An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer

Discussion on: “Simple Fractional Order Model Structures and their Applications in Control System Design”

Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay

The paper deals with the search for the interrelations between the parameters of the nonlinear object of control and the fractional order transfer function by which it is identified. A series excitation direct current motor is used as a nonlinear object. The moment of inertia and the moment of resistance on the motor shaft and the supply voltage were assumed to be the parameters of variation. Their change influences not only the quantitative indices of the transfer characteristic but also the qualitative ones. FOMCON MATLAB Toolbox is used for the identification of the coefficients of the fractional order transfer function. The obtained results testify to the existence of the relationship between the motor parameters and the coefficients of the fractal function. The obtained dependences are exponential for the moment of resistance and extreme for supply voltage and the moment of inertia.

The paper deals with the substantiation of the topicality of the problem of the creation of the high-quality and relatively simple control systems for electric drives with Switched reluctance motor (SRM) due to the continuous increase of the field of application of SRM in industry. The mathematical simulation method with the application of Matlab System Identification toolbox was used to determine that the sufficient convergence of the results can be obtained at the identification of SRM with a fractional rational transfer function having three zeros and four poles, R-squared value for this variant makes 86%. Such a high order of the transfer function of SRM causes the complexity of its regulator design. The authors worked out a method for the identification of SRM fractional measured transfer function based on the use of FOMCON MATLAB Toolbox. This approach provides higher accuracy of SRM identification. R-squared value for the proposed method makes 94 - 96%, which allows the simplification of the controller structure and the improvement of the accuracy of SRM control in the closed-loop control system. It is shown that the structure of the fractional measured transfer function, identifying the process of SRM start, does not depend on the electric drive inertia moment.

Stochastic fractal equilibrium optimizer with X-shaped dynamic transfer function for solving large-scale feature selection problems

On the robust stability of commensurate fractional-order systems

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer FunctionThis paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems for a given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.

In this paper, we have introduced nonlinear harvesting to study a fractional-order predator-prey model with Holling-II response. Existence of multiple equilibrium points of the model and their stability under different conditions are analyzed. Global stability analysis of the co-existence equilibrium point has examined by considering suitable Lyapunov function. we have observed that fractional-order model is more viable for the memory-based system than integer-order model. Our model exhibits Hopf bifurcation with respect to fractional-order of the derivative. Furthermore, we have investigated period of doubling bifurcation with respect to some other parameters. Numerical simulations have performed to verify the theoretical results using Adams-Bashforth-Moulton type scheme.KeywordsFractional-orderNonlinear harvestingStability analysisHopf bifurcation

In order to implement fractional order transfer function (FOTF) model in digital systems, transfer function discretization methods are developed to obtain discrete filters that provide acceptable amplitude or phase response approximations to FOTFs in operating frequency ranges. This paper presents an approach to improve discrete IIR filter approximations to FOTFs according to application requirements by using Particle Swarm Optimization (PSO). For this purpose, particles of PSO are initialized around the solution of a well-known analytical approximation method and then, these particles search stable IIR filter solutions in the filter design space to improve magnitude and phase response approximation performance over a desired frequency region. Specifically, PSO algorithm is used to fine-tune results of Tustin recursive discretization method according to a weighed multi-objective cost function. This cost function is expressed as the weighted sum of magnitude and phase response matching objectives with a frequency weighting. The frequency weighting is employed for prioritization of frequency regions in optimization. The proposed method also ensures the stability of optimized IIR filter approximations by enforcing particles to move into stable filter solution regions of the search space. This design approach can contribute to the digital realization of fractional order systems for practical applications.

In this paper, limit cycle frequency, pulse width and stability analysis are examined using different methods for relay feedback nonlinear control systems with integer or fractional order plant transfer functions. The describing function (DF), A loci, a time domain method formulated in state space notation and Matlab/Simulink simulations are used for the analysis. Comparisons of the results of using these methods are given in several examples. In addition, the work has been extended to fractional order systems with time delay. Programs have been developed in the Matlab environment for all the theoretical methods. In particular, Matlab programs have been written to obtain a graphical solution for the A loci method, which can precisely calculate the limit cycle frequency. The developed solution methods are shown in various examples. The major contribution is to look at finding limit cycles for relay feedback systems having plants with a fractional order transfer function (FOTF). However, en route to this goal new assessments of limit cycle stability have been done for a rational plant transfer function plus a time delay.

