Mohammad Haeri
Sharif University of Technology
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Publication
Featured researches published by Mohammad Haeri.
Mathematics and Computers in Simulation | 2009
Mohammad Saleh Tavazoei; Mohammad Haeri
In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems.
Applied Mathematics and Computation | 2007
Mohammad Saleh Tavazoei; Mohammad Haeri
The aim of this paper is to propose and compare different one-dimensional maps as chaotic search patterns in the constraint nonlinear optimization problems. For this purpose, about 10 one-dimensional maps are introduced that can be used as search pattern in chaos optimization algorithms. We apply these maps in specific optimization algorithm (weighted gradient direction based chaos optimization algorithm) and compare them based on numerical simulation results.
Automatica | 2009
Mohammad Saleh Tavazoei; Mohammad Haeri
The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputos definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems.
IEEE Transactions on Industrial Electronics | 2008
Mohammad Saleh Tavazoei; Mohammad Haeri; Saeid Jafari; Sadegh Bolouki; Milad Siami
This paper presents two different stabilization methods based on the fractional-calculus theory. The first method is proposed via using the fractional differentiator, and the other is constructed based on using the fractional integrator. It has been shown that the proposed techniques can be used to suppress chaotic oscillations in 3-D chaotic systems. To show the practical capability of the methods, some experimental results on the control of chaos in chaotic circuits are presented.
Journal of Vibration and Control | 2009
Mohammad Saleh Tavazoei; Mohammad Haeri; Mina Attari; Sadegh Bolouki; Milad Siami
This paper is devoted to the analysis of fractional order Van der Pol system studied in the literature. Based on the existing theorems on the stability of incommensurate fractional order systems, we determine parametric range for which a fractional order Van der Pol system with a specific order can perform as an undamped oscillator. Numerical simulations are presented to support the given analytical results. These results also illuminate a main difference between oscillations in a fractional order Van der Pol oscillator and its integer order counterpart. We show that contrary to integer order case, trajectories in a fractional Van der Pol oscillator do not converge to a unique cycle.
Automatica | 2010
Kamran Akbari Moornani; Mohammad Haeri
This paper deals with the analysis of robust BIBO-stability of LTI fractional order delay systems in the presence of real parametric uncertainties. Two large classes of these systems, namely retarded and neutral types, are considered. Two theorems are given to check the robust BIBO-stability of these two families of fractional order systems. One of these theorems provides necessary and sufficient conditions for the case of retarded type and another one presents only sufficient conditions for the case of neutral type. Furthermore, upper and lower bounds (cutoff frequencies) are provided for drawing the value sets. To illustrate the results, two numerical examples are presented.
Automatica | 2010
Mohammad Saleh Tavazoei; Mohammad Haeri
This paper deals with issues related to the use of rational approximations in the simulation of fractional-order systems and practical implementations of fractional-order dynamics and controllers. Based on the mathematical formulation of the problem, a descriptor model is found to describe the rational approximating model. This model is analyzed and compared with the original fractional-order system under the aspects which are important in their simulation and implementation. From the results achieved, one can determine in what applications the use of rational approximations would be unproblematic and in what applications it would lead to fallacious results. In order to clarify this point, some examples are presented in which the effects of using rational approximations are investigated.
Isa Transactions | 2011
Mahsan Tavakoli-Kakhki; Mohammad Haeri
Fractional order PI and PID controllers are the most common fractional order controllers used in practice. In this paper, a simple analytical method is proposed for tuning the parameters of these controllers. The proposed method is useful in designing fractional order PI and PID controllers for control of complicated fractional order systems. To achieve the goal, at first a reduction technique is presented for approximating complicated fractional order models. Then, based on the obtained reduced models some analytical rules are suggested to determine the parameters of fractional order PI and PID controllers. Finally, numerical results are given to show the efficiency of the proposed tuning algorithm.
SIAM Journal on Numerical Analysis | 2008
Mohammad Saleh Tavazoei; Mohammad Haeri; Sadegh Bolouki; Milad Siami
In this paper, the frequency domain-based numerical methods for simulation of fractional order systems are studied in the sense of stability preservation. First, the stability boundary curve is exactly determined for these methods. Then, this boundary is analyzed and compared with an accurate (ideal) boundary in different frequency ranges. Also, the critical regions in which the stability does not preserve are determined. Finally, the analytical achievements are confirmed via some numerical illustrations.
European Journal of Control | 2010
Mahsan Tavakoli-Kakhki; Mohammad Haeri; Mohammad Saleh Tavazoei
In this paper, firstly a four-parameter fractional order model structure is introduced to approximate processes having S-shaped step responses. Three different strategies are presented in order to determine the parameters of the proposed model. In a special case where the proposed model is not satisfactory, another fractional order model structure with five free parameters is introduced to improve the model approximation. Also in this case, a procedure is provided to estimate the parameters of the introduced five-parameter model. Then, some common classical integer order control design approaches are modified or extended to their fractional order counterparts in order to incorporate the proposed models in their design stage. Finally, some numerical examples are provided to show the applicability of the proposed procedures in estimating the parameters of the introduced models and evaluate the performance of the obtained models in the studied controllers.