Applications Of Fractional Order Calculus Research Articles

Fractional-Order Predictive Functional Control of Industrial Processes with Partial Actuator Failures

As the actuator faults in an industrial process cause damage or performance deterioration, the design issue of an optimal controller against these failures is of great importance. In this paper, a fractional-order predictive functional control method based on population extremal optimization is proposed to maintain the control performance against partial actuator failures. The proposed control strategy consists of two key ideas. The first one is the application of fractional-order calculus into the cost function of predictive functional control. Since the knowledge of analytical parameters including the prediction horizon, fractional-order parameter, and smoothing factor in fractional-order predictive functional control is not known, population extremal optimization is employed as the second key technique to search for these parameters. The effectiveness of the proposed controller is examined on two industrial processes, e.g., injection modeling batch process and process flow of coke furnace under constant faults, time-varying faults, and nonrepetitive unknown disturbance. The comprehensive simulation results demonstrate the performance of the proposed control method by comparing with a recently developed predictive functional control, genetic algorithm, and particle swarm optimization-based versions in terms of four performance indices.

ECG artifact cancellation in surface EMG signals by fractional order calculus application

Background and objectiveNew aspects for automatic electrocardiography artifact removal from surface electromyography signals by application of fractional order calculus in combination with linear and nonlinear moving window filters are explored. Surface electromyography recordings of skeletal trunk muscles are commonly contaminated with spike shaped artifacts. This artifact originates from electrical heart activity, recorded by electrocardiography, commonly present in the surface electromyography signals recorded in heart proximity. For appropriate assessment of neuromuscular changes by means of surface electromyography, application of a proper filtering technique of electrocardiography artifact is crucial. MethodsA novel method for automatic artifact cancellation in surface electromyography signals by applying fractional order calculus and nonlinear median filter is introduced. The proposed method is compared with the linear moving average filter, with and without prior application of fractional order calculus. 3D graphs for assessment of window lengths of the filters, crest factors, root mean square differences, and fractional calculus orders (called WFC and WRC graphs) have been introduced. For an appropriate quantitative filtering evaluation, the synthetic electrocardiography signal and analogous semi-synthetic dataset have been generated. The examples of noise removal in 10 able-bodied subjects and in one patient with muscle dystrophy are presented for qualitative analysis. ResultsThe crest factors, correlation coefficients, and root mean square differences of the recorded and semi-synthetic electromyography datasets showed that the most successful method was the median filter in combination with fractional order calculus of the order 0.9. Statistically more significant (p < 0.001) ECG peak reduction was obtained by the median filter application compared to the moving average filter in the cases of low level amplitude of muscle contraction compared to ECG spikes. ConclusionsThe presented results suggest that the novel method combining a median filter and fractional order calculus can be used for automatic filtering of electrocardiography artifacts in the surface electromyography signal envelopes recorded in trunk muscles.

Robust DC-motor speed control using a fractional adaptive PI&lt;SUP align="right"&gt;α&lt;/SUP&gt; regulator

Conventional adaptive PI controller is one of the most widely used controllers in industry, but the recent advancement in fractional calculus has introduced applications of fractional order calculus in control theory. One of the prime applications of fractional calculus is fractional adaptive PI controller and it has received a considerable attention in academic studies and in industrial applications. Fractional order adaptive PI controller is an advancement of classical integer order adaptive PI controller. In many a cases fractional order adaptive PI controller has outperformed classical integer order adaptive PI controller. Particularly for the problem of controlling the speed of DC-motors, it is very important use a suitable and efficient controller as any small change can lead to instability of the closed loop system. This research paper, studies the control aspect of fractional order controller in speed control of DC motor. A comparative study of classical adaptive PI controller and fractional order adaptive PI controller has been performed to illustrate the effectiveness and robustness of the proposed fractional adaptive control solution.

Implementation of fractional order integrator/differentiator on field programmable gate array

Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractional calculus i.e. fractional integrator and derivative, using Grünwald–Letnikov definition, on field programmable gate array (FPGA) in LabVIEW environment. The simulation and hardware implementation results for fractional order integrator and derivative of sinusoid and square waveform signals for some selected fractional orders have been presented. A close agreement between the simulated and the experimental results demonstrated the suitability of FPGA device in fractional order control and signal processing applications. LabVIEW being one of the finest tools for measurement and control, and signal processing applications the fractional order operator implementation is expected to further enhance the capability of the tool to cater to the needs of advanced experimental research employing fractional order operators.

Design of fractional order predictive functional control for fractional industrial processes

Many phenomena in practical processes cannot be accurately described by conventional differential equations, while fractional order differential equations can describe the characteristics of such processes more accurately. In this paper, the fractional order predictive functional control (FPFC) method is designed for a class of single-input single-output (SISO) fractional order linear systems. The Oustaloup approximation is employed to derive the approximate model of fractional order system. Meanwhile, the Grünwald–Letnikov (GL) definition and the fractional calculus operator are used in its cost function, which further extend the applications of fractional order calculus to the predictive functional control algorithm. And then the optimal control is obtained. Compared with traditional predictive functional control based on integer reduced order model, simulation results reveal that the fractional order controller yields improved control performance.

SOME APPLICATIONS OF FRACTIONAL ORDER CALCULUS TO DESIGN DIGITAL FILTERS FOR BIOMEDICAL SIGNAL PROCESSING

The goal of this paper is to describe some applications of fractional order calculus to biomedical signal processing with emphasis on the ability of this mathematical tool to remove noise, enhance useful information, and generate fractal signals. Three types of digital filters are considered, namely, lowpass differentiation filter, smoothing filter, and 1/fβ-noise generation filter. The filter impulse responses are functions of the fractional order and the sampling period only, and thus can be computed easily. Application examples are presented for illustrations.

The Application of Fractional Order Calculus in Closed-Loop System Control

A design method of fractional controller has been developed to meet the five different specifications, including for the closed-loop system robustness. The specifications of cross frequency, phase to get financing ϕ meters and robustness and complete performance curve based on level off the stage of open loop system, ensure damping is worse reaction time of model uncertainty gain change.

Some applications of fractional order calculus

Abstract. This paper presents some recent results in the area of application of fractional order system models. After the introduction to the dynamic systems modelling with the fractional order calculus the paper concentrates on the possibilities of using this approach to the modelling of real-world phenomena. Two examples of such systems are considered. First one is the ultracapacitor where fractional order models turn out to be more precise in the wider range of frequencies than other models used so far. Another example is the beam heating problem where again the fractional order model allows to obtain better modelling accuracy. The theroetical models were tested experimentally and the results of these experiments are described in the paper.