# Adaptive Feedback Control for Four-Phase Interleaved Boost Converter Used with PEM Fuel Cell +
## 1 Introduction
An interleaved boost converter (IBC) consists of multiple standard boost converters in parallel. This interleaved topology retains the structural simplicity of the standard boost converter while resolving issues of redundancy and ripple suppression, making it the preferred choice for fuel cell vehicles. Consequently, several research articles have been published on the use of IBC in PEMFC applications [12; 13; 14; 15]. However, designing a controller suitable for application to interleaved boost converters (IBC) intended for fuel cell vehicles is a highly complex task. On the one hand, there are specific requirements that must be considered, such as rejecting load disturbances, reducing ripples, and limiting current overshoots from the fuel cell. This entails additional demands on the robustness of the controller to meet the specified requirements. On the other hand, nonlinear terms appear in both the fuel cell and converter models, while uncertainties in the parameters of both systems add to the complexity of controller design. Although a double-loop controller based on the proportional-integral (PI) algorithm can ensure stability near a certain static operating point [16], it is necessary to design a controller capable of ensuring system stability over a wide operating range. Nonlinear controllers have already been used to address similar power control issues in general. However, the literature reports that by applying the small-signal model of the TAB converter and designing a system controller using a decoupling control method, the PEMFC power can be stabilized after a disturbance is injected across the entire frequency range tested. Furthermore, the lithium-ion battery can instantly track load variations during fluctuations, as referenced in [17]. The advantages of the proposed controller compared to those in the literature lie in its ability to offer enhanced stability not only after small-scale disturbances but also across a wider range of operating conditions. Unlike traditional decoupling approaches, our controller accounts for the complex dynamic interactions between the fuel cell and the load, ensuring a rapid response to sudden load variations while maintaining system robustness over time. Additionally, our approach incorporates nonlinear compensation mechanisms that increase resilience to input voltage fluctuations and parameter variations in the system, which significantly improves overall system performance compared to existing methods. [PERSON] et al. [18] proposed a double-loop sliding mode control (DL-STSM) for the interleaved converter, taking into account the performance of the fuel cell current, also demonstrating satisfactory robustness. [PERSON] et al. [19] also proposed robust disturbance rejection control based on fuzzy logic of four-phase interleaved boost converters. However, due to the nonlinear characteristics of the fuzzy logic model, this controller causes additional ripples in the fuel cell current. In [11], [PERSON] et al. proposed another controller based on a double-loop for the four-phase interleaved boost converter (IBC). An outer loop (voltage loop) based on the STSM algorithm is used to ensure the tracking of the output voltage to a desired reference voltage, and subsequently, generate an appropriate current reference. An inner loop (current loop) employing the backstepping control algorithm is utilized to indirectly control the fuel cell stack current to ensure system disturbance rejection and enhance its capability. The objectives of this controller are achieved. However, the system response time remains significant in this case. [PERSON] et al. [20] proposed a control system also based on a double loop with the \(H_{\infty}\) algorithm for a four-phase interleaved boost converter (IBC), which was validated using a fuel cell simulator. Although the efficiency of the control algorithm was confirmed through experiments, the lack of comparison with other control methods and the absence of a proof of reliability for the selected parameters could diminish its credibility.