Discrete ADRC method based on improved fal function and its application

Abstract

In this paper, to address the problem that the traditional fal function constitutes an active disturbance rejection control (ADRC) system that is greatly affected by feedback signal noise and the control output has jitter, propose a continuous and smooth Hfal function in the definition domain to improve the extended state observer and nonlinear error feedback control law in ADRC. Firstly, the characteristic curves and error gain curves of the fal function and Hfal function are compared and analyzed to prove the feasibility and superiority of the Hfal function; secondly, the convergence condition of the extended state observer improved by the Hfal function is analyzed theoretically, and the simulation of the improved extended state observer with glan , faln , and tanh function is compared in the observed signal containing noise to verify the improved extended state observer with Hfal function has higher observation accuracy; finally, the improved ADRC (IADRC) method is applied to the magnetically levitated sphere system model with a nonlinear, large time lag and strong coupling characteristics for discretization simulation experiments, and the results show that the proposed IADRC method solves the output jitter problem of the traditional ADRC method, has better stability, and has stronger robustness to large-amplitude control quantity step disturbances and feedback link noise. The proposed control method further improves the control performance of the system and has a good reference value for the control of other nonlinear systems with uncertain disturbances.