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Application of fractional order proportional-integral-derivative-acceleration PIλDμA controller to a bioreactor is presented and studied in this paper. The fractional order PIλDμA controller is an integer order PIDA controller whose integral and derivative orders are fractional numbers rather than integers. Design stage of the fractional order PIλDμA controller consists of determining six parameters...
The general Bagley-Torvik fractional order system is represented by the Bagley-Torvik equation with a real order derivative instead of 1/2 or 3/2 order derivative. This fractional order system can exhibit behaviors that range from relaxation to oscillation for different values of the real derivative order and the damping ratio-like parameters. For this reason, it is interesting to take this system...
In the last years, the electrocardiogram signal has become an important biometric modality due essentially to the physiological or/and behavioral characteristics variation of the heart among different individuals. The aim of this paper is to present a human identification approach using some time and frequency features of the QRS complex of the ECG signal. These features are extracted from a fractional...
In this paper, a new approach to a finite impulse response (FIR) closed form design of the digital fractional forward filter is presented. The design is based on the approximation of the fractional order systems. First, closed form digital infinite impulse response (IIR) fractional forward filter implementation has been derived from the analog rational function approximation, in a given frequency...
The electrocardiogram (ECG) signal may contain useful information about the nature of the diseases afflicting the heart. However, the cardiac abnormalities information cannot be easily and directly monitored by the human eye for large amount of ECG data. Hence, computer assisted methods are very important to monitor cardiac health easily and accurately. In this paper, ECG Normal beats (N), Premature...
In a recent article we have introduced and used the complex fractional wavelet for QRS complex detection in ECG signal. This complex fractional wavelet is derived from the Cole-Cole distribution which is widely used in the modeling of dielectrics by a fractional power pole. This work presents an extension of QRS detection scheme using the complex Morlet wavelet function. It consists of using the real...
Robust control based on fractional order calculus is gaining more and more interests from the control community. In this paper we present a fractional order adaptive high-gain based controllers with σ-modification concept for the class of linear, time-invariant, minimum phase, SISO systems of relative degree one. The basic idea of the proposed design is a further modification in the σ-modification...
The intelligent optimization method for designing Proportional Fractional Order Integral-Proportional Derivative (PIα-PD) controller based on Particle Swarm Optimization algorithm is presented in this paper. The proposed fractional order PIα-PD controller is a generalization of the regular PI-PD controller. Particle Swarm Optimization algorithm offers optimal solution to multidimensional rough objective...
The identification of fractional order systems is a more difficult problem than the integer one because it requires not only the estimation of the model coefficients but also the determination of the fractional orders with the tedious calculation of fractional order derivatives. This paper addresses the identification of linear fractional systems of commensurate order. The proposed identification...
A new method for numerical simulation and parameter identification of fractional order models is presented in this paper. A Digital Adjustable Fractional Integrator is proposed to improve the numerical simulation of fractional order systems. The main feature of this tool consists in: the important reduction of simulation run time, operate as a one-step forward predictor and, consequently, it can be...
Depolarization of the myocardial cells of the left and the right ventricles via the irregular but self-similar pattern of branching of the His-Purkinje tree produces the QRS complex on the surface electrocardiogram. The analysis of the power spectrum of the QRS complex has shown that it has the inverse power law or fractal behavior. This fractal behavior has been modeled in the frequency domain by...
In this paper a simple and an efficient approach for approximating the fractional delay operator z-a (0 <; a <; 0.5) using digital infinite impulse response (IIR) filters is proposed. In this technique, the coefficients of the closed form digital IIR filter derived for the approximation of the fractional delay operator, in a given frequency band, are based on the approximation of fractional...
In this paper we propose a fractional PIα-PDβ controller that tuned with integral performance criterion. The orders of the integral and derivative parts, α and β, respectively, are fractional. This controller is a generalization of a conventional PI-PD controller. This expansion could provide much more flexibility than a conventional PI-PD controller design. The tuning method is based on the solution...
In a recent paper we have introduced and used a real fractional wavelet for the detection of the QRS complex in ECG signal. This fractional wavelet is the second derivative of the Cole-Cole distribution which is widely used in the modelling of dielectrics by a fractional power pole. This work presents a QRS detection scheme using a complex fractional wavelet function. The absolute value of this wavelet...
In this paper, we introduce a control algorithm based on the delayed feedback control method to stabilize a fractional order system on an unstable fixed point. The control input is defined as the difference between the future, and current state. The gain matrix is obtained using the pole placement method. To illustrate the effectiveness of the proposed algorithm, we give simulation results of the...
This work deals with the fractional order differentiator sm and integrator s-m (0<m<1) and its analogue and numerical implementation. A new method is proposed, first the fractional order differentiator sm (0<m<1) is modeled by a fractional power zero (FPZ), in a given frequency band of practical interest. Next, this FPZ is approximated by a rational function, the same idea is used to model...
In this paper we demonstrate that a fractional adaptive controller based on the high gain output feedback stabilizes the class of linear, time-invariant, minimum phase, SISO systems of relative degree one. We generalize the stability theorem of integer controllers to fractional order controllers whose derivative order is a real number between one and two, and introduce a new tuning parameter for the...
The general stability theory of nonlinear receding horizon controllers has attracted much attention over the last fifteen years, and many algorithms have been proposed to ensure closed-loop stability. On the other hand many reports exist regarding the use of artificial neural network models in nonlinear receding horizon control. However, little attention has been given to the stability issue of these...
In this paper we examine the use of fractional wavelet for the detection of QRS complex in ECG signal. The wavelet we used is the second derivative of the Cole-Cole distribution that is widely used in mathematical modelling of dielectrics and viscoelastic dynamics and it's related to the fractional power pole (FPP). With the multiscale feature, the wavelet transform (WT) has provided more ability...
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