On fractional order adaptive observer

Wei, Yiheng; Sun, Zhenyuan; Hu, Yangsheng; Yong, Wang

doi:10.1007/s11633-015-0929-3

Cited by 13 publications

(6 citation statements)

References 24 publications

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“…, the same solution for (7) when ψ 0 ≡ 0. From (9) to 14, we obtain that,x (t) − x (t) = ξ t;ψ 0 , F, β − ξ (t; ψ 0 , F, α). Hence, lim t→∞x (t) − x (t) = 0 and lim t→∞ŷ (t) − y (t) = lim t→∞ c Tx (t) − c T x (t) = 0 accordingly to the choice of F.…”

Section: Non-adaptive Mixed Order Observer (Namoo)mentioning

confidence: 99%

“…In Section 2 we provide a mathematical framework for designing observer for LTIS, which includes systems defined by any generic fractional order derivative (GFOD) e.g., Caputo, Riemann-Liouville, etc. This is a subtle issue given the variety of fractional order derivatives (FOD) existent [7] and the fact that NMOO have been designed for specific type of derivatives [6,[8][9][10][11][12]. In this framework, the concept of initial conditions (IC) is unambiguously defined and linear properties (superposition and separation) are easily obtained.…”

mentioning

confidence: 99%

“…The conditions obtained meet those of the integer order observers (IOO) [4] when particularized to them, and constitutes a contribution in the non-mixed fractional order observers (FOO) literature for the adaptive case (cf. [8,9,13,14]), the latter being especially challenging, since currently there is not a fractional Lasalle theorem [15] available. The importance of this contribution is supported by the capability of fractional order systems (FOS) to model complex phenomena [10,16,17], whereby observers are needed since the internal variables are usually not accessible.…”

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confidence: 99%

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Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

et al. 2018

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Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

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Section: Non-adaptive Mixed Order Observer (Namoo)mentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

et al. 2018

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“…The performance of these controllers can be improved by using the fractional calculus. In fractional order (FO) controllers, the order of integral and derivative terms is not an integer [7]. The main advantage associated with FO controllers is flexibility in controlling purpose which helps to design a robust control system.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Pid Controller for Agc Loop of a Two-Area Solar-Thermal Deregulated Power System With RFB and Ipfc Unit

Baskar¹,

Paramasivam²

2019

IJEET

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This paper presents the Fractional Order Proportional-Integral-Derivative (FOPID) controller for Automatic Generation Control (AGC) of an interconnected twoarea solar-thermal deregulated power system. In this investigation, the thermal plants are considered with reheat tandem compound steam turbine rather than steam turbine dynamic model parameters are thought to be consistent. Concentrated solar power can store vitality in the type of thermal energy. The stored thermal energy can be utilized to produce electricity in the absence of solar irradiance. Thus, AGC of a multi-area power system incorporating solar thermal power plant (STPP) is vital for these examinations. A FOPID controller is an established PID aside from its derivative and integral orders are fractional numbers in place of being integers. The control parameters of FOPID controller are tuned utilizing Lightning Search Algorithm (LSA) and its execution is contrasted and Proportional-Integral (PI), Proportional-Integral-Derivative (PID) controllers based AGC loop. A sophisticated application of Redox Flow Batteries (RFB) coordinates with Interline Power Flow Controller (IPFC) for the improvement of AGC loop of a two-area solar-thermal power system is also considered. Simulation reveals that the proposed FOPID controller tuned with LSA algorithm liven up the dynamic output response of the test system as far as less pinnacle deviation and settling time of area frequencies and tie-line power oscillations in various exchanges of the deregulated power system. The execution of the RFB and IPFC unit captures the underlying fall in frequency and additionally the tie-line power deviations after a sudden load unsettling influence.

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“…Growing applications have attracted interest in studying the state estimation of fractional differential equations in a linear case [18][19][20][21] and in a nonlinear case [22][23][24][25]. It is well known that the study of the problem of stabilization of the fractional order system is particularly important for the synthesis of the observer [26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables

et al. 2019

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This paper presents a new procedure for designing a fractional order unknown input observer (FOUIO) for nonlinear systems represented by a fractional-order Takagi–Sugeno (FOTS) model with unmeasurable premise variables (UPV). Most of the current research on fractional order systems considers models using measurable premise variables (MPV) and therefore cannot be utilized when premise variables are not measurable. The concept of the proposed is to model the FOTS with UPV into an uncertain FOTS model by presenting the estimated state in the model. First, the fractional-order extension of Lyapunov theory is used to investigate the convergence conditions of the FOUIO, and the linear matrix inequalities (LMIs) provide the stability condition. Secondly, performances of the proposed FOUIO are improved by the reduction of bounded external disturbances. Finally, an example is provided to clarify the proposed method. The obtained results show that a good convergence of the outputs and the state estimation errors were observed using the new proposed FOUIO.

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On fractional order adaptive observer

Cited by 13 publications

References 24 publications

Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Fractional Order Pid Controller for Agc Loop of a Two-Area Solar-Thermal Deregulated Power System With RFB and Ipfc Unit

Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables

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