Journal of King Saud University – Engineering Sciences 31 (2019) 238–244

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Journal of King Saud University – Engineering Sciences

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Original article

Robust observer-based DC-DC converter control

Montadher S. Shaker ⇑, Asaad A. Kraidi
Department of Electrical Engineering, University of Technology, Baghdad, Iraq

a r t i c l e i n f o a b s t r a c t

Article history: This paper develops a novel robust control strategy for DC-DC buck converter subjected to varying load
Received 3 March 2017 and parameter uncertainty. The proposal exploits the robustness of the sliding mode control (SMC) incor-
Accepted 16 August 2017 porated with proportional-proportional-integral-observer (PPIO) to assure tight reference voltage track-
Available online 18 August 2017
ing under a wide range of load change scenarios. Within this framework, an integral sliding mode surface
based SMC (ISMC) is designed to guarantee closed-loop robustness against the matched and mismatched
Keywords: disturbance components of the load uncertainty. Subsequently, a novel control structure comprises ISMC
Sliding mode control
and PPIO is presented to overcome the design constraints and to mitigate the undesired transient
Proportional-proportional-integral-observer
(PPIO)
response accompany the response of the closed-loop system based ISMC. Stability analysis has clearly
DC-DC converter demonstrated using linear matrix inequality (LMI) and Lyapunov approach. To illustrate the effectiveness
Mismatched uncertainty of the proposal, a comparison between the closed-loop system responses of SMC, ISMC, and the combined
Robust control ISMC and PPIO are presented in the simulation results.
Ó 2017 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an
open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction control schemes in order to cope with the required control objec-
tives (El Fadil et al., 2009; Olalla et al., 2011; Nachidi et al., 2013;
The DC-DC converters are an important part in modern tech- Wang et al., 2015). In this context, the authors in (El Fadil et al.,
nologies that require reliable power supplies such as computer 2009) proposed a backstepping-based control design algorithm
systems and cellular phones or they could be used as power opti- that accounts for the effect of model parameter uncertainty. The
mizers in renewable energy such as photovoltaic and wind turbine work in (Olalla et al., 2011) exploits the potential of LMI-based
systems (Forsyth and Mollov, 1998). From circuit topology stand- multi-objective robust state feedback controller to account for
ing point, there are wide varieties of converter circuits ranging model uncertainty, nonlinearity, and exogenous input. An
from simple to complex configuration of buck, boost, or buck/boost H1 -based robust output feedback fuzzy control for DC-DC
converters (Forsyth and Mollov, 1998). converter is presented in (Nachidi et al., 2013) to account for the
From control design standing point, tackling the effects of load converter nonlinearity using Takagi–Sugeno fuzzy models.
variation and parameter uncertainty of DC-DC converter circuits On the other hand, recent publications have shown interest in
have drawn the attention to develop control strategies that ensure utilizing the relative design simplicity and the robustness of SMC
reliable converters. Additionally, the time response of the convert- to deal with DC-DC converter control problems (Gonzalez
ers must satisfy desired transient characteristics. However, owing Montoya et al., 2016, Kanimozhi and Shunmugalatha, 2013;
to the nonlinear characteristics of the DC-DC converters and their Liqun et al., 2015; Lopez-Santos et al., 2013; Oucheriah and
highly uncertain model parameters, several challenges regarding Liping, 2013; Salimi et al., 2015; Shen et al., 2015; Yue et al.,
their control have stimulated several researchers to exploit robust 2014; Wang et al., 2015). Specifically, the work presented in
Wang et al. (2015) combines the SMC and a disturbance observer
such that the converter circuit exhibits robustness against mis-
⇑ Corresponding author. matched uncertainties that have specific time behaviour. To guar-
E-mail addresses: 30211@uotechnology.edu.iq, montadher_979@yahoo.com antee robust reference voltage tracking of a converter circuit
(M.S. Shaker), asaadabdlbari@gmail.com (A.A. Kraidi). subjected to time varying external input, the authors in
Peer review under responsibility of King Saud University. Oucheriah and Liping (2013) developed an adaptive SMC scheme
to provide asymptotic stability of the boost converter system. A
sliding mode based boost converter control is presented in Yue
et al. (2014) to stabilize the DC power systems over the entire
Production and hosting by Elsevier operating range in the presence of significant variations in load

