High Order Sliding Mode Control for Power Regulation: Comparative

Insights with PI Controller CUK Converter Implementation

Muhammed Mahho

, Mehmet Yilmaz

and Muhammed Fatih C¸ orapsiz

Department of Electrical and Electronics Engineering, Ataturk University, Erzurum, Turkey

Keywords:

CUK Converter, Proportional-Integral (PI) Controller, High Order Sliding Mode Control (HOSMC), Energy

Conversion Efﬁciency.

Abstract:

In this study, the performance analysis of the Higher Order Sliding Mode Controller (HOSMC) and

Proportional-Integral (PI) controller for various scenarios was performed using the DC-DC CUK converter

topology. While performing the performance analysis, the current ripple at the converter output, voltage rise-

fall and convergence time were considered. While comparing the PI controller and HOSMC, the output voltage

boost for the 30V input voltage was evaluated to 60V in the ﬁrst scenario and to 45V in the second scenario.

In these scenarios, HOSMC showed superior performance compared to PI controller in a shorter time. In the

third scenario, the performance of the controllers was examined to obtain an output voltage lower than the in-

put voltage. In the third scenario, HOSMC provided the desired output voltage at the input voltage level within

0.05s. In this scenario, HOSMC gave more successful results than the PI controller. In the fourth scenario, the

input voltage was transferred to the output at different voltage levels at 1.5s intervals. In the fourth scenario,

for the ﬁrst 1.5 seconds, HOSMC has shorter settling time than the PI controller. In the second 1.5 seconds,

although the HOSMC experienced some deterioration in the transient state, the desired output voltage values

were reached in the same time as the PI controller.

1 INTRODUCTION

Rapid developments in medical devices, computer

systems and energy production technologies have in-

creasingly increased the importance of DC-DC con-

verters. Converters are among the basic components

that increase energy efﬁciency by providing different

voltage levels required by electronic devices and sys-

tems (Yılmaz et al., 2025). Used in a wide variety

of applications, from portable devices and electric ve-

hicles to renewable energy systems and communica-

tion infrastructures, these converters not only directly

contribute to design criteria such as size, weight, and

cost, but also improve system performance. The most

frequently preferred among switched non-isolated

DC-DC converters are; Boost converter, Buck con-

verter, Buck-Boost converter, CUK converter and

SEPIC converter. Non-isolated DC-DC converters of-

fer higher efﬁciency than isolated DC-DC converters

and the advantage of voltage increase/decrease via

a single switching control. Technological advance-

https://orcid.org/0009-0005-0938-7031

https://orcid.org/0000-0001-7624-4245

https://orcid.org/0000-0001-5692-8367

ments and increasing energy demand have enabled the

widespread use of these types of converters. DC-DC

converter topologies are frequently used to reduce en-

ergy conversion losses in charging systems and PV

energy generation systems (Fathabadi, 2016; Mahho

et al., 2025). In today’s conditions, especially in solar,

wind, proton exchange membrane fuel cells and sim-

ilar energy production systems, the energy produced

is low and the current is not constant (Refaat et al.,

2024). In such systems, DC-DC converters play a

critical role in ensuring that the produced energy is

made available for the load systems in a safe and ef-

ﬁcient manner (Xu et al., 2021). The CUK converter

was proposed by Slobodan

Cuk in 1977. This con-

verter is a type of converter that can operate in a step-

up/step-down mode without applying a pulse signal

to the capacitor in the middle and does not switch

from input to output (Ilman et al., 2019). Various con-

trol methods, including fuzzy logic (Balestrino et al.,

2002) and sliding mode control (Chen, 2012), have

been applied to the CUK converter to improve per-

formance criteria such as settling time, steady-state

error and overshoot. In (Chen, 2012), two differ-

ent control methods, Proportional-Integral (PI) con-

Mahho, M., Yilmaz, M. and Çorapsiz, M. F.

High Order Sliding Mode Control for Power Regulation: Comparative Insights with PI Controller CUK Converter Implementation.

DOI: 10.5220/0014285100004848

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd International Conference on Advances in Electrical, Electronics, Energy, and Computer Sciences (ICEEECS 2025), pages 147-152

ISBN: 978-989-758-783-2

147

trol and Sliding Mode Control (SMC), were used for

the CUK converter topology to evaluate the controller

performances to obtain constant output voltage. The

transient and steady-state performances of the system

were analyzed. It was obtained that SMC gave better

dynamic response than the PI controller, was supe-

rior in terms of stability and was more robust against

load changes. In this study, two different methods of

voltage control were implemented in the CUK con-

verter topology. These methods are High Order Slid-

ing Mode Control (HOSMC) and PI controller. The

two controllers were evaluated for four different sce-

narios. The scenarios include increasing/decreasing

the voltage and changing the voltage levels at certain

time intervals.

