# Comparison of the Performance of Photovoltaic Power Generation-Consumption System with Push-Pull Converter under the Effect of Five Different Types of Controllers

Authors: Hilmi Zenk
Journal: International Journal of Photoenergy
 (2019)

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## Abstract

In this study, a dynamic system has been modeled to efficiently use a photovoltaic generation and control system (PVGCS) for driving of a medium power off-grid electric machine. The measures have been taken to respond to three different disturbing factors in this system. First, the photovoltaic panels selected for energy generation have a variable solar radiation effect. Second, the DC motor load at the system output is assumed to have a variable torque. Third, a variable reference voltage, which is determined even in the case of time-varying energy generation and consumption of the system, is followed with minimum error. For this purpose, a push-pull converter has been chosen as a highly flexible structure since it is predicted that it can provide stable and effective variable DC voltage at increasing and decreasing level required for DC motor. The control of the DC voltage at different levels to be provided by the push-pull converter is performed by PI, fuzzy logic, fuzzy-tuned PI, 2-DOF PI, and fractional PID logic whose coefficients are selected by appropriate methods, respectively. The system efficiency and stability under the influence of these five different advanced controllers are compared. In the case of two disturbing factors affecting the system, the difference values (errors) of the voltage generated by each selected controller with the reference voltage are determined comparatively. The studies were carried out by using dynamic system modeling in MATLAB-SIMULINK software. In addition, the results of this study proved which type of controllers is more successful in controlling systems with the second order and more instability factors and which of them responds to sudden changes in errors more quickly.


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## Body

## 1. Introduction

One of the most effective ways to produce electricity without harming the environment is through the use of solar energy. Solar energy is described in the photovoltaic event, which is converted to electrical energy. A photovoltaic event is a physical phenomenon defined as the transformation of sunlight into electrical energy. Solar cells are semiconductors which can convert sunlight directly into their electrical energy. The solar cell operating with this principle produces voltage on the ends depending on the amount of light falling on it. The voltage produced varies directly depending on the amount of incoming sunlight.A number of solar cells are combined to form panels, and panels are combined to form PV power systems [1]. The output of solar panels is generated from DC electric energy. The DC voltage and power from solar panels can supply DC or AC loads with various power electronic converters.Solar cells can be manufactured from many materials, such as amorphous silicon, copper indium gallium selenide, and cadmium telluride [2]. There are many studies on cost and efficiency in solar panels. The efficiency of the current photovoltaic panel has been expressed many times, reaching 35% [3]. In plants with large power generation from solar energy-producing countries, the development of solar panel manufacturing techniques has become more economical with an increase in production and an increase in panel power values and efficiency [4].DC type electrical energy produced from photovoltaic solar panels must be converted into DC or AC electrical energy according to the purpose of use. A different type of converter is required for this. However, the converters need a control system.These converters are controlled by using classical and advanced control methods such as P, PI, PD, and PID controllers [5]; fuzzy logic controllers [6], fractional PID [7]; artificial neural networks [8]; vector control methods [9]; model predictive control [10]; and genetic algorithms [11].In this study, an off-grid system is recommended. The photovoltaic solar power generation system in this network is connected to the push-pull converter. The performance of the push-pull converter is compared to the performances of PI, fuzzy, and fuzzy-tuned PI controllers, while feeding the DC motor-containing loads, respectively. In the simulation, it was tried to create difficult conditions by constantly changing the irradiation level of the sun coming into the panels. In this environment, the performances of the controllers were tested and the results were compared and the contribution of the advanced control techniques was discussed. The whole simulation was performed in a MATLAB/Simulink environment.This paper is organized in four sections. Section1 is the introduction. The designed push-pull converter, controllers, and DC motor load are described in Section 2. Section 3 presents the simulation results. The last section gives some remarks and conclusion.


## 2. Materials and Methods

The general scheme of the system consisting of push-pull transducer and DC motor connected to PI, fuzzy, fuzzy-tuned PI, 2-DOF PI, and fractional PID controllers, respectively, is proposed in Figure1. The solar panels contained 40 parallel branches and 40 panels on each branch. The voltage from these panels feeds the DC motor with a push-pull type converter. The samples taken to control the voltage and speed of the motor in the desired reference range enter the controller unit. The control signals at the controller output turn into PWM signals and drive the push-pull converter switches.Figure 1
PVES with push-pull converter and DC motor.


### 2.1. PV Solar Cell Equivalent Circuit

Photovoltaic solar cells are semiconductor components that turn solar light to electrical energy [12]. In order to examine the behavior and electrical characteristics of photovoltaic solar cells, an equivalent circuit consisting of electrical circuit elements is needed [13]. Different equivalent circuit models for simple and advanced photovoltaic solar cells are found in the literature [14]. Because photovoltaic solar cells are not ideal elements, they are loss elements due to their physical structure. Therefore, losses are represented by resistances.A commonly used equivalent circuit model for a photovoltaic solar cell is seen in Figure2. The Iph current source shows the current generated by the photons and is constant under constant radiation and temperature. The parallel Rp resistance is used to represent the leakage current and the series Rs resistance to the voltage drop in the output. The efficiency of the conversion in the photovoltaic battery is sensitive to small changes in Rs. However, it is not sensitive to changes in Rp. A small increase in Rs significantly reduces the output of the photovoltaic module [15]. The output voltage of the PV cell is shown in equation (1) [16]. Descriptions of the variables used here are seen in Table 1.
(1)VPV=NλlnISC−IPV+MI0MI0−NMRsIPV.Figure 2
Equivalent circuit model of a PV solar cell.Table 1
The descriptions for PV cell.
Expression
Definition
Unit
VPV
:
Cell output voltage
V
IPH
:
Photocurrent, function of irradiation level, and junction of temperature
A
IPV
:
Cell output current
A
ISC
:
Cell short circuit current
A
I0
:
Reverse saturation current
A
RS
:
Series resistance of cell
Ω
N
:
Series cells per string
λ
:
Constant coefficient depends upon the cell material
M
:
Parallel strings


