The Implementation of Internal Mode Control Method to SEPIC Converter for Battery Charging Systems

In this paper, internal model control (IMC) method, which is model based approach that offers more robust and better reference tracking capability than conventional controllers for the unstable process, is applied to SEPIC topology used in battery charging system for military implementations. When a system is not based on a plant model, it is possible to encounter some problems such as dead time and non-linearity in controlling of the system. The purpose of the SEPIC topology is to eliminate the disadvantage of other converter types such as buck/boost and cúk converters that are used for similar applications in reversing the output voltage. In addition, a great amount of voltage and current stress on a component causes the power board to overheat in such converters and requires additional cooling equipment. These problems are not encountered in SEPIC topology. Also, this topology provides high efficiency, step-up/step-down voltage conversion, and excellent transient state response over a wide range. The performance of IMC method applied on SEPIC converter is detailed analyzed in terms of simulation studies that are obtained by using MATLAB/Simulink and experimental studies.

Aim (Amaç): When a system is not based on a model, it is possible to encounter some problems in the control of the system, such as dead time and non-linearity.This study provides better performance of the system by using model based control approach./ Bir sistem bir modele dayalı olmadığında, sistemin kontrolünde ölü zaman ve doğrusal olmama gibi bazı sorunlarla karşılaşmak mümkündür.Bu çalışma, model tabanlı kontrol yaklaşımı kullanarak sistemin daha iyi performans göstermesini sağlar.

INTRODUCTION (GİRİŞ)
DC-DC power converters are required to respond dynamically to sudden variations in frequency, load and input voltage.In addition, they must provide reliable and efficient output voltage without voltage sag and swell.Due to the heat, the efficiency of linear regulators (LRs) is lower than switching mode power supplies (SMPS) though they produce small ripples of output voltage.On the contrary, the LRs do not have a step-up capability, they are only step-down the voltage.Therefore, they are preferred in low power applications.The SMPS is used in all power applications due to high efficiency, lower X switching loss and the most important one is reliability.
SMPS stores energy using various energy storage components such as capacitor and inductor.The energy that is stored in these components can be transferred to the output using different control methods through switching elements.One of the popular methods for controlling turn-on and turnoff mode of a switching device to transfer energy to load side is Pulse Width Modulation (PWM) that involves adjusting the width of a high-frequency pulse signal.Different SMPS topologies are available to be used by power electronics societies for various purposes.Boost/buck/buck-boost converters, most widely used topologies, are called non-isolated topologies because the lack of galvanic isolation between input/output voltages.
The Cúk and SEPIC topologies have been improved by adding low-pass filter to conventional topologies [1].Output voltage ripple for this type of converter is reasonable and can be less than 2% [2].Since there are two inductors in these topologies, it is called a two-stage converter, and both input and output currents are naturally filtered with an LC low pass filter.Also, charging and discharging capacitors by means of inductors prevents high current increases and thistable 2 makes the topology efficient [3].Compared to Cúk converter, SEPIC converter has an advantage in that it produces an output voltage with rectified polarity.
In [4] and [5], Garcia de Viculia et al. analyzed the SEPIC converter in discontinuous conduction mode (DCM) and continuous conduction mode (CCM).In [6], transfer function of the SEPIC converter is calculated by state space averaging (SSA) method that is operated in CCM using feedback control design.In [7], R.There are situations where switching converter such as SEPIC topology may need to function as a power supply, as well as maintain batteries that are used in military applications.The SEPIC converter that is designed properly can supply several amps continuously if the load demands it.The control methods used can directly impact the output voltage of the SMPS, making the performance of these algorithms a crucial factor to consider.Due to its effectiveness and straightforwardness in linear systems, the Proportional-Integral-Derivative (PID) control method is commonly favored in SMPS topologies.There are also some problems such as non-linearity and dead time in controlling the dynamic plant of the model in the PID control method [8].The development of model-based control (MBC) approaches has been propelled by these concerns.Compared to the conventional ones, the Internal Mode Control (IMC) method, which is one of the MBC methods, shows a better reference tracking capability and more robustness for unbalanced applications [9].The IMC method estimates the plant output in parallel and according to the estimation, applies a corrective effect [10].In addition, the stability of IMC method depends on the plant and the controller such as the conventional control methods [11].
A new technique for obtaining a parallel model to the plant is presented in reference [9], a single-input single-output (SISO) system was then utilized by Garcia and Morari [10].This approach incorporates various conventional techniques such as the deadbeat controller, Dahlin method and Smith estimator.Afterwards, this approach is integrated into discrete-time multiple-input multiple-output (MIMO) systems [12].Reference [13] presents a boost-type DC-DC converter operating in CCM utilizes a two degrees of freedom (2DOF) IMC design to regulate the output voltage.Xiaodong Sun et al. analyzed a bearingless permanent magnet synchronous motor (BPMSM) by using IMC and inverse system technique in [14].In [15], a new controller is designed for permanent magnet synchronous motor (PMSM) using both support vector machine generalized inverse (SVMGI) and IMC.
In this paper, IMC method is implemented for a SEPIC converter for battery charging system used in military applications due to the better setpoint monitoring and more robustness for unstable process compared to conventional methods.The theory and principle of SEPIC converter are given in part 2. Control strategies of the IMC and its comparison with the conventional PI control method is described for the SEPIC converter in part 3. The design of the topology is given in part 4. Simulation and test bench results are presented in part 5 and 6, respectively.Conclusion part is also given in the last chapter.

