Fractional - order system modeling and its applications

In order to control or operate any system in a closed-loop, it is important to know its behavior in the form of mathematical models. In the last two decades, a fractional-order model has received more attention in system identification instead of classical integer-order model transfer function. Literature shows recently that some techniques on fractional calculus and fractional-order models have been presenting valuable contributions to real-world processes and achieved better results. Such new developments have impelled research into extensions of the classical identification techniques to advanced fields of science and engineering. This article surveys the recent methods in the field and other related challenges to implement the fractional-order derivatives and miss-matching with conventional science. The comprehensive discussion on available literature would help the readers to grasp the concept of fractional-order modeling and can facilitate future investigations. One can anticipate manifesting recent advances in fractional-order modeling in this paper and unlocking more opportunities for research

A single-step identification strategy for the coupled TITO process using fractional calculus

The reliable performance of a complete control system depends on accurate model information being used to represent each subsystem. The identification and modelling of multivariable systems are complex and challenging due to cross-coupling. Such a system may require multiple steps and decentralized testing to obtain full system models effectively. In this paper, a direct identification strategy is proposed for the coupled two-input two-output (TITO) system with measurable input–output signals. A well-known closed-loop relay test is utilized to generate a set of inputs–outputs data from a single run. Based on the collected data, four individual fractional-order transfer functions, two for main paths and two for cross-paths, are estimated from single-run test signals. The orthogonal series-based algebraic approach is adopted, namely the Haar wavelet operational matrix, to handle the fractional derivatives of the signal in a simple manner. A single-step strategy yields faster identification with accurate estimation. The simulation and experimental studies depict the efficiency and applicability of the proposed identification technique. The demonstrated results on the twin rotor multiple-input multiple- output (MIMO) system (TRMS) clearly reveal that the presented idea works well with the highly coupled system even in the presence of measurement noise

Design and practical implementation of a fractional order proportional integral controller (FOPI) for a poorly damped fractional order process with time delay

One of the most popular tuning procedures for the development of fractional order controllers is by imposing frequency domain constraints such as gain crossover frequency, phase margin and iso-damping properties. The present study extends the frequency domain tuning methodology to a generalized range of fractional order processes based on second order plus time delay (SOPDT) models. A fractional order PI controller is tuned for a real process that exhibits poorly damped dynamics characterized in terms of a fractional order transfer function with time delay. The obtained controller is validated on the experimental platform by analyzing staircase reference tracking, input disturbance rejection and robustness to process uncertainties. The paper focuses around the tuning methodology as well as the fractional order modeling of the process' dynamics

On the Selection of Tuning Methodology of FOPID Controllers for the Control of Higher Order Processes

In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modeling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is also presented. The time domain optimal tuning of FOPID controllers have also been carried out to handle these higher order processes by performing optimization with various integral performance indices. The paper highlights on the practical control system implementation issues like flexibility of online autotuning, reduced control signal and actuator size, capability of measurement noise filtration, load disturbance suppression, robustness against parameter uncertainties etc. in light of the above tuning methodologies.Comment: 27 pages, 10 figure