### 2.2. Push-Pull Converter

Figure3 shows the circuit diagram of the dc-dc converter using the push-pull structure. In this circuit diagram, the symmetrical structure of the output stage is clearly visible. The circuit uses two active power switches. The converter uses a transformer for voltage trimming and electrical isolation, and the output inductor is used for energy storage. Therefore, unlike the design of the transformer for the single-ended converter, where care must be taken in selecting the core material and geometry to design for proper magnetizing inductance, in the push-pull converter, the transformer is used as an ideal element.Figure 3
Equivalent circuit model of a push-pull converter.Since Sw1 and Sw2 share the current, the push-pull converter is used for higher power applications compared to the single-ended converters. Figure 4(a) illustrates the switching waveforms for Sw1 and Sw2 with a dead time during which both switches are open. The symmetrical structure of the push-pull stage permits two-sided use of the magnetic loop of the transformer [17]. The principle of push-pull converter operation is as follows. When the SW1 switch is turned on, the current passes through the primary of the TR1 transformer and the magnetic field at TR1 expands along the core. This operating state is shown in Figure 4(b). The expanding magnetic field in TR1 creates a voltage at the secondary TR1; the polarity is inversely biased so that the D2 diode is forward-oriented and the D1 diode is cut. D2 transmits and charges the output capacitor C through the L coil. L and C form an LC filter structure. The converter voltages are given by equation (2).
(2)Vs1=Vs2=ViN2N1,Vp1=Vp2=Vi,VL=ViN2N1−Vo.Figure 4
(a) Switching waveforms for Sw1 and Sw2. (b) Equivalent circuit when SW1 is on and Sw2 is off. (c) Equivalent circuit when SW1 is off and Sw2 is on. (d) Equivalent circuit when SW1 is off and Sw2 is off.
(a)
(b)
(c)
(d)When the Sw1 switch is off, the magnetic field in TR1 collapses, and after a dead time period (depending on the duty cycle of the PWM drive signal), the Sw2 switch is transmitted; the current passes through the primer of TR2, and the magnetic field at TR2 expands along the core. This operating state is shown in Figure 4(c). At this point, the direction of the magnetic flux is reversed from that produced by the transmission state of Sw1. The magnetic field emitted through the magnetic core forms a voltage in the secondary of TR2; the polarity is in the opposite direction, leading to the D1 diode and leading to the D2 diode. When the D1 diode is in transmission, C charges the output capacitor L. After some dead time, the Sw1 switch is back to on and the cycle is repeated [18]. The converter new voltages are given by equation (3).
(3)Vs1=Vs2=−N2N1Vi,Vp1=Vp2=−Vi,VL=−Vs2−Vo=N2N1Vi−Vo.There are two important considerations for the stable operation of push-pull converters. First, both switches should not be in the same position together, because this makes the source short circuit effectively. This means that the transmission time of each switch must not exceed half the total time for a full cycle; otherwise, the transmission will overlap. This operating state is shown in Figure4(d). The duty cycle (D) must be less than 50% so that the switches do not have a coincidence. Second, the magnetic behavior of the transformers and switches in the circuit must be the same. Otherwise, the transformer may go to saturation and this will cause damage to the Sw1 and Sw2 switches. This behavior requires that the Sw1 and Sw2 keys have exactly the same individual transmission times and that the centers are magnetically balanced with the interconnected primary and secondary transformer ends. These criteria must be met by the transformer with the control and drive circuit. The output voltage (Vo) of the push-pull converter is equal to equation (4). Electrical parameters of the push-pull converter are given in Table 2.
(4)Vo=2DViN2N1.Table 2
Push-pull converter parameters.
Expression
Definition
Value
Vi
:
Converter input voltage
0-1 kV
Vo
:
Converter output voltage
0-600 V
N1
:
Number of secondary windings
1000 turns
N2
:
Number of secondary windings
600 turns
L
:
Inductor
1 mH
C
:
Capacitor
10 mF
fSw
:
Switch frequency
1 kHz


### 2.3. DC Motor Model

Many features that are required to be in a motor are available in a DC motor. Some of these features include safety, durability, and cheapness and low voltage levels. DC motors are preferred in many applications. The electrical circuit and the electrical circuit diagram of the rotor of a direct current motor are shown in Figure5. The parameters and symbols used in the system are given in Table 3.Figure 5
Basic structure of DC motor equivalent circuit.Table 3
DC motor parameters.
Expression
Definition
Unit
Ra
:
Armature resistance
Ω
2.581
La
:
Armature inductance
H
0.028
Rf
:
Field resistance
Ω
281.3
Lf
:
Field inductance
H
156
Laf
:
Field-armature mutual inductance
H
0.9483
Jm
:
Total inertia
kg·m2
0.02215
B
:
Viscous friction coefficient
N·m·s
0.002953
Τ
:
Coulomb friction torque
N·m
0.5161
ɷrstart
:
Initial speed
rad/s
1
Ifstart
:
Initial field current
A
1According to Kirchhoff’s voltage law, the electrical equation of the DC motor is given in equation (5). Here, iat is the armature current, eat is back voltage, and Vst is the voltage source. In equation (6), the back emf voltage eat is expressed to be proportional to a constant, such as Ke, with the angular velocity of the rotor ɷt in the motor. Furthermore, the torque generated by the motor, Tm, is calculated by multiplying the torque constant Kt by the armature current as shown in equation (7).
(5)Vst=Ra·iat+Ladiatdt+eat,(6)eak=Ke·ωmt,(7)Tmt=Kt·iat.θ is the position of the shaft, and TL is the external load torque. The total torque of the motor must be zero; this is expressed in equation (8).
(8)dθdt=θ̇=ωt,Jmdωmdt+Bωm=Kt·ia−Bωm−TL.


### 2.4. PI Controller

The PI controller structure is simple and has a controller structure that provides very good results for many control systems. The control block diagram of the classical PI controller is given in Figure6. In this configuration, the control signal ut is the sum of two terms. Each of these terms is a function of the tracking error et. The term Kp indicates that this term is proportional to the error. The term Ki/s is an integral term. Each of the terms works independently of the other. According to DC converter reference voltage input circuit, output voltage is controlled by the PI controller. Activated equations are as follows:
(9)ut=Kpet+Ki∫etdt,(10)dutdt=Kpdetdt+Kiet.Figure 6
PI controller block diagram.If equation (10) is converted from the continuous time space t into the discrete time space k, then equation (11) is obtained.
(11)uk−uk−1Ts=Kpek−ek−1Ts+Kiek,uk=uk−1+Kpek−ek−1+Kiek.The optimalP and I coefficients for the PI controller in this system were found by using the closed loop Ziegler-Nichols method.


### 2.5. Fuzzy Logic Controller (FLC)

Fuzzy logic control algorithm is based on digitizing a set of heuristic control rules. It is important to note that fuzzy logic is used to evaluate uncertain, fuzzy sets and rules for expressing linguistic terms [19, 20]. The most important feature that distinguishes the concept of the fuzzy set from that of the classical set is that verbal variables are used instead of numerical variables. A fuzzy logic controller system is generally shown in Figure 7. As is known, the structure of the fuzzy logic controller consists of three parts. These sections are briefly mentioned in the “fuzzification” system phase, and the data obtained from the system are converted to fuzzy values. The second stage is “rule base,” where fuzzy data is processed by fuzzy rules. In the last stage, which is called “defuzzification,” the data is converted to the exact number of fuzzy results.Figure 7
Basic configuration of a FLC.The knowledge base unit consists of two units, the database and the rule base. The knowledge base can be divided into two parts: the database, in which the decision-making unit receives the information used in the rule base, and the rule base, where there are linguistic control rules for audit purposes. The set of rules determines the audit objectives and audit strategy. Information about the system being audited, fuzzification, processing of fuzzy data, membership function required during defuzzification operations, and rule table information are available in the "database" unit. Connections between inputs and outputs are established using rules in the rule base. In a system,e and de are inputs, and if μ is the output variable (if e=x and de=y, then u=z), defined by the rule, e and f take the value of the fuzzy value of the output determined. The rule table is shown in Figure 8.Figure 8
Rule base table.


