Discrete Bi-Bandwidth Extended State Observer for Systems with Measurement Noise

The goal of this research is to present a discrete extended state observer that can effectively track fast time-varying disturbances while maintaining low sensitivity to measurement noise. A novel disturbance estimation method, named the discrete bi-bandwidth extended state observer (DBESO), is proposed. The DBESO employs a bi-bandwidth gain pencil, which comprises a base bandwidth and a bi-bandwidth scaling factor, to adjust the bandwidth of the observer. Consequently, DBESO can achieves a better tradeoff between the disturbance estimation accuracy and noise suppression. Specific details of DBESO, including its general form and stability proof, are discussed. Furthermore, we proposed three bi-bandwidth gain pencil design methods. The simulation comparisons reveal that the smooth gain pencil exhibits superior estimation performance. Finally, we integrated the observer with PD control and applied it to the rudder deflection control platform. Moreover, the experimental results demonstrate its effectiveness in compensating for fast time-varying disturbances and suppressing measurement noise.