Input-output linearization of DC-DC converter with discrete sliding mode fuzzy control strategy

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 2, April 2022, pp. 1223~1232
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i2.pp1223-1232  1223
Journal homepage: http://ijece.iaescore.com
Input-output linearization of DC-DC converter with discrete
sliding mode fuzzy control strategy
Viji Karthikeyan1
, Anil Kumar Tiwari2
, Agalya Vedi1
, Buvana Devaraju3
1
Department of Electrical and Electronics Engineering, CMR Institute of Technology, Visvesvaraya Technological University,
Bengaluru, India
2
Department of Electronics and Communication, Amity School of Engineering and Technology, Amity University, Lucknow, India
3
Department of Electrical and Electronics Engineering, Dhanalakshmi College of Engineering, Anna University, Chennai, India
Article Info ABSTRACT
Article history:
Received Apr 29, 2021
Revised Sep 17, 2021
Accepted Oct 10, 2021
The major thrust of the paper is on designing a fuzzy logic approach has
been combined with a well-known robust technique discrete sliding mode
control (DSMC) to develop a new strategy for discrete sliding mode fuzzy
control (DSMFC) in direct current (DC-DC) converter. Proposed scheme
requires human expertise in the design of the rule base and is inherently
stable. It also overcomes the limitation of DSMC, which requires bounds of
uncertainty to be known for development of a DSMC control law. The
scheme is also applicable to higher order systems unlike model following
fuzzy control, where formation of rule base becomes difficult with rise in
number of error and error derivative inputs. In this paper the linearization of
input-output performance is carried out by the DSMFC algorithm for boost
converter. The DSMFC strategy minimizes the chattering problem faced by
the DSMC. The simulated performance of a discrete sliding mode fuzzy
controller is studied and the results are investigated.
Keywords:
Boost converter
DC-DC converter
Discrete sliding mode control
Fuzzy logic control
Sliding mode fuzzy control
This is an open access article under the CC BY-SA license.
Corresponding Author:
Viji Karthikeyan
Department of Electrical and Electronics Engineering, CMR Institute of Technology, Visvesvaraya
Technological University
AECS Layout, Bengaluru-560037, India
Email: kvijiperumal@gmail.com
1. INTRODUCTION
In the latest trends the usage of power electronic converters are increasing and a survey says that by
the end of next decade, more than 70% of electrical energy will be from power electronic equipment. Rapid
development of microelectronics has a pronounced influence on the development of power electronics by
constant improvement and making it economically reliable. Most commonly used applications are switched-
mode power supply (SMPS), personal computers and communication equipment [1]–[4]. These converters
are subjected to high load fluctuation because of increase in package density of on-board digital chips, which
deteriorate the converter performance. Hence there is a necessity for an efficient controller which can work
well during rapid load fluctuations [5], [6].
Power electronic converters are commonly used for easy implementation, high efficiency, improved
power factor, compact size, and flexibility in control. Boost converters are frequently used because of their
simple circuit design and their ease of implementation [7]–[10]. The fuzzy controller has been introduced to
overcome the chattering phenomena faced by the power converter by means of discrete sliding mode control
(DSMC) [11]–[14]. Further the ease of implementation of fuzzy systems has been exploited for hardware
implementation of the controller.