### 2.6. Fuzzy-Tuned PI Controller (FT-PIC)

The simplified block diagram of the fuzzy-tuned PI controller is shown in Figure9. Membership functions for this controller type input error (e), change of error (de), and controller output (du) are defined on the normalized domain [-1, 1] as shown in Figure 10. Membership functions (MF) of β are defined on [0, 1] as shown in Figure 11.Figure 9
Basic configuration of a FT-PIC.Figure 10
Membership functions of inputs (e, de) and output (du). Le=Lde=Ldu (NB: negative big; NM: negative medium; NS: negative small; Z: zero; PS: positive small; PM: positive medium; PB: positive big).Figure 11
Membership functions of gain updating factor,β, are mapped {ZE, VS, S, SB, MB, B, VB}.Symmetric triangles with equal base width and 50% overlap with neighboring MFs are used here due to its natural and unbiased nature. The term sets ofe, de, and du for PI type FLC contain the same linguistic expressions for the magnitude part of the linguistic values [21].The operation of a PI-type FLC as shown in Figure9 can be described by equation (12). Here, du is the incremental change in controller output. FT-PIC generates the nonlinear controller output (du) by modifying the output of the simple fuzzy-tuned PI controller (FT-PIC) as shown in Figure 9 and equation (13).
(12)uk=uk−1+duk,(13)du=βGuduN1.The weighted absolute average of the effective rules of the controller can be taken as the absolute output. For this rinsing process, the central method of areas where the center of gravity of the active areas given in equation (14) is taken can be used.
(14)duk=u∑i=a,b,c,dμRiduRduRRi∑i=1nuVR.where k is the sampling time, m is the degree of membership, ek is the control error, and k is the variation of this error in a sampling time. The Simulink model of the membership function related to weight coefficients according to the expression in the share portion of the central method of the fields given by equation (14) was prepared as shown in Figure 12.Figure 12
Simulink model of the central method of fields.


### 2.7. Two Degree Of Freedom (2-DOF) PI Controller

As with most industrial control applications, the desired value of the controlled variable or setpoint normally remains constant and needs to be changed. This control technique is mainly concerned with two free-grade (2-DOF) applications of PID control algorithms. The 2-DOF control algorithm provides additional parameter and regulative control performance, and the closed loop control system durability in mind to improve servo control behavior is used [22–26]. It is possible to incorporate this capability of Two Degree Of Freedom controllers into both PI-type and PID-type control algorithms.The 2-DOF controller structure has been developed for situations where a 1-DOF controller structure is insufficient. By adding theβ parameter to the controller structure, better performance is achieved in terms of maintaining reference distortion suppression performance and improving transient response. The structure of the 2-DOF PI controller is shown in Figure 13.Figure 13
2-DOF PI structure.The control signal for the 2-DOF PI controller is given in equation (15). Here, Ti shows the integral time constant, Td the derivative time constant, KP proportional gain, β reference weight ratio, Crs reference signal transfer function, and Cys feedback transfer function [27].
(15)uk=KPβ+1Tikrk−KP1+1Tikyk,uk=Crkrk−Cykyk.


### 2.8. Fractional PID Controller (PIλDμ)

Fractional type PID controllers can be described as the generalized form of PIDs. The output data can be summarized as a linear combination of the input, a fractional derivative of the input, and a fractional integral of the input [28]. Fractional PIDs are also known as PIλDμ controllers, where λ and μ are the integration and differentiation orders; if both values are 1, the result is a usual PID (henceforth called “integer” PID as opposed to a fractional PID). PIλDμ controllers are advanced controllers that can give better results than classical PI controllers. They are widely used because they are able to adjust more precisely than PID controllers. The best knowns are the descriptions of Shah and Agashe and Rasoanarivo and Sargos [29, 30]. The PIλDμ controller general block diagram is shown in Figure 14.Figure 14
General block diagram ofPIλDμ structure.In this study,λ and μ≥0, where λ is the order of integration and μ is the order of differentiator. KP, KI, and KD are the PID controller gains. Us and Es are the control and error signals, respectively. In this study, PIλDμ controller software was performed by FOMCON Toolbox [31]. System output, Ck, is as seen in
(16)Ck=KP+KIkλ+KDkμ.


## 2.1. PV Solar Cell Equivalent Circuit

Photovoltaic solar cells are semiconductor components that turn solar light to electrical energy [12]. In order to examine the behavior and electrical characteristics of photovoltaic solar cells, an equivalent circuit consisting of electrical circuit elements is needed [13]. Different equivalent circuit models for simple and advanced photovoltaic solar cells are found in the literature [14]. Because photovoltaic solar cells are not ideal elements, they are loss elements due to their physical structure. Therefore, losses are represented by resistances.A commonly used equivalent circuit model for a photovoltaic solar cell is seen in Figure2. The Iph current source shows the current generated by the photons and is constant under constant radiation and temperature. The parallel Rp resistance is used to represent the leakage current and the series Rs resistance to the voltage drop in the output. The efficiency of the conversion in the photovoltaic battery is sensitive to small changes in Rs. However, it is not sensitive to changes in Rp. A small increase in Rs significantly reduces the output of the photovoltaic module [15]. The output voltage of the PV cell is shown in equation (1) [16]. Descriptions of the variables used here are seen in Table 1.
(1)VPV=NλlnISC−IPV+MI0MI0−NMRsIPV.Figure 2
Equivalent circuit model of a PV solar cell.Table 1
The descriptions for PV cell.
Expression
Definition
Unit
VPV
:
Cell output voltage
V
IPH
:
Photocurrent, function of irradiation level, and junction of temperature
A
IPV
:
Cell output current
A
ISC
:
Cell short circuit current
A
I0
:
Reverse saturation current
A
RS
:
Series resistance of cell
Ω
N
:
Series cells per string
λ
:
Constant coefficient depends upon the cell material
M
:
Parallel strings


