Ryszard Kopka

Modeling and identification of fractional first-order systems with Laguerre-Grünwald-Letnikov fractional-order differences

This paper introduces a method for modeling and identification of a simple dynamical system described by fractional-order differential equation. The Grünwald-Letnikov fractional-order derivative is approximated by a discrete-time Laguerre-based model, giving rise to a new discrete-time integerorder equation modeling the considered system. An application example involves a supercapacitor charging circuit. High accuracy of parametric identification for the circuit model, under moderate computational effort, is achieved on a real-life experimental data.

Estimation of Supercapacitor Energy Storage Based on Fractional Differential Equations

In this paper, new results on using only voltage measurements on supercapacitor terminals for estimation of accumulated energy are presented. For this purpose, a study based on application of fractional–order models of supercapacitor charging/discharging circuits is undertaken. Parameter estimates of the models are then used to assess the amount of the energy accumulated in supercapacitor. The obtained results are compared with energy determined experimentally by measuring voltage and current on supercapacitor terminals. All the tests are repeated for various input signal shapes and parameters. Very high consistency between estimated and experimental results fully confirm suitability of the proposed approach and thus applicability of the fractional calculus to modelling of supercapacitor energy storage.

Modeling and identification of a simple fractional-order circuit via discrete-time Laguerre approximation to the GL fractional-order derivative

This paper presents a new method for modeling and identification of a simple electric circuit described by fractional-order differential equation. The Grunwald-Letnikov fractional-order derivative is approximated by its effective discrete-time model based on Laguerre filters, giving rise to a new discrete-time integer-order equation modeling the considered electric circuit. High accuracy of modeling and parameter estimation for the circuit, under moderate computational effort, is verified on a real-life experimental data.

Control Measurements at the Manufacturing of Metallic Products

This article presents the developed system for collecting, memorising and analysing of the measurements conducted in a production plant. It describes the algorithm of the software im-plemented on the control panel and managing the work of a single measurement cell. Moreover the procedure of collecting of the measurement results by two modes: automatically and manually and the procedure of estimating of product ratio quality. Mentioned are also the practices for controlling of the communication with the central computer as well as archiving of the collected measurement results.

A fractional model of supercapacitors for use in energy storage systems of next-generation shipboard electrical networks

The reduction of energy consumption and carbon dioxide emission has forced designers and manufacturers to develop new, more efficient ship propulsion systems. Traditional mechanical systems are replaced by hybrid or completely electric ones. In addition to the combustion, the electromechanical sources are considered. But in such small electric grids, in order to reduce the impact of load fluctuations on the power system, energy storage devices are proposed. Such devices are able to supply a peak power. As examples the batteries, flywheels, but primarily supercapacitors can be considered. Unfortunately, a very low voltage causes supercapacitors to work in stacks. This paper presents the results of analysis of the influence of changes in selected supercapacitor parameters changes on its terminal voltage during the cycles of charging and discharging. The model parameters are estimated based on the test measurements, while the differ-integral calculus of fractional order is used to derive the model output. It turns out that such an approach provides a very good fit for model responses even for its very simple structures. In addition, a very precise mathematical model allows to accurately estimate an amount of stored energy and estimate the supercapacitor reliability.

Reconfiguration of Control Allocation Module Based on Reliability Estimated by Stochastic Models

The paper presents the results of the regulation strategy based on the reconfiguration of the control allocation module steering redundant actuators. As the reconfiguration criterion the required level of system reliability was assumed at the end of the operating time, estimated by the means of stochastic differential equations. In this case, two tasks become the key. The first concerns the choice of the method of determining the pseudo inverse matrix taking into account the constraints on the control signal. The second concerns the prioritization of the actuators. i.e. the distribution of the increased demand for the control signal so that, this increase, in minimum way, decreases the reliability.

Model–Based Fault Diagnosis with Fractional Models

Paper presents the results of experimental research of fault detection based on difference signal of plant and model controllers output. The plant was simulated by electronic circuit with supercapacitor ’damaged’ by discharging it by the current source. The model of the plant was described by fractional order differential equations. Such approaches allowed for some processes and the newest technologies, obtain better modelling accuracy. Model parameters was derived used identification procedures based on step response signal. The fault detection problem of this paper can be used as simple benchmark example to test new fault detection rules before applying it to real systems.