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An adaptive back-stepping discrete sliding mode control (SMC) strategy is implemented for the
boost converter in [15] and it is implemented in real time to ensure the stability. Simulation and hardware
implementation is done successfully and validates that the behavior of the proposed system is superior to
conventional methods. An improved SMC technique is developed by combining a disturbance estimator with
continuous SMC to overcome the voltage linearization problem of the boost converter [16]. The robustness
of the algorithm is proved by simulation and practical results under voltage and load disturbance conditions.
An indirect SMC method is implemented in [17] to regulate single-ended primary-inductor converters
(SEPIC) voltage in which the sliding function is reframed by incorporating the current error. This technique
is simple to use and reduces the cost of the controller. The behavior of the prototype is verified under output
and input side fluctuation conditions in buck and boosts modes.
The nonlinear boost converter model is designed with a perturbed relay system is explained in [18];
this is implemented in industrial processes and the non-linear responses are analyzed. Theoretical model is
validated by experimental results. A new approach to maintain steady load power in boost, Cuk and SEPIC
converters is explained in [19]. A simple, cheap, and small prototype is set-up and the results are validated. A
dynamic SMC technique with type-2 neural network is implemented in [20] for boost converter voltage
regulation. A new dynamic sliding surface is defined with duty ratio and reference value. The implemented
error tracking system is stable under inductor and capacitor variations; the results are compared and validated
with experimental set-up. An adaptive SMC law is implemented for event-triggered communication systems
[21] by incorporating a stochastic semi-Markov switching function. This law is implemented successfully in
boost converter and verified with theoretical calculation.
Small-signal design of the boost converter is proposed in [22] for photovoltaic (PV) fed
applications. This paper is projecting the stability problems due to the additional input capacitor which is
required to couple the PV array with boost converter. This model is validated by experimental set-up under
continuous and dis-continuous current modes. A DSMC is implemented for PV fed Cuk converter [23];
stability of the proposed controller is verified by adding disturbance in input and load. A type-2 fuzzy
controller is proposed to overcome the stability problems due to negative impedance characteristics of DC-
DC converters [24]. This is a non-integer intelligent controller and improves the stability of the converters
connected to constant power loads. All these control techniques are robust but the chattering problem faced
by the SMC is not addressed.
From the literature survey it is clear that a smooth gain change can be achieved by merging SMC
with fuzzy which can overcome the chattering response of the system under uncertainties. This paper deals
with the new development and performance analysis of boost DC-DC converters with control (DSMFC) with
extended load and source regulation. The new control scheme is validated through computer simulation and
by comparing with existing techniques. In the block diagram as shown in Figure 1 the power converter used
is buck/boost converter and load used is a resistive load, controller is DSMFC. This paper develops the
design and the mathematical modeling of DSMFC for boost converters.
Figure 1. Block diagram representation of DSMFC
2. RESEARCH METHOD
2.1. Design of DSMC based boost converter
The circuit diagram of the boost converter is shown in Figure 2, where Vin is the supply voltage, L is
the inductor connected in series with the supply voltage, a switch S1 is in shunt with the source and a
capacitor C is connected across the load resistance R [9]. The discrete model of boost converter based SMC
is represented by the (1) and (2), represents the discrete model when the switch is ON, (2) represents the
discrete model when the switch is OFF [14].

Int J Elec & Comp Eng ISSN: 2088-8708 
Input-output linearization of DC-DC converter with … (Viji Karthikeyan)
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Figure 2. Circuit diagram of boost converter
x1[K + 1] = x1[K] +
T
L
[Vin − (1 − u)x2]
(1)
x2[K + 1] = x2[K] −
T
C
[
x2
R
− (1 − u)x1] (2)
Where Iref=
VrefiL
V0
The sliding surface is given by the (3),
S[k] = ep[k] + µ1
e1[k] + µ2
e2[k] (3)
S[k] = x1[k]x2[k] − x1refx2ref + µ1(x1[k] − x1ref) + µ2(x2[k] − x2ref) (4)
where e1 = (x1 − x1ref) , e2 = (x2 − x2ref) and ep = (x1x2 − x1refx2ref). Such that e1
̇ [k] = x1
̇ [k] and
e2
̇ [k] = x2
̇ [k] where e1 is the current error, e2 is the voltage error, ep is the power error, x1 is the inductor
current iL, x2 is the output voltage/capacitor voltage Vc and K is the positive integer.
The control law is given by the (5) where S is the sliding surface. The system has been converged
when 𝑆[𝑘 + 1] < 𝑆[𝑘], which can be obtained from Lyapunov stability criteria. That is when the future value
is less than the present value then the system is converging.
u =
1
2
(1 − sgn(S)) = {
0 if S > 0
1 if S < 0 (5)
2.2. Mathematical modeling of discrete sliding mode fuzzy control for boost converter
The DSMFC based boost converter block diagram is shown in Figure 3, the controller uses the
control signal 𝑢[𝑘] and change in control signal 𝑢[𝑘 + 1] as input to the controller. The foremost objective is
to guarantee Lyapunov stability which used to satisfy the following condition |S[k + 1]| < |S[k]| [23]. Let
the sliding surface be 𝑆[𝑘], the proposed DSMFC creates the derivative of the Lyapunov function as negative
in sign. The rule-based table is established for this situation. They are: i) if 𝑢[𝑘] and 𝑢 [𝑘 + 1] greater than
zero then the duty cycle has to be increased; ii) else 𝑢[𝑘] and 𝑢[𝑘 + 1] less than zero then the duty cycle has
to be decreased.
Thus, the control signal u[k] and its derivatives 𝑢[𝑘 + 1] are given as the input to the fuzzy
controller, the output of the controller is the change in switching signal ∆µ(𝑘). The proposed DSMFC uses
the sugeno fuzzy inference system (SFIS) from Simulink library. Fuzzification has been done by selecting
gbell membership functions as fuzzy sets with the limit range [0 1] for the control signal u[k] and the change
in control signal 𝑢[𝑘 + 1]. The output signal is denoted by ∆µ(k) where a set of rules are defined. The fuzzy
set membership functions are symbolized by in1mf1, in1mf2, in1mf3, in1mf4, in1mf5, in1mf6, in1mf7 for
input signals 𝑢[𝑘] and in2mf1, in2mf2, in2mf3, in2mf4, in2mf5, in2mf6, in2mf7 for u[k+1]. The change in
Controller output signal ∆u[k] is specified in (6).
u[k] = ∆u[k] + ∆u[k − 1] (6)