Fractional-order modeling and controller design by a simplified way is the demanding research area and is gearing more and more momentum. This paper is the attempt of application of fractional-order modeling and controller design for the power plant gas turbine. The Gas Turbine is most important equipment in power, aviation and automotive industry. It converts the thermal energy of fuel into the mechanical power. Therefore, important requirement of gas turbine system is to control the flow of input fuel. The existing identified model of the gas turbine between the input fuel flow and the output speed, is of high-order and integer type, which is reduced to the simple and compact integer-order (IO) and fractional-order (FO) models using local optimization technique. The fractional-order internal model controller (FO-IMC) is designed and to show the performance efficacy it is compared with integer-order internal model controller (IO-IMC), which is also designed using the same methodology and specification. Simulation results show that FO-IMC based controller gives better performance for the set point tracking, plant uncertainty and disturbance rejection than the IO-IMC. FO-IMC controller also satisfy the robust stability condition.

A causal and compact fractional-order model is developed for complementary metal-oxide-semiconductor (CMOS) on-chip transmission line (T-line) at Terahertz (THz) frequencies. With consideration of the loss from frequency-dependent dispersion and nonquasi-static effects at THz, good agreement of characteristic impedance is observed between the proposed fractional-order model and the measurement up to 110 GHz, while traditional integer-order model can only match up to 10 GHz. The developed fractional-order model is further deployed in the design and analysis of CMOS-based THz integrated circuits that utilize T-line, such as standing-wave oscillator, which has significantly improved accuracy with causality.

Active medical devices rely on a source of energy that is applied to the human body for specific purposes such as electrosurgery, ultrasounds for breaking up kidney stones (lithotripsy), laser irradiation, and other medical techniques and procedures that are extensively used. These systems must provide adequate working power with a commitment not to produce side effects on patients. Therefore, the materials used in these devices must effectively transmit energy, allow for security control, sense real-time variations in case of any issues, and ensure the implementation of closed-loop systems for control. This work extends to the experimental data adjustment of some different coating techniques based on plasma electro-oxidation (PEO) and thermal spray (TS) using fractional-order models. According to the physical structure of the coating in different coating techniques, Cole family models were selected. The experimental data were obtained by means of a vector network analyzer (VNA) in the frequency spectrum from 0.3 MHz to 5 MHz. The results show that some models from the Cole family (the single-dispersion model and inductive model) offered a goodness of fit to the experimental impedance in terms of RMSE error and a squared error R2 close to unity. The use of this type of fractional-order electrical model allows an adjustment with a very small number of elements compared to integer-order models, facilitating its use and a consequent reduction in instrumentation cost and the development of control devices that are more robust and easily miniaturized for embedded applications. Additionally, fractional-order models allow for more accurate assessment in industrial and medical applications.

The design of a non-minimal state space fractional-order predictive functional controller for fractional systems of arbitrary order

State of health (SOH) estimation of lithium-ion batteries is a key but challengeable technique for the application of electric vehicles. Due to the ambiguous aging mechanisms and sensitivity to the applied conditions of lithium-ion batteries, the recognition of aging mechanisms and SOH monitoring of the battery might be difficult. A novel SOH estimation and aging mechanism identification method is presented in this paper. First, considering the dispersion effect, a fractional-order model is constructed, and the parameter identification approach is proposed, and a comparison between integer-order model and fractional-order model has been done from the prospect of predicting accuracy. Then, based on the identified open-circuit voltage, the battery aging mechanism can be analyzed by the means of an incremental capacity analysis method. Moreover, the normalized incremental capacity peak is used to estimate the remaining capacity. Finally, the robustness of the SOH estimation method is validated by batteries aged at different conditions based on the idea of cross validation, and the estimation error of the remaining capacity can be reduced within 3.1%.