2 MATERIALS AND METHOD

2.1 DC-DC CUK Converter Topology

Power electronics gained an important role in semi-

conductor technology in the 1950s with the devel-

opment of silicon-controlled rectiﬁers (SCRs), MOS-

FETs and IGBTs for commercial and industrial ap-

plications. Fast switching and reduced losses have

become increasingly important for electronic devices

requiring large voltage and current control. The de-

velopment of power electronics technology has had

a signiﬁcant impact, especially in AC motor drives,

power control units and industrial applications. In re-

cent years, DC-DC converters have played an impor-

tant role in terms of energy efﬁciency, reliability and

sustainability, especially in renewable energy sources

(Mumtaz et al., 2021). CUK converters, which con-

sist of two inductors and two capacitances, are a

type of fourth-order DC-DC converter. CUK convert-

ers are circuit topologies that transfer the DC volt-

age level applied to the input to a higher or lower

level to the output by appropriate control methods

(Narayanaswamy and Mandava, 2023). CUK con-

verters have an output voltage in the opposite polarity

of the input voltage (Singh, 2017).

Figure 1: Cuk converter topology.

CUK converters are obtained by cascading the

Boost converter and Buck converter topologies. For

this reason, they have the ability to both increase and

decrease the input voltage. The most important ad-

vantage of these converters is the presence of induc-

tance at the input and output of the circuit. In this

way, current ﬂuctuations are reduced to a minimum

level. The visual of the CUK converter topology is

presented in Figure 1.

The CUK converter topology operates in two op-

erating modes, Pulse Width Modulation (PWM) ris-

ing edge and falling edge triggering. When the MOS-

FET is triggered by the rising edge, the inductance

is energized by the source voltage V

n and the en-

ergy is stored as a magnetic ﬁeld. Capacitor C

discharged to ground through the MOSFET and en-

ergizes inductor L

and the load, the diode exhibits

open circuit characteristics. The electrical equivalent

circuit of the CUK converter MOSFET on mode is

shown in Figure 2. The mathematical equations for

this case are given in Equation (1) (Yılmaz et al.,

2020).

−V

)

(−V

)



−













(1)

Figure 2: Switching element conduction state CUK con-

verter circuit topology.

When the MOSFET low pulse is triggered, the

energy stored in inductor L

is transferred to capac-

itor C

and indirectly in inductor L

. The diode is

in on mode for this situation. Energy is supplied to

the load through inductor L

.The electrical equivalent

circuit of the CUK converter MOSFET cut-off mode

is shown in Figure 3. The mathematical equations

for this case are given in Equation (2) (Yılmaz et al.,

2020).

ICEEECS 2025 - International Conference on Advances in Electrical, Electronics, Energy, and Computer Sciences

148

−V

)

(−V

)



−













(2)

Figure 3: Switching element cut-off status CUK converter

circuit topology.

Table 1 gives the mathematical expressions of the

electrical circuit parameters of the CUK converter

topology used in the study.

Table 1: Mathematical expressions of electrical circuit pa-

rameters of CUK converter topology.

Parameter Formula

Duty Cycle D =

+|V

Inductance L

∆i

Capacitance C

∆V

R f

D − 1

∆V

Load R

Switching Frequency f

2.2 High Order Sliding Mode Control

Higher order sliding mode control (HOSMC) is a con-

trol method developed from Sliding Mode Control

(SMC). It is used to provide simplicity, high perfor-

mance, stability and vibration reduction to nonlinear

systems. HOSMC includes tracking calculation, shift

calculation and supertwist calculation. Its advantages

over sliding mode controllers are that it is more ro-

bust against the uncertain behaviour of the system and

provides faster response and provides superior perfor-

mance by preventing the system from vibration. The

mathematical expressions used for HOSMC are given

in Equations 3-6 (Yılmaz and C¸ orapsız, 2025).

(t) = λ

|S|sign(S) (3)

(t) = λ

sign(S)dt (4)

(t) = λ

sign(S) (5)

u(t) = λ

|S|sign(S) + λ

sign(S)dt + λ

sign(S)

(6)

In Equation 3, it pulls the system quickly to the

sliding surface. It provides terminal attraction be-

haviour. In Equation 4, it is added so that the system

does not make permanent errors. It is known as inte-

gral sliding mode control and is more resistant to dis-

turbances. In Equation 5, it pulls the system quickly

to the sliding surface but can cause unwanted vibra-

tions called ﬂutter. In Equations 3-6,λ

, λ

,λ

the

coefﬁcients that provide the balance between conver-

gence speed, steady-state accuracy, and jitter reduc-

tion.

3 RESULTS AND DISCUSSION

In this study, the dynamic performance of the CUK

converter is evaluated using HOSMC and PI con-

troller. The dynamic performance of the CUK con-

verter is evaluated in detail for four different scenar-

ios. Considering the increase/decrease of the output

voltage, important performance criteria such as efﬁ-

ciency and settling time are analysed.

Figure 4: Simulation model of the CUK converter with PI

control and HOSMC.

