1. Introduction
DC-DC converters are employed in a variety of applications such as industrial controls, audio applications, power adapters and chargers, electric vehicles, electronic appliances, power supplies, renewable systems, aerospace equipment, and many other modern types of equipment that operate on DC [
1,
2,
3]. Flyback converters (FCs) are a frequently used type of DC converter which may operate over a broad range of unregulated DC voltage. FCs serve as energy storage as well as converter isolation because of a choke in their topology. This results in reduced noise interference and provided load protection [
4,
5]. FCs are able to achieve high efficiency, high stability, small size, lightweight, less cost, etc., and have more power capacity (usually in the range of 20 to 200 W [
6]) than other fundamental DC-DC converters. They are preferred for their outstanding features including output voltage waveform shape, power factor control optimization, and device miniaturization [
7,
8,
9,
10]. FCs exhibit non-minimum phase characteristics, i.e., the existence of a right half plane zero (RHPZ) in the voltage transfer function. This complicates the dynamics of FCs, as it results in increased gain and introduces additional phase lag, thus behaving as a pole. Thus, there is a need to design a feedback controller able to ensure the static and dynamic performance of the converter [
11].
There are several analog and digital methods, such as PID, fuzzy logic (FL), and sliding mode control (SMC), for regulating the output of DC-DC FCs [
12]. The feedback controller in a DC-DC converter is mainly responsible for delivering regulated supply, ideally with no steady-state error, less overshoot, and fast dynamic response while maintaining the highest possible efficiency [
13,
14]. Sliding mode control (SMC) based on the equivalent control method with a constant frequency has been applied to FCs in References [
5,
14]. In Reference [
15], a peak current control technique for a flyback converter’s power factor correction was proposed. Reference [
16] introduced average current mode control (ACM) for an FC, which employed an outer voltage feedback loop responsible for maintaining constant output voltage, and an inner loop engaged in sensing the input current. Quasi-resonant (QR) controllers for FCs have been presented in References [
8,
17,
18]. PI controllers [
19] and PID controllers [
20,
21] for FCs have also been reported in the literature. For example, in Reference [
22], an FC with a photovoltaic (PV) panel was controlled by a PI compensator. The problem with these controllers is that they may not be robust against disturbance and uncertainty. Dynamic modeling and quantitative controller design of a current-mode controlled FC with optocoupler isolation were presented in Reference [
23]. In Reference [
24], the FC operated with a natural switching surface (NSS) control. Derivation and implementation of NSS with the operation of FCs in boundary conduction mode (BCM) were presented. A detailed review of the controllers to date, including pulse frequency modulation (PFM) control, adaptive peak current value control, current estimation control, and duty cycle control for FCs is presented in Reference [
25].
Owing to features such as easier implementation and robustness characteristics, fuzzy logic controllers (FLCs) have also been employed to control FCs. FLCs are based on natural language and employ fuzzy “if-then” rules and fuzzy reasoning. They are tolerant of imprecise data, require fewer tuning parameters, and are flexible in such a way that they add more functionality without re-starting from the start [
26,
27]. Such an FLC can be employed to implement a central action for dealing with the variable structure nature of an FC. In Reference [
28], an FLC-based FC is presented where the FLC responds rapidly to changes in load current or input voltage to ensure better load regulation. The controller also offers robustness with a good dynamic response. In Reference [
29], a comparison was made between fuzzy and PI-based voltage controllers for an integrated buck flyback converter. Similarly, in Reference [
30], the performance of the FC compensated system was analyzed via a PID controller and FLC. In these references, FLCs have outshone PIDs in terms of performance. Although an FL can make decisions based on the knowledge supplied to it, due to the lack of a training mechanism, it cannot make its knowledge adaptive.