The Operation of SEPIC Converter (SEPIC Dönüştürücünün Çalışması)
The fact that it has a non-inverting structure has made the use of SEPIC converter popular.The SEPIC converter can maintain a stable output voltage despite variations in the input voltage, X moreover, it is possible for the output voltage to be higher or lower than the input voltage.Applied duty cycle of the switching device can be modified to achieve desired output voltage or source current.It is a fourth-order time-varying converter with two switching states, one MOSFET, one diode, two inductors and two capacitors.The topology diagram of a typical SEPIC converter is illustrated in Figure 1.
The input side of SEPIC converter consists of an inductor (L1) and switching element (S), like the standard boost converter, from which an output voltage higher than the input voltage can be obtained.When the switching element S is turnedon, the inductor L1 is charged by current   / 1 .Besides, due to the diode D has reverse biased, no current flows through it and therefore inductor L2 is charged by current  1 / 2 .
When the switching element S is turned-off, currents iL1 and iL2 flow to the load through diode D. Thus, the capacitor C1 charges through the inductor L1; Capacitor C2 charges through inductors L1 and L2.The voltage across the inductor L2 equals to -Vo during the turn-off state.In this mode, energy flows from inductors L1 and L2 to the load.Modulation Index (MI) that is related to duty cycle, input and output voltage is similar with Cûk converter without reverse polarity.The general state space equations are given in ( 2) and (3), respectively.

𝑥̇= 𝐴𝑥 + 𝐵
(2) Where,  represents state-space vector, ̇ represents state variable vector;  represents input signal;  represents output signal;  represents state matrix;  represents vector;  represents vector associated with the state variable and  represents vector relating input to the output.Also, both turn-on and turn-off modes are given in Figure 2  The state variables are considered as  1 =   1 ,  2 =   1 ,  3 =   2 and  4 =   2 .In Figure 2 (a), when switch is turn-on, SEPIC converter state space model is expressed ( 4) and (5).
In Figure 2 (b), when switching element is turn-off, SEPIC converter state space variables are expressed given ( 6) and (7).
During the model extraction, switching element is assumed ideal and the parasitic elements ( 1 ,  2 ,  1 ,  2 ) are assumed to be negligible, state space model is expressed as: where  =    and  − = 1 −  =    .DC and AC parts of the variables , ,  and  can be expressed given below: [ X  =  +  x =  +  ũ =   +  ̃  =   +  ̃ (10) The first terms in the equations represent the DC signal part, and the second terms represent the AC signal part.When these equations are put into a time-weighted average equation, they can be expressed as (11) and (12).
To determine a signal response, AC signal disturbances at the input ( ̃ ) are neglected as (13) and (14).To solve the equation, it needs to be transformed to the frequency domain given (15).The relationship between control and output can be calculated as (16).

THEORY AND PRINCIPLES OF IMC METHOD (IMC Metodunun Teorisi ve Prensipleri)
The conventional feedback model and a specific property of the proposed IMC method that implemented to the SEPIC converter is given in Figure 3  (() −  ̃()) (18) For stability, the roots of the characteristic functions given below should be in the unit cycle.

X
To provide that the system maintains robust against any distortion, low-pass filter is added to the controller as follows [12].
Therefore, ( 18) is transformed as: The filter design is expanded by [11] for the plant model given below: : Tuning parameter n : Relative order of minimum phase Distortion and variations can be evaluated against Integral Absolute Error (IAE) or Integral Square Error (ISE).IAE can be defined as the integral of absolute difference between reference and output signals and can be given as follows: where Ts is settling time and the factorization can be minimized by IAE as (30): ISE is equivalent to the integral of the squared difference between the reference and output signals.
This approach rapidly corrects errors while still allowing for minor errors to remain within an acceptable range.
where Ts is settling time and the factorization can be minimized by ISE as (32): Consequently, the complementary sensitivity equations can be calculated as follows: The L1 and L2 inductance values are calculated by minimum input voltage, which results a peak-topeak ripple current of around 30% of maximum current.For inductors considered equal to each other, the ripple current is expressed as: Besides, the inductance is calculated as follows:

Calculation of the Coupling Capacitor (𝑪 𝟏 ) (Kuplaj Kondansatörünün Hesaplanması)
The coupling capacitor's size is primarily determined by the RMS current, and the current flowing through the capacitor can be described as: Voltage ripple across coupling capacitor is defined peak-to-peak given below:

Calculatıon of Output Capacıtor (𝑪 𝟐 ) (Çıkış Kondansatörünün Hesaplanması)
When the switching element is turned-on, the loadside current is supplied by output capacitor, and RMS current flowing through output capacitor can be given below: Moreover, value of the output capacitor ( 2 ) can be expressed given below: According to design parameters and specifications, calculated values are given in Table 1.

