On the other hand, artificial neural networks (ANN) have emerged as a promising tool for enhancing power quality, owing to their simplicity and the absence of intricate control frameworks or system models. However, this technique is limited by its suboptimal real-time performance and its inability to guarantee convergence [9]. Most of the current UPQC control methods require precise model parameters, involve complex controller design, and have limited disturbance rejection capabilities, making it difficult to address the intermittent and stochastic nature of distributed generation. Linear active disturbance rejection control (LADRC) originated in 1998, proposed by Professor [PERSON] as active disturbance rejection control (ADRC) [10], and was later linearized by Professor [PERSON] to form LADRC [11]. Subsequently, a bandwidth tuning method for LADRC was introduced [12], simplifying the parameter tuning process by consolidating it into two bandwidth parameters. ADRC views all uncertainties in a system as unknown disturbances, which are estimated through an expansion state observer (ESO). The reference input is differentiated to obtain its higher-order differential state variables, which are then subjected to nonlinear state error feedback (NLSEF) from the states observed by the ESO, ultimately converting the system into a cascaded integrator form. The key difference between LADRC and ADRC is that the ESO and state feedback in LADRC are linear, which simplifies the parameter tuning by reducing it to the adjustment of two bandwidth parameters. Currently, LADRC is widely applied in electrical control fields, such as motor control, robotic control, aircraft control, and grid-connected inverter control [13; 14; 15; 16; 17]. In Ref. [18],LADRC was applied to wind power grid-connected inverters. In Ref. [19], LADRC was used to replace traditional PI control in phase-locked loop (PLL) design, effectively suppressing system oscillations. Furthermore, Ref. [20] improved the total disturbance observation gain coefficient in traditional LADRC by incorporating a proportional-differential element in the control gain and performing loop correction. This modification reduced the amplitude reduction and phase lag of the disturbance observation, effectively minimizing the fluctuations in the inverter's DC-link voltage. In Ref. [21], LADRC was applied to microgrid inverters, where a time-frequency domain LADRC controller was designed. Compared to traditional PI dual-loop control, this approach demonstrated better disturbance rejection and dynamic performance, with no need for decoupling design and reduced dependency on model parameters. Nowadays, neural network-based soft computing techniques are widely used in the field of power quality to develop adaptive control schemes. In Ref. [22], the least mean squares (LMS) algorithm was used for adaptive estimation of the reference signal required for a switched converter, implemented through weight update equations. Ref. [23] proposed a variable-step LMS algorithm to overcome the slow convergence issues caused by fixed-step algorithms. This paper proposes a novel control method for the DC-side voltage regulation of the UPQC system, aimed at mitigating voltage sags, swells, and harmonics in the power grid. The main contributions of this work are as follows:  
1. To address the control accuracy issues caused by noise and parameter variations in traditional LADRC control methods, an adaptive filter is introduced into the LADRC, enhancing the system's robustness and control precision. 2. To resolve the voltage sag problem introduced by the adaptive filter, the effects of both fixed-step and variable-step algorithms within the adaptive filter are analyzed, and the optimal control strategy is selected to maximize the stability of the DC-side voltage. 3. To validate the generalization ability of the proposed method, a photovoltaic power-generation system is incorporated, and the dynamic variations of solar irradiance in real-world conditions are simulated.