http://dx.doi.org/10.1016/j.jksues.2017.08.002
1018-3639/Ó 2017 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
 M.S. Shaker, A.A. Kraidi / Journal of King Saud University – Engineering Sciences 31 (2019) 238–244 239

power and input voltage. An output voltage control of buck/boost

converter based on a proportional-integral type hyper-plane SMC
L
is presented in Salimi et al. (2015) to provide robustness against
parameters uncertainties, load disturbance and variations of the
converter input voltage.
In the aforementioned literature, the authors presented con-
trollers that meet specific performance requirements and/or cope DC C R
with a variety of DC-DC robustness issues. For instance, the work
in Wang et al. (2015) does not present systematic control system
design procedure. Moreover, the proposal assumes pre knowledge
of the upper bound of the disturbance signal. Additionally, the Fig. 1b. the ideal switch is ON.
closed-loop robustness is constrained to step varying load change.
On the other hand, the complexity of the proposal in Nachidi et al.
(2013) is attributed to the use of multiple model control. In
L
(Kanimozhi and Shunmugalatha, 2013; Liqun et al., 2015; Lopez-
Santos et al., 2013; Oucheriah and Liping, 2013; Salimi et al.,
2015; Shen et al., 2015; Siew-Chong et al., 2006; Yue et al., 2014)
the proposed sliding mode controllers are insensitive to the
matched uncertainty and sensitive to the mismatched uncertainty.
Hence, developing a control strategy that characterized by design DC C R
simplicity and robustness against matched and time varying mis-
matched uncertainty is of significant contribution to the literature
of DC-DC converter control.
This work aims to design a robust control strategy to ensure
Fig. 1c. the ideal switch is OFF.
acceptable performance and robustness of DC-DC converter circuit
that affected by the variable load and/or parameter uncertainty. A
novel control structure that comprises the ISMC and PPIO has been where E in the input voltage, L is the inductance, iL is the inductor
proposed to ensure robustness against matched and mismatched current, v out is the output voltage, C is the capacitance, and R is
uncertainty. The proposal removes any offset caused by the mis- the resistance. The average model that encompasses Eqs. (1) and
matched uncertainty without the need for pre knowledge of the (2) is depicted in Eq. (3).
upper bound of the uncertainty. Moreover, unlike the work pre- )
sented in Wang et al. (2015), a systematic observer design is pre- Li_L ¼ lE  mout
ð3Þ
sented to ensure closed-loop robustness for a wide range of load C m_ out ¼ iL  mout
R
change scenarios.
The average model presented in Eq. (3) assumes ideal circuit
2. The DC-DC buck converter model components and fixed load resistance. However, in order to con-
sider the effects of load uncertainty, the model (3) has rewritten
This section establishes the state space model of a typical DC- in term of nominal load ðRo Þ as follows:
DC buck converter. The buck converter circuit comprises a transis- )
Li_L ¼ lE  mout
tor switch, inductor, capacitor, and variable load resistance can be ð4Þ
found in (Wang et al., 2015) (see Fig. 1a). The circuit reveals two C m_ out ¼ iL  mout
R
þ mRout  mRout
o o

models arising from the particular position, ON (see Fig. 1b) and  
OFF (see Fig. 1c), of the switch. Based on the direct application of Letting ðx1 ¼ mout  mr Þ and x2 ¼ iCL  mRout
oC
yield,
Kirchhoff’s voltage and current laws for the ON and OFF positions, )
the two models are given in Eqs. (1) and (2) respectively. x_ 1 ¼ x2 þ d1
) ð5Þ
x_ 2 ¼  LC
x1
 Rxo2C þ u þ d2
E ¼ Li_L þ mout
ð1Þ
C m_ out ¼ iL  mout
R where
) mout mout lE  m r 1
Li_L ¼ mout d1 ¼  ; u¼ ; and d2 ¼  d1 :
ð2Þ Ro C RC LC Ro C
C m_ out ¼ iL  mout
R
where v r is the reference voltage, and the components ðd1 Þ and ðd2 Þ
represent the mismatched ðd1 Þ and matched ðd2 Þ uncertainty.
Hence, the objective is to design a robust controller for the system
Q L (5) despite the effects caused by uncertain load resistance.