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Figure 3. Block diagram of DSMFC for boost converter
3. RESULTS AND DISCUSSION
3.1. Used DSMFC boost converter
The DSMFC based boost converter is developed and simulated. metal oxide semiconductor field
effect transistor (MOSFET) is recommended as a switch in this boost converter model because it has
extraordinary speed of response [7], [8]. The switching of the MOSFET is controlled by DSMFC. The SFIS
is composed of a fuzzification stage, a rule base table stage and a defuzzification stage. This can be achieved
by means of rule editor function block in which input and output control parameters are well-defined with the
assistance of membership functions. The rules are framed by choosing a suitable fuzzy set for each input
variable such as 𝑢[𝑘] and 𝑢[𝑘 + 1] and also choosing the function 𝑓(𝑢) for the output variable. The gbell
membership function has been used for both inputs in order to get smooth response for the corner values. The
output parameter is specified by ∆µ[𝑘] and it has well-defined functions. The control surface can be viewed
with the support of rule edit viewer function. The Figure 4 illustrates the simulated response of the control
surface. This surface has been taken from the surface viewer of the rule edit function, which explains the
controller output variation for different input combinations.
Figure 4. DSMFC control surface
The model of the DSMFC boost converter is simulated in the Simulink platform and the input
voltage, inductor current, reference voltage and output voltage responses are illustrated in Figure 5. Initially
Source
Boost
Converter Load
DSMC
Fuzzy
Logic
Control
Vo, iL
Vref
DSMFC
µ1, µ2 u[k], u[k+1]
u[k]

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input voltage is set as 5 V, during starting current response is started with a current spike of 12.5 A and
settled quickly. The waveform is smooth until there is any sudden change. Reference voltage is set as 12 V;
the output voltage is 12 V after a peak overshoot of 20.7852 V for the input of 5 V. A change in input voltage
of 8 V is given at 0.5 sec; the output follows the reference with 12 V. When a change in reference voltage of
12 to 15 V is made at 0.7 sec; then the output response can be able to track the change. But there is a spike of
3 A at the time of 0.7 sec when there is a step change in reference voltage. This validates the robustness of
the controller and the controller is able to track the reference even during sudden variations of the system
parameters. From the analysis and simulated response of the boost converter it is clear that output voltage is
more than or equal to the input excitation; and the simulation is conducted under discontinuous current mode.
Figure 5. Simulated response of DSMFC boost converter for step-up change
The model of DSMFC is simulated with reduced input and reference voltage values. The simulated
response of the boost converter has been plotted which is illustrated in Figure 6. Initially input voltage is set
as 8 V, during starting current response is started with a current spike of 15.5 A and settled quickly. The
waveform is smooth until it sees a change. Reference voltage is set as 15 V; the output voltage for the input
of 8 V is 15 V after a peak overshoot of 29.5 V. A step-down in input voltage of 5 V is given at 0.5 sec; the
output follows the reference with 14.5 V. A step-down in reference is introduced at 0.7 sec from 15 to 12 V;
the output voltage can be able to track the reference of 12 V. This proved the robustness of the controller
where the output is able to track the reference by sudden step-down variations of the system parameters.
Figure 6. Simulated response of DSMFC boost converter for step-down change
Input Voltage in V
Inductor Current in A
Input Voltage in V
Inductor Current in A
Output Voltage in V
Reference Voltage in V
Output Voltage in V
Reference Voltage in V

