Differential flatness‐based ADRC scheme for underactuated fractional‐order systems

Abstract

This article mainly studies the fractional-order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional-order systems (FOSs). The FOADRC framework for linear FOSs-based fractional proportion integration differentiation is constructed by using the fractional-order tracking differentiator and the fractional-order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example.

Enhanced extended state observer based prescribed time tracking control of wheeled mobile robot with slipping and skidding

“…Lemma 1 (38). For system (6), if there exists a continuous differential function  Remark 1. Most common disturbances can be seen as a different common signal combination.…”

“…They deal with the disturbances and uncertainties passively. Active disturbance rejection control (ADRC), mentioned as the second kind, has received extensive attention because it can estimate and compensate for the disturbance actively 6,7 . The extended state observer (ESO) usually combines with various controllers to realize different control purposes.…”

“…Active disturbance rejection control (ADRC), mentioned as the second kind, has received extensive attention because it can estimate and compensate for the disturbance actively. 6,7 The extended state observer 7314…”

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“…In order to deal with this problem, the extended state observer (ESO) can be used to estimate and compensate the high order approximation error terms in the FO Han (2009). Gao (2003) proposed a linear ESO based Active Disturbance Rejection Control (ADRC) tuning method to substantially simplify the original nonlinear controller in Han (2009) for practitioners, then this philosophy tremendously promotes the widespread application of ADRC Madonski et al (2019); Li et al (2020); Long et al (2017); Qiu et al (2014); Sun et al (2020); Piao et al (2020); Huang and Xue (2014); Zuo et al (2021). The linear ADRC is a linear control but its design concept is totally different from that of classical linear controllers and it can be applied to nonlinear, time-varying, and uncertain processes with very little model information.…”