## 2.2. Push-Pull Converter

Figure3 shows the circuit diagram of the dc-dc converter using the push-pull structure. In this circuit diagram, the symmetrical structure of the output stage is clearly visible. The circuit uses two active power switches. The converter uses a transformer for voltage trimming and electrical isolation, and the output inductor is used for energy storage. Therefore, unlike the design of the transformer for the single-ended converter, where care must be taken in selecting the core material and geometry to design for proper magnetizing inductance, in the push-pull converter, the transformer is used as an ideal element.Figure 3
Equivalent circuit model of a push-pull converter.Since Sw1 and Sw2 share the current, the push-pull converter is used for higher power applications compared to the single-ended converters. Figure 4(a) illustrates the switching waveforms for Sw1 and Sw2 with a dead time during which both switches are open. The symmetrical structure of the push-pull stage permits two-sided use of the magnetic loop of the transformer [17]. The principle of push-pull converter operation is as follows. When the SW1 switch is turned on, the current passes through the primary of the TR1 transformer and the magnetic field at TR1 expands along the core. This operating state is shown in Figure 4(b). The expanding magnetic field in TR1 creates a voltage at the secondary TR1; the polarity is inversely biased so that the D2 diode is forward-oriented and the D1 diode is cut. D2 transmits and charges the output capacitor C through the L coil. L and C form an LC filter structure. The converter voltages are given by equation (2).
(2)Vs1=Vs2=ViN2N1,Vp1=Vp2=Vi,VL=ViN2N1−Vo.Figure 4
(a) Switching waveforms for Sw1 and Sw2. (b) Equivalent circuit when SW1 is on and Sw2 is off. (c) Equivalent circuit when SW1 is off and Sw2 is on. (d) Equivalent circuit when SW1 is off and Sw2 is off.
(a)
(b)
(c)
(d)When the Sw1 switch is off, the magnetic field in TR1 collapses, and after a dead time period (depending on the duty cycle of the PWM drive signal), the Sw2 switch is transmitted; the current passes through the primer of TR2, and the magnetic field at TR2 expands along the core. This operating state is shown in Figure 4(c). At this point, the direction of the magnetic flux is reversed from that produced by the transmission state of Sw1. The magnetic field emitted through the magnetic core forms a voltage in the secondary of TR2; the polarity is in the opposite direction, leading to the D1 diode and leading to the D2 diode. When the D1 diode is in transmission, C charges the output capacitor L. After some dead time, the Sw1 switch is back to on and the cycle is repeated [18]. The converter new voltages are given by equation (3).
(3)Vs1=Vs2=−N2N1Vi,Vp1=Vp2=−Vi,VL=−Vs2−Vo=N2N1Vi−Vo.There are two important considerations for the stable operation of push-pull converters. First, both switches should not be in the same position together, because this makes the source short circuit effectively. This means that the transmission time of each switch must not exceed half the total time for a full cycle; otherwise, the transmission will overlap. This operating state is shown in Figure4(d). The duty cycle (D) must be less than 50% so that the switches do not have a coincidence. Second, the magnetic behavior of the transformers and switches in the circuit must be the same. Otherwise, the transformer may go to saturation and this will cause damage to the Sw1 and Sw2 switches. This behavior requires that the Sw1 and Sw2 keys have exactly the same individual transmission times and that the centers are magnetically balanced with the interconnected primary and secondary transformer ends. These criteria must be met by the transformer with the control and drive circuit. The output voltage (Vo) of the push-pull converter is equal to equation (4). Electrical parameters of the push-pull converter are given in Table 2.
(4)Vo=2DViN2N1.Table 2
Push-pull converter parameters.
Expression
Definition
Value
Vi
:
Converter input voltage
0-1 kV
Vo
:
Converter output voltage
0-600 V
N1
:
Number of secondary windings
1000 turns
N2
:
Number of secondary windings
600 turns
L
:
Inductor
1 mH
C
:
Capacitor
10 mF
fSw
:
Switch frequency
1 kHz


## 2.3. DC Motor Model

Many features that are required to be in a motor are available in a DC motor. Some of these features include safety, durability, and cheapness and low voltage levels. DC motors are preferred in many applications. The electrical circuit and the electrical circuit diagram of the rotor of a direct current motor are shown in Figure5. The parameters and symbols used in the system are given in Table 3.Figure 5
Basic structure of DC motor equivalent circuit.Table 3
DC motor parameters.
Expression
Definition
Unit
Ra
:
Armature resistance
Ω
2.581
La
:
Armature inductance
H
0.028
Rf
:
Field resistance
Ω
281.3
Lf
:
Field inductance
H
156
Laf
:
Field-armature mutual inductance
H
0.9483
Jm
:
Total inertia
kg·m2
0.02215
B
:
Viscous friction coefficient
N·m·s
0.002953
Τ
:
Coulomb friction torque
N·m
0.5161
ɷrstart
:
Initial speed
rad/s
1
Ifstart
:
Initial field current
A
1According to Kirchhoff’s voltage law, the electrical equation of the DC motor is given in equation (5). Here, iat is the armature current, eat is back voltage, and Vst is the voltage source. In equation (6), the back emf voltage eat is expressed to be proportional to a constant, such as Ke, with the angular velocity of the rotor ɷt in the motor. Furthermore, the torque generated by the motor, Tm, is calculated by multiplying the torque constant Kt by the armature current as shown in equation (7).
(5)Vst=Ra·iat+Ladiatdt+eat,(6)eak=Ke·ωmt,(7)Tmt=Kt·iat.θ is the position of the shaft, and TL is the external load torque. The total torque of the motor must be zero; this is expressed in equation (8).
(8)dθdt=θ̇=ωt,Jmdωmdt+Bωm=Kt·ia−Bωm−TL.


## 2.4. PI Controller

The PI controller structure is simple and has a controller structure that provides very good results for many control systems. The control block diagram of the classical PI controller is given in Figure6. In this configuration, the control signal ut is the sum of two terms. Each of these terms is a function of the tracking error et. The term Kp indicates that this term is proportional to the error. The term Ki/s is an integral term. Each of the terms works independently of the other. According to DC converter reference voltage input circuit, output voltage is controlled by the PI controller. Activated equations are as follows:
(9)ut=Kpet+Ki∫etdt,(10)dutdt=Kpdetdt+Kiet.Figure 6
PI controller block diagram.If equation (10) is converted from the continuous time space t into the discrete time space k, then equation (11) is obtained.
(11)uk−uk−1Ts=Kpek−ek−1Ts+Kiek,uk=uk−1+Kpek−ek−1+Kiek.The optimalP and I coefficients for the PI controller in this system were found by using the closed loop Ziegler-Nichols method.


## 2.5. Fuzzy Logic Controller (FLC)

Fuzzy logic control algorithm is based on digitizing a set of heuristic control rules. It is important to note that fuzzy logic is used to evaluate uncertain, fuzzy sets and rules for expressing linguistic terms [19, 20]. The most important feature that distinguishes the concept of the fuzzy set from that of the classical set is that verbal variables are used instead of numerical variables. A fuzzy logic controller system is generally shown in Figure 7. As is known, the structure of the fuzzy logic controller consists of three parts. These sections are briefly mentioned in the “fuzzification” system phase, and the data obtained from the system are converted to fuzzy values. The second stage is “rule base,” where fuzzy data is processed by fuzzy rules. In the last stage, which is called “defuzzification,” the data is converted to the exact number of fuzzy results.Figure 7
Basic configuration of a FLC.The knowledge base unit consists of two units, the database and the rule base. The knowledge base can be divided into two parts: the database, in which the decision-making unit receives the information used in the rule base, and the rule base, where there are linguistic control rules for audit purposes. The set of rules determines the audit objectives and audit strategy. Information about the system being audited, fuzzification, processing of fuzzy data, membership function required during defuzzification operations, and rule table information are available in the "database" unit. Connections between inputs and outputs are established using rules in the rule base. In a system,e and de are inputs, and if μ is the output variable (if e=x and de=y, then u=z), defined by the rule, e and f take the value of the fuzzy value of the output determined. The rule table is shown in Figure 8.Figure 8
Rule base table.