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The enlarged response of the DSMFC for the boost converter has been shown in Figure 7. It is
observed that the chattering problem has been efficiently addressed along with reduced ripple current.
Figure 8 illustrates the generated gate pulse of the simulated response of DSMFC for Boost converter along
with input voltage with step change. Initially the input voltage has been set as 8 V; the corresponding gate
pulse is shown in the second portion of the figure with pulse width of 10.9 µs. At a time of 0.5 sec; a step
change in input voltage of 5 V is introduced. The gate pulse width got changed into 9.9 µs after the
introduction of step change in input voltage.
Figure 7. Enlarged response of DSMFC boost converter shows reduced chattering
Figure 8. Gate pulse response of DSMFC for boost converter-input step change
Figure 9 illustrates the generated gate pulse of the simulated response of DSMFC for boost
converter along with reference voltage with step changes. Initially the reference voltage is set as 15 V; the
corresponding gate pulse is shown in the second portion of the figure with pulse width of 10.3 µs. At a time
of 0.7 sec; a change in reference value of 12 V is made. The gate pulse width got changed into 5 µs after the
incorporation of reference change. The reference voltages are selected according to the load voltage
requirement.
The results from DSMC and DSMFC have been compared and it is observed that current has
reduced ripple content with DSMFC. Figure 10 depicts the simulated results. Initially the input voltage is set

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as 15 V, the current of DSMC has a spike of 16 A but with DSMFC the spike is reduced to 12 A. When there
is a step change in input voltage of 5 V at 0.5 sec there is a rise in current of 1.5 A in DSMC but the current
is about 1 A in DSMFC, no spike introduced in both the controllers. When there is a step change in reference
voltage of 12 V at 0.7 sec a low voltage spike of about 2 A is introduced in DFSMC but DSMC is not
introducing any spike.
Figure 11 shows the enlarged response of the inductor currents of DSMC and DSMFC for boost
converter. From the plot it is clear that the peak overshoot of inductor current for DSMFC is less than the
DSMC; and also, the fluctuation of current is less due to change in input voltage for DSMFC. DSMFC for
boost converter has been investigated; they find application in power converter circuits such as switched
mode power converters, voltage regulators, battery operated vehicles and variable speed direct current (DC)
drives because it offers smooth control under fluctuating loads. The simulated performance has been
analyzed which is out of chattering. There is a boost in the output voltage for the given input voltage. When
there is a step change in the input of the controller, it takes a short time to recover its performance which
shows the robustness of the controller.
Figure 9. Gate pulse response of DSMFC for boost converter-reference step change
Figure 10. DSMC vs DSMFC comparative response for boost converter
DSMC DSMFC
Input Voltage in V Reference Voltage in V

