Fractional Order Model Identification Research Articles

A modified reptile search algorithm for parametric estimation of fractional order model of lithium battery

AbstractIn this paper, a Levy reptile search algorithm (LRSA) is proposed to improve the global search capability and convergence speed of reptile search algorithm which has advantages in solving single‐modal, multi‐modal and composite problems. Firstly, circle chaotic mapping is introduced to make the initial distribution of population more uniform and diversified. Secondly, Levy flight strategy is employed in the global search, which can improve the accuracy and convergence speed. In order to test and verify the optimization performance of the LRSA, 12 benchmark functions are tested and compared with four other intelligent optimization algorithms. It can be seen that LRSA is effective and advantageous in average convergence speed. In addition, the proposed LRSA is applied to a fractional order model identification of lithium battery with a very small error (less than 2%). The experimental results show that the LRSA can effectively estimate the parameters of the fractional order model and aid to state of charge and state of health estimation.

Nonlinear Fractional Order Model Identification of the Voltage Source Inverter Fed Induction Motor

This paper presents a new nonlinear fractional-order model identification of a two-level voltage source inverter fed induction motor (VSI-IM). The nonlinearities present in inverter and IM cause the failure of the sensorless controls and model predictive controls, which mainly depends on the VSI-IM model. In the proposed work, an attempt has been made to identify the exact nonlinear behavior of the VSI-IM model using the PWM signal injection method. The identified fractional-order VSI-IM model is helpful to provide more insight into the dynamic behavior of the IM drive in the speed controller design (sensorless and sensored) and in predictive controls (model-based and model-free). The fractional VSI-IM models are identified at low, medium, and high frequencies. The best fit of these models is compared to the integer-order identified VSI-IM models. The experimental study clearly shows that the fractional-order VSI-IM identified model is superior to the integer-order VSI-IM model in terms of best fit with the actual hardware speed response.

Fractional-order model identification and indirect internal model controller design for higher-order processes

Several studies have shown that fractional-order models with dead-time can be used to capture the dynamics of a wide range of processes. Also, there is more scope to improve the existing identification and control strategies. Hence, this work revisits the identification of fractional-order models (IDFOM) approach to augment the same with a robust indirect fractional-order internal model control (IFOIMC) method to formulate a new identification and control strategy. In this strategy, the fractional-order model obtained using the IDFOM approach is shifted in the frequency domain by a frequency-shifting parameter. With the help of IMC principles, the frequency-shifted model is used to design the IFOIMC controller with the frequency-shifting parameter as the only tuneable parameter. Thus, the frequency-shifting parameter/robustness parameter replaces the only tuning parameter of conventional IMC design. This frequency-shifting parameter is tuned based on maximum sensitivity considerations to ensure the robustness of the design. The resulting IFOIMC controller is further realized as a fractional-order proportional-integral controller in series with a fractional-order filter (FOPIFOF). The effectiveness of the proposed identification and control strategy is illustrated by comparing the closed-loop performance achieved by IFOIMC controllers designed using two widely used identification strategies.

Fractional Order Model Identification of a Person with Parkinson’s Disease for Wheelchair Control

The paper focuses on the design of an intelligent interface that compensates for the incapacity of a person with Parkinson’s disease to drive a wheelchair. The fractional order model that defines a person with Parkinson’s disease is investigated. An identification technique based on the analysis of the frequency behavior of the movement of a wheelchair driven by a with Parkinson’s disease person on the test trajectory is proposed and a delay time crossover model with fractional order exponent β=1.5 is inferred. The fractional dynamic model of the “disabled man-wheelchair” system is discussed and a control system is proposed to compensate for the inability of the wheelchair driver. The conditions that ensure the stability of the closed loop control system are inferred. An experimental technique for analyzing movement performance is developed and a quality index is proposed to evaluate these experiments. The values of this index on the tests performed on Parkinson’s patients are analyzed and discussed.