## 2.6. Fuzzy-Tuned PI Controller (FT-PIC)

The simplified block diagram of the fuzzy-tuned PI controller is shown in Figure9. Membership functions for this controller type input error (e), change of error (de), and controller output (du) are defined on the normalized domain [-1, 1] as shown in Figure 10. Membership functions (MF) of β are defined on [0, 1] as shown in Figure 11.Figure 9
Basic configuration of a FT-PIC.Figure 10
Membership functions of inputs (e, de) and output (du). Le=Lde=Ldu (NB: negative big; NM: negative medium; NS: negative small; Z: zero; PS: positive small; PM: positive medium; PB: positive big).Figure 11
Membership functions of gain updating factor,β, are mapped {ZE, VS, S, SB, MB, B, VB}.Symmetric triangles with equal base width and 50% overlap with neighboring MFs are used here due to its natural and unbiased nature. The term sets ofe, de, and du for PI type FLC contain the same linguistic expressions for the magnitude part of the linguistic values [21].The operation of a PI-type FLC as shown in Figure9 can be described by equation (12). Here, du is the incremental change in controller output. FT-PIC generates the nonlinear controller output (du) by modifying the output of the simple fuzzy-tuned PI controller (FT-PIC) as shown in Figure 9 and equation (13).
(12)uk=uk−1+duk,(13)du=βGuduN1.The weighted absolute average of the effective rules of the controller can be taken as the absolute output. For this rinsing process, the central method of areas where the center of gravity of the active areas given in equation (14) is taken can be used.
(14)duk=u∑i=a,b,c,dμRiduRduRRi∑i=1nuVR.where k is the sampling time, m is the degree of membership, ek is the control error, and k is the variation of this error in a sampling time. The Simulink model of the membership function related to weight coefficients according to the expression in the share portion of the central method of the fields given by equation (14) was prepared as shown in Figure 12.Figure 12
Simulink model of the central method of fields.


## 2.7. Two Degree Of Freedom (2-DOF) PI Controller

As with most industrial control applications, the desired value of the controlled variable or setpoint normally remains constant and needs to be changed. This control technique is mainly concerned with two free-grade (2-DOF) applications of PID control algorithms. The 2-DOF control algorithm provides additional parameter and regulative control performance, and the closed loop control system durability in mind to improve servo control behavior is used [22–26]. It is possible to incorporate this capability of Two Degree Of Freedom controllers into both PI-type and PID-type control algorithms.The 2-DOF controller structure has been developed for situations where a 1-DOF controller structure is insufficient. By adding theβ parameter to the controller structure, better performance is achieved in terms of maintaining reference distortion suppression performance and improving transient response. The structure of the 2-DOF PI controller is shown in Figure 13.Figure 13
2-DOF PI structure.The control signal for the 2-DOF PI controller is given in equation (15). Here, Ti shows the integral time constant, Td the derivative time constant, KP proportional gain, β reference weight ratio, Crs reference signal transfer function, and Cys feedback transfer function [27].
(15)uk=KPβ+1Tikrk−KP1+1Tikyk,uk=Crkrk−Cykyk.


## 2.8. Fractional PID Controller (PIλDμ)

Fractional type PID controllers can be described as the generalized form of PIDs. The output data can be summarized as a linear combination of the input, a fractional derivative of the input, and a fractional integral of the input [28]. Fractional PIDs are also known as PIλDμ controllers, where λ and μ are the integration and differentiation orders; if both values are 1, the result is a usual PID (henceforth called “integer” PID as opposed to a fractional PID). PIλDμ controllers are advanced controllers that can give better results than classical PI controllers. They are widely used because they are able to adjust more precisely than PID controllers. The best knowns are the descriptions of Shah and Agashe and Rasoanarivo and Sargos [29, 30]. The PIλDμ controller general block diagram is shown in Figure 14.Figure 14
General block diagram ofPIλDμ structure.In this study,λ and μ≥0, where λ is the order of integration and μ is the order of differentiator. KP, KI, and KD are the PID controller gains. Us and Es are the control and error signals, respectively. In this study, PIλDμ controller software was performed by FOMCON Toolbox [31]. System output, Ck, is as seen in
(16)Ck=KP+KIkλ+KDkμ.


## 3. Results and Discussion

First, the installed system was run uncontrolled. What happened in this case was investigated. Afterwards, PI, FLC fuzzy-tuned PI, 2-DOF PI, and fractional PID controllers are connected to the push-pull convertor connected system, and their results are shown. In all simulations, the solar radiation from the photovoltaic solar panels and the power of the drawn load were compared under the same conditions. In many practical applications, the system with the push-pull converter and fuzzy logic or PI controller gives the same results as computer simulations [32, 33].


### 3.1. Data of PV Panels

The selected solar panel is a BP SX3190 model and is easily available from the market. Table4 shows the information regarding silicon nitride multi crystalline silicon cell high efficiency photovoltaic module. In all simulations, the solar radiation level at 25°C ambient temperature is shown in Figure 15.Table 4
Photovoltaic solar panel parameters [34].
Value
Unit
Open circuit voltage
30.6021 V
Short-circuit current
8.51029 A
Maximum power
190 W
Voltage at maximum power point
24.3003 V
Current at maximum power point
7.82945 Α
Temperature coefficient of short circuit current
0.065±0.015%/°C
Temperature coefficient of open circuit voltage
-111±10mV/°C
Serial resistance
0.17514 ohm
Parallel resistance
755.51 ohm
Diode saturation current
1.0647e-6 A
Diode ideality factor
1.5Figure 15
Ambient solar irradiation level changes.For a PV powered power system that does not have a battery pack, it is not possible to achieve voltage stability of the loads with large solar radiation changes in 5 seconds. However, in this study, it also helps to show a good way to measure the response of the system to sudden power changes. The voltage stability of the push-pull converter used in the system is also examined under the variable load moment which is another disturbance under these radiation conditions. Comparing the five selected controllers in terms of system stability is very important for many practical applications.


### 3.2. Simulation Results and Discussion

The push-pull converter in the system is connected to the PI, FLC fuzzy-tuned PI, 2-DOF PI, and fractional PID controllers by manual switches. The reference voltage applied to these controllers is given in Figure16. It provides the voltage error between the reference voltage and the output voltage signal produced by the push-pull converter, which enables the transmission of power to the secondary winding by generating electrical docks for the primary windings of the transformers according to the PWM method with the control voltage of the control signals. According to the type of feedback signal of the controllers, the DC motor can control the voltage, current, torque, or speed effectively.Figure 16
The reference voltage.The sampling time of the system is 50μs. The output voltage of the PV panels ranges from 1000 V to 1225 V, and the output current is up to 240 A. The changes in the torque taken by the load connected to the motor in the system are shown in Figure 17.Figure 17
Time change of load torque (TL) applied to DC motor.The controllers controlling the push-pull converter are connected to the pulse generator, which operates a pair of pulse width modulation principles. The frequency of these pulse generators working with reverse pulse logic is 1 kHz and depends on the transformers by means of power electronics switches.


