A nonlinear extended state observer based on fractional power functions

Zhao, Zhi‐Liang; Guo, Bao‐Zhu

doi:10.1016/j.automatica.2017.03.002

Cited by 157 publications

(85 citation statements)

References 19 publications

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“…Moreover, the state could be bounded in many practical control systems such as those for faults diagnosis . Finally, since the observer is usually designed for feedback purpose, we can use observer‐based feedback to make the state be bounded …”

Section: Problem Formulationmentioning

confidence: 99%

“…During the past decades, several classes of observers, including but no limited to extended state observer (ESO), extended high‐gain observer (EHGO), unknown input observer (UIO), generalized extended state observer (GESO), proportional‐integral observer (PIO) and disturbance observer (DO) have been proposed to estimate state or uncertainty. Although using different names, these observers are based on the similar idea: expanding the state in the observer to include the uncertainty estimation.…”

Section: Introductionmentioning

confidence: 99%

“…Substantial researches have been produced to analyze these classes of observers theoretically. The convergence of nonlinear ESO with matched uncertainty has been studied in the work of Guo and Zhao . Under the assumption that the nonlinear system is minimum phase, Freidovich and Khalil prove that the closed‐loop system based on the EHGO‐based controller is stable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Bai

Chen

Huang

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, observers and observability for uncertain nonlinear systems are systematically discussed. It is shown that for the convergence of a large class of observers, featured with the augment state to estimate the uncertainty, it requires not only the observability condition for the augment matrix pair but, more importantly, requires a structural condition first proposed in this paper. Furthermore, it is demonstrated that the combination of this structural condition and the observability of the augment matrix pair is a necessary and sufficient condition for the convergence of the observers and the observability of the original uncertain nonlinear systems. This implies that both the structural condition and the observability condition of the augment matrix pair reveal essential feature of the observing problems for uncertain nonlinear systems. In addition, for unobservable uncertain nonlinear systems, which do not satisfy this necessary and sufficient condition, the biased estimation error is explicitly presented, which can be used to evaluate the estimation performance of this class of observers. The numerical simulations for three typical examples are carried out to validate our theoretical analysis.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Bai

Chen

Huang

et al. 2019

Intl J Robust & Nonlinear

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“…Here, only the d‐axis current i d and mechanical rotation speed ω m need to be measured. Lastly, the obtained control inputs are modulated by the sinusoidal pulse‐width modulation (SPWM) technique …”

Section: Afopid Control Design Of Pmsg For Mpptmentioning

confidence: 99%

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

Yang

Shu

et al. 2018

Int Trans Electr Energ Syst

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Summary This paper designs a novel adaptive fractional‐order PID (AFOPID) control of a permanent magnetic synchronous generator (PMSG)‐based wind energy conversion system, which attempts to extract the maximum wind power by using a linear perturbation observer. The combinatorial effect of generator nonlinearities and parameter uncertainties, unmodelled dynamics, and stochastic wind speed variation is aggregated into a perturbation, which is then estimated in real time by a linear extended‐state observer called high‐gain state and perturbation observer. Besides, the perturbation estimate is used as an auxiliary control signal which is fully compensated by a fractional‐order PID (FOPID) controller to achieve a globally robust control consistency, simple structure and high reliability, as well as an improved tracking performance compared to that of PID control. In addition, AFOPID does not require an accurate PMSG model while only the measurement of d‐axis current and mechanical rotation speed is required, in which parameter is optimally tuned by particle swarm optimization. Four case studies are carried out, including step change of wind speed, low‐turbulence stochastic wind speed, high‐turbulence stochastic wind speed, and generator parameter uncertainties, respectively. Simulation results verify the effectiveness and superiority of AFOPID compared to that of PID, FOPID, and nonlinear control.

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“…Remark Assumption is made based on the assumptions in the works of Zhao and Guo . With this assumption,

{\overset{ϕ}{true}}_{i}

is bounded as long as the synchronization errors are bounded (see Lemma for the proof).…”

Section: Problem Formulationmentioning

confidence: 99%

Output feedback semiglobal practical consensus of linear systems with relative state‐dependent uncertainties

Zhao

Zhang

2018

Intl J Robust & Nonlinear

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Summary This paper proposes an output feedback consensus control law for linear multiagent systems with relative state‐dependent uncertainties. To achieve output feedback control and uncertainty attenuation, the theories of extended high‐gain observer and structural decomposition are employed. Under the proposed control scheme, semiglobal practical consensus is achieved in the sense that the synchronization errors are ultimately bounded. Besides, the synchronization errors can be kept arbitrarily small by a proper choice of tuning parameters. Finally, a simulation example is provided to verify the theoretical results.

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A nonlinear extended state observer based on fractional power functions

Cited by 157 publications

References 19 publications

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

Output feedback semiglobal practical consensus of linear systems with relative state‐dependent uncertainties

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