Memory identification of fractional order systems: Background and theory

Li, Yan; Zhao, Yao

doi:10.1109/ccdc.2015.7162070

Cited by 6 publications

(3 citation statements)

References 36 publications

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“…This issue is theoretically challenging, since ϕ is infinite dimensional, and the analytical relationship between ϕ and its response signal Ψ is relatively complex. In this regard, some discretization based data-driven strategies are notable [44][45][46], as it is difficult to apply the analytical methods. In addition, for more complex initialized fractional order systems, it may be difficult to calculate ϕ d and u d .…”

Section: Examplementioning

confidence: 99%

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Xu,

Lu,

Chen

2024

Fractal Fract

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Iterative learning control is widely applied to address the tracking problem of dynamic systems. Although this strategy can be applied to fractional order systems, most existing studies neglected the impact of the system initialization on operation repeatability, which is a critical issue since memory effect is inherent for fractional operators. In response to the above deficiencies, this paper derives robust convergence conditions for iterative learning control under non-repetitive initialization functions, where the bound of the final tracking error depends on the shift degree of the initialization function. Model nonlinearity, initial error, and channel noises are also discussed in the derivation. On this basis, a novel initialization learning strategy is proposed to obtain perfect tracking performance and desired initialization trajectory simultaneously, providing a new approach for fractional order system design. Finally, two numerical examples are presented to illustrate the theoretical results and their potential applications.

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Section: Examplementioning

confidence: 99%

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Xu,

Lu,

Chen

2024

Fractal Fract

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“…Moreover, implementing FOPID controllers presents specific challenges, such as memory requirements. As non-integer integrators and differentiators necessitate an infinite memory capacity, conventional methods are inadequate for executing non-integer order controllers (Li & Zhao, 2015). Consequently, the efficient realization of FOPID controllers hinges on employing appropriate approximations.…”

Section: Fractional Order Pid (Fopid) Controllermentioning

confidence: 99%

FOPID Controller Design for a Buck Converter System Using a Novel Hybrid Cooperation Search Algorithm with Pattern Search for Parameter Tuning

ERSALI,

HEKİMOĞLU

2023

Gazi University Journal of Science Part A: Engineering and Innovation

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This research introduces a novel metaheuristic algorithm, OCSAPS, representing an upgraded cooperation search algorithm (CSA) version. OCSAPS incorporates opposition-based learning (OBL) and pattern search (PS) algorithms. The proposed algorithm's application aims to develop a fractional order proportional-integral-derivative (FOPID) controller tailored for a buck converter system. The efficacy of the proposed algorithm is assessed by statistical boxplot and convergence response analyses. Furthermore, the performance of the OCSAPS-based FOPID-controlled buck converter system is benchmarked against CSA, Harris hawk optimization (HHO), and genetic algorithm (GA). This comparative analysis encompasses transient and frequency responses, performance indices, and robustness analysis. The outcomes of this comparison highlight the distinctive advantages of the proposed approach-based system. Moreover, the proposed approach's performance was compared with six other approaches used to control buck converter systems similarly regarding both time and frequency domain responses. Overall, the findings underscore the efficacy of the OCSAPS algorithm as a robust solution for designing FOPID controllers in buck converter systems.

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“…In contrast, the system identification method uses the mathematical relation between the input and output of the system to establish a system model when the internal operating mechanism is fuzzy or the external disturbance is unknown, which considerably reduces the complexity of the modelling process. Li and Zhao (2015) modelled a fractional order system (FOS) using original data to determine its initialization function, and effectively identified the model parameters by use of iterative learning method. Malti et al (2004) used the fractional order Kautz orthogonal basis to describe the FOS, and proposed a method for identification of the output error criterion.…”

Section: Introductionmentioning

confidence: 99%

Fractional order system modelling with Legendre wavelet multi-resolution analysis

Wang

Liang

et al. 2021

Transactions of the Institute of Measurement and Control

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This paper proposes a method of fractional order system (FOS) modelling with Legendre wavelet multi-resolution analysis. The proposed method expands the input and output signals of the system in the form of a Legendre wavelet, and constructs the Legendre wavelet integration operational matrix by use of a block-pulse function. To address the problem of the considerable volume of system identification data and system noise in practical engineering applications, the multi-resolution characteristics of the wavelet are combined to build a wavelet integration operational matrix from the multi-scale space. By continuously discarding the high-frequency information to reduce the length of the identification data, the identification speed of the system is accelerated and the influence of noise on the identification accuracy is reduced. In addition, the least squares method is used to find the optimal order in the identification interval and further accelerate the FOS modelling process. The proposed method rapidly identifies the FOS parameters with high accuracy, and is thus feasible for engineering applications. Its effectiveness is verified by simulation and photoelectric stabilized sighting platform experiment.

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Memory identification of fractional order systems: Background and theory

Cited by 6 publications

References 36 publications

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

FOPID Controller Design for a Buck Converter System Using a Novel Hybrid Cooperation Search Algorithm with Pattern Search for Parameter Tuning

Fractional order system modelling with Legendre wavelet multi-resolution analysis

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