#### 3.2.1. Case 1: Push-Pull Converter with PI Controller

The results obtained when the indirect current control method with the PI controller is used to control of the push-pull converter output voltage signals are shown Figure18. The PI controllers used in the indirect current control method of the system under variable ambient conditions and constant change in load were set to KP=10 and KI=100. This coefficients for the system were found by using the closed loop Ziegler-Nichols method.Figure 18
Push-pull converter output voltage signal connected to PI controller and overvoltage values at some points.Table5 shows the output voltage signal of the push-pull converter connected to the PI controller shown in Figure 18 and the overvoltage values at some points.Table 5
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0600
255.40
200.00
-55.40
-27.70
2
1.5400
264.76
321.50
56.74
17.65
3
2.2800
336.32
450.00
113.68
25.26
4
2.8300
332.11
441.59
109.48
24.79
5
3.0720
428.34
335.68
-92.66
-27.60
6
4.0200
180.30
200.00
19.7
9.85The error voltage (ΔV) between the reference and output voltage signals in the Push-pull converter system with PI controller has been monitored. Accordingly, the five points where the error voltage is greatest is selected and it is calculated to be 22.14% when the percentage averages are taken according to the reference voltage.


#### 3.2.2. Case 2: Push-Pull Converter with Fuzzy Logic Controller

The results obtained when the indirect current control method with the fuzzy logic controller is used to control of the push-pull converter output voltage signals are shown Figure19.Figure 19
Push-pull converter output voltage signal connected to fuzzy logic controller and overvoltage values at some points.Table6 shows the output voltage signal of the push-pull converter connected to the FL controller shown in Figure 19 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with FL controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 12.52% when the percentage averages are taken according to the reference voltage.Table 6
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0065
297.72
200.00
-97.72
-48.86
2
1.006
317.84
280.36
-37.48
-13.37
3
2.0054
414.46
401.36
-13.1
-3.26
4
2.4133
433.63
450.00
16.37
3.64
5
3.5679
283.00
287.93
4.93
1.71
6
4.0200
200.00
209.02
9.02
4.32


#### 3.2.3. Case 3: Push-Pull Converter with Fuzzy-Tuned PI Controller

The results obtained when the indirect current control method with the fuzzy-tuned PI controller is used to control of the push-pull converter output voltage signals are shown Figure20.Figure 20
Push-pull converter output voltage signal connected to fuzzy-tuned PI controller and overvoltage values at some points.Table7 shows the output voltage signal of the push-pull converter connected to the fuzzy-tuned PI controller shown in Figure 20 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with fuzzy-tuned PI controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 15.99% when the percentage averages are taken according to the reference voltage.Table 7
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0064
314.13
200.00
-114.13
-57.07
2
1.0530
324.90
280.30
-44.60
-15.91
3
2.0034
412.90
400.85
-12.05
-3.01
4
2.6900
461.39
450.00
-11.39
-2.53
5
3.0135
323.67
339.19
15.52
4.58
6
4.0200
174.33
200.00
25.67
12.84


#### 3.2.4. Case 4: Push-Pull Converter with 2-DOF PID Controller

The results obtained when the indirect current control method with the 2-DOF PI controller is used to control of the push-pull converter output voltage signals are shown Figure21.Figure 21
Push-pull converter output voltage signal connected to 2-DOF PI controller and overvoltage values at some points.Table8 shows the output voltage signal of the push-pull converter connected to the 2-DOF PI controller shown in Figure 21 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with 2-DOF PI controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 18.94% when the percentage averages are taken according to the reference voltage.Table 8
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0061
234.28
200.00
-34.28
-17.14
2
1.7332
276.93
324.00
47.07
14.53
3
2.0190
289.42
404.72
115.30
28.49
4
2.8945
313.95
426.42
112.47
26.38
5
3.1420
403.50
331.48
-72.02
-21.73
6
4.0175
189.31
200.00
10.69
5.35


#### 3.2.5. Case 5: Push-Pull Converter with Fractional PID (PIλDμ) Controller

The results obtained when the indirect current control method with thePIλDμ controller is used to control of the push-pull converter output voltage signals are shown Figure 22. Table 9 shows the output voltage signal of the push-pull converter connected to the PIλDμ controller shown in Figure 22 and the overvoltage values at some points.Figure 22
Push-pull converter output voltage signal connected toPIλDμ controller and overvoltage values at some points.Table 9
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0070
233.19
200.00
-33.19
-16.60
2
1.9765
274.69
338.58
63.89
18.87
3
2.0525
303.18
413.12
109.94
26.61
4
2.8660
327.61
433.36
105.75
24.40
5
3.1605
270.00
330.35
60.35
18.27
6
4.0247
184.10
200.00
15.90
7.95The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system withPIλDμ controller has been monitored. Accordingly, the five points where the error voltage is greatest is selected and it is calculated to be 18.78% when the percentage averages are taken according to the reference voltage.Table10 gives the average of the percent (% e) of the absolute value of the error between the output voltage produced by the five different controllers obtained from the simulations and the reference of the system.Table 10
Average of the percentages (%e) of the absolute value of the error between the output voltage produced by the five different controllers and the reference of the system.
Point number
PI
Fuzzy logic(FLC)
Fuzzy-tuned PI(FT-PIC)
2-DOF PI
Fractional PID(PIλDμ)
1
-27.70
-48.86
-57.07
-17.14
-16.60
2
17.65
-13.37
-15.91
14.53
18.87
3
25.26
-3.26
-3.01
28.49
26.61
4
24.79
3.64
-2.53
26.38
24.40
5
-27.60
1.71
4.58
-21.73
18.27
6
9.85
4.32
12.84
5.35
7.95
(% e)
22.14
12.53
15.99
18.93
18.78


## 3.1. Data of PV Panels

The selected solar panel is a BP SX3190 model and is easily available from the market. Table4 shows the information regarding silicon nitride multi crystalline silicon cell high efficiency photovoltaic module. In all simulations, the solar radiation level at 25°C ambient temperature is shown in Figure 15.Table 4
Photovoltaic solar panel parameters [34].
Value
Unit
Open circuit voltage
30.6021 V
Short-circuit current
8.51029 A
Maximum power
190 W
Voltage at maximum power point
24.3003 V
Current at maximum power point
7.82945 Α
Temperature coefficient of short circuit current
0.065±0.015%/°C
Temperature coefficient of open circuit voltage
-111±10mV/°C
Serial resistance
0.17514 ohm
Parallel resistance
755.51 ohm
Diode saturation current
1.0647e-6 A
Diode ideality factor
1.5Figure 15
Ambient solar irradiation level changes.For a PV powered power system that does not have a battery pack, it is not possible to achieve voltage stability of the loads with large solar radiation changes in 5 seconds. However, in this study, it also helps to show a good way to measure the response of the system to sudden power changes. The voltage stability of the push-pull converter used in the system is also examined under the variable load moment which is another disturbance under these radiation conditions. Comparing the five selected controllers in terms of system stability is very important for many practical applications.


## 3.2. Simulation Results and Discussion

The push-pull converter in the system is connected to the PI, FLC fuzzy-tuned PI, 2-DOF PI, and fractional PID controllers by manual switches. The reference voltage applied to these controllers is given in Figure16. It provides the voltage error between the reference voltage and the output voltage signal produced by the push-pull converter, which enables the transmission of power to the secondary winding by generating electrical docks for the primary windings of the transformers according to the PWM method with the control voltage of the control signals. According to the type of feedback signal of the controllers, the DC motor can control the voltage, current, torque, or speed effectively.Figure 16
The reference voltage.The sampling time of the system is 50μs. The output voltage of the PV panels ranges from 1000 V to 1225 V, and the output current is up to 240 A. The changes in the torque taken by the load connected to the motor in the system are shown in Figure 17.Figure 17
Time change of load torque (TL) applied to DC motor.The controllers controlling the push-pull converter are connected to the pulse generator, which operates a pair of pulse width modulation principles. The frequency of these pulse generators working with reverse pulse logic is 1 kHz and depends on the transformers by means of power electronics switches.


