**Published at : ** 17 May 2024

**Volume :** **IJtech**
Vol 15, No 3 (2024)

**DOI :** https://doi.org/10.14716/ijtech.v15i3.5164

Attia, H., Suan, S.T.K., 2024. Robust Sliding Mode Controller Design for Boost Converter Applications.

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Hussain Attia | Department of Electrical & Electronics Engineering, American University of Ras Al Khaimah, Ras Al Khaimah, 72603, United Arab Emirates |

Freddy Tan Kheng Suan | Department of Electrical and Electronic Engineering, University of Nottingham Malaysia, Jalan Broga, 43500 Semenyih, Selangor |

Abstract

This
paper presents detailed steps to design an effective, robust sliding mode
controller for boost converter applications. Before that, the paper models a
boost converter circuit during a continuous conduction mode (CCM) operation,
obtains the related dynamic equations and explains the variation effects of the
circuit parameters on the converter performance. The design steps of the
proposed controller are illustrated, and the robustness of the controller is
demonstrated in terms of maintaining output voltage stability under input
voltage variations and load fluctuations. On the other hand, this paper shows a
fast and accurate dynamic response of the load voltage during different
reference voltages. Simulation results are collected, analyzed, and
demonstrated the robustness and correctness of the proposed controller design.

Boost converter; Converter modeling; Simulation; Sliding mode control

Introduction

Due to the advancement of technology in the
field of renewable energy sources, DC-DC converters largely penetrated in
implementing the power electronic systems to generate clean electricity (Andreas *et al.*, 2018; Setiawan and Setiawan, 2017;
Shafinaz *et al*., 2016; Rini *et al*., 2014). On the other
side, support for renewable energy sources is exemplified by microgrids, which
combine various renewable energy sources and can be interconnected with the
electrical grid (Rahul, 2023; Budiyanto *et al.*,
2011). DC-DC converter plays a major role in the standalone and/or grid-connected
power electronic systems by converting a variable DC link voltage to a desired
output-regulated DC voltage. The converter is stepping up the input voltage
using a DC-DC boost converter, stepping down the input voltage using a DC-DC
buck converter, or able to step up/step down the input voltage using a DC-DC
buck/boost converter (Shayeghi, Poujafar, and Sedaghati, 2020; Ali, Hossein, and Amir,*
*2014; Sulistiyanto, Rif’an, and Setyawati, 2014).

All converter circuits involve capacitors,
inductors, transistors, and diodes for energy storing and directing from the source
side to the load side (Deepak *et al*., 2018; Walker
and Sernia, 2004) showed an integrated comparison among converter types
and highlighted the functions of the converter parameters. Based on the
converter parameters, the converter can operate in either continuous conduction
mode CCM, in which the minimum inductor current will be more than zero amperes,
or the converter can operate in discontinuous conduction mode DCM, in which the
minimum inductor current can be zero amperes during a certain frequently switching period (Emerson *et al*., 2021; Philippe and Peter, 2020;
Saravana *et al.* 2014).

By considering the design difficulty of the DC-DC boost converter, the
successful controlling scheme should manipulate the variation in the input
voltage, the desired reference voltage, and the variation of the
connected load, in addition to the possibility of connected nonlinear
loads. So, a robust and accurate controller such as Sliding Mode Controller SMC
is necessary to have an effective converter performance (Makhloufi, Bousserhane, and Zegnoun, 2021; Sattianadan *et al.*,
2020).

At the same time, it deserves to be mentioned
that many research studies proposed a successful design to suppress the
chattering demerit in the controlling input voltage to the SM controller (Huayang *et al*., 2023; Xin, Huashan, and Wenke,*
*2021; Mobayen *et al.*, 2021; Amirzubir *et al.,* 2016).

This
paper models a DC-DC boost converter and demonstrates a detailed sliding mode
controller design suitable for controlling the boost converter. The study
started by modeling the converter, obtaining the dynamic equations, explaining
the design steps of the desired SMC, and then evaluating the converter
performance by analyzing the collected Simulink simulation results. The remainder
of this paper is as follows: modeling a DC-DC boost converter and driving the
related dynamic equations shown in Section 2, detailed design steps and
equations of a sliding mode controller explained in Section 3. Simulating the
proposed SMC with a DC-DC boost converter and collecting and analyzing the
collected simulation results are all demonstrated in Section 4. Section 5
summarizes the conclusion of this study.

