A Time Delay Estimation Interpretation of Extended State Observer-Based Controller With Application to Structural Vibration Suppression

Abstract

This paper aims to investigate the disturbance estimation mechanism of extended state observer (ESO) from a new perspective: a time-delay estimation (TDE) interpretation. By drawing the concept of input-output linearization, ESO is transformed into an equivalent TDE form in frequency domain. The establishment of this relationship can lead to an improved understanding of ESO’s principle. In addition, ESO’s parameters for disturbance estimation are given with explicitly physical meanings. Furthermore, theoretical analysis from this perspective also results in a quantitative relationship between ESO estimation performance and its two tuning parameters including control gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b_0$</tex-math> </inline-formula> and bandwidth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega _o$</tex-math> </inline-formula> . Theoretical results are evaluated by using an all-clamped plate structure with an inertial actuator, which is considered to be a typical benchmark for active vibration control. Extensive comparative experiments validate algorithm effectiveness. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was focused on the ability of extended state observer (ESO) to estimate total disturbances. The controlled system is a typical benchmark for active vibration control consisting of an all-clamped plate structure with an inertial actuator. The model uncertainties and external disturbances that bothers the system is compensated by the real-time estimation of the ESO. In order to facilitate practical engineering applications, the distinct physical meanings of ESO parameters are expounded with the help of the relationship between ESO and time delay estimation (TDE) established in frequency domain. Moreover, the influence of parameters control gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b_0$</tex-math> </inline-formula> and bandwidth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega _o$</tex-math> </inline-formula> on ESO is qualitatively established. Therefore, the engineer can avoid fall into a trial-and-error strategy that could be laborious and time-consuming. Thus, this paper proposed a convenient way for practitioners interested in developing anti-disturbance control strategies based on ESO. The simplicity and the partial-model-based characteristics are also profitable in practice. Potential applications include robotic systems, smart structures and electrical drives. In the future, the improvements of ESO based on the proposed method to deal with the intractable disturbances should be taken in an effort.