The parameters of the CUK converter used

in the simulation studies are; capacitors C

12.35 µF, C

= 10.42 µF, inductors L

= 800 µH

High Order Sliding Mode Control for Power Regulation: Comparative Insights with PI Controller CUK Converter Implementation

149

ve L

= 1600 µH and load R = 36 Ω The output volt-

age of the CUK converter is -60V in the ﬁrst scenario,

and -45V, -15V in the third scenario, ﬁrst in the fourth

scenario1.5per second-60V and next 1.5 per second

-45V. Figure 4 shows the CUK converter designed

in MATLAB/SIMULINK 2021b to evaluate the per-

formance of the controllers under different scenarios.

The input voltage for all scenarios is 30V was taken

as ﬁxed.

Figure 5: Load a) current-time b) voltage-time changes for

the ﬁrst scenario.

Figure 6: Load a) power-time b) duty cycle-time variations

for the ﬁrst scenario.

In the ﬁrst scenario, the input voltage is reverse

polarity. 60 VDC voltage. In this scenario, the PI

controller and HOSMC’s ability to increase the input

voltage by two times was evaluated. According to the

HOSMC PI controller, the duty cycles 0.04 It was ob-

served that the output voltage reached its steady state

by ﬁnding the best value in seconds. 0.01% tolerant

-60 DC nominal voltage is ﬁxed, and energy conver-

sion efﬁciency is measured as 100%. Figure 5 shows

the changes in load current and voltage with respect to

time. Figure 6 shows the changes in power and duty

cycle with respect to time.

Figure 7: Load a) current-time b) voltage-time changes for

the second scenario.

Figure 8: Load a) power-time b) duty cycle-time variations

for the second scenario.

In the second scenario, the voltage boost perfor-

mance of the controllers 30 V In this scenario, the

system’s transient behavior and steady-state perfor-

mance were observed. According to the PI controller,

the most optimum value of the HOSMC duty cycle

was 0.03 seconds and reached its steady state. Out-

put voltage %0, 01 tolerant −45V DC voltage value

was reached and energy conversion efﬁciency was ob-

tained as 100%. The changes of load current and volt-

age with respect to time are given in Figure 7. The

changes of power and duty cycle with respect to time

are shown in Figure 8.

In the third scenario, the performance of HOSMC

and PI controllers in reducing the input voltage level

by half is examined. While HOSMC reaches the most

optimum value of the duty cycle in 0.05 seconds, PI

controller reaches the most optimum value of the duty

ICEEECS 2025 - International Conference on Advances in Electrical, Electronics, Energy, and Computer Sciences

150

Figure 9: Load a) current-time b) voltage-time changes for

the third scenario.

Figure 10: Load a) current-time b) voltage-time changes for

the third scenario.

cycle in 0.15 seconds. HOSMC control structure not

only reaches the optimum duty cycle in a shorter time

to ensure the stability of the system, but also exhibits

superior performance in transient behaviors. In par-

ticular, the fact that the duty cycle becomes stable in

only 0.05 seconds reveals the fast response ability of

the system. The changes in the load current and volt-

age values with respect to time are given in Figure

9, and the changes in the power and duty cycle with

respect to time are given in Figure 10.

In the fourth scenario, the performances of the PI

controller and HOSMC were evaluated for different

voltage levels in different time periods. The input

voltage was increased from 30V to 60V for the ﬁrst

1.5 seconds. The voltage value of 60V was decreased

to 45V for the next 1.5 seconds. For this scenario, it

was observed that the HOSMC had a shorter settling

time compared to the PI controller in the ﬁrst 1.5 sec-

onds. The results of this scenario are shown in Figure

11 and Figure 12.

Figure 11: Load a) current-time b) voltage-time changes for

the second scenario.

Figure 12: Load a) power-time b) duty cycle-time variations

for the second scenario.

4 CONCLUSIONS

In this study, the dynamic behavior of PI controller

and HOSMC in CUK converter is comparatively an-

alyzed in terms of current, voltage, power and duty

cycle. Four different scenarios are evaluated in the

study. In all scenarios, HOSMC exhibits shorter con-

vergence time capability compared to PI controller.

In the ﬁrst two scenarios, the voltage boost feature

of CUK converter is evaluated, and in the third sce-

nario, the voltage reduction feature. In the fourth

scenario, the desired output voltage sudden change is

evaluated. In all scenarios, HOSMC and PI controller

reach 100% efﬁciency. HOSMC exhibits strong re-

sistance by behaving more robustly against uncertain-

ties and external disturbances in the system. In addi-

tion, it has the advantages of faster transient response,

lower overshoot and shorter settling time thanks to its

high-order derivative feedback structure. HOSMC’s

discrete-time operating structure and high accuracy

High Order Sliding Mode Control for Power Regulation: Comparative Insights with PI Controller CUK Converter Implementation

151

enable it to provide superior control performance es-

pecially in nonlinear and parameter-variable systems.

With these aspects, HOSMC gave more successful re-

sults than the PI controller in terms of both control

quality and system reliability

ACKNOWLEDGEMENTS

This work was supported by the Atat

urk Univer-

sity Coordination Unit of Scientiﬁc Research Projects

(Project No: FBA-2025-15043)

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