A cascade dead-zone extended state observer for a class of systems with measurement noise

Shihua Zhang; Xiaohui Qi; Sen Yang; Shihua Zhang; Xiaohui Qi; Sen Yang

doi:10.3934/math.2023732

AIMS Mathematics

2023, Volume 8, Issue 6: 14300-14320. doi: 10.3934/math.2023732

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A cascade dead-zone extended state observer for a class of systems with measurement noise

Shijiazhuang Campus, The Army Engineering University of PLA, Shijiazhuang, Hebei 050053, China

Received: 02 February 2023 Revised: 25 March 2023 Accepted: 03 April 2023 Published: 18 April 2023
MSC : 93B53, 93C10, 93D05

For high frequency noise, a new $ 2n $-th order cascade extended state observer with dynamic dead-zone structure is proposed in this paper. Dead zone dynamic consists of two parts. One is to "trim" the effect of noise by cutting off the part that falls in the dead zone. The other part pushes the dead zone amplitude to converge to 0 as soon as possible to ensure the convergence of the estimation error. Moreover, in the cascade structure, the high-gain parameter grows only to a second power, thus avoiding excessive amplification of the measurement noise and solving numerical implementation problems. The design procedure ensures that the extended state observer is input-to-state stable. Numerical simulations show the improvement in terms of total disturbance estimation and noise attenuation. The frequency-domain analysis of the proposed ESO using the describing function method investigates the effect of the dead zone nonlinear parameter on the performance of a closed-loop system.
- extended state observer,
- dead-zone,
- measurement noise,
- input-to-state stability,
- describing function method
Citation: Shihua Zhang, Xiaohui Qi, Sen Yang. A cascade dead-zone extended state observer for a class of systems with measurement noise[J]. AIMS Mathematics, 2023, 8(6): 14300-14320. doi: 10.3934/math.2023732

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Abstract

For high frequency noise, a new $ 2n $-th order cascade extended state observer with dynamic dead-zone structure is proposed in this paper. Dead zone dynamic consists of two parts. One is to "trim" the effect of noise by cutting off the part that falls in the dead zone. The other part pushes the dead zone amplitude to converge to 0 as soon as possible to ensure the convergence of the estimation error. Moreover, in the cascade structure, the high-gain parameter grows only to a second power, thus avoiding excessive amplification of the measurement noise and solving numerical implementation problems. The design procedure ensures that the extended state observer is input-to-state stable. Numerical simulations show the improvement in terms of total disturbance estimation and noise attenuation. The frequency-domain analysis of the proposed ESO using the describing function method investigates the effect of the dead zone nonlinear parameter on the performance of a closed-loop system.

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