### 3.2.1. Case 1: Push-Pull Converter with PI Controller

The results obtained when the indirect current control method with the PI controller is used to control of the push-pull converter output voltage signals are shown Figure18. The PI controllers used in the indirect current control method of the system under variable ambient conditions and constant change in load were set to KP=10 and KI=100. This coefficients for the system were found by using the closed loop Ziegler-Nichols method.Figure 18
Push-pull converter output voltage signal connected to PI controller and overvoltage values at some points.Table5 shows the output voltage signal of the push-pull converter connected to the PI controller shown in Figure 18 and the overvoltage values at some points.Table 5
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0600
255.40
200.00
-55.40
-27.70
2
1.5400
264.76
321.50
56.74
17.65
3
2.2800
336.32
450.00
113.68
25.26
4
2.8300
332.11
441.59
109.48
24.79
5
3.0720
428.34
335.68
-92.66
-27.60
6
4.0200
180.30
200.00
19.7
9.85The error voltage (ΔV) between the reference and output voltage signals in the Push-pull converter system with PI controller has been monitored. Accordingly, the five points where the error voltage is greatest is selected and it is calculated to be 22.14% when the percentage averages are taken according to the reference voltage.


### 3.2.2. Case 2: Push-Pull Converter with Fuzzy Logic Controller

The results obtained when the indirect current control method with the fuzzy logic controller is used to control of the push-pull converter output voltage signals are shown Figure19.Figure 19
Push-pull converter output voltage signal connected to fuzzy logic controller and overvoltage values at some points.Table6 shows the output voltage signal of the push-pull converter connected to the FL controller shown in Figure 19 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with FL controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 12.52% when the percentage averages are taken according to the reference voltage.Table 6
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0065
297.72
200.00
-97.72
-48.86
2
1.006
317.84
280.36
-37.48
-13.37
3
2.0054
414.46
401.36
-13.1
-3.26
4
2.4133
433.63
450.00
16.37
3.64
5
3.5679
283.00
287.93
4.93
1.71
6
4.0200
200.00
209.02
9.02
4.32


### 3.2.3. Case 3: Push-Pull Converter with Fuzzy-Tuned PI Controller

The results obtained when the indirect current control method with the fuzzy-tuned PI controller is used to control of the push-pull converter output voltage signals are shown Figure20.Figure 20
Push-pull converter output voltage signal connected to fuzzy-tuned PI controller and overvoltage values at some points.Table7 shows the output voltage signal of the push-pull converter connected to the fuzzy-tuned PI controller shown in Figure 20 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with fuzzy-tuned PI controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 15.99% when the percentage averages are taken according to the reference voltage.Table 7
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0064
314.13
200.00
-114.13
-57.07
2
1.0530
324.90
280.30
-44.60
-15.91
3
2.0034
412.90
400.85
-12.05
-3.01
4
2.6900
461.39
450.00
-11.39
-2.53
5
3.0135
323.67
339.19
15.52
4.58
6
4.0200
174.33
200.00
25.67
12.84


### 3.2.4. Case 4: Push-Pull Converter with 2-DOF PID Controller

The results obtained when the indirect current control method with the 2-DOF PI controller is used to control of the push-pull converter output voltage signals are shown Figure21.Figure 21
Push-pull converter output voltage signal connected to 2-DOF PI controller and overvoltage values at some points.Table8 shows the output voltage signal of the push-pull converter connected to the 2-DOF PI controller shown in Figure 21 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with 2-DOF PI controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 18.94% when the percentage averages are taken according to the reference voltage.Table 8
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0061
234.28
200.00
-34.28
-17.14
2
1.7332
276.93
324.00
47.07
14.53
3
2.0190
289.42
404.72
115.30
28.49
4
2.8945
313.95
426.42
112.47
26.38
5
3.1420
403.50
331.48
-72.02
-21.73
6
4.0175
189.31
200.00
10.69
5.35


### 3.2.5. Case 5: Push-Pull Converter with Fractional PID (PIλDμ) Controller

The results obtained when the indirect current control method with thePIλDμ controller is used to control of the push-pull converter output voltage signals are shown Figure 22. Table 9 shows the output voltage signal of the push-pull converter connected to the PIλDμ controller shown in Figure 22 and the overvoltage values at some points.Figure 22
Push-pull converter output voltage signal connected toPIλDμ controller and overvoltage values at some points.Table 9
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0070
233.19
200.00
-33.19
-16.60
2
1.9765
274.69
338.58
63.89
18.87
3
2.0525
303.18
413.12
109.94
26.61
4
2.8660
327.61
433.36
105.75
24.40
5
3.1605
270.00
330.35
60.35
18.27
6
4.0247
184.10
200.00
15.90
7.95The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system withPIλDμ controller has been monitored. Accordingly, the five points where the error voltage is greatest is selected and it is calculated to be 18.78% when the percentage averages are taken according to the reference voltage.Table10 gives the average of the percent (% e) of the absolute value of the error between the output voltage produced by the five different controllers obtained from the simulations and the reference of the system.Table 10
Average of the percentages (%e) of the absolute value of the error between the output voltage produced by the five different controllers and the reference of the system.
Point number
PI
Fuzzy logic(FLC)
Fuzzy-tuned PI(FT-PIC)
2-DOF PI
Fractional PID(PIλDμ)
1
-27.70
-48.86
-57.07
-17.14
-16.60
2
17.65
-13.37
-15.91
14.53
18.87
3
25.26
-3.26
-3.01
28.49
26.61
4
24.79
3.64
-2.53
26.38
24.40
5
-27.60
1.71
4.58
-21.73
18.27
6
9.85
4.32
12.84
5.35
7.95
(% e)
22.14
12.53
15.99
18.93
18.78


## 3.2.1. Case 1: Push-Pull Converter with PI Controller

The results obtained when the indirect current control method with the PI controller is used to control of the push-pull converter output voltage signals are shown Figure18. The PI controllers used in the indirect current control method of the system under variable ambient conditions and constant change in load were set to KP=10 and KI=100. This coefficients for the system were found by using the closed loop Ziegler-Nichols method.Figure 18
Push-pull converter output voltage signal connected to PI controller and overvoltage values at some points.Table5 shows the output voltage signal of the push-pull converter connected to the PI controller shown in Figure 18 and the overvoltage values at some points.Table 5
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0600
255.40
200.00
-55.40
-27.70
2
1.5400
264.76
321.50
56.74
17.65
3
2.2800
336.32
450.00
113.68
25.26
4
2.8300
332.11
441.59
109.48
24.79
5
3.0720
428.34
335.68
-92.66
-27.60
6
4.0200
180.30
200.00
19.7
9.85The error voltage (ΔV) between the reference and output voltage signals in the Push-pull converter system with PI controller has been monitored. Accordingly, the five points where the error voltage is greatest is selected and it is calculated to be 22.14% when the percentage averages are taken according to the reference voltage.


