Parameter Estimation of Fractional Wiener Systems with the Application of Photovoltaic Cell Models

Abstract

Fractional differential equations are used to construct mathematical models and can describe the characteristics of real systems. In this paper, the parameter estimation problem of a fractional Wiener system is studied by designing linear filters which can obtain smaller tunable parameters and maintain the stability of the parameters in any case. To improve the identification performance of the stochastic gradient algorithm, this paper derives two modified stochastic gradient algorithms for the fractional nonlinear Wiener systems with colored noise. By introducing the forgetting factor, a forgetting factor stochastic gradient algorithm is deduced to improve the convergence rate. To achieve more efficient and accurate algorithms, we propose a multi-innovation forgetting factor stochastic gradient algorithm by means of the multi-innovation theory, which expands the scalar innovation into the innovation vector. To test the developed algorithms, a fractional-order dynamic photovoltaic model is employed in the simulation, and the dynamic elements of this photovoltaic model are estimated using the modified algorithms. Concurrently, a numerical example is given, and the simulation results verify the feasibility and effectiveness of the proposed procedures.

Application of Fractional Calculus for Parameter Estimation of Nonlinear Wiener Systems With Time Delay

“…The fuzzy-weighted differential evolution [31] was proposed for the identification of time-delay fractional-order Wiener system, whereby linear subsystem was considered with the commensurate fractional orders. The parameter identification method for the fractional order Wiener system was developed and validated on a photovoltaic cell in [32], which is applicable to the Wiener system with commensurate orders and without time delay. The technique to identify the fractional Hammerstein-Wiener MISO system was illustrated in [33].…”

Fast Nonlinear Predictive Control Using Classical and Parallel Wiener Models: A Comparison for a Neutralization Reactor Process

“…A great advantage of the Wiener model is the fact that it can efficiently approximate the properties of different processes using a limited number of parameters. Let us name a few examples reported in the literature: distillation columns [17], chemical reactors [18][19][20], gasifiers [21], chromato-graphic separation processes [22], fuel cells [23,24], photovoltaic cells [25], the relaxation processes during anesthesia [26], the arterial pulse transmission phenomena [27]. Additionally, due to the specialized structure of the Wiener model, we can derive a set of computationally efficient MPC algorithms in which fast quadratic optimization is used rather than complicated nonlinear programming [16].…”