3. The proposed control structure

u This section explains the design steps of the proposed robust

DC D C R control structure that integrates the ISMC and PPIO within a feed-
back loop. The proposal follows the observer based robust control
design methodology (Nazir et al., 2017; Sami and Patton, 2012) to
tolerate a wide range of disturbance scenarios (i.e. load and param-
eter uncertainty). The closed-loop control system structure is
Fig. 1a. DC-DC buck converter. shown in Fig. 2.
240 M.S. Shaker, A.A. Kraidi / Journal of King Saud University – Engineering Sciences 31 (2019) 238–244

To maintain sliding motion (i.e. S_ ¼ 0), one could simply realize that
the required control signal (u) should has the form:
   
1 1
u¼ þ k2 x1  k1  x2  ðd2 þ k1 d1 Þ ð9Þ
LC Ro C
Clearly, the unknown disturbance terms makes the control signal
(9) unrealistic. However, making use of Assumption 1, a realistic
form of the signal (u) is given in Eq. (10).
   
1 1
u¼ þ k2 x1  k1  x2  bsgnðSÞ ð10Þ
LC Ro C
Proper design of control (10) makes the sliding surface attracts
the state of the system (5) into the sliding manifold within finite
Fig. 2. the proposed control structure.
time ðt ¼ t o Þ. Additionally, the states will remain within the sliding
manifold for all t > to .
Where E is the DC input, u is the control signal, v r is the refer- Now, consider a candidate Lyapunov function of the following
ence DC voltage, and d ^1 is the estimation of the mismatched uncer- form:
tainty d1 . Section 3.1 presents the ISMC design methodology for the 1
buck converter model (5). On the other hand, Section 3.2 will pre- D ¼ S2 ð11Þ
2
sent a new control structure that combines the ISMC and PPIO in
order to relax ISMC design constraints and performance limitation. the time derivative of Eq. (11) gives:
_
D_ ¼ SS ð12Þ
3.1. Sliding mode controller design
For the control law (10), Eq. (13) gives simplified form of Eq. (8):
The ability of SMC to compensate matched disturbances has S_ ¼ bsgnðSÞ þ ðd2 þ k1 d1 Þ ð13Þ
clearly investigated in the literature. Basically, the SMC design pro-
cedure encompasses two steps (Edwards and Spurgeon, 1998); (1) Combining Eqs. (12) and (13) yields:
sliding surface design to which the states are confined during the
D_ ¼ bsgnðSÞS þ ðd2 þ k1 d1 ÞS ð14Þ
sliding phase. (2) The control signal that makes the sliding surface
attracts the states during the reaching phase. Specifically, the con- Eq. (14) can be rewritten into an inequality form as follows:
trol law has two feedback control terms; (i) a linear control term,
and (ii) a discontinuous term. While the linear control term guar-
D_ 6 jSjðb þ jðd2 þ k1 d1 ÞjÞ ð15Þ
antees the reachability condition, the discontinuous control term Using Assumption 1 gives:
ensures the sliding condition.
D_ 6 djSj ð16Þ
Remark 1. The proposed SMC needs the following assumption. Inequality (16) implies that, for initial condition outside the
sliding manifold, i.e.Sðt ¼ 0Þ–0, the solution to (16) becomes zero
Assumption 1. The load uncertainty tackled by the proposed SMC in finite time. Clearly, the consequence of (16) and (11) is:
pffiffiffi
must satisfy: D_ ¼  2dD1=2 ; ð17Þ
which has the following solution:
1. b > d þ jðd2 þ k1 d1 Þj, where ðbÞ is the upper bound of uncer- pffiffiffi
D ¼ D1=2 ð0Þ  2dt ð18Þ
tainty, ðdÞ is a small positive constant and k1 is a design variable.
2. The term d1 satisfies the limit limt!1 d_ 1 ¼ 0 (i.e. has constant
1=2
Therefore, at time t ¼ t o ¼ D pffiffi2ð0Þ
d
, the states of system (5) reaches
steady state value). the surface (6).
Hence, using control law (10), the states of system (5) will
The objective is to guarantee acceptable system performance converge toward the sliding surface (6) at time t o provided that the
whilst the system confines into the sliding regime. Hence, to _ < 0).
control gain satisfiesb > d þ jðd2 þ k1 d1 Þj (i.e. SS
ensure acceptable sliding motion despite the effects of the
While the state of (5) remains within the sliding vicinity, the
matched and mismatched uncertainties (i.e. d1 and d2 ) the
dynamics of system (5) become:
following sliding surface has been proposed.
Z
S ¼ x2 þ k 1 x1 þ k 2 x1 dt ð6Þ €x1 þ k1 x_ 1 þ k2 x1 ¼ d_ 1 ð19Þ

