Performance Evaluation of PID, Fuzzy, and ANFIS Controllers for DC–DC Buck Converters under Reference and Load Disturbances

DC–DC buck converters are commonly used as efficient step-down stages in regulated DC supplies for embedded electronics, telecommunications, point-of-load regulation, automotive auxiliaries, and various power-electronic interfaces. Due to their switched nonlinear dynamics, sudden load changes, and component tolerances, buck converters can display overshoot, ripple, and slow recovery if the feedback controller is not designed to ensure proper damping and disturbance rejection. Thus, achieving fast transient response with low steady-state error and minimal voltage/current ripple remains a key control goal for buck converters, especially during reference changes and load disturbances [1, 2].

Conventional proportional-integral-derivative (PID) control remains popular because of its simple structure and ease of real-time implementation. However, fixed PID gains can reduce performance when operating conditions change or unmodeled dynamics and parameter uncertainties occur. To address these issues, intelligent control strategies such as Fuzzy Logic Controller (FLC) and adaptive neuro-fuzzy inference systems (ANFIS)-based controllers are increasingly studied for power converters to enhance robustness and transient response.

A brief review of control techniques in the literature is provided below. Yusoff et al. [3] compared FLC and PID with other control methods for a DC-DC buck converter. They indicated that FLC achieved reduced settling time and less overshoot at operating points. The paper highlights the strong, dynamic performance of FLC, which demonstrates tight voltage regulation. Swathy et al. [4] evaluated an FLC for closed-loop regulation of a DC–DC buck converter and benchmarked it against conventional linear controllers such as PID. The study reports that FLC yields improved transient behavior, characterized by reduced overshoot and shorter settling time, while maintaining tighter output-voltage regulation and stronger robustness to operating-point and load variations. Fudoli et al [5] compared a classical Proportional-Integral (PI) controller with a fuzzy-logic PI scheme for buck-converter output-voltage regulation. Using step and load-disturbance scenarios, they assessed overshoot and settling time. The fuzzy PI consistently delivered shorter settling time and reduced overshoot, implying superior closed-loop stability and robustness compared to the classical PI. Guiza et al. [6] proposed a Takagi–Sugeno fuzzy tracking controller for a DC–DC buck converter using an exact T–S fuzzy model and virtual desired variables. Controller gains were derived via LMI conditions, yielding faster rise and settling times and zero overshoot compared to a baseline PI regulator. Bhat et al. [7] compared PI and fuzzy-logic control for a DC-DC buck converter. They report that fuzzy control achieves faster transient response with minimal overshoot and reduced voltage and current ripple, providing tighter output-voltage regulation than conventional PI across operating conditions. Martínez et al. [8] proposed an advanced fuzzy inference–based control scheme for synchronous buck converters in renewable-energy applications. By combining adaptive, feedforward, and multivariable fuzzy reasoning, the controller improves voltage regulation and closed-loop stability, achieving faster settling, lower overshoot, and smaller steady-state error than a conventional PID under load and input-voltage variations. Shaikh et al. [9] introduced hybrid ANFIS–PID control structures for buck converters, including a novel product-type hybrid that multiplies ANFIS and PID outputs. Comparative results against classical PID indicate improved tracking quality, with reduced steady-state error and marginal overshoot reduction, alongside a higher peak efficiency (96.5%) across load conditions. Shabaninia et al. [10] developed a neuro-fuzzy PD controller for a Pulse-Width Modulation (PWM) buck converter and, through simulation (using ANFIS-based), demonstrated strong performance with improved transients (lower overshoot) and shorter settling times compared to standard fuzzy PID/PD versions. Nejad et al. [11] developed an ANFIS-based controller for a DC-DC buck converter. They demonstrated strong noise tracking, supply, and load response, and compared it with fuzzy-PID and Particle Swarm Optimization (PSO)-PID, which had faster responses and higher disturbance rejection.

This paper addresses the above gap by providing a unified simulation-based benchmark of three controllers-PID, FLC, and an ANFIS-based neuro-fuzzy controller-applied to the same buck-converter plant with the same operating constraints and switching conditions. The controllers are evaluated under strictly identical reference-step and load-disturbance scenarios. Performance is quantified using consistent metrics, including rise time, settling time, overshoot/undershoot, steady-state error, output-voltage ripple, inductor-current ripple, and disturbance rejection.