More intelligence can be introduced to fuzzy rules by retuning them with artificial neural networks (ANN). ANFIS is the fusion of ANN and FL and utilizes the salient features of neural and fuzzy networks, respectively. The main advantage of ANFIS is that it converges quickly since it minimizes the search space dimensions of the backpropagation method used in NN [
31,
32,
33]. An ANFIS-based maximum power point tracking (MPPT) system for a PV module with a DC-DC converter is presented in References [
34,
35,
36,
37]. In Reference [
38], the authors proposed an ANFIS-based MPPT system comprising a PV module connected to a load through a DC-DC Ćuk converter to track the maximum power point (MPP). The MATLAB/Simulink environment was used to simulate the proposed model. Very limited research can be found in the literature regarding the control of switching converters using ANFIS. This paper thus proposes an ANFIS-based controller to regulate and improve the output voltage of FC. Line and load regulation and response to reference voltage changes are presented and the static and dynamic performance of the proposed controller is analyzed. Furthermore, its performance was also compared with FLC and PID controllers to validate its superiority.
The paper is organized as follows.
Section 2 describes the modeling of an FC in continuous conduction mode (CCM). The design parameter selection of the FC used throughout the paper for the design of the controllers is described in
Section 3.
Section 4 presents the detailed controller design procedure for the FLC, ANFIS-based controller, and PID controller.
Section 5 shows the results obtained after performing the simulations of FC with feedback controllers. Finally, the results are concluded in
Section 6.
2. Modeling of Flyback Converter
The block diagram of the complete system, along with the circuit diagram of the FC, is presented in
Figure 1. FC behaves like a plant to be controlled. To develop a controller for it, its dynamics must be known.
Figure 1 shows the FC circuit consisting of a DC voltage source “
E”, a power MOSFET “S”, transformer “
T” for isolation purposes, diode “
D”, capacitor “
C”, and load and magnetizing inductance of transformer “
LM”. The DC voltage source can be the output of an uncontrolled rectifier (after filtering) that converts AC to DC. The switching MOSFET S is fed with a PWM at high frequency. The purpose of the transformer is also to provide better matching between input and output voltage and current requirements. The diode
D rectifies the secondary voltage of the transformer
T. The capacitor
C is for filtration purposes.
For determining FC dynamics in CCM, a state-space averaging technique was employed [
5,
24,
28]. Inductor current
and voltage across the capacitor
were considered as independent state variables of the state vector
. Thus,
The independent input vector
is expressed in Equation (2) with input voltage
and voltage across the diode
as constraints.
The output vector consists of input current
and output voltage
, since in the modeling procedure, input and output are to be modeled, which are dependent quantities.
CCM operation occurs in two modes:
Mode 1: When the switching MOSFET
S is in ON state, current flows through the primary side of the transformer with magnitude
, and the diode is reversed biased at the secondary side. Therefore, no current flows in the secondary of the transformer. The capacitor’s stored energy supplies the output voltage. The state conditions for Mode 1 are:
where
is the magnetizing inductance of transformer,
is the rate of change of current in the primary of the transformer,
is the supply voltage,
is the supply current,
is the resistance of the switch S,
is the capacitance,
is the rate of change of capacitor voltage,
is the capacitor voltage,
is the load resistance,
is the internal resistance of capacitor, and
is the output voltage. Thus, the state-space representation for Mode 1 is as follows:
where
is a state vector,
is the state vector derivative with regard to time,
is the system matrix,
is the input matrix,
is the input or control vector,
is the output vector,
is the output matrix, and
is the disturbance matrix.
Mode 2: When the switching MOSFET S is in OFF state, current flows through the secondary of the transformer and the diode is forward biased. The energy stored in the magnetizing inductance is transferred to the load and output capacitor.
The state conditions for Mode 2 are:
where
is the turn ratio of the transformer. Thus, the state-space representation for Mode 2 is as follows:
Now, the state-space averaged model for CCM can be written as [
5]:
Leading towards the derivation of the transfer function, the small-signal model was employed to approximate the behavior of the FC model. In the state-space model (SSM), state variables and control input are comprised of DC and AC quantities. Capital subscripts represent DC steady-state values, and small subscripts represent AC perturbations.
Inserting the above quantities into the state-space averaged model (SSAM) and hence taking Laplace transforms results in the voltage transfer function expressed in Equation (21).
The negative sign in the numerator with the term ‘s’ indicates that it is a non-minimum phase system, i.e., it has a right half plane zero (RHPZ).