Fractional extended state observer for balancing noise suppression and disturbance rejection: Theoretical analysis with numerical validation

This paper proposes a fractional‐order cascade extended state observer to alleviate the fundamental trade‐off between disturbance rejection and noise amplification in integer‐order observer‐based control. By incorporating fractional calculus into the cascade observer architecture, the fractional order serves as a continuous tuning parameter that captures system memory and long‐term disturbance dynamics more accurately. Frequency‐domain and stability analyses demonstrate enhanced disturbance rejection and improved noise attenuation compared with the conventional integer‐order cascade extended state observer. Numerical simulations on a 4‐degree‐of‐freedom robotic manipulator validate accurate disturbance estimation and robustness under sensor noise. The proposed approach introduces an additional degree of tuning freedom to balance performance and robustness without increasing observer structural complexity.