The main contributions of this work are summarized as follows:

1. A standardized benchmarking framework for PID, FLC, and ANFIS-based neuro-fuzzy control applied to the same DC–DC buck converter under identical operating constraints and disturbance scenarios (constant-reference regulation, reference-step change, and step load disturbance), enabling direct quantitative comparison.
2. A documented neuro-fuzzy controller development process in which the ANFIS model is initialized from the designed FLC rule base; training input–output pairs are generated from the FLC mapping (e and de to duty-cycle command), and ANFIS training refines the membership functions and consequent parameters, with the resulting changes linked to the control surface and closed-loop performance.
3. A comprehensive evaluation protocol that reports output-voltage tracking, error dynamics, and duty-cycle behavior using unified time-domain and ripple-related performance indices, providing a consistent basis to assess transient response, steady-state accuracy, ripple, and disturbance rejection.

In this section, three control paradigms for regulating the buck DC–DC converter's output voltage is considered: a conventional PID controller, a classical FLC, and a neuro-fuzzy controller (ANFIS). The PID controller is characterized by its proportional, integral, and derivative gains, which are tuned to achieve the desired closed-loop dynamics. The FLC is defined by its linguistic variables, membership functions, and rule base. The ANFIS employs an ANFIS-like structure that combines fuzzy inference with neural network learning, enabling data-driven parameter adaptation.

3.1 Proportional-integral-derivative-based controller design

To ensure a principled and reproducible tuning procedure, the PID gains were initialized using the averaged small-signal model of the buck converter operating in continuous-conduction mode (CCM), and subsequently verified through time-domain tests. By linearizing the averaged state-space equations around the nominal operating point, the duty-cycle–to–output-voltage transfer function is obtained as

${Gvd}(s)=\frac{{Vin}}{\left(L C s^2+\left(\frac{L}{R}\right) s+1\right)}$                (9)

which adequately represents the dominant output-filter dynamics within the frequency range of interest.

A frequency-domain loop-shaping strategy was employed to determine the controller parameters. The target closed-loop bandwidth was deliberately selected to be well below the PWM switching frequency $(f s=20 k H z)$ to preserve the validity of the averaged-model approximation and to mitigate high-frequency duty-cycle chatter. The adopted compensator has the standard PID form:

$C(s)=K p+\frac{K i}{s}+K d s$               (10)

The placement of controller zeros was guided by the plant dynamics: integral action provides low-frequency gain to eliminate steady-state regulation error, whereas the derivative term introduces phase lead to enhance damping and transient performance. In particular, the controller zero frequencies are $\omega z i=K i / K p$ and $\omega z d=K p / K d$, which were positioned to support robust tracking while maintaining adequate phase characteristics near the unity-gain crossover.

Using the final gains $(K p=0.15, K i=10, K d=$ 0.005 ), the open-loop transfer function $L(s)= C(s) \operatorname{Gvd}(s)$ exhibits a unity-gain crossover frequency of $\omega c \approx 34 \mathrm{rad} / \mathrm{s}$ and an estimated phase margin of approximately $80^{\circ}$, indicating a robust stability buffer against modelling uncertainty and operating-point variations. Moreover, the gain margin is effectively large because the open-loop phase does not approach $-180^{\circ}$ over the frequency range relevant to the designed bandwidth. Following this model-based initialisation, limited time-domain simulations under reference-step and load-step disturbances were performed only as a final validation stage, ensuring that transient indices and ripple-related performance metrics satisfy the study’s requirements without relying on trial-and-error as the primary design method.

The closed-loop PID regulation structure adopted in this study is depicted in Figure 2.

Figure 2. Proportional-integral-derivative (PID) controller

3.2 Fuzzy Logic Controller-based controller design

The FLC regulates the buck-converter output by mapping the instantaneous voltage error and its rate of change to a duty-cycle command. The input variables are defined as

$e(t)=\operatorname{vref}(t)-v o(t), e^{\prime}(t)=\frac{d e(t)}{d t}$           (11)

where, e represents the tracking error and $e^{\prime}$ provides derivative-sensitive information for damping.

The overall FLC-based closed-loop regulation scheme is illustrated in Figure 3.

Figure 3. Fuzzy Logic Controller (FLC)

Universes of discourse: The input universes are selected to cover the maximum expected excursions under the standardized reference-step and load-disturbance scenarios used in this paper, with an additional safety margin to prevent saturation. Accordingly, the error universe is set to $e \in[-5,5]$, which safely covers the largest anticipated deviation from the setpoint (including margin), while the change-of-error universe is set to $e^{\prime} \in[-10,10]$, chosen to encompass the maximum expected error slope during the transient (based on the controller update interval and the observed worst-case response). These ranges provide high sensitivity near the setpoint and sufficient coverage under large disturbances.