Experimental Methods

**Modelling
of DC-DC Boost Converter**

A boost converter
or a step-up converter works on having a regulated output load voltage of a
level greater than the input voltage level. This converter has been implemented
by adding an LC low-pass filter to a basic converter circuit (Farzin, 2021; Attia, 2020a; 2020b; Daniel and Hart,
2011; Rashid, 2001). Figure 1 shows
the circuit of the DC-DC boost converter. In this converter, the diode will be
reverse-biased when the switch is ON, whereas the diode is directing the
inductor current during the OFF state of the switch.

Figure 2(a) shows the equivalent converter circuit when the switch is ON and the diode is reverse biased, whereas Figure 2 (b) shows the equivalent converter circuit when the switch is OFF and the diode is forward biased.

When the switch is ON (close), the source voltage across the inductor is shown in Equation 1, whereas Equation 2 demonstrates the inductor current derivative.

The
behavior of the current derivative is linear and positive during the switch
closing, Equation 3 demonstrates this current derivative during this period.
Equation 4 shows the variation in inductor current with respect to the duty
ratio *D.*

When
the switch is open, the diode becomes forward-biased to provide a path for
inductor current, which cannot change instantaneously. By assuming constant
output voltage the
voltage across the inductor is shown in Equation 5, and based on that the
inductor current during opening the switch is demonstrated by Equation 6.

**Figure 1 **DC-DC boost converter circuit

Equation 7 shows the inductor current derivative during the switch
OFF (open), whereas Equation 8 shows the inductor current change with respect
to duty ratio *D*.

During steady-state operation, the net change in inductor current for each one switching period is zero as demonstrated Equation 9, and it can demonstrated after variables replacement as shown in Equation 10. Based on that Equation 11 shows the converter output voltage.

Or,

From Equation 11, the
boost converter produces an output voltage that is greater than or equal to the
input voltage based on the instantaneous value of the Duty cycle (*D*).

The instantaneous value of the inductor current
variation equal
to the summation of By considering the duty cycle (*DT)* is (*u)* for the switch ON time, (*T*-*DT**)* is (*1-u)** *for
the switch OFF time, the dynamic equation of can be written as shown
in Equation 12, and can be rearrange as shown in Equation 13.

When the switch is OFF (open), the inductor current equals to the summation of the capacitor and the resistor current as shown in Equation 14. Based on that Equation 15 demonstrates the capacitor current, and it can be written by considering the capacitor voltage derivative multiplying by the capacitance value as shown in Equation 16. Equation 17 shows the expression of the capacitor derivative by moving the capacitance to the right side.

Or,

Equations (13) and (17) represent the dynamic equations of the inductor current and output voltage of the DC-DC boost converter, respectively.

**Design of Sliding Mode Controller**

The function of the Sliding
Mode (SM) controller is to decide the switching state *u* of the converter switch (Tahri, Tahri, and Flazi,*
*2014; Saad *et al.,* 2011; Guldemir, 2011; Guldemir, 2005; Trushev *et
al.*, 2005). The sliding surface *S* of the boost converter can be represented by the summation of
error in the output voltage as shown in Equation 18, which is the difference
between the reference voltage and actual output voltage** **which is the change of the
error of the output voltage *dx _{1}/dt
*as

Replace in Equation 19 yields sliding surface in circuit parameters form as shown in Equation 20, and Equation 21.

Or,

Sliding
mode control depends on the objective of the slide mode *S*, and
the derivative of the surface *to be zero value as
indicated in Equation 22.*

So can be determined by doing derivative to the surface as shown in Equation 23.

Replacing
Equation 13 and Equation 17 in Equation 23 yields Equation 24 which
demonstrates the derivative of

The general structure of the
controlling state *u* includes two components as shown in Equation 25:
equivalent controlling component and the nonlinear component (Tahri,
Tahri, and Flazi,* *2014; Saad *et al.*, 2011; Guldemir, 2011);

Equaling to zero yields the equivalent cntrol of switching ON state *u*_{eq }as demonstrated in Equation 26.

where
the equivalent values of the parameters A, B, and F are demonstrated in
Equation 27, Equation 28, and Equation 29 respectively.

The
nonlinear component can be defined as shown in Equation 30.