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3.2. Comparative analysis of DSMFC with DSMC for boost converter
Table 1 shows the results of a boost converter with DSMFC and DSMC techniques. Table 2 shows
the improvements for the boost converter. In the voltage response of DSMFC, the rise time is 0.3 msec faster,
the settling time is 3 msec faster, the peak time is 1.12 msec faster and percentage overshoot is 10% reduced
as compared to DSMC. In the current response of DSMFC the rise time is 0.106 msec faster, the settling time
is 2 msec faster, the peak time is 3.2 msec faster compared to DSMC. The SMC suppresses the oscillations in
less than 10 sec [25], but the DSMC and DSMFC can reduce the oscillations in less than 20 msec of time.
Figure 11. Comparison of DSMFC and DSMC inductor currents
Table 1. DSMFC-boost converter response (Vin=5 to 8 V, Vref=12 to 15 V)
No. Parameter DSMFC DSMC
Voltage response Current response Voltage response Current response
1 Rise Time 0.9 msec 0.18 msec 1.2 msec 0.286 msec
2 Settling Time 17 msec 10 msec 20 msec 12 msec
3 Peak 20.7852 V 12.5 A 21.9852 V 12.503 A
4 Peak Time 8.0 msec 2.8 msec 9.12 msec 6.0 msec
Table 2. Improvement table for boost converter
No. Response Parameter DSMFC DSMC Improvement Percentage Improvement
1 Voltage Response Rise Time 0.9 msec 1.2 msec 0.3 msec faster rise time 25%
Settling Time 17 msec 20 msec 3 msec faster settling time 15%
Peak Time 8.0 msec 9.12 msec 1.12 msec faster peak time 12.3%
% overshoot 73.21% 83.21% 10% 10% reduced
2 Current Response Rise Time 0.18 msec 0.286 msec 0.106 msec faster rise time 37%
settling time 10 msec 12 msec 2 msec faster settling time 16.7%
Peak Time 2.8 msec 6.0 msec 3.2 msec faster Peak Time 53.33%
4. CONCLUSION
In this paper control strategy based on DSMFC has been implemented for boost power converters
which can be used for power converter applications such as switched mode power supplies. In both the cases
such as change in reference and input; the output is able to track the reference, the chattering problem of
DSMC strategy has been reduced by the incorporation of fuzzy logic. The robustness of the system has been
investigated by introducing sudden change in input and reference voltages. The comparative analysis of this
controller with DSMC has also been analyzed. It is observed that the DSMFC gives linearized output.
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BIOGRAPHIES OF AUTHORS
Viji Karthikeyan has completed her Ph.D. in Visvesvaraya Technological
University, India, currently she is working as an Assistant Professor, in Department of
Electrical and Electronics Engineering, CMR Institute of Technology, Bengaluru, India. She
completed her B.E. (Distinction) from Manonmaniam Sundaranar University India, M.E.
(Distinction) from Anna University India. Her area of research is Advanced Control
Systems, Power Electronics and Renewable Energy Sources. She is a Life Member of ISTE
and member of IEI. She can be contacted at email: kvijiperumal@gmail.com.

 ISSN: 2088-8708
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Anil Kumar Tiwari has completed his B.E. (Hons) from Thapar University
Patiala India, M.E. (Distinction) from Pune University, India, PhD from Motilal Nehru
National Institute of Technology Allahabad India. A passionate teacher and researcher he has
been Head, Faculty of Electronics and is currently Director of AMITY School of
Engineering & Technology AMITY University Uttar Pradesh Lucknow Campus. His current
area of research are Advanced Nonlinear Control Theory, Sliding mode Control theory,
Intelligent Control, aerospace Control, Microwave and Radar, Photonics sensors and
Devices. He can be contacted at email: akumar3@lko.amity.edu.
Agalya Vedi has completed Ph.D. in Electrical Engineering from Anna
University, Chennai. She has completed master degree in power electronics drives from
SVCE, Chennai. She has completed UG degree in B.E from VKMV, Salem. She has
published 15 papers in international and national journals. She is a member in LISTE, IEEE.
She has received many awards and rewards during her teaching carrier. Currently working as
an associate professor in CMRIT, Bengaluru. Her area of interest in Power Electronics,
Biomedical Engineering, Artificial intelligence techniques and VLSI. She can be contacted
at email: agalya@cmrit.ac.in.
Buvana Devaraju has completed B.E./EEE in the year 2002 and M.E/PED in
the year 2006. She has sixteen years of teaching experience. She has completed her Ph.D. in
2019 in the area of DC to DC converters. Currently, she is a working as a Professor at the
Faculty of Electrical and Electronics Engineering in Dhanalakshmi College of Engineering,
Chennai, Tamilnadu, India. She can be contacted at email: gcebuvana@gmail.com.

Input-output linearization of DC-DC converter with discrete sliding mode fuzzy control strategy

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Input-output linearization of DC-DC converter with discrete sliding mode fuzzy control strategy