. 9. Sim
TABLE Vs 2
The performa st tested for the
018, 3054-3059
Sliding Mode ven in Figure is obtained by r signal. The FSM controlle
Fig. 7. Duty
Fig. 8. F
VII. SIM
o implement mance even w hat system sh der different op M control appro ance rejection oop controller ics of the curre a fuzzy sliding p. The output y the duty ra . FSM control Figure 9 show
t converter. T DC boost conv
es, under inp oost converter for the simulati
mulink block of th
II. PARAME (V) L (mH) 20 4
ance of the FS e reference vo
9
Control of DC- e 7. The pulse
y comparing t Simulink rep er is given in F
y cycle calculation
FSM controller.
MULATIONS
a robust cont with input volt ould have an perating condit oach is implem
and tracking r is a linear ent is much fa g mode contro
voltage of DC atio of the sw
ller is used to s the block di The performa erter is monit put voltage va
r with the pa ions.
he FSM controlled
TERS OF BOOST C C (F) R
1200
SM controlled oltage change.
3057
-DC Boost Con e width modu the signal d w presentation o Figure 8.
n.
troller with a tage variations invariant dyn tions. A casca mented to imp performance PI type contr ster than that o oller is used i C-D boost conv
witch used in obtain the de iagram of the ance of the ored with diff ariations, and arameters give
d boost converter.
CONVERTER R ()
200
d boost conver The output vo
verter ulated with a of the
good s and namic ade PI prove . The roller.
of the in the verter n the esired
FSM ferent FSM load en in
.
rter is oltage
and current waveforms are shown in Figure 10 for a step change in the desired reference voltage from 30V to 40V at time t=0.5s. Load variation is applied to the FSM controlled boost converter to test its robustness under load variation.
Figure 11 shows the voltage and current waveforms when the load resistance is changed from R=200 to R=100 at time t=0.5s. 30 V output voltage is maintained during the load change. Test for the input voltage change is also made to see the effects of the input voltage variations on the output voltage.
A step change in input voltage is made when the converter is at steady state with a 30V output voltage. The performance of the controlled system is shown in Figure 12 and Figure 13 when a change in input voltage from 20V to 15V and 20V to 25V occurs at the time t=5s. In Figure 12, a decrease in input voltage occurs and in Figure 13, an increase in input voltage occurs at t=0.5s. Figures 10-13 prove the robustness of the FSM control against changes in the load and input voltage. The recovering feature of the FSM controlled boost converter can be clearly seen.
Fig. 10. Output voltage and output and input current waveforms for step change in reference voltage.
Fig. 11. Output voltage and output and input current waveforms for step load variations.
Fig. 12. Output voltage and output and input current waveforms when input voltage decreased from 20V to 15V.
Fig. 13. Output voltage and output and input current waveforms when input voltage increased from 20V to 25V.
VIII. CONCLUSIONS
A sliding mode fuzzy controller designed and simulated for a DC-DC boost converter to improve the performance and achieve robustness. The error obtained from the load current and the reference current which is the sliding surface and its derivative are used as inputs to the fuzzy controller which controls the duty ratio of the signal driving the switch in the converter circuit. Matlab/Simulink programming environment is used for the simulations. The obtained results show that the controlled system is robust against load and input voltage variations. A good dynamic performance is also achieved.
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