Figure 3 demonstrates
the DC-DC boost converter circuit controlled by the designed sliding mode
controller through the Pulse Width Modulation PWM technique to generate the
drive pulses.

Results and Discussion

**Simulation
with Results Analysis**

Simulation of the boost converter is done using MATLAB®/Simulink®
version 2015b after selecting a fixed switching frequency of 15 kHz. Many
practical research studies have been focused on using a low switching frequency
starting from 1.2 kHz in power converter applications to have an effective
power electronic system with low switching losses (Busacca
*et al.* 2022; Rohten *et al.* 2021; Ye, Malysz, and Emadi, 2015; Abrishamifar,
Ahmad, and Mohamadian, 2012). Table 1 shows the simulated converter
parameters, which were selected by considering the work of (Abouchabana *et al.*, 2021; Attia, 2020a; Attia,
2020b). Table 1 also demonstrates the range of simulated input voltage,
reference voltage, connected load, and converter parameters, which are
determined through the relationships of (Sreedhar and
Basavaraju, 2018).

**Figure 3** Block diagram of the proposed
Sliding Mode Controller SMC for DC-DC boost converter

**Table 1** Parameters for testing the SMC-based
converter

Figure 4 shows the MATLAB/Simulink simulation of the proposed converter controlled by the designed sliding mode controller, whereas Figure 4(b) shows the details of the calculated SMC parameters.

**Figure 4** MATLAB/Simulink simulation of proposed system, (a) The SM
controller with DC-DC boost converter, (b) Simulation of the designed SM
controller with the calculated parameters

Figure 5 illustrates the robustness and accuracy of the controller under a fixed source voltage of 20 Volts, focusing on load voltage regulation. The load voltage is maintained at 30 V while the load varies from 24for the initial 0.5 seconds of simulation to 12 for the subsequent 0.5 seconds, covering the entire simulation time of 1 second. Figure 5(b) shows a zoom-in of the starting transient response, in which the increments in load current and load voltage are clearly noticeable at each step of sampling time 0.5with soft starting without any overshoot in the load voltage and load current. Figure 5(c) shows a zoom-in view of the system response during a steady period, in which measuring a short period approximately equals 67(14.9 kHz), whereas measuring a long period approximately equals 133(7.5 kHz). Figure 5(d) shows a zoom-in view of the system response during the same steady period, in which measuring a long period approximately equals 133 µsec (7.5 kHz). In other words, the sliding mode controller controls the switching frequency of the PWM drive pulses based on the status of the sliding surface and, consequently, the instantaneous level of the duty cycle.

**Figure 5** Load voltage and current when load resistor 24 then
12 (a) Results of 1 sec simulation period, (b)
Zoom in during the transient period, (c) Zoom in during steady period with time
measuring of the high switching frequency range, (d) Zoom in during steady
period with time measuring of the low switching frequency

Figure 6 illustrates the controller response at various reference voltages. The simulation initiates with a reference voltage of 30 Volts for the first quarter of the 1-second simulation period. Subsequently, reference voltages of 35 Volts, 40 Volts, and 35 Volts are applied for the remaining three-quarters of the simulation period. As depicted in Figure 6, the load voltage accurately tracks the reference voltage. Figure 7 demonstrates the controller's effectiveness and response during the variation of input source voltage.

**Figure 6** Load voltage and current at different *V _{ref}*

**Figure 7** Load voltage and current at different Vs (24 V, 15 V) when load
resistor 12

Conclusion

The
paper has presented a comprehensive demonstration of the detailed steps
involved in designing a sliding mode controller for DC-DC boost converters.
Initially, the paper covered the modeling of the converter circuit during
continuous conduction mode (CCM) operation. Subsequently, the paper outlines
the design steps of a robust SM controller to decide the instantaneous value of
the controlling state involving the effects of equivalent controlling
components and nonlinear components. Simulation results have been collected and
analyzed using MATLAB/Simulink software. The study's
findings and analysis underscore the effectiveness and robustness of the
designed controller, particularly in coping with variations in source voltage
and connected loads. Furthermore, it is demonstrated that the controller
adeptly tracks the instantaneous reference voltage.

Acknowledgement

The author expresses
gratitude for the financial support received from the Office of Research &
Community Service at the American University of Ras Al Khaimah, UAE, https://aurak.ac.ae/en/academics/office-of-research-community-service/.

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