The implemented FIS configuration in the MATLAB Fuzzy Designer is shown in Figure 4. Each input is partitioned into nine Gaussian membership functions (NB, NM, NS, NVS, Z, PVS, PS, PM, PB), as shown in Figures 5 and 6. Nine membership functions are adopted as a compromise between control resolution and rule-base complexity: the “very small” regions (NVS/PVS) around zero enable fine corrective action near regulation to reduce ripple, while the additional granularity away from zero improves transient damping and overshoot control. Gaussian membership functions are selected because their smooth overlap yields a smooth duty-cycle command and avoids abrupt control variations.

Figure 4. Fuzzy designer

Figure 5. Gaussian membership function of the input variable "e"

Figure 6. Gaussian membership function of the input variable "$e^{\prime}$"

The Gaussian membership functions used for the input variables e and e′ are presented in Figures 5 and 6, while the output representation is shown in Figure 7.

Figure 7. Membership function of the output variable

Table 2. The fuzzy control rules

Figure 8. Control surface of Fuzzy Logic Controller (FLC)

Inference and output computation (consistency clarification): The implemented FLC is a zero-order Sugeno (TSK) FIS. The rule base (Table 2) generates singleton consequents for the duty-cycle command D. The firing strength of each rule is computed from the input MF degrees using a standard T-norm (e.g., product or min), and the crisp output is obtained by the Sugeno weighted-average:

$D=(\Sigma w i \cdot D i) /(\Sigma w i)$              (12)

where, $w_i$ is the firing strength of the i-th rule, and Di is the corresponding singleton consequent. The duty-cycle command is finally limited to a safe operating range [Dmin,Dmax] before driving the PWM stage. The resulting rule surface (Figure 8) is monotonic and derivative-sensitive, providing stronger correction far from the setpoint and gentler action near regulation, which helps reduce overshoot and ripple.

3.3 Adaptive neuro-fuzzy inference system-based controller design

The buck DC–DC converter exhibits nonlinear and switching-dependent dynamics; therefore, intelligent control techniques can provide improved regulation performance compared to fixed-gain classical controllers under varying operating conditions [13]. In this work, a neuro-fuzzy controller is developed using an ANFIS. The ANFIS combines the interpretability of fuzzy rules with data-driven parameter adaptation, enabling an enhanced nonlinear mapping from the error signals to the duty-cycle command [14, 15]. Figure 9 illustrates the ANFIS structure adopted in this study. A first-order Sugeno (TSK) ANFIS is used, with two inputs and one output. The inputs are the voltage tracking error and its change:

$e(t)=\operatorname{vref}(t)-\operatorname{vo}(t), e^{\prime}(t)=\frac{d e(t)}{d t}$               (13)

And the ANFIS output is the duty-cycle increment ΔD (bounded to the safe range [Dmin, Dmax] before driving the PWM).

Figure 9. Structure of adaptive neuro-fuzzy inference system (ANFIS)

First-order Sugeno ANFIS rules and layer computations for a first-order Sugeno ANFIS, the i-th rule is expressed as [13]:

If $X$ is $A_i$ and $Y$ is $B_i$, then

$f_i=p_i x+q_i y+r_i$           (14)

where, $X \triangleq e$ and $\mathrm{Y} \triangleq \mathrm{e}^{\prime}$. The parameters $\left(p_i, q_i, r_i\right)$ are the consequent parameters, while $A_i$ and $B_i$are the premise (input) membership functions (MFs). The overall ANFIS computation can be described layer-by-layer as follows (the input layer is counted separately, hence a six-layer representation including inputs, consistent with Figure 10:

Layer 1 (premise MFs): Each node computes the MF grade of the inputs:

$O_{1, i}=\mu_{A_i}(x), \quad i=1,2, \ldots, M$            (15)

$O_{2, i}=\mu_{B_i}(y), \quad j=1,2, \ldots, K$             (16)

where, M and K are the numbers of MFs assigned to X and Y, respectively.

Layer 2 (rule firing): Each node computes the firing strength of a rule using a T-norm (product is used here):

$w_i=\mu_{A_i}(x) \cdot \mu_{B_i}(y) i=1,2, \cdots, 5 N r$              (17)

where, Nr is the number of rules.

Layer 3 (normalization): The firing strengths are normalized:

$\bar{w} i=w i /(\Sigma w i), i=1,2, \ldots, N r$                 (18)

Layer 4 (rule outputs): Each node computes the weighted rule output:

$O_{4, i}=\bar{w} i f i=\bar{w} i(p i X+q i Y+r i)$                (19)

Layer 5 (aggregation/output): The final crisp output is obtained by summing all rule contributions:

$\Delta D=\Sigma w i f i=(\Sigma w i f i) /(\Sigma w i)$                (20)

Unlike Mamdani FIS, a first-order Sugeno ANFIS represents the output through rule consequents (linear functions) rather than output membership functions; therefore, training refines the premise (input MF) parameters and the consequent coefficients.