Estimation of state of charge of lithium battery based on parameter identification of fractional order model

Accurate estimation of state of charge of lithium battery is one of the important performance parameters for safe and reliable operation of lithium battery. A fractional order second-order Thevenin equivalent circuit model was proposed by based on the improvement of the traditional Thevenin equivalent circuit model for accurately estimating the state of charge of lithium-ion battery. In order to overcome the shortcomings of the least square method easily enter into local convergence or even unable to converge, an adaptive genetic algorithm is proposed to identify the parameters of lithium battery model, and global parameter identification is carried out to improve the convergence of the algorithm. Matlab simulation shows that the parameters of fractional order model of the second-order Thevenin equivalent circuit identified by adaptive genetic algorithm are better than those of integer order model identified by least square method. Combined with extended Kalman filter, the estimation of state of charge accuracy control is realized, with the accuracy error being within 1.61%.

Identification of fractional order model for a voltammetric E-tongue system

A method to estimate the fractional order model of a voltammetric electronic tongue (E-tongue) system with five working electrodes has been presented in this paper. The method uses fractional order system (FOS) identification to obtain a fractional order transfer function (FOTF) from the process data itself. Model quality measures of the proposed FOTF have been compared with that of the integral order transfer function (IOTF) which is based upon the Randles model for an electrochemical cell. It is found that FOTF produces better model performance than that of IOTF. The parameter estimation of the FOTF has been performed using the E-tongue response for five tea samples with different working electrodes. The cross-validation of FOTF has been carried out by obtaining the impedance spectra of the working electrodes. The efficacy of discrimination for the identified fractional model has been assessed by studying the clusters of response data for various tea samples.

Fractional order model identification using the sinusoidal input

An output error optimization approach for identification of parsimonious fractional order models using multi-frequency sinusoids as input is proposed. The algorithm simultaneously estimates orders, parameters and the delay of simple models with fractional orders using the Gauss–Newton optimization approach. Optimization-based methods for fractional order model identification require evaluation of the sensitivity functions which include the logarithmic derivatives of the input signal. In the existing literature, central difference or similar methods are used to numerically calculate the Jacobian matrix due to difficulties with numerical simulation of the logarithmic derivatives. We assume deterministic input signals and provide analytical expressions for the logarithmic derivatives of single and multiple frequency sinusoids. Relevant mathematical derivations are presented and the analytical expressions are used to evaluate the Jacobian. Effects of noise to signal ratio, input frequency and sampling intervals are studied in simulation to demonstrate the efficacy of the method. Convergence and robustness of the method is also studied. In theory, the approach is applicable for models with large set of parameters; however, convergence of the optimization scheme needs to be addressed.

Fractional Order Model Identification for a Billet Unloading Robotic Arm

This paper presents a fractional model identification for a billet unloading robotic arm’s positioning system. First, an integer order model is obtained using a graphical identification method based on a set of experimental data. The experimental data represents the robotic arm’s position, measured using an encoder, at a constant billet displacement. The integer order model was obtained based on the overall performances of the measured robotic arm’s step response. The mean square error between the measured data and the model step response is high, thus, in order to decrease the error and to obtain a more accurate model, a fractional order model is determined using an iterative procedure.

Fractional models for modeling complex linear systems under poor frequency resolution measurements

When modeling a linear system in a parametric way, one needs to deal with (i) model structure selection, (ii) model order selection as well as (iii) an accurate fit of the model. The most popular model structure for linear systems has a rational form which reveals crucial physical information and insight due to the accessibility of poles and zeros. In the model order selection step, one needs to specify the number of poles and zeros in the model. Automated model order selectors like Akaikeʼs Information Criterion (AIC) and the Minimum Description Length (MDL) are popular choices. A large model order in combination with poles and zeros lying closer to each other in frequency than the frequency resolution indicates that the modeled system exhibits some fractional behavior. Classical integer order techniques cannot handle this fractional behavior due to the fact that the poles and zeros are lying to close to each other to be resolvable and not enough data is available for the classical integer order identification procedure. In this paper, we study the use of fractional order poles and zeros and introduce a fully automated algorithm which (i) estimates a large integer order model, (ii) detects the fractional behavior, and (iii) identifies a fractional order system. ► Complexity reduction integer order models. ► Automated fractional order model identification. ► Fractional order model selection. ► Dealing with high order systems. ► Dealing with closely spaced poles and zeros.