where ðSÞ is the sliding variable, and k1 and k2 are design variables. In fact, Eq. (19) becomes a homogeneous differential equation if
Before proceeding with the second design step, analysis of system the term d_ 1 satisfies the limit of Assumption 1. This implies that;
motion equation is given first. While the dynamics of system (5) while sliding, the state in (5) moves toward the equilibrium point
confined into the sliding surface, the sliding variable must satisfies asymptotically.
S_ ¼ S ¼ 0. Hence, taking the time derivative of Eq. (6) yields:

S_ ¼ x_ 2 þ k1 x_ 1 þ k2 x1 ð7Þ Remark 2.

Combining Eqs. (5) and (7) gives:  From Eq. (10), it should be noted that the model parameter
    uncertainty (i.e. the changes of L; C) represent matched uncer-
1 1
S_ ¼ u þ þ k2 x1 þ k1  x2 þ ðd2 þ k1 d1 Þ ð8Þ tainty and hence can be tolerated via the control law (10).
LC Ro C
 M.S. Shaker, A.A. Kraidi / Journal of King Saud University – Engineering Sciences 31 (2019) 238–244 241


 While the control law (10) is capable of eliminating the steady ~¼ A  LC Ed
A ;
state offset caused by (d1 ), conventional SMC lacks the capabil- PK o1 CA þ PK o1 CLC  PK o2 C PK o1 CEd
ity to remove this offset. For comparison, consider the following  
e ~¼ 0
conventional SMC: ~ea ¼ x ; ~z ¼ d_ 1 ; N
ed I
Strad ¼ x2 þ k1 x1 ð20Þ Now the objective is to compute the gains L; K o1 ; and K o2 that atten-
  uate the effects of the input ~z, in eq. (27), on the estimation error via
1 1 minimizing the L2 norm ðk ~z 2 kÞ below desired level c.
u¼ x1  k 1  x2  gsgnðStrad Þ ð21Þ
LC Ro C
Remark 4. decoupling the effects is of ð~zÞ is beyond the scope of
where Strad is the conventional sliding surface, (g) is the upper
this paper. However, based on the available information of Ed , the
bound of the unknown input. If (g) is properly designed, the sliding
following theorem ensures L2 norm minimization of ð~zÞ on ~ea .
motion will possess the dynamics (22):
x_ 1 ¼ k1 x þ d1 ð22Þ
Theorem 1. The augmented estimation error in (27) is stable and the
Clearly, it is impossible to eliminate the offset using conven- L2 performance is guaranteed with an attenuation level c, Provided
tional SMC.
that the signals ðd_ 1 Þ are bounded, rankðCE Þ ¼ m , and the pair (A,
d d
C) is observable, if there exists a symmetric positive definite matrices
Remark 3. The constraints listed in Assumption 1 limit the appli- P1 ; P 1 and G matrices H; K o1 ; K o2 , and a scalar lo satisfying the fol-
cability of the control law (10) because: lowing LMI constraint:
Minimize c such that
2 3
W11 W12 0 0 W15 0
 The upper bound of the unknown input (i.e. 6  W22 W23 W24 0 0 7
6 7
b > d þ jðd2 þ k1 d1 Þj) increases the switching gain an thereby 6 I 7
6   c 0 0 0 7
the negative effects of chattering. 6 7<0 ð28Þ
6    G1 0 7
 The robustness of the closed-loop system in Section 3.1 is 6 0 7
6 7
restricted against disturbances that possess constant time beha- 4     2lo P 1 lo I 5
viour (i.e. limt!1 d_ 1 ¼ 0).      G
pffiffiffi
where L ¼ P1
1 H; c ¼ c; W11 ¼ P1 A þ ðP1 AÞT  HC  ðHCÞT þ w1 ;
3.2. The design of LMI-based PPIO
W12 ¼ P1 Ed  AT C T K To1  C T K To2 ; W15 ¼ ðHCÞT ; W22 ¼ K o1 CEd 
ðK o1 CEd Þ þ w2 ; W23 ¼ P 1 ; W24 ¼ K o1 C
T
This section presents the PPIO design steps and the vital role of
PPIO in relaxing the constraints of Section 3.1 (see Remark 3). The
converter system (5) can be rewritten in the following general Proof.. See (Shaker, 2015). It is worth remarking that to tune the
form: L2 performance against the exogenous input ~z, the weighting