Training-data generation (N = 100 samples) to avoid a black-box training description, the ANFIS training dataset is generated offline from the baseline FLC mapping (not from closed-loop time-series). Specifically, the defined input universes of discourse are sampled to produce N = 100 input pairs $\left(X_K, Y_K\right)$ over the ranges used in the fuzzy design. For each sampled pair, the baseline FLC is evaluated to generate the target output $y_K=\Delta D_{-} F L C, k$. Hence, the dataset is:

$\left(X_K, Y_K\right) \rightarrow y_K$ for $k=1, \ldots, 100$           (21)

Figure 10. Loading training data into the neuro-fuzzy designer

Figure 10 shows the imported training dataset used within the neuro-fuzzy designer.

Learning algorithm, objective function, and training settings

Training is performed using the standard ANFIS hybrid learning algorithm in MATLAB: in the forward pass, the consequent parameters ($\left(p_i, q_i, r_i\right)$ are identified via least-squares estimation (LSE), while in the backward pass the premise parameters of the input Gaussian MFs (centers and spreads) are updated via gradient descent/backpropagation to reduce the fitting error [16]. The optimization objective is the mean-squared error (MSE):

$J=\left(\frac{1}{N}\right) \Sigma \mathrm{k}(y A N F I S, k-y k)^2$            (22)

As shown in Figure 11, the training error converges rapidly within the first iterations and stabilizes by 100 epochs, indicating a consistent fit to the target mapping. The training dataset used for the ANFIS model is provided in the Appendix.

Figure 11. Adaptive neuro-fuzzy inference system (ANFIS) training error (MSE) versus epochs

Figure 12 shows a neural network that explains the structure of the ANFIS model, with two inputs and one output. Each input has a set of membership functions assigned to it, and combining these with the AND operation forms fuzzy rules. For each rule, a value is generated, and these values are summed to produce a final single value.

Figure 12. Neural network diagram

Effect of training on MFs and control surface. After training, a new FIS is obtained. The learned ANFIS slightly adjusts the input MF parameters and the consequent coefficients to better approximate the target nonlinear mapping. The resulting trained control surface is shown in Figure 13. Compared with the baseline FLC surface (Figure 8), the trained surface preserves the same global monotonic/derivative-sensitive behavior, while introducing refined nonlinear shaping in specific regions of the $\left(e, e^{\prime}\right)$ plane. This adjustment modifies the local slope (effective control gain) of the mapping, which is reflected in the improved transient damping and disturbance recovery reported in the comparative results under identical test scenarios.

Figure 13 shows the ANFIS control surface after learning. Relative to the baseline FLC surface (Figure 9), the ANFIS surface exhibits refined nonlinear shaping (modified local slope) while preserving the global monotonicity and derivative sensitivity.

Figure 13. New rules surface after training in adaptive neuro-fuzzy inference system (ANFIS)

This paper compared PID, FLC, and an ANFIS-based neuro-fuzzy controller for output-voltage regulation of a DC–DC buck converter under identical reference-step and load-disturbance scenarios. The observed trends align with fundamental control principles. PID offers linear fixed-gain compensation: integral action removes steady-state error, and derivative action enhances damping, but constant gains limit adaptability when the plant's dynamics change. FLC implements a nonlinear mapping from (e, e′) to the duty-cycle command that effectively performs gain scheduling—delivering strong correction for large deviations and gentler action near regulation—thus improving damping and reducing ripple. ANFIS extends this ability by training its premise membership functions and consequent coefficients, resulting in smoother interpolation and locally adjusted surface slopes that boost disturbance rejection and transient recovery. From a practical standpoint, PID is suitable for low-cost implementations with moderate performance needs and a narrow operating range. FLC is beneficial when an accurate model isn't available and moderate complexity is acceptable; it can be designed from expert knowledge and remains understandable. ANFIS is recommended for performance-critical regulation, but it requires representative training data, extra computation, and explicit checks for generalization across operating conditions. These trade-offs directly influence controller choice in real-world buck-converter applications. This study is limited to simulation with nominal parameters. Parameter uncertainties and converter non-idealities (e.g., ESR, quantization, sensor noise, and computation delay) were not systematically examined, and no hardware prototype validation was performed. Additionally, the comparative study considers only a single nominal converter design; broader operating ranges and uncertainty analyses will be explored in future work.

This study can be enhanced by incorporating artificial intelligence (AI) to improve the performance of voltage regulation [16-21]. Moreover, other control techniques can be suggested to compare to the proposed controller in this study [22-30].