<![CDATA[Accurate estimation of unknown and time-varying disturbances is essential for achieving high-performance control of nonlinear systems. This paper investigates the design and comparative evaluation of finite-time disturbance observers with different gain adaptation mechanisms. First, a conventional fixed-gain finite-time disturbance observer and a linearly adaptive finite-time disturbance observer are presented. Then, an adaptive finite-time disturbance observer based on fuzzy logic control is developed to automatically adjust observer gains according to the disturbance estimation error and its rate of change, thereby reducing gain sensitivity and improving transient performance. Finite-time stability of the closed-loop system is rigorously analyzed using Lyapunov theory, and sufficient conditions for convergence are derived. Extensive simulation studies on a nonlinear system subject to high-frequency time-varying disturbances demonstrate the effectiveness of the proposed approach. Quantitative results show that the adaptive finite-time disturbance observer based on fuzzy logic control reduces tracking error and disturbance estimation root mean square error by more than 75% compared with the conventional finite-time disturbance observer and by over 50% compared with the linearly adaptive observer, while yielding smoother control inputs. These results confirm that the adaptive finite-time disturbance observer based on fuzzy logic control significantly enhances robustness and estimation accuracy, making the proposed observer suitable for practical nonlinear control applications under severe disturbance conditions.]]>