 w1 0
x_ ¼ Ax þ Bu þ Ed d1 matrix W ¼ has been nominated in the LMI
0 w2
ð23Þ
y ¼ Cx formulation.
The estimated disturbance ðd ~ Þ plays a vital role in enhancing
1
where Ed 2 Rnmd ¼ ½ 1 1=Ro C T and x 2 Rn ¼ ½ x1 x2 T . The PPIO the overall closed loop performance. Specifically, the sliding
is given as follows: surface (6) is modified to the following form:
9 Z
^x_ ¼ A^x þ Bu þ Ed d ^ þ Lðy  y ^Þ >
> ^
1 = S ¼ x2 þ k1 x1 þ k2 x1 dt þ d 1 ð29Þ
^ ¼ C ^x
y ð24Þ
>
>
^_ 1 ðtÞ ¼ P½K o1 C e_ x þ K o2 Cex  ;
d To maintain sliding motion (i.e. S_ ¼ 0), the new control signal (u)
has the form:
where K o1 and K o2 are the proportional and integral gains respec-    
tively, and P is a symmetric positive definite matrix. After subtract- 1 1
u¼ þ k2 x1  k1  x2  ðd2 þ k1 d1 Þ
ing the observer in (24) from the system (23) the state estimation LC Ro C
error (ex ) will be defined as: þ ðd ^_ 1  b sgnðSÞ
^1 Þ  d
^2 þ k1 d ð30Þ
new

e_ x ¼ ðA  LCÞex þ Ed ed
ð25Þ Following the procedure of Section 3.1, the closed-loop system
ey ¼ Cex stability can easily derive and hence omitted here. h
Using Eq. (24) the disturbance estimation error dynamics will
become: ^1
Remark 5. The control signal in Eq. (30), the estimation d
^_ 1
e_ d ¼ d_ 1  d compensates the effect of load uncertainty. Consequently, the
design parameter bnew can be selected much smaller than b,
¼ d_ 1  PK o1 CAex þ PK o1 CLCex  PK o2 Cex  PK o1 CEd ed ð26Þ thereby minimising the chattering effect.
by combining Eqs. (25) and (26), the augmented estimation error
dynamics can be constructed as defined in Eq. (27): 4. Simulation results
~e_ a ðtÞ ¼ A
~ ~ea þ N
~ ~z ð27Þ
In this section, the proposed SMC strategy has verified based on
where Matlab/Simulink software. Table 1 gives details of the considered
242 M.S. Shaker, A.A. Kraidi / Journal of King Saud University – Engineering Sciences 31 (2019) 238–244

Table 1
the parameters of the buck converter.

