A Time-Varying Disturbance Rejection Method for LADRC Based on Disturbance-Derivative Extended Observation

To address the degraded accuracy of the conventional linear extended state observer (LESO) under time-varying disturbances and the consequent limitation on linear active disturbance rejection control (LADRC), a disturbance derivative compensation linear extended state observer (DDC-LESO) based on disturbance-derivative extended observation and a corresponding disturbance derivative compensation linear active disturbance rejection control (DDC-LADRC) method are proposed. Unlike methods relying on frequency-domain compensation, adaptive adjustment, or composite structures, DDC-LESO introduces the total-disturbance derivative as an extended state while retaining the conventional LADRC control law and bandwidth-tuning method, enabling simultaneous estimation of the total disturbance and its derivative and enhancing online compensation for low-frequency time-varying disturbances. Under low-order polynomial disturbances, DDC-LESO achieves zero-steady-state-error observation of first-order polynomial disturbances, extending the capability of conventional LESO from zeroth-order constant disturbances to first-order polynomial disturbances, while significantly reducing and bounding the observation error for second-order polynomial disturbances. The DDC-LADRC closed-loop model is established to analyze steady-state disturbance rejection. Simulations show that, compared with conventional LADRC, DDC-LADRC reduces the maximum deviation and integral of time multiplied by absolute error (ITAE) by about 83% and 96% under a first-order ramp disturbance, respectively, and reduces ITAE by about 93% under a second-order acceleration disturbance, demonstrating stronger rejection of low-frequency time-varying disturbances.