## 3.2.2. Case 2: Push-Pull Converter with Fuzzy Logic Controller

The results obtained when the indirect current control method with the fuzzy logic controller is used to control of the push-pull converter output voltage signals are shown Figure19.Figure 19
Push-pull converter output voltage signal connected to fuzzy logic controller and overvoltage values at some points.Table6 shows the output voltage signal of the push-pull converter connected to the FL controller shown in Figure 19 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with FL controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 12.52% when the percentage averages are taken according to the reference voltage.Table 6
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0065
297.72
200.00
-97.72
-48.86
2
1.006
317.84
280.36
-37.48
-13.37
3
2.0054
414.46
401.36
-13.1
-3.26
4
2.4133
433.63
450.00
16.37
3.64
5
3.5679
283.00
287.93
4.93
1.71
6
4.0200
200.00
209.02
9.02
4.32


## 3.2.3. Case 3: Push-Pull Converter with Fuzzy-Tuned PI Controller

The results obtained when the indirect current control method with the fuzzy-tuned PI controller is used to control of the push-pull converter output voltage signals are shown Figure20.Figure 20
Push-pull converter output voltage signal connected to fuzzy-tuned PI controller and overvoltage values at some points.Table7 shows the output voltage signal of the push-pull converter connected to the fuzzy-tuned PI controller shown in Figure 20 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with fuzzy-tuned PI controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 15.99% when the percentage averages are taken according to the reference voltage.Table 7
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0064
314.13
200.00
-114.13
-57.07
2
1.0530
324.90
280.30
-44.60
-15.91
3
2.0034
412.90
400.85
-12.05
-3.01
4
2.6900
461.39
450.00
-11.39
-2.53
5
3.0135
323.67
339.19
15.52
4.58
6
4.0200
174.33
200.00
25.67
12.84


## 3.2.4. Case 4: Push-Pull Converter with 2-DOF PID Controller

The results obtained when the indirect current control method with the 2-DOF PI controller is used to control of the push-pull converter output voltage signals are shown Figure21.Figure 21
Push-pull converter output voltage signal connected to 2-DOF PI controller and overvoltage values at some points.Table8 shows the output voltage signal of the push-pull converter connected to the 2-DOF PI controller shown in Figure 21 and the overvoltage values at some points. The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system with 2-DOF PI controller has been monitored. Accordingly, the six points where the error voltage is greatest is selected and it is calculated to be 18.94% when the percentage averages are taken according to the reference voltage.Table 8
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0061
234.28
200.00
-34.28
-17.14
2
1.7332
276.93
324.00
47.07
14.53
3
2.0190
289.42
404.72
115.30
28.49
4
2.8945
313.95
426.42
112.47
26.38
5
3.1420
403.50
331.48
-72.02
-21.73
6
4.0175
189.31
200.00
10.69
5.35


## 3.2.5. Case 5: Push-Pull Converter with Fractional PID (PIλDμ) Controller

The results obtained when the indirect current control method with thePIλDμ controller is used to control of the push-pull converter output voltage signals are shown Figure 22. Table 9 shows the output voltage signal of the push-pull converter connected to the PIλDμ controller shown in Figure 22 and the overvoltage values at some points.Figure 22
Push-pull converter output voltage signal connected toPIλDμ controller and overvoltage values at some points.Table 9
Percentage (%) of error between output voltage and reference of the system.
Point number
Time (s)
Output voltage (Vo)
Reference voltage (Vref)
ΔV=Vref‐Vo
% error
1
0.0070
233.19
200.00
-33.19
-16.60
2
1.9765
274.69
338.58
63.89
18.87
3
2.0525
303.18
413.12
109.94
26.61
4
2.8660
327.61
433.36
105.75
24.40
5
3.1605
270.00
330.35
60.35
18.27
6
4.0247
184.10
200.00
15.90
7.95The error voltage (delta) between the reference and output voltage signals in the Push-pull converter system withPIλDμ controller has been monitored. Accordingly, the five points where the error voltage is greatest is selected and it is calculated to be 18.78% when the percentage averages are taken according to the reference voltage.Table10 gives the average of the percent (% e) of the absolute value of the error between the output voltage produced by the five different controllers obtained from the simulations and the reference of the system.Table 10
Average of the percentages (%e) of the absolute value of the error between the output voltage produced by the five different controllers and the reference of the system.
Point number
PI
Fuzzy logic(FLC)
Fuzzy-tuned PI(FT-PIC)
2-DOF PI
Fractional PID(PIλDμ)
1
-27.70
-48.86
-57.07
-17.14
-16.60
2
17.65
-13.37
-15.91
14.53
18.87
3
25.26
-3.26
-3.01
28.49
26.61
4
24.79
3.64
-2.53
26.38
24.40
5
-27.60
1.71
4.58
-21.73
18.27
6
9.85
4.32
12.84
5.35
7.95
(% e)
22.14
12.53
15.99
18.93
18.78


## 4. Conclusion

In the study, the performance of the system connected to the push-pull converter was investigated using different controllers. The success of the system is to compare the variable load current demand with variable reference voltage in the variable solar radiation of the loads fed by the grid independent solar panels.The energy generation of the system is provided by photovoltaic solar panels. However, during the simulation, there is production under a variable solar radiation. The load of the system is designed as a DC motor which draws a lot of current. If the system design is made a little more difficult and the third variable is the push-pull converter, the output voltage is required to follow the reference given. Under these variables, PI, fuzzy logic, fuzzy-tuned PI-based, 2-DOF PI, and fractional PID control elements were the successors of the control system.Fuzzy logic and fuzzy-tuned PI-based controllers were the most effective of the reference signal from these controllers. It was seen that these two controllers were removed from the total of six points during the 5-second simulation. There is no significant difference between the percentages of voltage differences at these points. However, the classic fuzzy-based controller (FLC) performed slightly better. The most failed controller was the PI controller.During the simulations, large fault voltages were observed many times in all of the controllers. The point with a high error voltage occurred at the beginning of the simulation. However, based on the selected points, the FT-PIC gave a large error voltage of 57.07%. Considering all this information, fuzzy logic (FL) is the most successful controller used for this system. The mean values of 2-DOF PI and fractional PID controllers were very close to each other and yielded an average result. When the largest fluctuations in the selected regions are averaged, the PI controller gave the worst response.This is because there are three unknown and constantly changing situations in the system. The success of conventional controllers in systems above the second order is decreasing. Well-designed fuzzy logic-based control systems have proven to react more quickly to sudden changes in error.The most important contribution of this study is that a designed photovoltaic power generation and motor load-dependent system has shown the best push-pull converter and controller pair that will provide reference voltage under two different influences. These adverse effects are variable sunlight radiation and variable motor load. Controllers are based on PI, Fuzzy, fuzzy-tuned PI, 2-DOF PI, and fractional PID.



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*Source: 3810970-2019-12-07.xml*