Input voltage (E) 20 V

Desired voltage (v r ) 10 V
Capacitance (C) 1000 lF
Inductance (L) 4.7 mH
Load resistance (R) 60 O–140 O

converter parameter. The uncertain resistive load varies in the

range (60–140 O) has subjected to the buck converter.
In the first simulation scenario, the results compare the output
response of conventional SMC and SMC with integral action based
buck converter control.
The first design step of controller (10) is determining the Fig. 4. The tracking performance of the buck converter when subjected to step-
switching gain ðbÞ and the sliding surface parameters (k1 , k2 ). The varying load.
holding of Assumption 1 ensures sliding motion governed by the
dynamics of Eq. (19). Consequently, the performance parameters
(the damping ratio ðfÞ and natural undamped frequency ðxn Þ) of
this system are adopted such that the maximum settling time
ðT s Þ satisfies T s 6 1 sec and maximum peak time ðT p Þ satisfies
T p 6 0:5 sec. Hence,

1 2
T s 6 1 sec ) 6 1 sec ) 6 1 sec ) 2 6 k1
fxn k1

p p
T p 6 0:5 sec ) pffiffiffiffiffiffiffiffiffiffiffiffiffi 6 0:5 sec ) 6 0:25 sec
xn 1  f2 k2 ð1  f2 Þ
4p
) 6 k2
ð1  f2 Þ

,which led to k1 ¼ 25, k2 ¼ 250. On the other hand, the design Fig. 5. The tracking performance of the buck converter when subjected to fast-
parameter b ¼ 500 is selected to satisfy reachability condition (i.e. varying load change.
_ < 0).In order to investigate controller
b > d þ jðd2 þ k1 d1 Þj ) SS
robustness, the converter has subjected to nominal (100O), step-
controllers (10) and (21) are unable to maintain reference tracking
varying, and fast-varying load.
when the unmatched disturbance does not satisfy the limit
Fig. 3 shows tracking performance of the converter (5) when
subjected to nominal load (100O). In this scenario, the controllers limt!1 d_ 1 ¼ 0.
(10) and (21) can force the converter dynamics to start the sliding As mentioned in Remark 2, the proposed ISMC and the SMC
motion at time t o that depends on the variabled (and consequently possess the ability to tolerate the converter parameter uncertainty.
b). Fig. 6 obviously demonstrates the closed-loop robustness against
Fig. 4 shows the output response of the buck converter when the following parameter change scenario:
feeding a step-varying load. As demonstrated in Remark 2, the tra-
)
x_ 1 ¼ x2 þ d1
ditional SMC is incapable of compensating the unmatched compo- ð32Þ
x_ 2 ¼ a LC
x1
 a Rxo2C þ u þ d2
nent d1 . On the other hand, while the conditionlimt!1 d_ 1 ¼ 0 holds
for this scenario, the ISMC can compensate the effects of the where ðaÞ represents the multiplicative uncertainty factor of the
unmatched component d1 . However, the closed-loop system based system (5).
ISMC exhibit undesired transient response that disturbs the The second simulation scenario highlights on the advantages of
smoothness of the output voltage.Fig. 5 demonstrates how the integrating the closed-loop system based-ISMC with the PPIO.

Fig. 3. The tracking performance of the buck converter when subjected to nominal
load. Fig. 6. The controller robustness against model parameter uncertainty.
 M.S. Shaker, A.A. Kraidi / Journal of King Saud University – Engineering Sciences 31 (2019) 238–244 243

(a) Time varying load change

(b) Step varying load change

Fig. 7. (a and b): PPIO and ESO based load change estimation. a) Time varying load
change. b) Step varying load change.

(b)
Fig. 9. (a and b): Duty ratio of the Buck converter. (a) Duty ratio for step-varying
load. (b) Duty ratio for fast-varying load.

