Comparison of the methods for the calculation of fractional-order differential equations

Dorcak, Eubomir; Valsa, Juraj; Terpák, Ján; Gonzalez, Emmanuel A.

doi:10.1109/carpathiancc.2011.5945820

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…Then, fractionalorder control strategies are more widely used in nonlinear system control [25]. Some new control algorithms and strategies are proposed [26][27][28][29], such as fractional order PID control, fractional order sliding mode control, fractional order differential equation-based control, adaptive fractional order control, etc. Some scholars and experts demonstrated that inductance and capacitance are essentially fractional orders [30], so existing PMSM systems suffer from non-integer orders in kinetic processes with memory and hereditary mass diffusion or heat conduction [31], and fractional order theory has been increasingly applied to PMSM control with good results in recent years.…”

Section: Introductionmentioning

confidence: 99%

Research on PMSM Speed Performance Based on Fractional Order Adaptive Fuzzy Backstepping Control

Zhang,

Ma,

et al. 2023

Energies

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A permanent magnet synchronous motor (PMSM) is a nonlinear, strongly coupled, controlled object with time-varying, fractional-order characteristics. It is difficult to achieve the ideal control effect by using the traditional control method when motor parameter changes and load perturbations occur during the operation of the PMSM, so a fractional-order adaptive fuzzy backstepping control method is proposed to improve the system’s fast response and anti-jamming ability in the case of sudden changes in rotational speed, load perturbations and other conditions. Initially, the fractional order theory is introduced, backstepping control is utilized to decompose the system into multiple subsystems, and a fractional order-based Lyapunov function is designed for each subsystem to ensure the system’s stability. Suitable control laws, as well as parameter adaptive laws, are derived through rigorous mathematical derivation. Finally, a fractional order adaptive fuzzy backstepping controller (FOAB-FPID) is designed by combining the advantages of fuzzy control. Then a mechanical simulation model of the PMSM is established to verify the validity of the designed controller, followed by three sets of comparative experiments: PID, fuzzy PID (F-PID), and integer-order adaptive fuzzy backstepping (IOAB-FPID), which are selected to simulate the PMSM under the control of the four controllers. Finally, it is validated on the constructed PMSM experimental platform. Simulation and experimental results show that FOAB-FPID can adaptively adjust system parameters during sudden speed changes, achieve real-time speed tracking, and maintain speed stability under load perturbations and internal parameter uptake. Compared with the three control strategies, reached PMSM system has better acceleration, fast response performance, and better anti-disturbance ability, which proves the rationality and effectiveness of the FOAB-FPID control method.

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Section: Introductionmentioning

confidence: 99%

Research on PMSM Speed Performance Based on Fractional Order Adaptive Fuzzy Backstepping Control

Zhang,

Ma,

et al. 2023

Energies

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“…Grünwald-Letnikov (GL) definition of fractional order differentiation has been widely utilized for the numerical solution of fractional order differential equations, solution of fractional order system models in state space form and calculation of time response of fractional order transfer functions [7,8,9,10,11,12]. Numerical calculation methods based on Grünwald-Letnikov definition are commonly used to develop fractional-order system analysis tools [7,10].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Reduced Order Equivalent Circuit Model Parameters of Batteries from Noisy Current and Voltage Measurements

Alagöz

Alisoy

2018

Balkan Journal of Electrical and Computer Engineering

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Identification of reduced order equivalent circuit battery model from current and voltage measurements allows modeling, classification and monitoring of batteries, and these tasks are very essential for battery management systems. This study presents a theoretical study to investigate performance of computer-aided identification of the reduced order equivalent circuit battery model from noisy current and voltage measurement data. The battery model is expressed in the form of fractional order differential equation and time domain numerical solution of this model is numerically calculated according to Grünwald-Letnikov definition of fractional-order derivative. Paper demonstrates an application of this numerical solution so that it can fit noisy current and voltage measurement data, and thus parameters of the equivalent circuit battery model can be estimated. Particle swarm optimization (PSO) method is used to solve this model fitting problem. Performance of the parameter estimation method is investigated for various noise levels of the synthetically generated current and voltage profiles.Index Terms-Battery model, fractional order system model, Grünwald-Letnikov definition, PSO.

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Verification of the system for indirect temperatures measurement in the massive batch

Laciak

Kačur

Durdán

2012

Proceedings of the 13th International Carpathian Control Conference (ICCC)

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Comparison of the methods for the calculation of fractional-order differential equations

Cited by 5 publications

References 3 publications

Research on PMSM Speed Performance Based on Fractional Order Adaptive Fuzzy Backstepping Control

Research on PMSM Speed Performance Based on Fractional Order Adaptive Fuzzy Backstepping Control

Estimation of Reduced Order Equivalent Circuit Model Parameters of Batteries from Noisy Current and Voltage Measurements

Verification of the system for indirect temperatures measurement in the massive batch

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