IMC Controller Design (IMC Kontrolcüsünün Tasarımı)
As a result of the design calculation, relation between small signal duty cycle and output is expressed as (41).The matrices of the zeros and poles can be defined as ( 42) and (43).The reversible part of the equation according to the ISE criterion is: Also, the irreversible part is expressed as in (45).Elimination of unstable poles makes the controller as in (46).As a result, the filter is designed in the following manner: (47)

SIMULATION RESULTS (SİMÜLASYON SONUÇLARI)
In order to avoid overshoot in output voltage and to keep voltage fluctuations within the desired limits, simulation of the IMC method implemented to SEPIC topology is depicted in Figure 4.In addition, simulation studies are performed by using MATLAB/Simulink program.
Waveforms of output voltage, the zoom view of output voltage and output current at minimum input voltage and maximum duty cycle by using IMC method are illustrated in Figure 5, respectively.This study examines the response of the SEPIC converter under different load conditions while in a steady-state.Therefore, input/output voltages, input/output currents, coupling capacitor voltage, VGS and VDS voltages of MOSFET are observed under the steady-state condition.All experimental data in this study is gathered using an oscilloscope and then translated into graphs using Microsoft Excel.Under the 10 Ω resistive load conditions and 32 V input voltage, Figure 9  Output voltage overshoot ratios for proposed and conventional PI control methods in transient have been observed under different load and input voltage conditions and these data are presented in Table 2.
the transient state and load variation from 20Ω to 10Ω with 32 V input voltage, Figure 13 (

CONCLUSION (SONUÇ)
The primary objective of this study is to design a controller that ensures the robust performance of the SEPIC converter, suitable for battery charging in military applications.To achieve this objective, an optimal internal model control (IMC) controller is developed to overcome improved setpoint tracking and minimal disturbance in SEPIC converter.Thus, problems faced in parameter setting of the PID controller, which is frequently used today, with the IMC controller have been compensated.The results obtained from the topology have been validated by simulation and experiments.
Simulation and experimental outcomes of SEPIC converter controlled by IMC technique revealed controller's robustness in both transient and steadystate conditions, when compared to the conventional PI method.Therefore, IMC can be regarded as a suitable control method for conventional power supplies that provide quick response and steady-state benefits.

DECLARATION OF ETHICAL STANDARDS
(ETİK STANDARTLARIN BEYANI) The author of this article declares that the materials and methods they use in their work do not require ethical committee approval and/or legal-specific permission.
Ahmet KARAARSLAN: He conducted the conception, design and supervision process.

Zafer ORTATEPE:
He performed the interpretation, writing and critical review process.

CONFLICT OF INTEREST (ÇIKAR ÇATIŞMASI)
There is no conflict of interest in this stud

Figure A :
Figure A: The laboratory setup of the SEPIC board /Şekil A:.SEPIC bordunun laboratuvar kurulumu

Figure 2 .
Figure 2. Operating modes of SEPIC converter (a) the switch is turn-on state, (b) the switch is turn-off state

Figure 3 .
Figure 3 (b) shows that the plant model  ̃() is positioned in parallel with G(z), which enables it to make predictions.When the plant model  ̃() is equivalent to the plant G(z), any disturbance in the plant is solely caused by the disturbance d(z).According to the Figure 3 (b), the transfer functions of () and () for the IMC method are calculated as follows: () =

Figure 9 .Figure 11 .XFig. 12 .
Figure 9. Waveforms under the 32 V input voltage and 10 Ω resistive load condition (a) input voltage (orange), output voltage (blue) and coupling capacitor voltage (grey) waveforms (b) input (orange) and output (blue) current waveforms Under the 10 Ω resistive load and 32 V input voltage condition, Figure 10 (a) illustrates the voltage waveforms of the MOSFET VDS and VGS for the SEPIC converter.Besides, Figure 10 (b) displays the waveforms of the input/output and coupling capacitor voltages of the SEPIC converter when subjected to 10 Ω resistive load and 13 V input voltage conditions.

Figure 13 .
a) illustrates the waveforms of input/output voltages of SEPIC converter.Besides, Figure 13 (b) shows the waveforms of input/output voltages of SEPIC converter under the transient state and load variation from 10Ω to 20Ω with 32 V input voltage.Input (orange)/output voltage (blue) waveforms under the 32V input voltage and resistive load variation (from 20Ω to 10Ω) (greystep change) (b) input (orange)/output voltage (blue) waveforms under the 32V input voltage and resistive load variation (from 10Ω to 20Ω) (greystep change)

Table 1 .
Parameters and specifications of the SEPIC converter

Table 2 .
Voltage overshoot ratios for proposed and conventional PI control methods in transient state Under the transient state and load variation from 20Ω to 15Ω with 15 V input voltage, Figure 14 (a) displays the waveforms of input/output voltages of SEPIC converter.In addition, Figure 14 (b) illustrates the waveforms of input/output voltages of SEPIC converter under transient state and load variation from 15Ω to 20Ω with 15 V input voltage.

Table 3 .
Output voltage overshoot ratios under different voltage and load variations for proposed and conventional PI control methods in transient state