Using the Matlab LMI toolbox, the gains of the PPIO are obtained as
follows:
c ¼ 0:059; K o1 ¼ ½ 0:185 3:248 ; K o2 ¼ ½ 0:003 6:916 ;

0:046 0:001
L¼ :
1:616 9:954

Remark 6.

 The ISMC parameters (k1 , k2 ) are maintained as given above

(i.e.k1 ¼ 25, k2 ¼ 250). However, in the combined ISMC and
PPIO scheme, it becomes possible to reduce the switching gain
to bnew ¼ 380 (see Remarks 3 and 5).
 While the PPIO guarantees precise estimation of load change
when d_ 1 –0, the extended state observer (ESO) proposed in
Wang et al. (2015) is restricted to the case of d_ 1 ¼ 0. Fig. 7
shows the accuracy of PPIO, compared with the ESO, for esti-
mating d1 component.

Fig. 8 (a and b) shows the reference voltage tracking accuracy of

buck converter-based SMC, ISMC, and combined ISMC and PPIO.
Specifically, while tolerating the effects of time varying load
change (i.e. d_ 1 –0) is not possible via SMC and ISMC, the combined
ISMC and PPIO has showed robust tracking performance against
load change despite the fact that d_ 1 –0.
(b) With reference to Fig. 7, it is clear that utilizing PPIO for load
Fig. 8. (a and b): Reference voltage tracking performance. (a) Reference voltage
change estimation and compensation minimises the undesired
tracking for step-varying load. (b) Reference voltage tracking for fast-varying load. transient response of ISMC.
244 M.S. Shaker, A.A. Kraidi / Journal of King Saud University – Engineering Sciences 31 (2019) 238–244

Table 2 References
SMC, ISMC, and ISMC + PPIO controller performance for step load change.

Min Max Mean STD Edwards, C., Spurgeon, S., 1998. Sliding Mode Control: Theory and Applications.
Taylor & Francis.
SMC 9.087 10.72 9.983 0.3208 El Fadil, H., Giri, F., el Magueri, O., Chaoui, F.Z., 2009. Control of DC–DC power
ISMC 9.355 11.21 10 0.0767 converters in the presence of coil magnetic saturation. Control Eng. Pract. 17 (7),
ISMC + PPIO 9.913 10.1 10 0.0095 849–862.
Forsyth, A.J., Mollov, S.V., 1998. Modelling and control of DC-DC converters. Power
Eng. J. 12 (5), 229–236.
Gonzalez Montoya, D., Ramos-Paja, C.A., Giral, R., 2016. Improved design of sliding-
mode controllers based on the requirements of mppt techniques. IEEE Trans.
Table 3 Power Electron. 31 (1), 235–247.
SMC, ISMC, and ISMC + PPIO controller performance for time varying load change. Kanimozhi, K., Shunmugalatha, A., 2013. Published. Pulse Width Modulation based
sliding mode controller for boost converter. Int. Conference on Power, Energy
Min Max Mean STD and Control (ICPEC), 6-8 Feb. 2013, pp. 341–345.
Liqun, S., Lu, D.D.C., Chengwei, L., 2015. Adaptive sliding mode control method for
SMC 9.849 10.15 10 0.0728 DC-DC converters. IET Power Electron. 8 (9), 1723–1732.
ISMC 9.902 10.1 9.998 0.0256 Lopez-Santos, O., Martinez-Salamero, L., Garcia, G., Valderrama-Blavi, H., Mercuri, D.
ISMC + PPIO 9.967 10.11 10 0.0066 O., 2013. Efficiency analysis of a sliding-mode controlled quadratic boost
converter. Power Electron., IET 6 (2), 364–373.
Nachidi, M., el Hajjaji, A., Bosche, J., 2013. An enhanced control approach for DC–DC
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sired transient performance. Therefore, the proposal integrates based sliding-mode voltage controllers for basic DC-DC converters in
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controller is capable of compensating the effects of load uncer-
tainty regardless the time behaviour of the unmatched component.